TSTP Solution File: ALG397-1 by iProverMo---2.5-0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : ALG397-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 14 17:12:04 EDT 2022
% Result : Unsatisfiable 0.20s 0.56s
% Output : CNFRefutation 0.42s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named input)
% Comments :
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy Equiv(ClausalAll)
% Orienting axioms whose shape is orientable
cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
hBOOL(c_fequal(V_x,V_x,T_a)),
input ).
fof(cls_ATP__Linkup_Oequal__imp__fequal_0_0,plain,
! [T_a,V_x] :
( hBOOL(c_fequal(V_x,V_x,T_a))
| $false ),
inference(orientation,[status(thm)],[cls_ATP__Linkup_Oequal__imp__fequal_0]) ).
cnf(clsarity_Complex__Ocomplex__HOL_Ozero,axiom,
class_HOL_Ozero(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__HOL_Ozero_0,plain,
( class_HOL_Ozero(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__HOL_Ozero]) ).
cnf(clsarity_Complex__Ocomplex__Power_Opower,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__Power_Opower_0,plain,
( class_Power_Opower(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__Power_Opower]) ).
cnf(clsarity_Complex__Ocomplex__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__Int_Onumber__ring_0,plain,
( class_Int_Onumber__ring(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__Int_Onumber__ring]) ).
cnf(clsarity_Complex__Ocomplex__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__Int_Oring__char__0_0,plain,
( class_Int_Oring__char__0(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__Int_Oring__char__0]) ).
cnf(clsarity_Complex__Ocomplex__Nat_Osemiring__char__0,axiom,
class_Nat_Osemiring__char__0(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__Nat_Osemiring__char__0_0,plain,
( class_Nat_Osemiring__char__0(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__Nat_Osemiring__char__0]) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom_0,plain,
( class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Oidom]) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Oring_0,plain,
( class_Ring__and__Field_Oring(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Oring]) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1,axiom,
class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1_0,plain,
( class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1]) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add_0,plain,
( class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add]) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add_0,plain,
( class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add]) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring,axiom,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring_0,plain,
( class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring]) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult_0,plain,
( class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult]) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero,axiom,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero_0,plain,
( class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero]) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add_0,plain,
( class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add]) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0,axiom,
class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0_0,plain,
( class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0]) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__1,axiom,
class_Ring__and__Field_Osemiring__1(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__1_0,plain,
( class_Ring__and__Field_Osemiring__1(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__1]) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Osemigroup__add,axiom,
class_OrderedGroup_Osemigroup__add(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__OrderedGroup_Osemigroup__add_0,plain,
( class_OrderedGroup_Osemigroup__add(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Osemigroup__add]) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one_0,plain,
( class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one]) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add_0,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add]) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring_0,plain,
( class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring]) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add_0,plain,
( class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add]) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult_0,plain,
( class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult]) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector_0,plain,
( class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult_0,plain,
( class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult]) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra_0,plain,
( class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra]) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0_0,plain,
( class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0]) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1_0,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1]) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors_0,plain,
( class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors]) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add_0,plain,
( class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add]) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add_0,plain,
( class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add]) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors_0,plain,
( class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors]) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors_0,plain,
( class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors]) ).
cnf(clsarity_RealDef__Oreal__HOL_Ozero,axiom,
class_HOL_Ozero(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__HOL_Ozero_0,plain,
( class_HOL_Ozero(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__HOL_Ozero]) ).
cnf(clsarity_RealDef__Oreal__Power_Opower,axiom,
class_Power_Opower(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__Power_Opower_0,plain,
( class_Power_Opower(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__Power_Opower]) ).
cnf(clsarity_RealDef__Oreal__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__Int_Onumber__ring_0,plain,
( class_Int_Onumber__ring(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__Int_Onumber__ring]) ).
cnf(clsarity_RealDef__Oreal__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__Int_Oring__char__0_0,plain,
( class_Int_Oring__char__0(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__Int_Oring__char__0]) ).
cnf(clsarity_RealDef__Oreal__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__Orderings_Oorder_0,plain,
( class_Orderings_Oorder(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__Orderings_Oorder]) ).
cnf(clsarity_RealDef__Oreal__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__Orderings_Olinorder_0,plain,
( class_Orderings_Olinorder(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__Orderings_Olinorder]) ).
cnf(clsarity_RealDef__Oreal__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__Orderings_Opreorder_0,plain,
( class_Orderings_Opreorder(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__Orderings_Opreorder]) ).
cnf(clsarity_RealDef__Oreal__Nat_Osemiring__char__0,axiom,
class_Nat_Osemiring__char__0(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__Nat_Osemiring__char__0_0,plain,
( class_Nat_Osemiring__char__0(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__Nat_Osemiring__char__0]) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oidom,axiom,
class_Ring__and__Field_Oidom(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__Ring__and__Field_Oidom_0,plain,
( class_Ring__and__Field_Oidom(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Oidom]) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oring,axiom,
class_Ring__and__Field_Oring(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__Ring__and__Field_Oring_0,plain,
( class_Ring__and__Field_Oring(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Oring]) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oring__1,axiom,
class_Ring__and__Field_Oring__1(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__Ring__and__Field_Oring__1_0,plain,
( class_Ring__and__Field_Oring__1(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Oring__1]) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add_0,plain,
( class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add]) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add,axiom,
class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add_0,plain,
( class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add]) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Osemiring,axiom,
class_Ring__and__Field_Osemiring(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__Ring__and__Field_Osemiring_0,plain,
( class_Ring__and__Field_Osemiring(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Osemiring]) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult,axiom,
class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult_0,plain,
( class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult]) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono,axiom,
class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono_0,plain,
( class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono]) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero,axiom,
class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero_0,plain,
( class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero]) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add,axiom,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add_0,plain,
( class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add]) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1,axiom,
class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1_0,plain,
( class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1]) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__0,axiom,
class_Ring__and__Field_Osemiring__0(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__0_0,plain,
( class_Ring__and__Field_Osemiring__0(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__0]) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__1,axiom,
class_Ring__and__Field_Osemiring__1(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__1_0,plain,
( class_Ring__and__Field_Osemiring__1(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__1]) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Osemigroup__add,axiom,
class_OrderedGroup_Osemigroup__add(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__OrderedGroup_Osemigroup__add_0,plain,
( class_OrderedGroup_Osemigroup__add(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Osemigroup__add]) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom,axiom,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom_0,plain,
( class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom]) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one_0,plain,
( class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one]) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add_0,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add]) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring_0,plain,
( class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring]) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring,axiom,
class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring_0,plain,
( class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring]) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add_0,plain,
( class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add]) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult_0,plain,
( class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult]) ).
cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector_0,plain,
( class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector]) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult_0,plain,
( class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult]) ).
cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra_0,plain,
( class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra]) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__0,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__0_0,plain,
( class_Ring__and__Field_Ocomm__semiring__0(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__0]) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1_0,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1]) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom,axiom,
class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom_0,plain,
( class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom]) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors_0,plain,
( class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors]) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring,axiom,
class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring_0,plain,
( class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring]) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring,axiom,
class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring_0,plain,
( class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring]) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add_0,plain,
( class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add]) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add,axiom,
class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add_0,plain,
( class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add]) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add_0,plain,
( class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add]) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add_0,plain,
( class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add]) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict_0,plain,
( class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict]) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add_0,plain,
( class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add]) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors_0,plain,
( class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors]) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add_0,plain,
( class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add]) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add_0,plain,
( class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add]) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict_0,plain,
( class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict]) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oring__1__no__zero__divisors,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__Ring__and__Field_Oring__1__no__zero__divisors_0,plain,
( class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Oring__1__no__zero__divisors]) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring_0,plain,
( class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring]) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict_0,plain,
( class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict]) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le_0,plain,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le]) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add_0,plain,
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add]) ).
cnf(clsarity_nat__HOL_Ozero,axiom,
class_HOL_Ozero(tc_nat),
input ).
fof(clsarity_nat__HOL_Ozero_0,plain,
( class_HOL_Ozero(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__HOL_Ozero]) ).
cnf(clsarity_nat__Power_Opower,axiom,
class_Power_Opower(tc_nat),
input ).
fof(clsarity_nat__Power_Opower_0,plain,
( class_Power_Opower(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Power_Opower]) ).
cnf(clsarity_nat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_nat),
input ).
fof(clsarity_nat__Orderings_Oorder_0,plain,
( class_Orderings_Oorder(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Orderings_Oorder]) ).
cnf(clsarity_nat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_nat),
input ).
fof(clsarity_nat__Orderings_Olinorder_0,plain,
( class_Orderings_Olinorder(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Orderings_Olinorder]) ).
cnf(clsarity_nat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_nat),
input ).
fof(clsarity_nat__Orderings_Opreorder_0,plain,
( class_Orderings_Opreorder(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Orderings_Opreorder]) ).
cnf(clsarity_nat__Nat_Osemiring__char__0,axiom,
class_Nat_Osemiring__char__0(tc_nat),
input ).
fof(clsarity_nat__Nat_Osemiring__char__0_0,plain,
( class_Nat_Osemiring__char__0(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Nat_Osemiring__char__0]) ).
cnf(clsarity_nat__OrderedGroup_Omonoid__add,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
input ).
fof(clsarity_nat__OrderedGroup_Omonoid__add_0,plain,
( class_OrderedGroup_Omonoid__add(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Omonoid__add]) ).
cnf(clsarity_nat__Ring__and__Field_Osemiring,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
input ).
fof(clsarity_nat__Ring__and__Field_Osemiring_0,plain,
( class_Ring__and__Field_Osemiring(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Osemiring]) ).
cnf(clsarity_nat__OrderedGroup_Omonoid__mult,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
input ).
fof(clsarity_nat__OrderedGroup_Omonoid__mult_0,plain,
( class_OrderedGroup_Omonoid__mult(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Omonoid__mult]) ).
cnf(clsarity_nat__Ring__and__Field_Omult__mono,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
input ).
fof(clsarity_nat__Ring__and__Field_Omult__mono_0,plain,
( class_Ring__and__Field_Omult__mono(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Omult__mono]) ).
cnf(clsarity_nat__Ring__and__Field_Omult__zero,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
input ).
fof(clsarity_nat__Ring__and__Field_Omult__zero_0,plain,
( class_Ring__and__Field_Omult__zero(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Omult__zero]) ).
cnf(clsarity_nat__Ring__and__Field_Omult__mono1,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
input ).
fof(clsarity_nat__Ring__and__Field_Omult__mono1_0,plain,
( class_Ring__and__Field_Omult__mono1(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Omult__mono1]) ).
cnf(clsarity_nat__Ring__and__Field_Osemiring__0,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
input ).
fof(clsarity_nat__Ring__and__Field_Osemiring__0_0,plain,
( class_Ring__and__Field_Osemiring__0(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Osemiring__0]) ).
cnf(clsarity_nat__Ring__and__Field_Osemiring__1,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
input ).
fof(clsarity_nat__Ring__and__Field_Osemiring__1_0,plain,
( class_Ring__and__Field_Osemiring__1(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Osemiring__1]) ).
cnf(clsarity_nat__OrderedGroup_Osemigroup__add,axiom,
class_OrderedGroup_Osemigroup__add(tc_nat),
input ).
fof(clsarity_nat__OrderedGroup_Osemigroup__add_0,plain,
( class_OrderedGroup_Osemigroup__add(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Osemigroup__add]) ).
cnf(clsarity_nat__Ring__and__Field_Ozero__neq__one,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
input ).
fof(clsarity_nat__Ring__and__Field_Ozero__neq__one_0,plain,
( class_Ring__and__Field_Ozero__neq__one(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Ozero__neq__one]) ).
cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
input ).
fof(clsarity_nat__OrderedGroup_Ocomm__monoid__add_0,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Ocomm__monoid__add]) ).
cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
input ).
fof(clsarity_nat__Ring__and__Field_Ocomm__semiring_0,plain,
( class_Ring__and__Field_Ocomm__semiring(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Ocomm__semiring]) ).
cnf(clsarity_nat__OrderedGroup_Oab__semigroup__add,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
input ).
fof(clsarity_nat__OrderedGroup_Oab__semigroup__add_0,plain,
( class_OrderedGroup_Oab__semigroup__add(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Oab__semigroup__add]) ).
cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__mult,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
input ).
fof(clsarity_nat__OrderedGroup_Ocomm__monoid__mult_0,plain,
( class_OrderedGroup_Ocomm__monoid__mult(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Ocomm__monoid__mult]) ).
cnf(clsarity_nat__OrderedGroup_Oab__semigroup__mult,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
input ).
fof(clsarity_nat__OrderedGroup_Oab__semigroup__mult_0,plain,
( class_OrderedGroup_Oab__semigroup__mult(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Oab__semigroup__mult]) ).
cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__0,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
input ).
fof(clsarity_nat__Ring__and__Field_Ocomm__semiring__0_0,plain,
( class_Ring__and__Field_Ocomm__semiring__0(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Ocomm__semiring__0]) ).
cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
input ).
fof(clsarity_nat__Ring__and__Field_Ocomm__semiring__1_0,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Ocomm__semiring__1]) ).
cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
input ).
fof(clsarity_nat__Ring__and__Field_Oordered__semidom_0,plain,
( class_Ring__and__Field_Oordered__semidom(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Oordered__semidom]) ).
cnf(clsarity_nat__Ring__and__Field_Ono__zero__divisors,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
input ).
fof(clsarity_nat__Ring__and__Field_Ono__zero__divisors_0,plain,
( class_Ring__and__Field_Ono__zero__divisors(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Ono__zero__divisors]) ).
cnf(clsarity_nat__Ring__and__Field_Oordered__semiring,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
input ).
fof(clsarity_nat__Ring__and__Field_Oordered__semiring_0,plain,
( class_Ring__and__Field_Oordered__semiring(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Oordered__semiring]) ).
cnf(clsarity_nat__Ring__and__Field_Opordered__semiring,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
input ).
fof(clsarity_nat__Ring__and__Field_Opordered__semiring_0,plain,
( class_Ring__and__Field_Opordered__semiring(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Opordered__semiring]) ).
cnf(clsarity_nat__OrderedGroup_Ocancel__semigroup__add,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
input ).
fof(clsarity_nat__OrderedGroup_Ocancel__semigroup__add_0,plain,
( class_OrderedGroup_Ocancel__semigroup__add(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Ocancel__semigroup__add]) ).
cnf(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
input ).
fof(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add_0,plain,
( class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add]) ).
cnf(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
input ).
fof(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add_0,plain,
( class_OrderedGroup_Opordered__comm__monoid__add(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__comm__monoid__add]) ).
cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
input ).
fof(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add_0,plain,
( class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add]) ).
cnf(clsarity_nat__Ring__and__Field_Oordered__semiring__strict,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
input ).
fof(clsarity_nat__Ring__and__Field_Oordered__semiring__strict_0,plain,
( class_Ring__and__Field_Oordered__semiring__strict(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Oordered__semiring__strict]) ).
cnf(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
input ).
fof(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring_0,plain,
( class_Ring__and__Field_Opordered__cancel__semiring(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Opordered__cancel__semiring]) ).
cnf(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
input ).
fof(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict_0,plain,
( class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict]) ).
cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
input ).
fof(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le_0,plain,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le]) ).
cnf(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
input ).
fof(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add_0,plain,
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add]) ).
cnf(clsarity_nat__OrderedGroup_Ocancel__comm__monoid__add,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_nat),
input ).
fof(clsarity_nat__OrderedGroup_Ocancel__comm__monoid__add_0,plain,
( class_OrderedGroup_Ocancel__comm__monoid__add(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Ocancel__comm__monoid__add]) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring,axiom,
class_Ring__and__Field_Ocomm__ring(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring_0,plain,
( class_Ring__and__Field_Ocomm__ring(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring]) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring__1,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring__1_0,plain,
( class_Ring__and__Field_Ocomm__ring__1(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring__1]) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__comm__monoid__add,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
input ).
fof(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__comm__monoid__add_0,plain,
( class_OrderedGroup_Ocancel__comm__monoid__add(tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Ocancel__comm__monoid__add]) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring_0,plain,
( class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring]) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1_0,plain,
( class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1]) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
input ).
fof(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add_0,plain,
( class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add]) ).
cnf(cls_CHAINED_0,axiom,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(v_q____,tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex),
input ).
fof(cls_CHAINED_0_0,plain,
( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(v_q____,tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[cls_CHAINED_0]) ).
cnf(cls_nc_0,axiom,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(v_pa____,tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex),
input ).
fof(cls_nc_0_0,plain,
( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(v_pa____,tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[cls_nc_0]) ).
cnf(cls_q_I2_J_0,axiom,
hAPP(c_Polynomial_Opoly(v_q____,tc_Complex_Ocomplex),V_x) = hAPP(c_Polynomial_Opoly(v_pa____,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),v_c____),V_x)),
input ).
fof(cls_q_I2_J_0_0,plain,
! [V_x] :
( hAPP(c_Polynomial_Opoly(v_q____,tc_Complex_Ocomplex),V_x) = hAPP(c_Polynomial_Opoly(v_pa____,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),v_c____),V_x))
| $false ),
inference(orientation,[status(thm)],[cls_q_I2_J_0]) ).
cnf(cls_q_I1_J_0,axiom,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_q____,tc_Complex_Ocomplex) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_pa____,tc_Complex_Ocomplex),
input ).
fof(cls_q_I1_J_0_0,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_q____,tc_Complex_Ocomplex) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_pa____,tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[cls_q_I1_J_0]) ).
cnf(cls_assms_0,axiom,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex),
input ).
fof(cls_assms_0_0,plain,
( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[cls_assms_0]) ).
cnf(cls_poly__offset_1,axiom,
hAPP(c_Polynomial_Opoly(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1(V_a,V_p),tc_Complex_Ocomplex),V_q) = hAPP(c_Polynomial_Opoly(V_p,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),V_a),V_q)),
input ).
fof(cls_poly__offset_1_0,plain,
! [V_a,V_p,V_q] :
( hAPP(c_Polynomial_Opoly(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1(V_a,V_p),tc_Complex_Ocomplex),V_q) = hAPP(c_Polynomial_Opoly(V_p,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),V_a),V_q))
| $false ),
inference(orientation,[status(thm)],[cls_poly__offset_1]) ).
cnf(cls_n_0,axiom,
v_n____ = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_pa____,tc_Complex_Ocomplex),
input ).
fof(cls_n_0_0,plain,
( v_n____ = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_pa____,tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[cls_n_0]) ).
cnf(cls_c_0,axiom,
c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(c_Polynomial_Opoly(v_pa____,tc_Complex_Ocomplex),v_c____),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(hAPP(c_Polynomial_Opoly(v_pa____,tc_Complex_Ocomplex),V_w),tc_Complex_Ocomplex),tc_RealDef_Oreal),
input ).
fof(cls_c_0_0,plain,
! [V_w] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(c_Polynomial_Opoly(v_pa____,tc_Complex_Ocomplex),v_c____),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(hAPP(c_Polynomial_Opoly(v_pa____,tc_Complex_Ocomplex),V_w),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[cls_c_0]) ).
cnf(cls_poly__offset_0,axiom,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1(V_a,V_p),tc_Complex_Ocomplex) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(V_p,tc_Complex_Ocomplex),
input ).
fof(cls_poly__offset_0_0,plain,
! [V_a,V_p] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1(V_a,V_p),tc_Complex_Ocomplex) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(V_p,tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[cls_poly__offset_0]) ).
cnf(cls_pc0_0,axiom,
hAPP(c_Polynomial_Opoly(v_pa____,tc_Complex_Ocomplex),v_c____) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
input ).
fof(cls_pc0_0_0,plain,
( hAPP(c_Polynomial_Opoly(v_pa____,tc_Complex_Ocomplex),v_c____) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| $false ),
inference(orientation,[status(thm)],[cls_pc0_0]) ).
cnf(cls_plus__nat_Oadd__0_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n) = V_n,
input ).
fof(cls_plus__nat_Oadd__0_0_0,plain,
! [V_n] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n) = V_n
| $false ),
inference(orientation,[status(thm)],[cls_plus__nat_Oadd__0_0]) ).
cnf(cls_Nat_Oadd__0__right_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_HOL_Ozero__class_Ozero(tc_nat)) = V_m,
input ).
fof(cls_Nat_Oadd__0__right_0_0,plain,
! [V_m] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_HOL_Ozero__class_Ozero(tc_nat)) = V_m
| $false ),
inference(orientation,[status(thm)],[cls_Nat_Oadd__0__right_0]) ).
cnf(cls_natgb_Oadd__r0__iff_1,axiom,
V_x = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),c_HOL_Ozero__class_Ozero(tc_nat)),
input ).
fof(cls_natgb_Oadd__r0__iff_1_0,plain,
! [V_x] :
( V_x = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),c_HOL_Ozero__class_Ozero(tc_nat))
| $false ),
inference(orientation,[status(thm)],[cls_natgb_Oadd__r0__iff_1]) ).
cnf(cls_nat__add__left__commute_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_z)),
input ).
fof(cls_nat__add__left__commute_0_0,plain,
! [V_x,V_y,V_z] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_z))
| $false ),
inference(orientation,[status(thm)],[cls_nat__add__left__commute_0]) ).
cnf(cls_nat__add__assoc_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)),V_k) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k)),
input ).
fof(cls_nat__add__assoc_0_0,plain,
! [V_k,V_m,V_n] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)),V_k) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k))
| $false ),
inference(orientation,[status(thm)],[cls_nat__add__assoc_0]) ).
cnf(cls_add__is__0_2,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat),
input ).
fof(cls_add__is__0_2_0,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_add__is__0_2]) ).
cnf(cls_Suc__eq__plus1_0,axiom,
c_Suc(V_n) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),c_HOL_Oone__class_Oone(tc_nat)),
input ).
fof(cls_Suc__eq__plus1_0_0,plain,
! [V_n] :
( c_Suc(V_n) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),c_HOL_Oone__class_Oone(tc_nat))
| $false ),
inference(orientation,[status(thm)],[cls_Suc__eq__plus1_0]) ).
cnf(cls_Suc__eq__plus1__left_0,axiom,
c_Suc(V_n) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),V_n),
input ).
fof(cls_Suc__eq__plus1__left_0_0,plain,
! [V_n] :
( c_Suc(V_n) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),V_n)
| $false ),
inference(orientation,[status(thm)],[cls_Suc__eq__plus1__left_0]) ).
cnf(cls_add__is__1_4,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
input ).
fof(cls_add__is__1_4_0,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| $false ),
inference(orientation,[status(thm)],[cls_add__is__1_4]) ).
cnf(cls_add__is__1_5,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
input ).
fof(cls_add__is__1_5_0,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| $false ),
inference(orientation,[status(thm)],[cls_add__is__1_5]) ).
cnf(cls_real__le__refl_0,axiom,
c_lessequals(V_w,V_w,tc_RealDef_Oreal),
input ).
fof(cls_real__le__refl_0_0,plain,
! [V_w] :
( c_lessequals(V_w,V_w,tc_RealDef_Oreal)
| $false ),
inference(orientation,[status(thm)],[cls_real__le__refl_0]) ).
cnf(cls_power_Opower_Opower__0_0,axiom,
hAPP(hAPP(c_Power_Opower_Opower(V_one,V_times,T_a),V_a),c_HOL_Ozero__class_Ozero(tc_nat)) = V_one,
input ).
fof(cls_power_Opower_Opower__0_0_0,plain,
! [T_a,V_a,V_one,V_times] :
( hAPP(hAPP(c_Power_Opower_Opower(V_one,V_times,T_a),V_a),c_HOL_Ozero__class_Ozero(tc_nat)) = V_one
| $false ),
inference(orientation,[status(thm)],[cls_power_Opower_Opower__0_0]) ).
cnf(cls_nat_Osimps_I3_J_0,axiom,
c_Suc(V_nat_H) != c_HOL_Ozero__class_Ozero(tc_nat),
input ).
fof(cls_nat_Osimps_I3_J_0_0,plain,
! [V_nat_H] :
( c_Suc(V_nat_H) != c_HOL_Ozero__class_Ozero(tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_nat_Osimps_I3_J_0]) ).
cnf(cls_Suc__neq__Zero_0,axiom,
c_Suc(V_m) != c_HOL_Ozero__class_Ozero(tc_nat),
input ).
fof(cls_Suc__neq__Zero_0_0,plain,
! [V_m] :
( c_Suc(V_m) != c_HOL_Ozero__class_Ozero(tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_Suc__neq__Zero_0]) ).
cnf(cls_one__is__add_4,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)),
input ).
fof(cls_one__is__add_4_0,plain,
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))
| $false ),
inference(orientation,[status(thm)],[cls_one__is__add_4]) ).
cnf(cls_One__nat__def_0,axiom,
c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
input ).
fof(cls_One__nat__def_0_0,plain,
( c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| $false ),
inference(orientation,[status(thm)],[cls_One__nat__def_0]) ).
cnf(cls_Zero__neq__Suc_0,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m),
input ).
fof(cls_Zero__neq__Suc_0_0,plain,
! [V_m] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m)
| $false ),
inference(orientation,[status(thm)],[cls_Zero__neq__Suc_0]) ).
cnf(cls_nat_Osimps_I2_J_0,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H),
input ).
fof(cls_nat_Osimps_I2_J_0_0,plain,
! [V_nat_H] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H)
| $false ),
inference(orientation,[status(thm)],[cls_nat_Osimps_I2_J_0]) ).
cnf(cls_n__not__Suc__n_0,axiom,
V_n != c_Suc(V_n),
input ).
fof(cls_n__not__Suc__n_0_0,plain,
! [V_n] :
( V_n != c_Suc(V_n)
| $false ),
inference(orientation,[status(thm)],[cls_n__not__Suc__n_0]) ).
cnf(cls_Suc__n__not__n_0,axiom,
c_Suc(V_n) != V_n,
input ).
fof(cls_Suc__n__not__n_0_0,plain,
! [V_n] :
( c_Suc(V_n) != V_n
| $false ),
inference(orientation,[status(thm)],[cls_Suc__n__not__n_0]) ).
cnf(cls_power_Opower_Opower__Suc_0,axiom,
hAPP(hAPP(c_Power_Opower_Opower(V_one,V_times,T_a),V_a),c_Suc(V_n)) = hAPP(hAPP(V_times,V_a),hAPP(hAPP(c_Power_Opower_Opower(V_one,V_times,T_a),V_a),V_n)),
input ).
fof(cls_power_Opower_Opower__Suc_0_0,plain,
! [T_a,V_a,V_n,V_one,V_times] :
( hAPP(hAPP(c_Power_Opower_Opower(V_one,V_times,T_a),V_a),c_Suc(V_n)) = hAPP(hAPP(V_times,V_a),hAPP(hAPP(c_Power_Opower_Opower(V_one,V_times,T_a),V_a),V_n))
| $false ),
inference(orientation,[status(thm)],[cls_power_Opower_Opower__Suc_0]) ).
cnf(cls_nat__add__commute_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),
input ).
fof(cls_nat__add__commute_0_0,plain,
! [V_m,V_n] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m)
| $false ),
inference(orientation,[status(thm)],[cls_nat__add__commute_0]) ).
cnf(cls_add__Suc__right_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_Suc(V_n)) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)),
input ).
fof(cls_add__Suc__right_0_0,plain,
! [V_m,V_n] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_Suc(V_n)) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n))
| $false ),
inference(orientation,[status(thm)],[cls_add__Suc__right_0]) ).
cnf(cls_add__Suc_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(V_m)),V_n) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)),
input ).
fof(cls_add__Suc_0_0,plain,
! [V_m,V_n] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(V_m)),V_n) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n))
| $false ),
inference(orientation,[status(thm)],[cls_add__Suc_0]) ).
cnf(cls_one__is__add_5,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
input ).
fof(cls_one__is__add_5_0,plain,
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))
| $false ),
inference(orientation,[status(thm)],[cls_one__is__add_5]) ).
cnf(cls_add__Suc__shift_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(V_m)),V_n) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_Suc(V_n)),
input ).
fof(cls_add__Suc__shift_0_0,plain,
! [V_m,V_n] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(V_m)),V_n) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_Suc(V_n))
| $false ),
inference(orientation,[status(thm)],[cls_add__Suc__shift_0]) ).
fof(def_lhs_atom1,axiom,
! [V_n,V_m] :
( lhs_atom1(V_n,V_m)
<=> hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(V_m)),V_n) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_Suc(V_n)) ),
inference(definition,[],]) ).
fof(to_be_clausified_0,plain,
! [V_m,V_n] :
( lhs_atom1(V_n,V_m)
| $false ),
inference(fold_definition,[status(thm)],[cls_add__Suc__shift_0_0,def_lhs_atom1]) ).
fof(def_lhs_atom2,axiom,
( lhs_atom2
<=> c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(definition,[],]) ).
fof(to_be_clausified_1,plain,
( lhs_atom2
| $false ),
inference(fold_definition,[status(thm)],[cls_one__is__add_5_0,def_lhs_atom2]) ).
fof(def_lhs_atom3,axiom,
! [V_n,V_m] :
( lhs_atom3(V_n,V_m)
<=> hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(V_m)),V_n) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)) ),
inference(definition,[],]) ).
fof(to_be_clausified_2,plain,
! [V_m,V_n] :
( lhs_atom3(V_n,V_m)
| $false ),
inference(fold_definition,[status(thm)],[cls_add__Suc_0_0,def_lhs_atom3]) ).
fof(def_lhs_atom4,axiom,
! [V_n,V_m] :
( lhs_atom4(V_n,V_m)
<=> hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_Suc(V_n)) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)) ),
inference(definition,[],]) ).
fof(to_be_clausified_3,plain,
! [V_m,V_n] :
( lhs_atom4(V_n,V_m)
| $false ),
inference(fold_definition,[status(thm)],[cls_add__Suc__right_0_0,def_lhs_atom4]) ).
fof(def_lhs_atom5,axiom,
! [V_n,V_m] :
( lhs_atom5(V_n,V_m)
<=> hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m) ),
inference(definition,[],]) ).
fof(to_be_clausified_4,plain,
! [V_m,V_n] :
( lhs_atom5(V_n,V_m)
| $false ),
inference(fold_definition,[status(thm)],[cls_nat__add__commute_0_0,def_lhs_atom5]) ).
fof(def_lhs_atom6,axiom,
! [V_times,V_one,V_n,V_a,T_a] :
( lhs_atom6(V_times,V_one,V_n,V_a,T_a)
<=> hAPP(hAPP(c_Power_Opower_Opower(V_one,V_times,T_a),V_a),c_Suc(V_n)) = hAPP(hAPP(V_times,V_a),hAPP(hAPP(c_Power_Opower_Opower(V_one,V_times,T_a),V_a),V_n)) ),
inference(definition,[],]) ).
fof(to_be_clausified_5,plain,
! [T_a,V_a,V_n,V_one,V_times] :
( lhs_atom6(V_times,V_one,V_n,V_a,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_power_Opower_Opower__Suc_0_0,def_lhs_atom6]) ).
fof(def_lhs_atom7,axiom,
! [V_n] :
( lhs_atom7(V_n)
<=> c_Suc(V_n) != V_n ),
inference(definition,[],]) ).
fof(to_be_clausified_6,plain,
! [V_n] :
( lhs_atom7(V_n)
| $false ),
inference(fold_definition,[status(thm)],[cls_Suc__n__not__n_0_0,def_lhs_atom7]) ).
fof(def_lhs_atom8,axiom,
! [V_n] :
( lhs_atom8(V_n)
<=> V_n != c_Suc(V_n) ),
inference(definition,[],]) ).
fof(to_be_clausified_7,plain,
! [V_n] :
( lhs_atom8(V_n)
| $false ),
inference(fold_definition,[status(thm)],[cls_n__not__Suc__n_0_0,def_lhs_atom8]) ).
fof(def_lhs_atom9,axiom,
! [V_nat_H] :
( lhs_atom9(V_nat_H)
<=> c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H) ),
inference(definition,[],]) ).
fof(to_be_clausified_8,plain,
! [V_nat_H] :
( lhs_atom9(V_nat_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_nat_Osimps_I2_J_0_0,def_lhs_atom9]) ).
fof(def_lhs_atom10,axiom,
! [V_m] :
( lhs_atom10(V_m)
<=> c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m) ),
inference(definition,[],]) ).
fof(to_be_clausified_9,plain,
! [V_m] :
( lhs_atom10(V_m)
| $false ),
inference(fold_definition,[status(thm)],[cls_Zero__neq__Suc_0_0,def_lhs_atom10]) ).
fof(def_lhs_atom11,axiom,
( lhs_atom11
<=> c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(definition,[],]) ).
fof(to_be_clausified_10,plain,
( lhs_atom11
| $false ),
inference(fold_definition,[status(thm)],[cls_One__nat__def_0_0,def_lhs_atom11]) ).
fof(def_lhs_atom12,axiom,
( lhs_atom12
<=> c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(definition,[],]) ).
fof(to_be_clausified_11,plain,
( lhs_atom12
| $false ),
inference(fold_definition,[status(thm)],[cls_one__is__add_4_0,def_lhs_atom12]) ).
fof(def_lhs_atom13,axiom,
! [V_m] :
( lhs_atom13(V_m)
<=> c_Suc(V_m) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_12,plain,
! [V_m] :
( lhs_atom13(V_m)
| $false ),
inference(fold_definition,[status(thm)],[cls_Suc__neq__Zero_0_0,def_lhs_atom13]) ).
fof(def_lhs_atom14,axiom,
! [V_nat_H] :
( lhs_atom14(V_nat_H)
<=> c_Suc(V_nat_H) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_13,plain,
! [V_nat_H] :
( lhs_atom14(V_nat_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_nat_Osimps_I3_J_0_0,def_lhs_atom14]) ).
fof(def_lhs_atom15,axiom,
! [V_times,V_one,V_a,T_a] :
( lhs_atom15(V_times,V_one,V_a,T_a)
<=> hAPP(hAPP(c_Power_Opower_Opower(V_one,V_times,T_a),V_a),c_HOL_Ozero__class_Ozero(tc_nat)) = V_one ),
inference(definition,[],]) ).
fof(to_be_clausified_14,plain,
! [T_a,V_a,V_one,V_times] :
( lhs_atom15(V_times,V_one,V_a,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_power_Opower_Opower__0_0_0,def_lhs_atom15]) ).
fof(def_lhs_atom16,axiom,
! [V_w] :
( lhs_atom16(V_w)
<=> c_lessequals(V_w,V_w,tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_15,plain,
! [V_w] :
( lhs_atom16(V_w)
| $false ),
inference(fold_definition,[status(thm)],[cls_real__le__refl_0_0,def_lhs_atom16]) ).
fof(def_lhs_atom17,axiom,
( lhs_atom17
<=> hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(definition,[],]) ).
fof(to_be_clausified_16,plain,
( lhs_atom17
| $false ),
inference(fold_definition,[status(thm)],[cls_add__is__1_5_0,def_lhs_atom17]) ).
fof(def_lhs_atom18,axiom,
( lhs_atom18
<=> hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(definition,[],]) ).
fof(to_be_clausified_17,plain,
( lhs_atom18
| $false ),
inference(fold_definition,[status(thm)],[cls_add__is__1_4_0,def_lhs_atom18]) ).
fof(def_lhs_atom19,axiom,
! [V_n] :
( lhs_atom19(V_n)
<=> c_Suc(V_n) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),V_n) ),
inference(definition,[],]) ).
fof(to_be_clausified_18,plain,
! [V_n] :
( lhs_atom19(V_n)
| $false ),
inference(fold_definition,[status(thm)],[cls_Suc__eq__plus1__left_0_0,def_lhs_atom19]) ).
fof(def_lhs_atom20,axiom,
! [V_n] :
( lhs_atom20(V_n)
<=> c_Suc(V_n) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(definition,[],]) ).
fof(to_be_clausified_19,plain,
! [V_n] :
( lhs_atom20(V_n)
| $false ),
inference(fold_definition,[status(thm)],[cls_Suc__eq__plus1_0_0,def_lhs_atom20]) ).
fof(def_lhs_atom21,axiom,
( lhs_atom21
<=> hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_20,plain,
( lhs_atom21
| $false ),
inference(fold_definition,[status(thm)],[cls_add__is__0_2_0,def_lhs_atom21]) ).
fof(def_lhs_atom22,axiom,
! [V_n,V_m,V_k] :
( lhs_atom22(V_n,V_m,V_k)
<=> hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)),V_k) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k)) ),
inference(definition,[],]) ).
fof(to_be_clausified_21,plain,
! [V_k,V_m,V_n] :
( lhs_atom22(V_n,V_m,V_k)
| $false ),
inference(fold_definition,[status(thm)],[cls_nat__add__assoc_0_0,def_lhs_atom22]) ).
fof(def_lhs_atom23,axiom,
! [V_z,V_y,V_x] :
( lhs_atom23(V_z,V_y,V_x)
<=> hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_z)) ),
inference(definition,[],]) ).
fof(to_be_clausified_22,plain,
! [V_x,V_y,V_z] :
( lhs_atom23(V_z,V_y,V_x)
| $false ),
inference(fold_definition,[status(thm)],[cls_nat__add__left__commute_0_0,def_lhs_atom23]) ).
fof(def_lhs_atom24,axiom,
! [V_x] :
( lhs_atom24(V_x)
<=> V_x = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(definition,[],]) ).
fof(to_be_clausified_23,plain,
! [V_x] :
( lhs_atom24(V_x)
| $false ),
inference(fold_definition,[status(thm)],[cls_natgb_Oadd__r0__iff_1_0,def_lhs_atom24]) ).
fof(def_lhs_atom25,axiom,
! [V_m] :
( lhs_atom25(V_m)
<=> hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_HOL_Ozero__class_Ozero(tc_nat)) = V_m ),
inference(definition,[],]) ).
fof(to_be_clausified_24,plain,
! [V_m] :
( lhs_atom25(V_m)
| $false ),
inference(fold_definition,[status(thm)],[cls_Nat_Oadd__0__right_0_0,def_lhs_atom25]) ).
fof(def_lhs_atom26,axiom,
! [V_n] :
( lhs_atom26(V_n)
<=> hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n) = V_n ),
inference(definition,[],]) ).
fof(to_be_clausified_25,plain,
! [V_n] :
( lhs_atom26(V_n)
| $false ),
inference(fold_definition,[status(thm)],[cls_plus__nat_Oadd__0_0_0,def_lhs_atom26]) ).
fof(def_lhs_atom27,axiom,
( lhs_atom27
<=> hAPP(c_Polynomial_Opoly(v_pa____,tc_Complex_Ocomplex),v_c____) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_26,plain,
( lhs_atom27
| $false ),
inference(fold_definition,[status(thm)],[cls_pc0_0_0,def_lhs_atom27]) ).
fof(def_lhs_atom28,axiom,
! [V_p,V_a] :
( lhs_atom28(V_p,V_a)
<=> c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1(V_a,V_p),tc_Complex_Ocomplex) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(V_p,tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_27,plain,
! [V_a,V_p] :
( lhs_atom28(V_p,V_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_poly__offset_0_0,def_lhs_atom28]) ).
fof(def_lhs_atom29,axiom,
! [V_w] :
( lhs_atom29(V_w)
<=> c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(c_Polynomial_Opoly(v_pa____,tc_Complex_Ocomplex),v_c____),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(hAPP(c_Polynomial_Opoly(v_pa____,tc_Complex_Ocomplex),V_w),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_28,plain,
! [V_w] :
( lhs_atom29(V_w)
| $false ),
inference(fold_definition,[status(thm)],[cls_c_0_0,def_lhs_atom29]) ).
fof(def_lhs_atom30,axiom,
( lhs_atom30
<=> v_n____ = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_pa____,tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_29,plain,
( lhs_atom30
| $false ),
inference(fold_definition,[status(thm)],[cls_n_0_0,def_lhs_atom30]) ).
fof(def_lhs_atom31,axiom,
! [V_q,V_p,V_a] :
( lhs_atom31(V_q,V_p,V_a)
<=> hAPP(c_Polynomial_Opoly(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1(V_a,V_p),tc_Complex_Ocomplex),V_q) = hAPP(c_Polynomial_Opoly(V_p,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),V_a),V_q)) ),
inference(definition,[],]) ).
fof(to_be_clausified_30,plain,
! [V_a,V_p,V_q] :
( lhs_atom31(V_q,V_p,V_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_poly__offset_1_0,def_lhs_atom31]) ).
fof(def_lhs_atom32,axiom,
( lhs_atom32
<=> ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_31,plain,
( lhs_atom32
| $false ),
inference(fold_definition,[status(thm)],[cls_assms_0_0,def_lhs_atom32]) ).
fof(def_lhs_atom33,axiom,
( lhs_atom33
<=> c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_q____,tc_Complex_Ocomplex) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_pa____,tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_32,plain,
( lhs_atom33
| $false ),
inference(fold_definition,[status(thm)],[cls_q_I1_J_0_0,def_lhs_atom33]) ).
fof(def_lhs_atom34,axiom,
! [V_x] :
( lhs_atom34(V_x)
<=> hAPP(c_Polynomial_Opoly(v_q____,tc_Complex_Ocomplex),V_x) = hAPP(c_Polynomial_Opoly(v_pa____,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),v_c____),V_x)) ),
inference(definition,[],]) ).
fof(to_be_clausified_33,plain,
! [V_x] :
( lhs_atom34(V_x)
| $false ),
inference(fold_definition,[status(thm)],[cls_q_I2_J_0_0,def_lhs_atom34]) ).
fof(def_lhs_atom35,axiom,
( lhs_atom35
<=> ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(v_pa____,tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_34,plain,
( lhs_atom35
| $false ),
inference(fold_definition,[status(thm)],[cls_nc_0_0,def_lhs_atom35]) ).
fof(def_lhs_atom36,axiom,
( lhs_atom36
<=> ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(v_q____,tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_35,plain,
( lhs_atom36
| $false ),
inference(fold_definition,[status(thm)],[cls_CHAINED_0_0,def_lhs_atom36]) ).
fof(def_lhs_atom37,axiom,
( lhs_atom37
<=> class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_36,plain,
( lhs_atom37
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add_0,def_lhs_atom37]) ).
fof(def_lhs_atom38,axiom,
( lhs_atom38
<=> class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_37,plain,
( lhs_atom38
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1_0,def_lhs_atom38]) ).
fof(def_lhs_atom39,axiom,
( lhs_atom39
<=> class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_38,plain,
( lhs_atom39
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring_0,def_lhs_atom39]) ).
fof(def_lhs_atom40,axiom,
( lhs_atom40
<=> class_OrderedGroup_Ocancel__comm__monoid__add(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_39,plain,
( lhs_atom40
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Ocancel__comm__monoid__add_0,def_lhs_atom40]) ).
fof(def_lhs_atom41,axiom,
( lhs_atom41
<=> class_Ring__and__Field_Ocomm__ring__1(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_40,plain,
( lhs_atom41
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring__1_0,def_lhs_atom41]) ).
fof(def_lhs_atom42,axiom,
( lhs_atom42
<=> class_Ring__and__Field_Ocomm__ring(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_41,plain,
( lhs_atom42
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring_0,def_lhs_atom42]) ).
fof(def_lhs_atom43,axiom,
( lhs_atom43
<=> class_OrderedGroup_Ocancel__comm__monoid__add(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_42,plain,
( lhs_atom43
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Ocancel__comm__monoid__add_0,def_lhs_atom43]) ).
fof(def_lhs_atom44,axiom,
( lhs_atom44
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_43,plain,
( lhs_atom44
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add_0,def_lhs_atom44]) ).
fof(def_lhs_atom45,axiom,
( lhs_atom45
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_44,plain,
( lhs_atom45
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le_0,def_lhs_atom45]) ).
fof(def_lhs_atom46,axiom,
( lhs_atom46
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_45,plain,
( lhs_atom46
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict_0,def_lhs_atom46]) ).
fof(def_lhs_atom47,axiom,
( lhs_atom47
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_46,plain,
( lhs_atom47
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Opordered__cancel__semiring_0,def_lhs_atom47]) ).
fof(def_lhs_atom48,axiom,
( lhs_atom48
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_47,plain,
( lhs_atom48
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Oordered__semiring__strict_0,def_lhs_atom48]) ).
fof(def_lhs_atom49,axiom,
( lhs_atom49
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_48,plain,
( lhs_atom49
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add_0,def_lhs_atom49]) ).
fof(def_lhs_atom50,axiom,
( lhs_atom50
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_49,plain,
( lhs_atom50
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__comm__monoid__add_0,def_lhs_atom50]) ).
fof(def_lhs_atom51,axiom,
( lhs_atom51
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_50,plain,
( lhs_atom51
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add_0,def_lhs_atom51]) ).
fof(def_lhs_atom52,axiom,
( lhs_atom52
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_51,plain,
( lhs_atom52
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Ocancel__semigroup__add_0,def_lhs_atom52]) ).
fof(def_lhs_atom53,axiom,
( lhs_atom53
<=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_52,plain,
( lhs_atom53
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Opordered__semiring_0,def_lhs_atom53]) ).
fof(def_lhs_atom54,axiom,
( lhs_atom54
<=> class_Ring__and__Field_Oordered__semiring(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_53,plain,
( lhs_atom54
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Oordered__semiring_0,def_lhs_atom54]) ).
fof(def_lhs_atom55,axiom,
( lhs_atom55
<=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_54,plain,
( lhs_atom55
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Ono__zero__divisors_0,def_lhs_atom55]) ).
fof(def_lhs_atom56,axiom,
( lhs_atom56
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_55,plain,
( lhs_atom56
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Oordered__semidom_0,def_lhs_atom56]) ).
fof(def_lhs_atom57,axiom,
( lhs_atom57
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_56,plain,
( lhs_atom57
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Ocomm__semiring__1_0,def_lhs_atom57]) ).
fof(def_lhs_atom58,axiom,
( lhs_atom58
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_57,plain,
( lhs_atom58
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Ocomm__semiring__0_0,def_lhs_atom58]) ).
fof(def_lhs_atom59,axiom,
( lhs_atom59
<=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_58,plain,
( lhs_atom59
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Oab__semigroup__mult_0,def_lhs_atom59]) ).
fof(def_lhs_atom60,axiom,
( lhs_atom60
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_59,plain,
( lhs_atom60
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Ocomm__monoid__mult_0,def_lhs_atom60]) ).
fof(def_lhs_atom61,axiom,
( lhs_atom61
<=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_60,plain,
( lhs_atom61
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Oab__semigroup__add_0,def_lhs_atom61]) ).
fof(def_lhs_atom62,axiom,
( lhs_atom62
<=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_61,plain,
( lhs_atom62
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Ocomm__semiring_0,def_lhs_atom62]) ).
fof(def_lhs_atom63,axiom,
( lhs_atom63
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_62,plain,
( lhs_atom63
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Ocomm__monoid__add_0,def_lhs_atom63]) ).
fof(def_lhs_atom64,axiom,
( lhs_atom64
<=> class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_63,plain,
( lhs_atom64
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Ozero__neq__one_0,def_lhs_atom64]) ).
fof(def_lhs_atom65,axiom,
( lhs_atom65
<=> class_OrderedGroup_Osemigroup__add(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_64,plain,
( lhs_atom65
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Osemigroup__add_0,def_lhs_atom65]) ).
fof(def_lhs_atom66,axiom,
( lhs_atom66
<=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_65,plain,
( lhs_atom66
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Osemiring__1_0,def_lhs_atom66]) ).
fof(def_lhs_atom67,axiom,
( lhs_atom67
<=> class_Ring__and__Field_Osemiring__0(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_66,plain,
( lhs_atom67
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Osemiring__0_0,def_lhs_atom67]) ).
fof(def_lhs_atom68,axiom,
( lhs_atom68
<=> class_Ring__and__Field_Omult__mono1(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_67,plain,
( lhs_atom68
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Omult__mono1_0,def_lhs_atom68]) ).
fof(def_lhs_atom69,axiom,
( lhs_atom69
<=> class_Ring__and__Field_Omult__zero(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_68,plain,
( lhs_atom69
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Omult__zero_0,def_lhs_atom69]) ).
fof(def_lhs_atom70,axiom,
( lhs_atom70
<=> class_Ring__and__Field_Omult__mono(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_69,plain,
( lhs_atom70
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Omult__mono_0,def_lhs_atom70]) ).
fof(def_lhs_atom71,axiom,
( lhs_atom71
<=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_70,plain,
( lhs_atom71
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Omonoid__mult_0,def_lhs_atom71]) ).
fof(def_lhs_atom72,axiom,
( lhs_atom72
<=> class_Ring__and__Field_Osemiring(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_71,plain,
( lhs_atom72
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Osemiring_0,def_lhs_atom72]) ).
fof(def_lhs_atom73,axiom,
( lhs_atom73
<=> class_OrderedGroup_Omonoid__add(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_72,plain,
( lhs_atom73
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Omonoid__add_0,def_lhs_atom73]) ).
fof(def_lhs_atom74,axiom,
( lhs_atom74
<=> class_Nat_Osemiring__char__0(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_73,plain,
( lhs_atom74
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Nat_Osemiring__char__0_0,def_lhs_atom74]) ).
fof(def_lhs_atom75,axiom,
( lhs_atom75
<=> class_Orderings_Opreorder(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_74,plain,
( lhs_atom75
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Opreorder_0,def_lhs_atom75]) ).
fof(def_lhs_atom76,axiom,
( lhs_atom76
<=> class_Orderings_Olinorder(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_75,plain,
( lhs_atom76
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Olinorder_0,def_lhs_atom76]) ).
fof(def_lhs_atom77,axiom,
( lhs_atom77
<=> class_Orderings_Oorder(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_76,plain,
( lhs_atom77
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Oorder_0,def_lhs_atom77]) ).
fof(def_lhs_atom78,axiom,
( lhs_atom78
<=> class_Power_Opower(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_77,plain,
( lhs_atom78
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Power_Opower_0,def_lhs_atom78]) ).
fof(def_lhs_atom79,axiom,
( lhs_atom79
<=> class_HOL_Ozero(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_78,plain,
( lhs_atom79
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__HOL_Ozero_0,def_lhs_atom79]) ).
fof(def_lhs_atom80,axiom,
( lhs_atom80
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_79,plain,
( lhs_atom80
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add_0,def_lhs_atom80]) ).
fof(def_lhs_atom81,axiom,
( lhs_atom81
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_80,plain,
( lhs_atom81
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le_0,def_lhs_atom81]) ).
fof(def_lhs_atom82,axiom,
( lhs_atom82
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_81,plain,
( lhs_atom82
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict_0,def_lhs_atom82]) ).
fof(def_lhs_atom83,axiom,
( lhs_atom83
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_82,plain,
( lhs_atom83
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring_0,def_lhs_atom83]) ).
fof(def_lhs_atom84,axiom,
( lhs_atom84
<=> class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_83,plain,
( lhs_atom84
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Oring__1__no__zero__divisors_0,def_lhs_atom84]) ).
fof(def_lhs_atom85,axiom,
( lhs_atom85
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_84,plain,
( lhs_atom85
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict_0,def_lhs_atom85]) ).
fof(def_lhs_atom86,axiom,
( lhs_atom86
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_85,plain,
( lhs_atom86
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add_0,def_lhs_atom86]) ).
fof(def_lhs_atom87,axiom,
( lhs_atom87
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_86,plain,
( lhs_atom87
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add_0,def_lhs_atom87]) ).
fof(def_lhs_atom88,axiom,
( lhs_atom88
<=> class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_87,plain,
( lhs_atom88
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors_0,def_lhs_atom88]) ).
fof(def_lhs_atom89,axiom,
( lhs_atom89
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_88,plain,
( lhs_atom89
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add_0,def_lhs_atom89]) ).
fof(def_lhs_atom90,axiom,
( lhs_atom90
<=> class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_89,plain,
( lhs_atom90
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict_0,def_lhs_atom90]) ).
fof(def_lhs_atom91,axiom,
( lhs_atom91
<=> class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_90,plain,
( lhs_atom91
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add_0,def_lhs_atom91]) ).
fof(def_lhs_atom92,axiom,
( lhs_atom92
<=> class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_91,plain,
( lhs_atom92
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add_0,def_lhs_atom92]) ).
fof(def_lhs_atom93,axiom,
( lhs_atom93
<=> class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_92,plain,
( lhs_atom93
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add_0,def_lhs_atom93]) ).
fof(def_lhs_atom94,axiom,
( lhs_atom94
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_93,plain,
( lhs_atom94
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add_0,def_lhs_atom94]) ).
fof(def_lhs_atom95,axiom,
( lhs_atom95
<=> class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_94,plain,
( lhs_atom95
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring_0,def_lhs_atom95]) ).
fof(def_lhs_atom96,axiom,
( lhs_atom96
<=> class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_95,plain,
( lhs_atom96
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring_0,def_lhs_atom96]) ).
fof(def_lhs_atom97,axiom,
( lhs_atom97
<=> class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_96,plain,
( lhs_atom97
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors_0,def_lhs_atom97]) ).
fof(def_lhs_atom98,axiom,
( lhs_atom98
<=> class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_97,plain,
( lhs_atom98
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom_0,def_lhs_atom98]) ).
fof(def_lhs_atom99,axiom,
( lhs_atom99
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_98,plain,
( lhs_atom99
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1_0,def_lhs_atom99]) ).
fof(def_lhs_atom100,axiom,
( lhs_atom100
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_99,plain,
( lhs_atom100
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__0_0,def_lhs_atom100]) ).
fof(def_lhs_atom101,axiom,
( lhs_atom101
<=> class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_100,plain,
( lhs_atom101
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra_0,def_lhs_atom101]) ).
fof(def_lhs_atom102,axiom,
( lhs_atom102
<=> class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_101,plain,
( lhs_atom102
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult_0,def_lhs_atom102]) ).
fof(def_lhs_atom103,axiom,
( lhs_atom103
<=> class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_102,plain,
( lhs_atom103
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector_0,def_lhs_atom103]) ).
fof(def_lhs_atom104,axiom,
( lhs_atom104
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_103,plain,
( lhs_atom104
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult_0,def_lhs_atom104]) ).
fof(def_lhs_atom105,axiom,
( lhs_atom105
<=> class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_104,plain,
( lhs_atom105
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add_0,def_lhs_atom105]) ).
fof(def_lhs_atom106,axiom,
( lhs_atom106
<=> class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_105,plain,
( lhs_atom106
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring_0,def_lhs_atom106]) ).
fof(def_lhs_atom107,axiom,
( lhs_atom107
<=> class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_106,plain,
( lhs_atom107
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring_0,def_lhs_atom107]) ).
fof(def_lhs_atom108,axiom,
( lhs_atom108
<=> class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_107,plain,
( lhs_atom108
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add_0,def_lhs_atom108]) ).
fof(def_lhs_atom109,axiom,
( lhs_atom109
<=> class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_108,plain,
( lhs_atom109
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one_0,def_lhs_atom109]) ).
fof(def_lhs_atom110,axiom,
( lhs_atom110
<=> class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_109,plain,
( lhs_atom110
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom_0,def_lhs_atom110]) ).
fof(def_lhs_atom111,axiom,
( lhs_atom111
<=> class_OrderedGroup_Osemigroup__add(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_110,plain,
( lhs_atom111
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Osemigroup__add_0,def_lhs_atom111]) ).
fof(def_lhs_atom112,axiom,
( lhs_atom112
<=> class_Ring__and__Field_Osemiring__1(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_111,plain,
( lhs_atom112
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__1_0,def_lhs_atom112]) ).
fof(def_lhs_atom113,axiom,
( lhs_atom113
<=> class_Ring__and__Field_Osemiring__0(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_112,plain,
( lhs_atom113
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__0_0,def_lhs_atom113]) ).
fof(def_lhs_atom114,axiom,
( lhs_atom114
<=> class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_113,plain,
( lhs_atom114
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1_0,def_lhs_atom114]) ).
fof(def_lhs_atom115,axiom,
( lhs_atom115
<=> class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_114,plain,
( lhs_atom115
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add_0,def_lhs_atom115]) ).
fof(def_lhs_atom116,axiom,
( lhs_atom116
<=> class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_115,plain,
( lhs_atom116
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero_0,def_lhs_atom116]) ).
fof(def_lhs_atom117,axiom,
( lhs_atom117
<=> class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_116,plain,
( lhs_atom117
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono_0,def_lhs_atom117]) ).
fof(def_lhs_atom118,axiom,
( lhs_atom118
<=> class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_117,plain,
( lhs_atom118
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult_0,def_lhs_atom118]) ).
fof(def_lhs_atom119,axiom,
( lhs_atom119
<=> class_Ring__and__Field_Osemiring(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_118,plain,
( lhs_atom119
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Osemiring_0,def_lhs_atom119]) ).
fof(def_lhs_atom120,axiom,
( lhs_atom120
<=> class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_119,plain,
( lhs_atom120
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add_0,def_lhs_atom120]) ).
fof(def_lhs_atom121,axiom,
( lhs_atom121
<=> class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_120,plain,
( lhs_atom121
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add_0,def_lhs_atom121]) ).
fof(def_lhs_atom122,axiom,
( lhs_atom122
<=> class_Ring__and__Field_Oring__1(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_121,plain,
( lhs_atom122
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Oring__1_0,def_lhs_atom122]) ).
fof(def_lhs_atom123,axiom,
( lhs_atom123
<=> class_Ring__and__Field_Oring(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_122,plain,
( lhs_atom123
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Oring_0,def_lhs_atom123]) ).
fof(def_lhs_atom124,axiom,
( lhs_atom124
<=> class_Ring__and__Field_Oidom(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_123,plain,
( lhs_atom124
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Oidom_0,def_lhs_atom124]) ).
fof(def_lhs_atom125,axiom,
( lhs_atom125
<=> class_Nat_Osemiring__char__0(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_124,plain,
( lhs_atom125
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__Nat_Osemiring__char__0_0,def_lhs_atom125]) ).
fof(def_lhs_atom126,axiom,
( lhs_atom126
<=> class_Orderings_Opreorder(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_125,plain,
( lhs_atom126
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__Orderings_Opreorder_0,def_lhs_atom126]) ).
fof(def_lhs_atom127,axiom,
( lhs_atom127
<=> class_Orderings_Olinorder(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_126,plain,
( lhs_atom127
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__Orderings_Olinorder_0,def_lhs_atom127]) ).
fof(def_lhs_atom128,axiom,
( lhs_atom128
<=> class_Orderings_Oorder(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_127,plain,
( lhs_atom128
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__Orderings_Oorder_0,def_lhs_atom128]) ).
fof(def_lhs_atom129,axiom,
( lhs_atom129
<=> class_Int_Oring__char__0(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_128,plain,
( lhs_atom129
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__Int_Oring__char__0_0,def_lhs_atom129]) ).
fof(def_lhs_atom130,axiom,
( lhs_atom130
<=> class_Int_Onumber__ring(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_129,plain,
( lhs_atom130
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__Int_Onumber__ring_0,def_lhs_atom130]) ).
fof(def_lhs_atom131,axiom,
( lhs_atom131
<=> class_Power_Opower(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_130,plain,
( lhs_atom131
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__Power_Opower_0,def_lhs_atom131]) ).
fof(def_lhs_atom132,axiom,
( lhs_atom132
<=> class_HOL_Ozero(tc_RealDef_Oreal) ),
inference(definition,[],]) ).
fof(to_be_clausified_131,plain,
( lhs_atom132
| $false ),
inference(fold_definition,[status(thm)],[clsarity_RealDef__Oreal__HOL_Ozero_0,def_lhs_atom132]) ).
fof(def_lhs_atom133,axiom,
( lhs_atom133
<=> class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_132,plain,
( lhs_atom133
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors_0,def_lhs_atom133]) ).
fof(def_lhs_atom134,axiom,
( lhs_atom134
<=> class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_133,plain,
( lhs_atom134
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors_0,def_lhs_atom134]) ).
fof(def_lhs_atom135,axiom,
( lhs_atom135
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_134,plain,
( lhs_atom135
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add_0,def_lhs_atom135]) ).
fof(def_lhs_atom136,axiom,
( lhs_atom136
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_135,plain,
( lhs_atom136
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add_0,def_lhs_atom136]) ).
fof(def_lhs_atom137,axiom,
( lhs_atom137
<=> class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_136,plain,
( lhs_atom137
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors_0,def_lhs_atom137]) ).
fof(def_lhs_atom138,axiom,
( lhs_atom138
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_137,plain,
( lhs_atom138
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1_0,def_lhs_atom138]) ).
fof(def_lhs_atom139,axiom,
( lhs_atom139
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_138,plain,
( lhs_atom139
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0_0,def_lhs_atom139]) ).
fof(def_lhs_atom140,axiom,
( lhs_atom140
<=> class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_139,plain,
( lhs_atom140
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra_0,def_lhs_atom140]) ).
fof(def_lhs_atom141,axiom,
( lhs_atom141
<=> class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_140,plain,
( lhs_atom141
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult_0,def_lhs_atom141]) ).
fof(def_lhs_atom142,axiom,
( lhs_atom142
<=> class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_141,plain,
( lhs_atom142
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector_0,def_lhs_atom142]) ).
fof(def_lhs_atom143,axiom,
( lhs_atom143
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_142,plain,
( lhs_atom143
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult_0,def_lhs_atom143]) ).
fof(def_lhs_atom144,axiom,
( lhs_atom144
<=> class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_143,plain,
( lhs_atom144
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add_0,def_lhs_atom144]) ).
fof(def_lhs_atom145,axiom,
( lhs_atom145
<=> class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_144,plain,
( lhs_atom145
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring_0,def_lhs_atom145]) ).
fof(def_lhs_atom146,axiom,
( lhs_atom146
<=> class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_145,plain,
( lhs_atom146
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add_0,def_lhs_atom146]) ).
fof(def_lhs_atom147,axiom,
( lhs_atom147
<=> class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_146,plain,
( lhs_atom147
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one_0,def_lhs_atom147]) ).
fof(def_lhs_atom148,axiom,
( lhs_atom148
<=> class_OrderedGroup_Osemigroup__add(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_147,plain,
( lhs_atom148
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Osemigroup__add_0,def_lhs_atom148]) ).
fof(def_lhs_atom149,axiom,
( lhs_atom149
<=> class_Ring__and__Field_Osemiring__1(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_148,plain,
( lhs_atom149
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__1_0,def_lhs_atom149]) ).
fof(def_lhs_atom150,axiom,
( lhs_atom150
<=> class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_149,plain,
( lhs_atom150
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0_0,def_lhs_atom150]) ).
fof(def_lhs_atom151,axiom,
( lhs_atom151
<=> class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_150,plain,
( lhs_atom151
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add_0,def_lhs_atom151]) ).
fof(def_lhs_atom152,axiom,
( lhs_atom152
<=> class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_151,plain,
( lhs_atom152
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero_0,def_lhs_atom152]) ).
fof(def_lhs_atom153,axiom,
( lhs_atom153
<=> class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_152,plain,
( lhs_atom153
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult_0,def_lhs_atom153]) ).
fof(def_lhs_atom154,axiom,
( lhs_atom154
<=> class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_153,plain,
( lhs_atom154
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring_0,def_lhs_atom154]) ).
fof(def_lhs_atom155,axiom,
( lhs_atom155
<=> class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_154,plain,
( lhs_atom155
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add_0,def_lhs_atom155]) ).
fof(def_lhs_atom156,axiom,
( lhs_atom156
<=> class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_155,plain,
( lhs_atom156
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add_0,def_lhs_atom156]) ).
fof(def_lhs_atom157,axiom,
( lhs_atom157
<=> class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_156,plain,
( lhs_atom157
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1_0,def_lhs_atom157]) ).
fof(def_lhs_atom158,axiom,
( lhs_atom158
<=> class_Ring__and__Field_Oring(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_157,plain,
( lhs_atom158
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Oring_0,def_lhs_atom158]) ).
fof(def_lhs_atom159,axiom,
( lhs_atom159
<=> class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_158,plain,
( lhs_atom159
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Oidom_0,def_lhs_atom159]) ).
fof(def_lhs_atom160,axiom,
( lhs_atom160
<=> class_Nat_Osemiring__char__0(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_159,plain,
( lhs_atom160
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__Nat_Osemiring__char__0_0,def_lhs_atom160]) ).
fof(def_lhs_atom161,axiom,
( lhs_atom161
<=> class_Int_Oring__char__0(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_160,plain,
( lhs_atom161
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__Int_Oring__char__0_0,def_lhs_atom161]) ).
fof(def_lhs_atom162,axiom,
( lhs_atom162
<=> class_Int_Onumber__ring(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_161,plain,
( lhs_atom162
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__Int_Onumber__ring_0,def_lhs_atom162]) ).
fof(def_lhs_atom163,axiom,
( lhs_atom163
<=> class_Power_Opower(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_162,plain,
( lhs_atom163
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__Power_Opower_0,def_lhs_atom163]) ).
fof(def_lhs_atom164,axiom,
( lhs_atom164
<=> class_HOL_Ozero(tc_Complex_Ocomplex) ),
inference(definition,[],]) ).
fof(to_be_clausified_163,plain,
( lhs_atom164
| $false ),
inference(fold_definition,[status(thm)],[clsarity_Complex__Ocomplex__HOL_Ozero_0,def_lhs_atom164]) ).
fof(def_lhs_atom165,axiom,
! [V_x,T_a] :
( lhs_atom165(V_x,T_a)
<=> hBOOL(c_fequal(V_x,V_x,T_a)) ),
inference(definition,[],]) ).
fof(to_be_clausified_164,plain,
! [T_a,V_x] :
( lhs_atom165(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_ATP__Linkup_Oequal__imp__fequal_0_0,def_lhs_atom165]) ).
% Start CNF derivation
fof(c_0_0,axiom,
! [X3,X4,X1,X5,X6] :
( lhs_atom6(X3,X4,X1,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_5) ).
fof(c_0_1,axiom,
! [X3,X4,X5,X6] :
( lhs_atom15(X3,X4,X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_14) ).
fof(c_0_2,axiom,
! [X14,X13,X5] :
( lhs_atom31(X14,X13,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_30) ).
fof(c_0_3,axiom,
! [X10,X11,X12] :
( lhs_atom23(X10,X11,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_22) ).
fof(c_0_4,axiom,
! [X1,X2,X9] :
( lhs_atom22(X1,X2,X9)
| ~ $true ),
file('<stdin>',to_be_clausified_21) ).
fof(c_0_5,axiom,
! [X12,X6] :
( lhs_atom165(X12,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_164) ).
fof(c_0_6,axiom,
! [X13,X5] :
( lhs_atom28(X13,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_27) ).
fof(c_0_7,axiom,
! [X1,X2] :
( lhs_atom5(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_4) ).
fof(c_0_8,axiom,
! [X1,X2] :
( lhs_atom4(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_3) ).
fof(c_0_9,axiom,
! [X1,X2] :
( lhs_atom3(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_2) ).
fof(c_0_10,axiom,
! [X1,X2] :
( lhs_atom1(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_0) ).
fof(c_0_11,axiom,
! [X12] :
( lhs_atom34(X12)
| ~ $true ),
file('<stdin>',to_be_clausified_33) ).
fof(c_0_12,axiom,
! [X8] :
( lhs_atom29(X8)
| ~ $true ),
file('<stdin>',to_be_clausified_28) ).
fof(c_0_13,axiom,
! [X1] :
( lhs_atom26(X1)
| ~ $true ),
file('<stdin>',to_be_clausified_25) ).
fof(c_0_14,axiom,
! [X2] :
( lhs_atom25(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_24) ).
fof(c_0_15,axiom,
! [X12] :
( lhs_atom24(X12)
| ~ $true ),
file('<stdin>',to_be_clausified_23) ).
fof(c_0_16,axiom,
! [X1] :
( lhs_atom20(X1)
| ~ $true ),
file('<stdin>',to_be_clausified_19) ).
fof(c_0_17,axiom,
! [X1] :
( lhs_atom19(X1)
| ~ $true ),
file('<stdin>',to_be_clausified_18) ).
fof(c_0_18,axiom,
! [X8] :
( lhs_atom16(X8)
| ~ $true ),
file('<stdin>',to_be_clausified_15) ).
fof(c_0_19,axiom,
! [X7] :
( lhs_atom14(X7)
| ~ $true ),
file('<stdin>',to_be_clausified_13) ).
fof(c_0_20,axiom,
! [X2] :
( lhs_atom13(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_12) ).
fof(c_0_21,axiom,
! [X2] :
( lhs_atom10(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_9) ).
fof(c_0_22,axiom,
! [X7] :
( lhs_atom9(X7)
| ~ $true ),
file('<stdin>',to_be_clausified_8) ).
fof(c_0_23,axiom,
! [X1] :
( lhs_atom8(X1)
| ~ $true ),
file('<stdin>',to_be_clausified_7) ).
fof(c_0_24,axiom,
! [X1] :
( lhs_atom7(X1)
| ~ $true ),
file('<stdin>',to_be_clausified_6) ).
fof(c_0_25,axiom,
( lhs_atom164
| ~ $true ),
file('<stdin>',to_be_clausified_163) ).
fof(c_0_26,axiom,
( lhs_atom163
| ~ $true ),
file('<stdin>',to_be_clausified_162) ).
fof(c_0_27,axiom,
( lhs_atom162
| ~ $true ),
file('<stdin>',to_be_clausified_161) ).
fof(c_0_28,axiom,
( lhs_atom161
| ~ $true ),
file('<stdin>',to_be_clausified_160) ).
fof(c_0_29,axiom,
( lhs_atom160
| ~ $true ),
file('<stdin>',to_be_clausified_159) ).
fof(c_0_30,axiom,
( lhs_atom159
| ~ $true ),
file('<stdin>',to_be_clausified_158) ).
fof(c_0_31,axiom,
( lhs_atom158
| ~ $true ),
file('<stdin>',to_be_clausified_157) ).
fof(c_0_32,axiom,
( lhs_atom157
| ~ $true ),
file('<stdin>',to_be_clausified_156) ).
fof(c_0_33,axiom,
( lhs_atom156
| ~ $true ),
file('<stdin>',to_be_clausified_155) ).
fof(c_0_34,axiom,
( lhs_atom155
| ~ $true ),
file('<stdin>',to_be_clausified_154) ).
fof(c_0_35,axiom,
( lhs_atom154
| ~ $true ),
file('<stdin>',to_be_clausified_153) ).
fof(c_0_36,axiom,
( lhs_atom153
| ~ $true ),
file('<stdin>',to_be_clausified_152) ).
fof(c_0_37,axiom,
( lhs_atom152
| ~ $true ),
file('<stdin>',to_be_clausified_151) ).
fof(c_0_38,axiom,
( lhs_atom151
| ~ $true ),
file('<stdin>',to_be_clausified_150) ).
fof(c_0_39,axiom,
( lhs_atom150
| ~ $true ),
file('<stdin>',to_be_clausified_149) ).
fof(c_0_40,axiom,
( lhs_atom149
| ~ $true ),
file('<stdin>',to_be_clausified_148) ).
fof(c_0_41,axiom,
( lhs_atom148
| ~ $true ),
file('<stdin>',to_be_clausified_147) ).
fof(c_0_42,axiom,
( lhs_atom147
| ~ $true ),
file('<stdin>',to_be_clausified_146) ).
fof(c_0_43,axiom,
( lhs_atom146
| ~ $true ),
file('<stdin>',to_be_clausified_145) ).
fof(c_0_44,axiom,
( lhs_atom145
| ~ $true ),
file('<stdin>',to_be_clausified_144) ).
fof(c_0_45,axiom,
( lhs_atom144
| ~ $true ),
file('<stdin>',to_be_clausified_143) ).
fof(c_0_46,axiom,
( lhs_atom143
| ~ $true ),
file('<stdin>',to_be_clausified_142) ).
fof(c_0_47,axiom,
( lhs_atom142
| ~ $true ),
file('<stdin>',to_be_clausified_141) ).
fof(c_0_48,axiom,
( lhs_atom141
| ~ $true ),
file('<stdin>',to_be_clausified_140) ).
fof(c_0_49,axiom,
( lhs_atom140
| ~ $true ),
file('<stdin>',to_be_clausified_139) ).
fof(c_0_50,axiom,
( lhs_atom139
| ~ $true ),
file('<stdin>',to_be_clausified_138) ).
fof(c_0_51,axiom,
( lhs_atom138
| ~ $true ),
file('<stdin>',to_be_clausified_137) ).
fof(c_0_52,axiom,
( lhs_atom137
| ~ $true ),
file('<stdin>',to_be_clausified_136) ).
fof(c_0_53,axiom,
( lhs_atom136
| ~ $true ),
file('<stdin>',to_be_clausified_135) ).
fof(c_0_54,axiom,
( lhs_atom135
| ~ $true ),
file('<stdin>',to_be_clausified_134) ).
fof(c_0_55,axiom,
( lhs_atom134
| ~ $true ),
file('<stdin>',to_be_clausified_133) ).
fof(c_0_56,axiom,
( lhs_atom133
| ~ $true ),
file('<stdin>',to_be_clausified_132) ).
fof(c_0_57,axiom,
( lhs_atom132
| ~ $true ),
file('<stdin>',to_be_clausified_131) ).
fof(c_0_58,axiom,
( lhs_atom131
| ~ $true ),
file('<stdin>',to_be_clausified_130) ).
fof(c_0_59,axiom,
( lhs_atom130
| ~ $true ),
file('<stdin>',to_be_clausified_129) ).
fof(c_0_60,axiom,
( lhs_atom129
| ~ $true ),
file('<stdin>',to_be_clausified_128) ).
fof(c_0_61,axiom,
( lhs_atom128
| ~ $true ),
file('<stdin>',to_be_clausified_127) ).
fof(c_0_62,axiom,
( lhs_atom127
| ~ $true ),
file('<stdin>',to_be_clausified_126) ).
fof(c_0_63,axiom,
( lhs_atom126
| ~ $true ),
file('<stdin>',to_be_clausified_125) ).
fof(c_0_64,axiom,
( lhs_atom125
| ~ $true ),
file('<stdin>',to_be_clausified_124) ).
fof(c_0_65,axiom,
( lhs_atom124
| ~ $true ),
file('<stdin>',to_be_clausified_123) ).
fof(c_0_66,axiom,
( lhs_atom123
| ~ $true ),
file('<stdin>',to_be_clausified_122) ).
fof(c_0_67,axiom,
( lhs_atom122
| ~ $true ),
file('<stdin>',to_be_clausified_121) ).
fof(c_0_68,axiom,
( lhs_atom121
| ~ $true ),
file('<stdin>',to_be_clausified_120) ).
fof(c_0_69,axiom,
( lhs_atom120
| ~ $true ),
file('<stdin>',to_be_clausified_119) ).
fof(c_0_70,axiom,
( lhs_atom119
| ~ $true ),
file('<stdin>',to_be_clausified_118) ).
fof(c_0_71,axiom,
( lhs_atom118
| ~ $true ),
file('<stdin>',to_be_clausified_117) ).
fof(c_0_72,axiom,
( lhs_atom117
| ~ $true ),
file('<stdin>',to_be_clausified_116) ).
fof(c_0_73,axiom,
( lhs_atom116
| ~ $true ),
file('<stdin>',to_be_clausified_115) ).
fof(c_0_74,axiom,
( lhs_atom115
| ~ $true ),
file('<stdin>',to_be_clausified_114) ).
fof(c_0_75,axiom,
( lhs_atom114
| ~ $true ),
file('<stdin>',to_be_clausified_113) ).
fof(c_0_76,axiom,
( lhs_atom113
| ~ $true ),
file('<stdin>',to_be_clausified_112) ).
fof(c_0_77,axiom,
( lhs_atom112
| ~ $true ),
file('<stdin>',to_be_clausified_111) ).
fof(c_0_78,axiom,
( lhs_atom111
| ~ $true ),
file('<stdin>',to_be_clausified_110) ).
fof(c_0_79,axiom,
( lhs_atom110
| ~ $true ),
file('<stdin>',to_be_clausified_109) ).
fof(c_0_80,axiom,
( lhs_atom109
| ~ $true ),
file('<stdin>',to_be_clausified_108) ).
fof(c_0_81,axiom,
( lhs_atom108
| ~ $true ),
file('<stdin>',to_be_clausified_107) ).
fof(c_0_82,axiom,
( lhs_atom107
| ~ $true ),
file('<stdin>',to_be_clausified_106) ).
fof(c_0_83,axiom,
( lhs_atom106
| ~ $true ),
file('<stdin>',to_be_clausified_105) ).
fof(c_0_84,axiom,
( lhs_atom105
| ~ $true ),
file('<stdin>',to_be_clausified_104) ).
fof(c_0_85,axiom,
( lhs_atom104
| ~ $true ),
file('<stdin>',to_be_clausified_103) ).
fof(c_0_86,axiom,
( lhs_atom103
| ~ $true ),
file('<stdin>',to_be_clausified_102) ).
fof(c_0_87,axiom,
( lhs_atom102
| ~ $true ),
file('<stdin>',to_be_clausified_101) ).
fof(c_0_88,axiom,
( lhs_atom101
| ~ $true ),
file('<stdin>',to_be_clausified_100) ).
fof(c_0_89,axiom,
( lhs_atom100
| ~ $true ),
file('<stdin>',to_be_clausified_99) ).
fof(c_0_90,axiom,
( lhs_atom99
| ~ $true ),
file('<stdin>',to_be_clausified_98) ).
fof(c_0_91,axiom,
( lhs_atom98
| ~ $true ),
file('<stdin>',to_be_clausified_97) ).
fof(c_0_92,axiom,
( lhs_atom97
| ~ $true ),
file('<stdin>',to_be_clausified_96) ).
fof(c_0_93,axiom,
( lhs_atom96
| ~ $true ),
file('<stdin>',to_be_clausified_95) ).
fof(c_0_94,axiom,
( lhs_atom95
| ~ $true ),
file('<stdin>',to_be_clausified_94) ).
fof(c_0_95,axiom,
( lhs_atom94
| ~ $true ),
file('<stdin>',to_be_clausified_93) ).
fof(c_0_96,axiom,
( lhs_atom93
| ~ $true ),
file('<stdin>',to_be_clausified_92) ).
fof(c_0_97,axiom,
( lhs_atom92
| ~ $true ),
file('<stdin>',to_be_clausified_91) ).
fof(c_0_98,axiom,
( lhs_atom91
| ~ $true ),
file('<stdin>',to_be_clausified_90) ).
fof(c_0_99,axiom,
( lhs_atom90
| ~ $true ),
file('<stdin>',to_be_clausified_89) ).
fof(c_0_100,axiom,
( lhs_atom89
| ~ $true ),
file('<stdin>',to_be_clausified_88) ).
fof(c_0_101,axiom,
( lhs_atom88
| ~ $true ),
file('<stdin>',to_be_clausified_87) ).
fof(c_0_102,axiom,
( lhs_atom87
| ~ $true ),
file('<stdin>',to_be_clausified_86) ).
fof(c_0_103,axiom,
( lhs_atom86
| ~ $true ),
file('<stdin>',to_be_clausified_85) ).
fof(c_0_104,axiom,
( lhs_atom85
| ~ $true ),
file('<stdin>',to_be_clausified_84) ).
fof(c_0_105,axiom,
( lhs_atom84
| ~ $true ),
file('<stdin>',to_be_clausified_83) ).
fof(c_0_106,axiom,
( lhs_atom83
| ~ $true ),
file('<stdin>',to_be_clausified_82) ).
fof(c_0_107,axiom,
( lhs_atom82
| ~ $true ),
file('<stdin>',to_be_clausified_81) ).
fof(c_0_108,axiom,
( lhs_atom81
| ~ $true ),
file('<stdin>',to_be_clausified_80) ).
fof(c_0_109,axiom,
( lhs_atom80
| ~ $true ),
file('<stdin>',to_be_clausified_79) ).
fof(c_0_110,axiom,
( lhs_atom79
| ~ $true ),
file('<stdin>',to_be_clausified_78) ).
fof(c_0_111,axiom,
( lhs_atom78
| ~ $true ),
file('<stdin>',to_be_clausified_77) ).
fof(c_0_112,axiom,
( lhs_atom77
| ~ $true ),
file('<stdin>',to_be_clausified_76) ).
fof(c_0_113,axiom,
( lhs_atom76
| ~ $true ),
file('<stdin>',to_be_clausified_75) ).
fof(c_0_114,axiom,
( lhs_atom75
| ~ $true ),
file('<stdin>',to_be_clausified_74) ).
fof(c_0_115,axiom,
( lhs_atom74
| ~ $true ),
file('<stdin>',to_be_clausified_73) ).
fof(c_0_116,axiom,
( lhs_atom73
| ~ $true ),
file('<stdin>',to_be_clausified_72) ).
fof(c_0_117,axiom,
( lhs_atom72
| ~ $true ),
file('<stdin>',to_be_clausified_71) ).
fof(c_0_118,axiom,
( lhs_atom71
| ~ $true ),
file('<stdin>',to_be_clausified_70) ).
fof(c_0_119,axiom,
( lhs_atom70
| ~ $true ),
file('<stdin>',to_be_clausified_69) ).
fof(c_0_120,axiom,
( lhs_atom69
| ~ $true ),
file('<stdin>',to_be_clausified_68) ).
fof(c_0_121,axiom,
( lhs_atom68
| ~ $true ),
file('<stdin>',to_be_clausified_67) ).
fof(c_0_122,axiom,
( lhs_atom67
| ~ $true ),
file('<stdin>',to_be_clausified_66) ).
fof(c_0_123,axiom,
( lhs_atom66
| ~ $true ),
file('<stdin>',to_be_clausified_65) ).
fof(c_0_124,axiom,
( lhs_atom65
| ~ $true ),
file('<stdin>',to_be_clausified_64) ).
fof(c_0_125,axiom,
( lhs_atom64
| ~ $true ),
file('<stdin>',to_be_clausified_63) ).
fof(c_0_126,axiom,
( lhs_atom63
| ~ $true ),
file('<stdin>',to_be_clausified_62) ).
fof(c_0_127,axiom,
( lhs_atom62
| ~ $true ),
file('<stdin>',to_be_clausified_61) ).
fof(c_0_128,axiom,
( lhs_atom61
| ~ $true ),
file('<stdin>',to_be_clausified_60) ).
fof(c_0_129,axiom,
( lhs_atom60
| ~ $true ),
file('<stdin>',to_be_clausified_59) ).
fof(c_0_130,axiom,
( lhs_atom59
| ~ $true ),
file('<stdin>',to_be_clausified_58) ).
fof(c_0_131,axiom,
( lhs_atom58
| ~ $true ),
file('<stdin>',to_be_clausified_57) ).
fof(c_0_132,axiom,
( lhs_atom57
| ~ $true ),
file('<stdin>',to_be_clausified_56) ).
fof(c_0_133,axiom,
( lhs_atom56
| ~ $true ),
file('<stdin>',to_be_clausified_55) ).
fof(c_0_134,axiom,
( lhs_atom55
| ~ $true ),
file('<stdin>',to_be_clausified_54) ).
fof(c_0_135,axiom,
( lhs_atom54
| ~ $true ),
file('<stdin>',to_be_clausified_53) ).
fof(c_0_136,axiom,
( lhs_atom53
| ~ $true ),
file('<stdin>',to_be_clausified_52) ).
fof(c_0_137,axiom,
( lhs_atom52
| ~ $true ),
file('<stdin>',to_be_clausified_51) ).
fof(c_0_138,axiom,
( lhs_atom51
| ~ $true ),
file('<stdin>',to_be_clausified_50) ).
fof(c_0_139,axiom,
( lhs_atom50
| ~ $true ),
file('<stdin>',to_be_clausified_49) ).
fof(c_0_140,axiom,
( lhs_atom49
| ~ $true ),
file('<stdin>',to_be_clausified_48) ).
fof(c_0_141,axiom,
( lhs_atom48
| ~ $true ),
file('<stdin>',to_be_clausified_47) ).
fof(c_0_142,axiom,
( lhs_atom47
| ~ $true ),
file('<stdin>',to_be_clausified_46) ).
fof(c_0_143,axiom,
( lhs_atom46
| ~ $true ),
file('<stdin>',to_be_clausified_45) ).
fof(c_0_144,axiom,
( lhs_atom45
| ~ $true ),
file('<stdin>',to_be_clausified_44) ).
fof(c_0_145,axiom,
( lhs_atom44
| ~ $true ),
file('<stdin>',to_be_clausified_43) ).
fof(c_0_146,axiom,
( lhs_atom43
| ~ $true ),
file('<stdin>',to_be_clausified_42) ).
fof(c_0_147,axiom,
( lhs_atom42
| ~ $true ),
file('<stdin>',to_be_clausified_41) ).
fof(c_0_148,axiom,
( lhs_atom41
| ~ $true ),
file('<stdin>',to_be_clausified_40) ).
fof(c_0_149,axiom,
( lhs_atom40
| ~ $true ),
file('<stdin>',to_be_clausified_39) ).
fof(c_0_150,axiom,
( lhs_atom39
| ~ $true ),
file('<stdin>',to_be_clausified_38) ).
fof(c_0_151,axiom,
( lhs_atom38
| ~ $true ),
file('<stdin>',to_be_clausified_37) ).
fof(c_0_152,axiom,
( lhs_atom37
| ~ $true ),
file('<stdin>',to_be_clausified_36) ).
fof(c_0_153,axiom,
( lhs_atom36
| ~ $true ),
file('<stdin>',to_be_clausified_35) ).
fof(c_0_154,axiom,
( lhs_atom35
| ~ $true ),
file('<stdin>',to_be_clausified_34) ).
fof(c_0_155,axiom,
( lhs_atom33
| ~ $true ),
file('<stdin>',to_be_clausified_32) ).
fof(c_0_156,axiom,
( lhs_atom32
| ~ $true ),
file('<stdin>',to_be_clausified_31) ).
fof(c_0_157,axiom,
( lhs_atom30
| ~ $true ),
file('<stdin>',to_be_clausified_29) ).
fof(c_0_158,axiom,
( lhs_atom27
| ~ $true ),
file('<stdin>',to_be_clausified_26) ).
fof(c_0_159,axiom,
( lhs_atom21
| ~ $true ),
file('<stdin>',to_be_clausified_20) ).
fof(c_0_160,axiom,
( lhs_atom18
| ~ $true ),
file('<stdin>',to_be_clausified_17) ).
fof(c_0_161,axiom,
( lhs_atom17
| ~ $true ),
file('<stdin>',to_be_clausified_16) ).
fof(c_0_162,axiom,
( lhs_atom12
| ~ $true ),
file('<stdin>',to_be_clausified_11) ).
fof(c_0_163,axiom,
( lhs_atom11
| ~ $true ),
file('<stdin>',to_be_clausified_10) ).
fof(c_0_164,axiom,
( lhs_atom2
| ~ $true ),
file('<stdin>',to_be_clausified_1) ).
fof(c_0_165,plain,
! [X3,X4,X1,X5,X6] : lhs_atom6(X3,X4,X1,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_166,plain,
! [X3,X4,X5,X6] : lhs_atom15(X3,X4,X5,X6),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_167,plain,
! [X14,X13,X5] : lhs_atom31(X14,X13,X5),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_168,plain,
! [X10,X11,X12] : lhs_atom23(X10,X11,X12),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_169,plain,
! [X1,X2,X9] : lhs_atom22(X1,X2,X9),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_170,plain,
! [X12,X6] : lhs_atom165(X12,X6),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_171,plain,
! [X13,X5] : lhs_atom28(X13,X5),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_172,plain,
! [X1,X2] : lhs_atom5(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_173,plain,
! [X1,X2] : lhs_atom4(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_174,plain,
! [X1,X2] : lhs_atom3(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_175,plain,
! [X1,X2] : lhs_atom1(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_176,plain,
! [X12] : lhs_atom34(X12),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_177,plain,
! [X8] : lhs_atom29(X8),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_178,plain,
! [X1] : lhs_atom26(X1),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_179,plain,
! [X2] : lhs_atom25(X2),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_180,plain,
! [X12] : lhs_atom24(X12),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_181,plain,
! [X1] : lhs_atom20(X1),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_182,plain,
! [X1] : lhs_atom19(X1),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_183,plain,
! [X8] : lhs_atom16(X8),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_184,plain,
! [X7] : lhs_atom14(X7),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_185,plain,
! [X2] : lhs_atom13(X2),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
fof(c_0_186,plain,
! [X2] : lhs_atom10(X2),
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_187,plain,
! [X7] : lhs_atom9(X7),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_188,plain,
! [X1] : lhs_atom8(X1),
inference(fof_simplification,[status(thm)],[c_0_23]) ).
fof(c_0_189,plain,
! [X1] : lhs_atom7(X1),
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_190,plain,
lhs_atom164,
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_191,plain,
lhs_atom163,
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_192,plain,
lhs_atom162,
inference(fof_simplification,[status(thm)],[c_0_27]) ).
fof(c_0_193,plain,
lhs_atom161,
inference(fof_simplification,[status(thm)],[c_0_28]) ).
fof(c_0_194,plain,
lhs_atom160,
inference(fof_simplification,[status(thm)],[c_0_29]) ).
fof(c_0_195,plain,
lhs_atom159,
inference(fof_simplification,[status(thm)],[c_0_30]) ).
fof(c_0_196,plain,
lhs_atom158,
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_197,plain,
lhs_atom157,
inference(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_198,plain,
lhs_atom156,
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_199,plain,
lhs_atom155,
inference(fof_simplification,[status(thm)],[c_0_34]) ).
fof(c_0_200,plain,
lhs_atom154,
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_201,plain,
lhs_atom153,
inference(fof_simplification,[status(thm)],[c_0_36]) ).
fof(c_0_202,plain,
lhs_atom152,
inference(fof_simplification,[status(thm)],[c_0_37]) ).
fof(c_0_203,plain,
lhs_atom151,
inference(fof_simplification,[status(thm)],[c_0_38]) ).
fof(c_0_204,plain,
lhs_atom150,
inference(fof_simplification,[status(thm)],[c_0_39]) ).
fof(c_0_205,plain,
lhs_atom149,
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_206,plain,
lhs_atom148,
inference(fof_simplification,[status(thm)],[c_0_41]) ).
fof(c_0_207,plain,
lhs_atom147,
inference(fof_simplification,[status(thm)],[c_0_42]) ).
fof(c_0_208,plain,
lhs_atom146,
inference(fof_simplification,[status(thm)],[c_0_43]) ).
fof(c_0_209,plain,
lhs_atom145,
inference(fof_simplification,[status(thm)],[c_0_44]) ).
fof(c_0_210,plain,
lhs_atom144,
inference(fof_simplification,[status(thm)],[c_0_45]) ).
fof(c_0_211,plain,
lhs_atom143,
inference(fof_simplification,[status(thm)],[c_0_46]) ).
fof(c_0_212,plain,
lhs_atom142,
inference(fof_simplification,[status(thm)],[c_0_47]) ).
fof(c_0_213,plain,
lhs_atom141,
inference(fof_simplification,[status(thm)],[c_0_48]) ).
fof(c_0_214,plain,
lhs_atom140,
inference(fof_simplification,[status(thm)],[c_0_49]) ).
fof(c_0_215,plain,
lhs_atom139,
inference(fof_simplification,[status(thm)],[c_0_50]) ).
fof(c_0_216,plain,
lhs_atom138,
inference(fof_simplification,[status(thm)],[c_0_51]) ).
fof(c_0_217,plain,
lhs_atom137,
inference(fof_simplification,[status(thm)],[c_0_52]) ).
fof(c_0_218,plain,
lhs_atom136,
inference(fof_simplification,[status(thm)],[c_0_53]) ).
fof(c_0_219,plain,
lhs_atom135,
inference(fof_simplification,[status(thm)],[c_0_54]) ).
fof(c_0_220,plain,
lhs_atom134,
inference(fof_simplification,[status(thm)],[c_0_55]) ).
fof(c_0_221,plain,
lhs_atom133,
inference(fof_simplification,[status(thm)],[c_0_56]) ).
fof(c_0_222,plain,
lhs_atom132,
inference(fof_simplification,[status(thm)],[c_0_57]) ).
fof(c_0_223,plain,
lhs_atom131,
inference(fof_simplification,[status(thm)],[c_0_58]) ).
fof(c_0_224,plain,
lhs_atom130,
inference(fof_simplification,[status(thm)],[c_0_59]) ).
fof(c_0_225,plain,
lhs_atom129,
inference(fof_simplification,[status(thm)],[c_0_60]) ).
fof(c_0_226,plain,
lhs_atom128,
inference(fof_simplification,[status(thm)],[c_0_61]) ).
fof(c_0_227,plain,
lhs_atom127,
inference(fof_simplification,[status(thm)],[c_0_62]) ).
fof(c_0_228,plain,
lhs_atom126,
inference(fof_simplification,[status(thm)],[c_0_63]) ).
fof(c_0_229,plain,
lhs_atom125,
inference(fof_simplification,[status(thm)],[c_0_64]) ).
fof(c_0_230,plain,
lhs_atom124,
inference(fof_simplification,[status(thm)],[c_0_65]) ).
fof(c_0_231,plain,
lhs_atom123,
inference(fof_simplification,[status(thm)],[c_0_66]) ).
fof(c_0_232,plain,
lhs_atom122,
inference(fof_simplification,[status(thm)],[c_0_67]) ).
fof(c_0_233,plain,
lhs_atom121,
inference(fof_simplification,[status(thm)],[c_0_68]) ).
fof(c_0_234,plain,
lhs_atom120,
inference(fof_simplification,[status(thm)],[c_0_69]) ).
fof(c_0_235,plain,
lhs_atom119,
inference(fof_simplification,[status(thm)],[c_0_70]) ).
fof(c_0_236,plain,
lhs_atom118,
inference(fof_simplification,[status(thm)],[c_0_71]) ).
fof(c_0_237,plain,
lhs_atom117,
inference(fof_simplification,[status(thm)],[c_0_72]) ).
fof(c_0_238,plain,
lhs_atom116,
inference(fof_simplification,[status(thm)],[c_0_73]) ).
fof(c_0_239,plain,
lhs_atom115,
inference(fof_simplification,[status(thm)],[c_0_74]) ).
fof(c_0_240,plain,
lhs_atom114,
inference(fof_simplification,[status(thm)],[c_0_75]) ).
fof(c_0_241,plain,
lhs_atom113,
inference(fof_simplification,[status(thm)],[c_0_76]) ).
fof(c_0_242,plain,
lhs_atom112,
inference(fof_simplification,[status(thm)],[c_0_77]) ).
fof(c_0_243,plain,
lhs_atom111,
inference(fof_simplification,[status(thm)],[c_0_78]) ).
fof(c_0_244,plain,
lhs_atom110,
inference(fof_simplification,[status(thm)],[c_0_79]) ).
fof(c_0_245,plain,
lhs_atom109,
inference(fof_simplification,[status(thm)],[c_0_80]) ).
fof(c_0_246,plain,
lhs_atom108,
inference(fof_simplification,[status(thm)],[c_0_81]) ).
fof(c_0_247,plain,
lhs_atom107,
inference(fof_simplification,[status(thm)],[c_0_82]) ).
fof(c_0_248,plain,
lhs_atom106,
inference(fof_simplification,[status(thm)],[c_0_83]) ).
fof(c_0_249,plain,
lhs_atom105,
inference(fof_simplification,[status(thm)],[c_0_84]) ).
fof(c_0_250,plain,
lhs_atom104,
inference(fof_simplification,[status(thm)],[c_0_85]) ).
fof(c_0_251,plain,
lhs_atom103,
inference(fof_simplification,[status(thm)],[c_0_86]) ).
fof(c_0_252,plain,
lhs_atom102,
inference(fof_simplification,[status(thm)],[c_0_87]) ).
fof(c_0_253,plain,
lhs_atom101,
inference(fof_simplification,[status(thm)],[c_0_88]) ).
fof(c_0_254,plain,
lhs_atom100,
inference(fof_simplification,[status(thm)],[c_0_89]) ).
fof(c_0_255,plain,
lhs_atom99,
inference(fof_simplification,[status(thm)],[c_0_90]) ).
fof(c_0_256,plain,
lhs_atom98,
inference(fof_simplification,[status(thm)],[c_0_91]) ).
fof(c_0_257,plain,
lhs_atom97,
inference(fof_simplification,[status(thm)],[c_0_92]) ).
fof(c_0_258,plain,
lhs_atom96,
inference(fof_simplification,[status(thm)],[c_0_93]) ).
fof(c_0_259,plain,
lhs_atom95,
inference(fof_simplification,[status(thm)],[c_0_94]) ).
fof(c_0_260,plain,
lhs_atom94,
inference(fof_simplification,[status(thm)],[c_0_95]) ).
fof(c_0_261,plain,
lhs_atom93,
inference(fof_simplification,[status(thm)],[c_0_96]) ).
fof(c_0_262,plain,
lhs_atom92,
inference(fof_simplification,[status(thm)],[c_0_97]) ).
fof(c_0_263,plain,
lhs_atom91,
inference(fof_simplification,[status(thm)],[c_0_98]) ).
fof(c_0_264,plain,
lhs_atom90,
inference(fof_simplification,[status(thm)],[c_0_99]) ).
fof(c_0_265,plain,
lhs_atom89,
inference(fof_simplification,[status(thm)],[c_0_100]) ).
fof(c_0_266,plain,
lhs_atom88,
inference(fof_simplification,[status(thm)],[c_0_101]) ).
fof(c_0_267,plain,
lhs_atom87,
inference(fof_simplification,[status(thm)],[c_0_102]) ).
fof(c_0_268,plain,
lhs_atom86,
inference(fof_simplification,[status(thm)],[c_0_103]) ).
fof(c_0_269,plain,
lhs_atom85,
inference(fof_simplification,[status(thm)],[c_0_104]) ).
fof(c_0_270,plain,
lhs_atom84,
inference(fof_simplification,[status(thm)],[c_0_105]) ).
fof(c_0_271,plain,
lhs_atom83,
inference(fof_simplification,[status(thm)],[c_0_106]) ).
fof(c_0_272,plain,
lhs_atom82,
inference(fof_simplification,[status(thm)],[c_0_107]) ).
fof(c_0_273,plain,
lhs_atom81,
inference(fof_simplification,[status(thm)],[c_0_108]) ).
fof(c_0_274,plain,
lhs_atom80,
inference(fof_simplification,[status(thm)],[c_0_109]) ).
fof(c_0_275,plain,
lhs_atom79,
inference(fof_simplification,[status(thm)],[c_0_110]) ).
fof(c_0_276,plain,
lhs_atom78,
inference(fof_simplification,[status(thm)],[c_0_111]) ).
fof(c_0_277,plain,
lhs_atom77,
inference(fof_simplification,[status(thm)],[c_0_112]) ).
fof(c_0_278,plain,
lhs_atom76,
inference(fof_simplification,[status(thm)],[c_0_113]) ).
fof(c_0_279,plain,
lhs_atom75,
inference(fof_simplification,[status(thm)],[c_0_114]) ).
fof(c_0_280,plain,
lhs_atom74,
inference(fof_simplification,[status(thm)],[c_0_115]) ).
fof(c_0_281,plain,
lhs_atom73,
inference(fof_simplification,[status(thm)],[c_0_116]) ).
fof(c_0_282,plain,
lhs_atom72,
inference(fof_simplification,[status(thm)],[c_0_117]) ).
fof(c_0_283,plain,
lhs_atom71,
inference(fof_simplification,[status(thm)],[c_0_118]) ).
fof(c_0_284,plain,
lhs_atom70,
inference(fof_simplification,[status(thm)],[c_0_119]) ).
fof(c_0_285,plain,
lhs_atom69,
inference(fof_simplification,[status(thm)],[c_0_120]) ).
fof(c_0_286,plain,
lhs_atom68,
inference(fof_simplification,[status(thm)],[c_0_121]) ).
fof(c_0_287,plain,
lhs_atom67,
inference(fof_simplification,[status(thm)],[c_0_122]) ).
fof(c_0_288,plain,
lhs_atom66,
inference(fof_simplification,[status(thm)],[c_0_123]) ).
fof(c_0_289,plain,
lhs_atom65,
inference(fof_simplification,[status(thm)],[c_0_124]) ).
fof(c_0_290,plain,
lhs_atom64,
inference(fof_simplification,[status(thm)],[c_0_125]) ).
fof(c_0_291,plain,
lhs_atom63,
inference(fof_simplification,[status(thm)],[c_0_126]) ).
fof(c_0_292,plain,
lhs_atom62,
inference(fof_simplification,[status(thm)],[c_0_127]) ).
fof(c_0_293,plain,
lhs_atom61,
inference(fof_simplification,[status(thm)],[c_0_128]) ).
fof(c_0_294,plain,
lhs_atom60,
inference(fof_simplification,[status(thm)],[c_0_129]) ).
fof(c_0_295,plain,
lhs_atom59,
inference(fof_simplification,[status(thm)],[c_0_130]) ).
fof(c_0_296,plain,
lhs_atom58,
inference(fof_simplification,[status(thm)],[c_0_131]) ).
fof(c_0_297,plain,
lhs_atom57,
inference(fof_simplification,[status(thm)],[c_0_132]) ).
fof(c_0_298,plain,
lhs_atom56,
inference(fof_simplification,[status(thm)],[c_0_133]) ).
fof(c_0_299,plain,
lhs_atom55,
inference(fof_simplification,[status(thm)],[c_0_134]) ).
fof(c_0_300,plain,
lhs_atom54,
inference(fof_simplification,[status(thm)],[c_0_135]) ).
fof(c_0_301,plain,
lhs_atom53,
inference(fof_simplification,[status(thm)],[c_0_136]) ).
fof(c_0_302,plain,
lhs_atom52,
inference(fof_simplification,[status(thm)],[c_0_137]) ).
fof(c_0_303,plain,
lhs_atom51,
inference(fof_simplification,[status(thm)],[c_0_138]) ).
fof(c_0_304,plain,
lhs_atom50,
inference(fof_simplification,[status(thm)],[c_0_139]) ).
fof(c_0_305,plain,
lhs_atom49,
inference(fof_simplification,[status(thm)],[c_0_140]) ).
fof(c_0_306,plain,
lhs_atom48,
inference(fof_simplification,[status(thm)],[c_0_141]) ).
fof(c_0_307,plain,
lhs_atom47,
inference(fof_simplification,[status(thm)],[c_0_142]) ).
fof(c_0_308,plain,
lhs_atom46,
inference(fof_simplification,[status(thm)],[c_0_143]) ).
fof(c_0_309,plain,
lhs_atom45,
inference(fof_simplification,[status(thm)],[c_0_144]) ).
fof(c_0_310,plain,
lhs_atom44,
inference(fof_simplification,[status(thm)],[c_0_145]) ).
fof(c_0_311,plain,
lhs_atom43,
inference(fof_simplification,[status(thm)],[c_0_146]) ).
fof(c_0_312,plain,
lhs_atom42,
inference(fof_simplification,[status(thm)],[c_0_147]) ).
fof(c_0_313,plain,
lhs_atom41,
inference(fof_simplification,[status(thm)],[c_0_148]) ).
fof(c_0_314,plain,
lhs_atom40,
inference(fof_simplification,[status(thm)],[c_0_149]) ).
fof(c_0_315,plain,
lhs_atom39,
inference(fof_simplification,[status(thm)],[c_0_150]) ).
fof(c_0_316,plain,
lhs_atom38,
inference(fof_simplification,[status(thm)],[c_0_151]) ).
fof(c_0_317,plain,
lhs_atom37,
inference(fof_simplification,[status(thm)],[c_0_152]) ).
fof(c_0_318,plain,
lhs_atom36,
inference(fof_simplification,[status(thm)],[c_0_153]) ).
fof(c_0_319,plain,
lhs_atom35,
inference(fof_simplification,[status(thm)],[c_0_154]) ).
fof(c_0_320,plain,
lhs_atom33,
inference(fof_simplification,[status(thm)],[c_0_155]) ).
fof(c_0_321,plain,
lhs_atom32,
inference(fof_simplification,[status(thm)],[c_0_156]) ).
fof(c_0_322,plain,
lhs_atom30,
inference(fof_simplification,[status(thm)],[c_0_157]) ).
fof(c_0_323,plain,
lhs_atom27,
inference(fof_simplification,[status(thm)],[c_0_158]) ).
fof(c_0_324,plain,
lhs_atom21,
inference(fof_simplification,[status(thm)],[c_0_159]) ).
fof(c_0_325,plain,
lhs_atom18,
inference(fof_simplification,[status(thm)],[c_0_160]) ).
fof(c_0_326,plain,
lhs_atom17,
inference(fof_simplification,[status(thm)],[c_0_161]) ).
fof(c_0_327,plain,
lhs_atom12,
inference(fof_simplification,[status(thm)],[c_0_162]) ).
fof(c_0_328,plain,
lhs_atom11,
inference(fof_simplification,[status(thm)],[c_0_163]) ).
fof(c_0_329,plain,
lhs_atom2,
inference(fof_simplification,[status(thm)],[c_0_164]) ).
fof(c_0_330,plain,
! [X7,X8,X9,X10,X11] : lhs_atom6(X7,X8,X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_165]) ).
fof(c_0_331,plain,
! [X7,X8,X9,X10] : lhs_atom15(X7,X8,X9,X10),
inference(variable_rename,[status(thm)],[c_0_166]) ).
fof(c_0_332,plain,
! [X15,X16,X17] : lhs_atom31(X15,X16,X17),
inference(variable_rename,[status(thm)],[c_0_167]) ).
fof(c_0_333,plain,
! [X13,X14,X15] : lhs_atom23(X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_168]) ).
fof(c_0_334,plain,
! [X10,X11,X12] : lhs_atom22(X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_169]) ).
fof(c_0_335,plain,
! [X13,X14] : lhs_atom165(X13,X14),
inference(variable_rename,[status(thm)],[c_0_170]) ).
fof(c_0_336,plain,
! [X14,X15] : lhs_atom28(X14,X15),
inference(variable_rename,[status(thm)],[c_0_171]) ).
fof(c_0_337,plain,
! [X3,X4] : lhs_atom5(X3,X4),
inference(variable_rename,[status(thm)],[c_0_172]) ).
fof(c_0_338,plain,
! [X3,X4] : lhs_atom4(X3,X4),
inference(variable_rename,[status(thm)],[c_0_173]) ).
fof(c_0_339,plain,
! [X3,X4] : lhs_atom3(X3,X4),
inference(variable_rename,[status(thm)],[c_0_174]) ).
fof(c_0_340,plain,
! [X3,X4] : lhs_atom1(X3,X4),
inference(variable_rename,[status(thm)],[c_0_175]) ).
fof(c_0_341,plain,
! [X13] : lhs_atom34(X13),
inference(variable_rename,[status(thm)],[c_0_176]) ).
fof(c_0_342,plain,
! [X9] : lhs_atom29(X9),
inference(variable_rename,[status(thm)],[c_0_177]) ).
fof(c_0_343,plain,
! [X2] : lhs_atom26(X2),
inference(variable_rename,[status(thm)],[c_0_178]) ).
fof(c_0_344,plain,
! [X3] : lhs_atom25(X3),
inference(variable_rename,[status(thm)],[c_0_179]) ).
fof(c_0_345,plain,
! [X13] : lhs_atom24(X13),
inference(variable_rename,[status(thm)],[c_0_180]) ).
fof(c_0_346,plain,
! [X2] : lhs_atom20(X2),
inference(variable_rename,[status(thm)],[c_0_181]) ).
fof(c_0_347,plain,
! [X2] : lhs_atom19(X2),
inference(variable_rename,[status(thm)],[c_0_182]) ).
fof(c_0_348,plain,
! [X9] : lhs_atom16(X9),
inference(variable_rename,[status(thm)],[c_0_183]) ).
fof(c_0_349,plain,
! [X8] : lhs_atom14(X8),
inference(variable_rename,[status(thm)],[c_0_184]) ).
fof(c_0_350,plain,
! [X3] : lhs_atom13(X3),
inference(variable_rename,[status(thm)],[c_0_185]) ).
fof(c_0_351,plain,
! [X3] : lhs_atom10(X3),
inference(variable_rename,[status(thm)],[c_0_186]) ).
fof(c_0_352,plain,
! [X8] : lhs_atom9(X8),
inference(variable_rename,[status(thm)],[c_0_187]) ).
fof(c_0_353,plain,
! [X2] : lhs_atom8(X2),
inference(variable_rename,[status(thm)],[c_0_188]) ).
fof(c_0_354,plain,
! [X2] : lhs_atom7(X2),
inference(variable_rename,[status(thm)],[c_0_189]) ).
fof(c_0_355,plain,
lhs_atom164,
c_0_190 ).
fof(c_0_356,plain,
lhs_atom163,
c_0_191 ).
fof(c_0_357,plain,
lhs_atom162,
c_0_192 ).
fof(c_0_358,plain,
lhs_atom161,
c_0_193 ).
fof(c_0_359,plain,
lhs_atom160,
c_0_194 ).
fof(c_0_360,plain,
lhs_atom159,
c_0_195 ).
fof(c_0_361,plain,
lhs_atom158,
c_0_196 ).
fof(c_0_362,plain,
lhs_atom157,
c_0_197 ).
fof(c_0_363,plain,
lhs_atom156,
c_0_198 ).
fof(c_0_364,plain,
lhs_atom155,
c_0_199 ).
fof(c_0_365,plain,
lhs_atom154,
c_0_200 ).
fof(c_0_366,plain,
lhs_atom153,
c_0_201 ).
fof(c_0_367,plain,
lhs_atom152,
c_0_202 ).
fof(c_0_368,plain,
lhs_atom151,
c_0_203 ).
fof(c_0_369,plain,
lhs_atom150,
c_0_204 ).
fof(c_0_370,plain,
lhs_atom149,
c_0_205 ).
fof(c_0_371,plain,
lhs_atom148,
c_0_206 ).
fof(c_0_372,plain,
lhs_atom147,
c_0_207 ).
fof(c_0_373,plain,
lhs_atom146,
c_0_208 ).
fof(c_0_374,plain,
lhs_atom145,
c_0_209 ).
fof(c_0_375,plain,
lhs_atom144,
c_0_210 ).
fof(c_0_376,plain,
lhs_atom143,
c_0_211 ).
fof(c_0_377,plain,
lhs_atom142,
c_0_212 ).
fof(c_0_378,plain,
lhs_atom141,
c_0_213 ).
fof(c_0_379,plain,
lhs_atom140,
c_0_214 ).
fof(c_0_380,plain,
lhs_atom139,
c_0_215 ).
fof(c_0_381,plain,
lhs_atom138,
c_0_216 ).
fof(c_0_382,plain,
lhs_atom137,
c_0_217 ).
fof(c_0_383,plain,
lhs_atom136,
c_0_218 ).
fof(c_0_384,plain,
lhs_atom135,
c_0_219 ).
fof(c_0_385,plain,
lhs_atom134,
c_0_220 ).
fof(c_0_386,plain,
lhs_atom133,
c_0_221 ).
fof(c_0_387,plain,
lhs_atom132,
c_0_222 ).
fof(c_0_388,plain,
lhs_atom131,
c_0_223 ).
fof(c_0_389,plain,
lhs_atom130,
c_0_224 ).
fof(c_0_390,plain,
lhs_atom129,
c_0_225 ).
fof(c_0_391,plain,
lhs_atom128,
c_0_226 ).
fof(c_0_392,plain,
lhs_atom127,
c_0_227 ).
fof(c_0_393,plain,
lhs_atom126,
c_0_228 ).
fof(c_0_394,plain,
lhs_atom125,
c_0_229 ).
fof(c_0_395,plain,
lhs_atom124,
c_0_230 ).
fof(c_0_396,plain,
lhs_atom123,
c_0_231 ).
fof(c_0_397,plain,
lhs_atom122,
c_0_232 ).
fof(c_0_398,plain,
lhs_atom121,
c_0_233 ).
fof(c_0_399,plain,
lhs_atom120,
c_0_234 ).
fof(c_0_400,plain,
lhs_atom119,
c_0_235 ).
fof(c_0_401,plain,
lhs_atom118,
c_0_236 ).
fof(c_0_402,plain,
lhs_atom117,
c_0_237 ).
fof(c_0_403,plain,
lhs_atom116,
c_0_238 ).
fof(c_0_404,plain,
lhs_atom115,
c_0_239 ).
fof(c_0_405,plain,
lhs_atom114,
c_0_240 ).
fof(c_0_406,plain,
lhs_atom113,
c_0_241 ).
fof(c_0_407,plain,
lhs_atom112,
c_0_242 ).
fof(c_0_408,plain,
lhs_atom111,
c_0_243 ).
fof(c_0_409,plain,
lhs_atom110,
c_0_244 ).
fof(c_0_410,plain,
lhs_atom109,
c_0_245 ).
fof(c_0_411,plain,
lhs_atom108,
c_0_246 ).
fof(c_0_412,plain,
lhs_atom107,
c_0_247 ).
fof(c_0_413,plain,
lhs_atom106,
c_0_248 ).
fof(c_0_414,plain,
lhs_atom105,
c_0_249 ).
fof(c_0_415,plain,
lhs_atom104,
c_0_250 ).
fof(c_0_416,plain,
lhs_atom103,
c_0_251 ).
fof(c_0_417,plain,
lhs_atom102,
c_0_252 ).
fof(c_0_418,plain,
lhs_atom101,
c_0_253 ).
fof(c_0_419,plain,
lhs_atom100,
c_0_254 ).
fof(c_0_420,plain,
lhs_atom99,
c_0_255 ).
fof(c_0_421,plain,
lhs_atom98,
c_0_256 ).
fof(c_0_422,plain,
lhs_atom97,
c_0_257 ).
fof(c_0_423,plain,
lhs_atom96,
c_0_258 ).
fof(c_0_424,plain,
lhs_atom95,
c_0_259 ).
fof(c_0_425,plain,
lhs_atom94,
c_0_260 ).
fof(c_0_426,plain,
lhs_atom93,
c_0_261 ).
fof(c_0_427,plain,
lhs_atom92,
c_0_262 ).
fof(c_0_428,plain,
lhs_atom91,
c_0_263 ).
fof(c_0_429,plain,
lhs_atom90,
c_0_264 ).
fof(c_0_430,plain,
lhs_atom89,
c_0_265 ).
fof(c_0_431,plain,
lhs_atom88,
c_0_266 ).
fof(c_0_432,plain,
lhs_atom87,
c_0_267 ).
fof(c_0_433,plain,
lhs_atom86,
c_0_268 ).
fof(c_0_434,plain,
lhs_atom85,
c_0_269 ).
fof(c_0_435,plain,
lhs_atom84,
c_0_270 ).
fof(c_0_436,plain,
lhs_atom83,
c_0_271 ).
fof(c_0_437,plain,
lhs_atom82,
c_0_272 ).
fof(c_0_438,plain,
lhs_atom81,
c_0_273 ).
fof(c_0_439,plain,
lhs_atom80,
c_0_274 ).
fof(c_0_440,plain,
lhs_atom79,
c_0_275 ).
fof(c_0_441,plain,
lhs_atom78,
c_0_276 ).
fof(c_0_442,plain,
lhs_atom77,
c_0_277 ).
fof(c_0_443,plain,
lhs_atom76,
c_0_278 ).
fof(c_0_444,plain,
lhs_atom75,
c_0_279 ).
fof(c_0_445,plain,
lhs_atom74,
c_0_280 ).
fof(c_0_446,plain,
lhs_atom73,
c_0_281 ).
fof(c_0_447,plain,
lhs_atom72,
c_0_282 ).
fof(c_0_448,plain,
lhs_atom71,
c_0_283 ).
fof(c_0_449,plain,
lhs_atom70,
c_0_284 ).
fof(c_0_450,plain,
lhs_atom69,
c_0_285 ).
fof(c_0_451,plain,
lhs_atom68,
c_0_286 ).
fof(c_0_452,plain,
lhs_atom67,
c_0_287 ).
fof(c_0_453,plain,
lhs_atom66,
c_0_288 ).
fof(c_0_454,plain,
lhs_atom65,
c_0_289 ).
fof(c_0_455,plain,
lhs_atom64,
c_0_290 ).
fof(c_0_456,plain,
lhs_atom63,
c_0_291 ).
fof(c_0_457,plain,
lhs_atom62,
c_0_292 ).
fof(c_0_458,plain,
lhs_atom61,
c_0_293 ).
fof(c_0_459,plain,
lhs_atom60,
c_0_294 ).
fof(c_0_460,plain,
lhs_atom59,
c_0_295 ).
fof(c_0_461,plain,
lhs_atom58,
c_0_296 ).
fof(c_0_462,plain,
lhs_atom57,
c_0_297 ).
fof(c_0_463,plain,
lhs_atom56,
c_0_298 ).
fof(c_0_464,plain,
lhs_atom55,
c_0_299 ).
fof(c_0_465,plain,
lhs_atom54,
c_0_300 ).
fof(c_0_466,plain,
lhs_atom53,
c_0_301 ).
fof(c_0_467,plain,
lhs_atom52,
c_0_302 ).
fof(c_0_468,plain,
lhs_atom51,
c_0_303 ).
fof(c_0_469,plain,
lhs_atom50,
c_0_304 ).
fof(c_0_470,plain,
lhs_atom49,
c_0_305 ).
fof(c_0_471,plain,
lhs_atom48,
c_0_306 ).
fof(c_0_472,plain,
lhs_atom47,
c_0_307 ).
fof(c_0_473,plain,
lhs_atom46,
c_0_308 ).
fof(c_0_474,plain,
lhs_atom45,
c_0_309 ).
fof(c_0_475,plain,
lhs_atom44,
c_0_310 ).
fof(c_0_476,plain,
lhs_atom43,
c_0_311 ).
fof(c_0_477,plain,
lhs_atom42,
c_0_312 ).
fof(c_0_478,plain,
lhs_atom41,
c_0_313 ).
fof(c_0_479,plain,
lhs_atom40,
c_0_314 ).
fof(c_0_480,plain,
lhs_atom39,
c_0_315 ).
fof(c_0_481,plain,
lhs_atom38,
c_0_316 ).
fof(c_0_482,plain,
lhs_atom37,
c_0_317 ).
fof(c_0_483,plain,
lhs_atom36,
c_0_318 ).
fof(c_0_484,plain,
lhs_atom35,
c_0_319 ).
fof(c_0_485,plain,
lhs_atom33,
c_0_320 ).
fof(c_0_486,plain,
lhs_atom32,
c_0_321 ).
fof(c_0_487,plain,
lhs_atom30,
c_0_322 ).
fof(c_0_488,plain,
lhs_atom27,
c_0_323 ).
fof(c_0_489,plain,
lhs_atom21,
c_0_324 ).
fof(c_0_490,plain,
lhs_atom18,
c_0_325 ).
fof(c_0_491,plain,
lhs_atom17,
c_0_326 ).
fof(c_0_492,plain,
lhs_atom12,
c_0_327 ).
fof(c_0_493,plain,
lhs_atom11,
c_0_328 ).
fof(c_0_494,plain,
lhs_atom2,
c_0_329 ).
cnf(c_0_495,plain,
lhs_atom6(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_330]) ).
cnf(c_0_496,plain,
lhs_atom15(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_331]) ).
cnf(c_0_497,plain,
lhs_atom31(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_332]) ).
cnf(c_0_498,plain,
lhs_atom23(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_333]) ).
cnf(c_0_499,plain,
lhs_atom22(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_334]) ).
cnf(c_0_500,plain,
lhs_atom165(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_335]) ).
cnf(c_0_501,plain,
lhs_atom28(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_336]) ).
cnf(c_0_502,plain,
lhs_atom5(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_337]) ).
cnf(c_0_503,plain,
lhs_atom4(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_338]) ).
cnf(c_0_504,plain,
lhs_atom3(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_339]) ).
cnf(c_0_505,plain,
lhs_atom1(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_340]) ).
cnf(c_0_506,plain,
lhs_atom34(X1),
inference(split_conjunct,[status(thm)],[c_0_341]) ).
cnf(c_0_507,plain,
lhs_atom29(X1),
inference(split_conjunct,[status(thm)],[c_0_342]) ).
cnf(c_0_508,plain,
lhs_atom26(X1),
inference(split_conjunct,[status(thm)],[c_0_343]) ).
cnf(c_0_509,plain,
lhs_atom25(X1),
inference(split_conjunct,[status(thm)],[c_0_344]) ).
cnf(c_0_510,plain,
lhs_atom24(X1),
inference(split_conjunct,[status(thm)],[c_0_345]) ).
cnf(c_0_511,plain,
lhs_atom20(X1),
inference(split_conjunct,[status(thm)],[c_0_346]) ).
cnf(c_0_512,plain,
lhs_atom19(X1),
inference(split_conjunct,[status(thm)],[c_0_347]) ).
cnf(c_0_513,plain,
lhs_atom16(X1),
inference(split_conjunct,[status(thm)],[c_0_348]) ).
cnf(c_0_514,plain,
lhs_atom14(X1),
inference(split_conjunct,[status(thm)],[c_0_349]) ).
cnf(c_0_515,plain,
lhs_atom13(X1),
inference(split_conjunct,[status(thm)],[c_0_350]) ).
cnf(c_0_516,plain,
lhs_atom10(X1),
inference(split_conjunct,[status(thm)],[c_0_351]) ).
cnf(c_0_517,plain,
lhs_atom9(X1),
inference(split_conjunct,[status(thm)],[c_0_352]) ).
cnf(c_0_518,plain,
lhs_atom8(X1),
inference(split_conjunct,[status(thm)],[c_0_353]) ).
cnf(c_0_519,plain,
lhs_atom7(X1),
inference(split_conjunct,[status(thm)],[c_0_354]) ).
cnf(c_0_520,plain,
lhs_atom164,
inference(split_conjunct,[status(thm)],[c_0_355]) ).
cnf(c_0_521,plain,
lhs_atom163,
inference(split_conjunct,[status(thm)],[c_0_356]) ).
cnf(c_0_522,plain,
lhs_atom162,
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_523,plain,
lhs_atom161,
inference(split_conjunct,[status(thm)],[c_0_358]) ).
cnf(c_0_524,plain,
lhs_atom160,
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_525,plain,
lhs_atom159,
inference(split_conjunct,[status(thm)],[c_0_360]) ).
cnf(c_0_526,plain,
lhs_atom158,
inference(split_conjunct,[status(thm)],[c_0_361]) ).
cnf(c_0_527,plain,
lhs_atom157,
inference(split_conjunct,[status(thm)],[c_0_362]) ).
cnf(c_0_528,plain,
lhs_atom156,
inference(split_conjunct,[status(thm)],[c_0_363]) ).
cnf(c_0_529,plain,
lhs_atom155,
inference(split_conjunct,[status(thm)],[c_0_364]) ).
cnf(c_0_530,plain,
lhs_atom154,
inference(split_conjunct,[status(thm)],[c_0_365]) ).
cnf(c_0_531,plain,
lhs_atom153,
inference(split_conjunct,[status(thm)],[c_0_366]) ).
cnf(c_0_532,plain,
lhs_atom152,
inference(split_conjunct,[status(thm)],[c_0_367]) ).
cnf(c_0_533,plain,
lhs_atom151,
inference(split_conjunct,[status(thm)],[c_0_368]) ).
cnf(c_0_534,plain,
lhs_atom150,
inference(split_conjunct,[status(thm)],[c_0_369]) ).
cnf(c_0_535,plain,
lhs_atom149,
inference(split_conjunct,[status(thm)],[c_0_370]) ).
cnf(c_0_536,plain,
lhs_atom148,
inference(split_conjunct,[status(thm)],[c_0_371]) ).
cnf(c_0_537,plain,
lhs_atom147,
inference(split_conjunct,[status(thm)],[c_0_372]) ).
cnf(c_0_538,plain,
lhs_atom146,
inference(split_conjunct,[status(thm)],[c_0_373]) ).
cnf(c_0_539,plain,
lhs_atom145,
inference(split_conjunct,[status(thm)],[c_0_374]) ).
cnf(c_0_540,plain,
lhs_atom144,
inference(split_conjunct,[status(thm)],[c_0_375]) ).
cnf(c_0_541,plain,
lhs_atom143,
inference(split_conjunct,[status(thm)],[c_0_376]) ).
cnf(c_0_542,plain,
lhs_atom142,
inference(split_conjunct,[status(thm)],[c_0_377]) ).
cnf(c_0_543,plain,
lhs_atom141,
inference(split_conjunct,[status(thm)],[c_0_378]) ).
cnf(c_0_544,plain,
lhs_atom140,
inference(split_conjunct,[status(thm)],[c_0_379]) ).
cnf(c_0_545,plain,
lhs_atom139,
inference(split_conjunct,[status(thm)],[c_0_380]) ).
cnf(c_0_546,plain,
lhs_atom138,
inference(split_conjunct,[status(thm)],[c_0_381]) ).
cnf(c_0_547,plain,
lhs_atom137,
inference(split_conjunct,[status(thm)],[c_0_382]) ).
cnf(c_0_548,plain,
lhs_atom136,
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_549,plain,
lhs_atom135,
inference(split_conjunct,[status(thm)],[c_0_384]) ).
cnf(c_0_550,plain,
lhs_atom134,
inference(split_conjunct,[status(thm)],[c_0_385]) ).
cnf(c_0_551,plain,
lhs_atom133,
inference(split_conjunct,[status(thm)],[c_0_386]) ).
cnf(c_0_552,plain,
lhs_atom132,
inference(split_conjunct,[status(thm)],[c_0_387]) ).
cnf(c_0_553,plain,
lhs_atom131,
inference(split_conjunct,[status(thm)],[c_0_388]) ).
cnf(c_0_554,plain,
lhs_atom130,
inference(split_conjunct,[status(thm)],[c_0_389]) ).
cnf(c_0_555,plain,
lhs_atom129,
inference(split_conjunct,[status(thm)],[c_0_390]) ).
cnf(c_0_556,plain,
lhs_atom128,
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_557,plain,
lhs_atom127,
inference(split_conjunct,[status(thm)],[c_0_392]) ).
cnf(c_0_558,plain,
lhs_atom126,
inference(split_conjunct,[status(thm)],[c_0_393]) ).
cnf(c_0_559,plain,
lhs_atom125,
inference(split_conjunct,[status(thm)],[c_0_394]) ).
cnf(c_0_560,plain,
lhs_atom124,
inference(split_conjunct,[status(thm)],[c_0_395]) ).
cnf(c_0_561,plain,
lhs_atom123,
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_562,plain,
lhs_atom122,
inference(split_conjunct,[status(thm)],[c_0_397]) ).
cnf(c_0_563,plain,
lhs_atom121,
inference(split_conjunct,[status(thm)],[c_0_398]) ).
cnf(c_0_564,plain,
lhs_atom120,
inference(split_conjunct,[status(thm)],[c_0_399]) ).
cnf(c_0_565,plain,
lhs_atom119,
inference(split_conjunct,[status(thm)],[c_0_400]) ).
cnf(c_0_566,plain,
lhs_atom118,
inference(split_conjunct,[status(thm)],[c_0_401]) ).
cnf(c_0_567,plain,
lhs_atom117,
inference(split_conjunct,[status(thm)],[c_0_402]) ).
cnf(c_0_568,plain,
lhs_atom116,
inference(split_conjunct,[status(thm)],[c_0_403]) ).
cnf(c_0_569,plain,
lhs_atom115,
inference(split_conjunct,[status(thm)],[c_0_404]) ).
cnf(c_0_570,plain,
lhs_atom114,
inference(split_conjunct,[status(thm)],[c_0_405]) ).
cnf(c_0_571,plain,
lhs_atom113,
inference(split_conjunct,[status(thm)],[c_0_406]) ).
cnf(c_0_572,plain,
lhs_atom112,
inference(split_conjunct,[status(thm)],[c_0_407]) ).
cnf(c_0_573,plain,
lhs_atom111,
inference(split_conjunct,[status(thm)],[c_0_408]) ).
cnf(c_0_574,plain,
lhs_atom110,
inference(split_conjunct,[status(thm)],[c_0_409]) ).
cnf(c_0_575,plain,
lhs_atom109,
inference(split_conjunct,[status(thm)],[c_0_410]) ).
cnf(c_0_576,plain,
lhs_atom108,
inference(split_conjunct,[status(thm)],[c_0_411]) ).
cnf(c_0_577,plain,
lhs_atom107,
inference(split_conjunct,[status(thm)],[c_0_412]) ).
cnf(c_0_578,plain,
lhs_atom106,
inference(split_conjunct,[status(thm)],[c_0_413]) ).
cnf(c_0_579,plain,
lhs_atom105,
inference(split_conjunct,[status(thm)],[c_0_414]) ).
cnf(c_0_580,plain,
lhs_atom104,
inference(split_conjunct,[status(thm)],[c_0_415]) ).
cnf(c_0_581,plain,
lhs_atom103,
inference(split_conjunct,[status(thm)],[c_0_416]) ).
cnf(c_0_582,plain,
lhs_atom102,
inference(split_conjunct,[status(thm)],[c_0_417]) ).
cnf(c_0_583,plain,
lhs_atom101,
inference(split_conjunct,[status(thm)],[c_0_418]) ).
cnf(c_0_584,plain,
lhs_atom100,
inference(split_conjunct,[status(thm)],[c_0_419]) ).
cnf(c_0_585,plain,
lhs_atom99,
inference(split_conjunct,[status(thm)],[c_0_420]) ).
cnf(c_0_586,plain,
lhs_atom98,
inference(split_conjunct,[status(thm)],[c_0_421]) ).
cnf(c_0_587,plain,
lhs_atom97,
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_588,plain,
lhs_atom96,
inference(split_conjunct,[status(thm)],[c_0_423]) ).
cnf(c_0_589,plain,
lhs_atom95,
inference(split_conjunct,[status(thm)],[c_0_424]) ).
cnf(c_0_590,plain,
lhs_atom94,
inference(split_conjunct,[status(thm)],[c_0_425]) ).
cnf(c_0_591,plain,
lhs_atom93,
inference(split_conjunct,[status(thm)],[c_0_426]) ).
cnf(c_0_592,plain,
lhs_atom92,
inference(split_conjunct,[status(thm)],[c_0_427]) ).
cnf(c_0_593,plain,
lhs_atom91,
inference(split_conjunct,[status(thm)],[c_0_428]) ).
cnf(c_0_594,plain,
lhs_atom90,
inference(split_conjunct,[status(thm)],[c_0_429]) ).
cnf(c_0_595,plain,
lhs_atom89,
inference(split_conjunct,[status(thm)],[c_0_430]) ).
cnf(c_0_596,plain,
lhs_atom88,
inference(split_conjunct,[status(thm)],[c_0_431]) ).
cnf(c_0_597,plain,
lhs_atom87,
inference(split_conjunct,[status(thm)],[c_0_432]) ).
cnf(c_0_598,plain,
lhs_atom86,
inference(split_conjunct,[status(thm)],[c_0_433]) ).
cnf(c_0_599,plain,
lhs_atom85,
inference(split_conjunct,[status(thm)],[c_0_434]) ).
cnf(c_0_600,plain,
lhs_atom84,
inference(split_conjunct,[status(thm)],[c_0_435]) ).
cnf(c_0_601,plain,
lhs_atom83,
inference(split_conjunct,[status(thm)],[c_0_436]) ).
cnf(c_0_602,plain,
lhs_atom82,
inference(split_conjunct,[status(thm)],[c_0_437]) ).
cnf(c_0_603,plain,
lhs_atom81,
inference(split_conjunct,[status(thm)],[c_0_438]) ).
cnf(c_0_604,plain,
lhs_atom80,
inference(split_conjunct,[status(thm)],[c_0_439]) ).
cnf(c_0_605,plain,
lhs_atom79,
inference(split_conjunct,[status(thm)],[c_0_440]) ).
cnf(c_0_606,plain,
lhs_atom78,
inference(split_conjunct,[status(thm)],[c_0_441]) ).
cnf(c_0_607,plain,
lhs_atom77,
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_608,plain,
lhs_atom76,
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_609,plain,
lhs_atom75,
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_610,plain,
lhs_atom74,
inference(split_conjunct,[status(thm)],[c_0_445]) ).
cnf(c_0_611,plain,
lhs_atom73,
inference(split_conjunct,[status(thm)],[c_0_446]) ).
cnf(c_0_612,plain,
lhs_atom72,
inference(split_conjunct,[status(thm)],[c_0_447]) ).
cnf(c_0_613,plain,
lhs_atom71,
inference(split_conjunct,[status(thm)],[c_0_448]) ).
cnf(c_0_614,plain,
lhs_atom70,
inference(split_conjunct,[status(thm)],[c_0_449]) ).
cnf(c_0_615,plain,
lhs_atom69,
inference(split_conjunct,[status(thm)],[c_0_450]) ).
cnf(c_0_616,plain,
lhs_atom68,
inference(split_conjunct,[status(thm)],[c_0_451]) ).
cnf(c_0_617,plain,
lhs_atom67,
inference(split_conjunct,[status(thm)],[c_0_452]) ).
cnf(c_0_618,plain,
lhs_atom66,
inference(split_conjunct,[status(thm)],[c_0_453]) ).
cnf(c_0_619,plain,
lhs_atom65,
inference(split_conjunct,[status(thm)],[c_0_454]) ).
cnf(c_0_620,plain,
lhs_atom64,
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_621,plain,
lhs_atom63,
inference(split_conjunct,[status(thm)],[c_0_456]) ).
cnf(c_0_622,plain,
lhs_atom62,
inference(split_conjunct,[status(thm)],[c_0_457]) ).
cnf(c_0_623,plain,
lhs_atom61,
inference(split_conjunct,[status(thm)],[c_0_458]) ).
cnf(c_0_624,plain,
lhs_atom60,
inference(split_conjunct,[status(thm)],[c_0_459]) ).
cnf(c_0_625,plain,
lhs_atom59,
inference(split_conjunct,[status(thm)],[c_0_460]) ).
cnf(c_0_626,plain,
lhs_atom58,
inference(split_conjunct,[status(thm)],[c_0_461]) ).
cnf(c_0_627,plain,
lhs_atom57,
inference(split_conjunct,[status(thm)],[c_0_462]) ).
cnf(c_0_628,plain,
lhs_atom56,
inference(split_conjunct,[status(thm)],[c_0_463]) ).
cnf(c_0_629,plain,
lhs_atom55,
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_630,plain,
lhs_atom54,
inference(split_conjunct,[status(thm)],[c_0_465]) ).
cnf(c_0_631,plain,
lhs_atom53,
inference(split_conjunct,[status(thm)],[c_0_466]) ).
cnf(c_0_632,plain,
lhs_atom52,
inference(split_conjunct,[status(thm)],[c_0_467]) ).
cnf(c_0_633,plain,
lhs_atom51,
inference(split_conjunct,[status(thm)],[c_0_468]) ).
cnf(c_0_634,plain,
lhs_atom50,
inference(split_conjunct,[status(thm)],[c_0_469]) ).
cnf(c_0_635,plain,
lhs_atom49,
inference(split_conjunct,[status(thm)],[c_0_470]) ).
cnf(c_0_636,plain,
lhs_atom48,
inference(split_conjunct,[status(thm)],[c_0_471]) ).
cnf(c_0_637,plain,
lhs_atom47,
inference(split_conjunct,[status(thm)],[c_0_472]) ).
cnf(c_0_638,plain,
lhs_atom46,
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_639,plain,
lhs_atom45,
inference(split_conjunct,[status(thm)],[c_0_474]) ).
cnf(c_0_640,plain,
lhs_atom44,
inference(split_conjunct,[status(thm)],[c_0_475]) ).
cnf(c_0_641,plain,
lhs_atom43,
inference(split_conjunct,[status(thm)],[c_0_476]) ).
cnf(c_0_642,plain,
lhs_atom42,
inference(split_conjunct,[status(thm)],[c_0_477]) ).
cnf(c_0_643,plain,
lhs_atom41,
inference(split_conjunct,[status(thm)],[c_0_478]) ).
cnf(c_0_644,plain,
lhs_atom40,
inference(split_conjunct,[status(thm)],[c_0_479]) ).
cnf(c_0_645,plain,
lhs_atom39,
inference(split_conjunct,[status(thm)],[c_0_480]) ).
cnf(c_0_646,plain,
lhs_atom38,
inference(split_conjunct,[status(thm)],[c_0_481]) ).
cnf(c_0_647,plain,
lhs_atom37,
inference(split_conjunct,[status(thm)],[c_0_482]) ).
cnf(c_0_648,plain,
lhs_atom36,
inference(split_conjunct,[status(thm)],[c_0_483]) ).
cnf(c_0_649,plain,
lhs_atom35,
inference(split_conjunct,[status(thm)],[c_0_484]) ).
cnf(c_0_650,plain,
lhs_atom33,
inference(split_conjunct,[status(thm)],[c_0_485]) ).
cnf(c_0_651,plain,
lhs_atom32,
inference(split_conjunct,[status(thm)],[c_0_486]) ).
cnf(c_0_652,plain,
lhs_atom30,
inference(split_conjunct,[status(thm)],[c_0_487]) ).
cnf(c_0_653,plain,
lhs_atom27,
inference(split_conjunct,[status(thm)],[c_0_488]) ).
cnf(c_0_654,plain,
lhs_atom21,
inference(split_conjunct,[status(thm)],[c_0_489]) ).
cnf(c_0_655,plain,
lhs_atom18,
inference(split_conjunct,[status(thm)],[c_0_490]) ).
cnf(c_0_656,plain,
lhs_atom17,
inference(split_conjunct,[status(thm)],[c_0_491]) ).
cnf(c_0_657,plain,
lhs_atom12,
inference(split_conjunct,[status(thm)],[c_0_492]) ).
cnf(c_0_658,plain,
lhs_atom11,
inference(split_conjunct,[status(thm)],[c_0_493]) ).
cnf(c_0_659,plain,
lhs_atom2,
inference(split_conjunct,[status(thm)],[c_0_494]) ).
cnf(c_0_660,plain,
lhs_atom6(X1,X2,X3,X4,X5),
c_0_495,
[final] ).
cnf(c_0_661,plain,
lhs_atom15(X1,X2,X3,X4),
c_0_496,
[final] ).
cnf(c_0_662,plain,
lhs_atom31(X1,X2,X3),
c_0_497,
[final] ).
cnf(c_0_663,plain,
lhs_atom23(X1,X2,X3),
c_0_498,
[final] ).
cnf(c_0_664,plain,
lhs_atom22(X1,X2,X3),
c_0_499,
[final] ).
cnf(c_0_665,plain,
lhs_atom165(X1,X2),
c_0_500,
[final] ).
cnf(c_0_666,plain,
lhs_atom28(X1,X2),
c_0_501,
[final] ).
cnf(c_0_667,plain,
lhs_atom5(X1,X2),
c_0_502,
[final] ).
cnf(c_0_668,plain,
lhs_atom4(X1,X2),
c_0_503,
[final] ).
cnf(c_0_669,plain,
lhs_atom3(X1,X2),
c_0_504,
[final] ).
cnf(c_0_670,plain,
lhs_atom1(X1,X2),
c_0_505,
[final] ).
cnf(c_0_671,plain,
lhs_atom34(X1),
c_0_506,
[final] ).
cnf(c_0_672,plain,
lhs_atom29(X1),
c_0_507,
[final] ).
cnf(c_0_673,plain,
lhs_atom26(X1),
c_0_508,
[final] ).
cnf(c_0_674,plain,
lhs_atom25(X1),
c_0_509,
[final] ).
cnf(c_0_675,plain,
lhs_atom24(X1),
c_0_510,
[final] ).
cnf(c_0_676,plain,
lhs_atom20(X1),
c_0_511,
[final] ).
cnf(c_0_677,plain,
lhs_atom19(X1),
c_0_512,
[final] ).
cnf(c_0_678,plain,
lhs_atom16(X1),
c_0_513,
[final] ).
cnf(c_0_679,plain,
lhs_atom14(X1),
c_0_514,
[final] ).
cnf(c_0_680,plain,
lhs_atom13(X1),
c_0_515,
[final] ).
cnf(c_0_681,plain,
lhs_atom10(X1),
c_0_516,
[final] ).
cnf(c_0_682,plain,
lhs_atom9(X1),
c_0_517,
[final] ).
cnf(c_0_683,plain,
lhs_atom8(X1),
c_0_518,
[final] ).
cnf(c_0_684,plain,
lhs_atom7(X1),
c_0_519,
[final] ).
cnf(c_0_685,plain,
lhs_atom164,
c_0_520,
[final] ).
cnf(c_0_686,plain,
lhs_atom163,
c_0_521,
[final] ).
cnf(c_0_687,plain,
lhs_atom162,
c_0_522,
[final] ).
cnf(c_0_688,plain,
lhs_atom161,
c_0_523,
[final] ).
cnf(c_0_689,plain,
lhs_atom160,
c_0_524,
[final] ).
cnf(c_0_690,plain,
lhs_atom159,
c_0_525,
[final] ).
cnf(c_0_691,plain,
lhs_atom158,
c_0_526,
[final] ).
cnf(c_0_692,plain,
lhs_atom157,
c_0_527,
[final] ).
cnf(c_0_693,plain,
lhs_atom156,
c_0_528,
[final] ).
cnf(c_0_694,plain,
lhs_atom155,
c_0_529,
[final] ).
cnf(c_0_695,plain,
lhs_atom154,
c_0_530,
[final] ).
cnf(c_0_696,plain,
lhs_atom153,
c_0_531,
[final] ).
cnf(c_0_697,plain,
lhs_atom152,
c_0_532,
[final] ).
cnf(c_0_698,plain,
lhs_atom151,
c_0_533,
[final] ).
cnf(c_0_699,plain,
lhs_atom150,
c_0_534,
[final] ).
cnf(c_0_700,plain,
lhs_atom149,
c_0_535,
[final] ).
cnf(c_0_701,plain,
lhs_atom148,
c_0_536,
[final] ).
cnf(c_0_702,plain,
lhs_atom147,
c_0_537,
[final] ).
cnf(c_0_703,plain,
lhs_atom146,
c_0_538,
[final] ).
cnf(c_0_704,plain,
lhs_atom145,
c_0_539,
[final] ).
cnf(c_0_705,plain,
lhs_atom144,
c_0_540,
[final] ).
cnf(c_0_706,plain,
lhs_atom143,
c_0_541,
[final] ).
cnf(c_0_707,plain,
lhs_atom142,
c_0_542,
[final] ).
cnf(c_0_708,plain,
lhs_atom141,
c_0_543,
[final] ).
cnf(c_0_709,plain,
lhs_atom140,
c_0_544,
[final] ).
cnf(c_0_710,plain,
lhs_atom139,
c_0_545,
[final] ).
cnf(c_0_711,plain,
lhs_atom138,
c_0_546,
[final] ).
cnf(c_0_712,plain,
lhs_atom137,
c_0_547,
[final] ).
cnf(c_0_713,plain,
lhs_atom136,
c_0_548,
[final] ).
cnf(c_0_714,plain,
lhs_atom135,
c_0_549,
[final] ).
cnf(c_0_715,plain,
lhs_atom134,
c_0_550,
[final] ).
cnf(c_0_716,plain,
lhs_atom133,
c_0_551,
[final] ).
cnf(c_0_717,plain,
lhs_atom132,
c_0_552,
[final] ).
cnf(c_0_718,plain,
lhs_atom131,
c_0_553,
[final] ).
cnf(c_0_719,plain,
lhs_atom130,
c_0_554,
[final] ).
cnf(c_0_720,plain,
lhs_atom129,
c_0_555,
[final] ).
cnf(c_0_721,plain,
lhs_atom128,
c_0_556,
[final] ).
cnf(c_0_722,plain,
lhs_atom127,
c_0_557,
[final] ).
cnf(c_0_723,plain,
lhs_atom126,
c_0_558,
[final] ).
cnf(c_0_724,plain,
lhs_atom125,
c_0_559,
[final] ).
cnf(c_0_725,plain,
lhs_atom124,
c_0_560,
[final] ).
cnf(c_0_726,plain,
lhs_atom123,
c_0_561,
[final] ).
cnf(c_0_727,plain,
lhs_atom122,
c_0_562,
[final] ).
cnf(c_0_728,plain,
lhs_atom121,
c_0_563,
[final] ).
cnf(c_0_729,plain,
lhs_atom120,
c_0_564,
[final] ).
cnf(c_0_730,plain,
lhs_atom119,
c_0_565,
[final] ).
cnf(c_0_731,plain,
lhs_atom118,
c_0_566,
[final] ).
cnf(c_0_732,plain,
lhs_atom117,
c_0_567,
[final] ).
cnf(c_0_733,plain,
lhs_atom116,
c_0_568,
[final] ).
cnf(c_0_734,plain,
lhs_atom115,
c_0_569,
[final] ).
cnf(c_0_735,plain,
lhs_atom114,
c_0_570,
[final] ).
cnf(c_0_736,plain,
lhs_atom113,
c_0_571,
[final] ).
cnf(c_0_737,plain,
lhs_atom112,
c_0_572,
[final] ).
cnf(c_0_738,plain,
lhs_atom111,
c_0_573,
[final] ).
cnf(c_0_739,plain,
lhs_atom110,
c_0_574,
[final] ).
cnf(c_0_740,plain,
lhs_atom109,
c_0_575,
[final] ).
cnf(c_0_741,plain,
lhs_atom108,
c_0_576,
[final] ).
cnf(c_0_742,plain,
lhs_atom107,
c_0_577,
[final] ).
cnf(c_0_743,plain,
lhs_atom106,
c_0_578,
[final] ).
cnf(c_0_744,plain,
lhs_atom105,
c_0_579,
[final] ).
cnf(c_0_745,plain,
lhs_atom104,
c_0_580,
[final] ).
cnf(c_0_746,plain,
lhs_atom103,
c_0_581,
[final] ).
cnf(c_0_747,plain,
lhs_atom102,
c_0_582,
[final] ).
cnf(c_0_748,plain,
lhs_atom101,
c_0_583,
[final] ).
cnf(c_0_749,plain,
lhs_atom100,
c_0_584,
[final] ).
cnf(c_0_750,plain,
lhs_atom99,
c_0_585,
[final] ).
cnf(c_0_751,plain,
lhs_atom98,
c_0_586,
[final] ).
cnf(c_0_752,plain,
lhs_atom97,
c_0_587,
[final] ).
cnf(c_0_753,plain,
lhs_atom96,
c_0_588,
[final] ).
cnf(c_0_754,plain,
lhs_atom95,
c_0_589,
[final] ).
cnf(c_0_755,plain,
lhs_atom94,
c_0_590,
[final] ).
cnf(c_0_756,plain,
lhs_atom93,
c_0_591,
[final] ).
cnf(c_0_757,plain,
lhs_atom92,
c_0_592,
[final] ).
cnf(c_0_758,plain,
lhs_atom91,
c_0_593,
[final] ).
cnf(c_0_759,plain,
lhs_atom90,
c_0_594,
[final] ).
cnf(c_0_760,plain,
lhs_atom89,
c_0_595,
[final] ).
cnf(c_0_761,plain,
lhs_atom88,
c_0_596,
[final] ).
cnf(c_0_762,plain,
lhs_atom87,
c_0_597,
[final] ).
cnf(c_0_763,plain,
lhs_atom86,
c_0_598,
[final] ).
cnf(c_0_764,plain,
lhs_atom85,
c_0_599,
[final] ).
cnf(c_0_765,plain,
lhs_atom84,
c_0_600,
[final] ).
cnf(c_0_766,plain,
lhs_atom83,
c_0_601,
[final] ).
cnf(c_0_767,plain,
lhs_atom82,
c_0_602,
[final] ).
cnf(c_0_768,plain,
lhs_atom81,
c_0_603,
[final] ).
cnf(c_0_769,plain,
lhs_atom80,
c_0_604,
[final] ).
cnf(c_0_770,plain,
lhs_atom79,
c_0_605,
[final] ).
cnf(c_0_771,plain,
lhs_atom78,
c_0_606,
[final] ).
cnf(c_0_772,plain,
lhs_atom77,
c_0_607,
[final] ).
cnf(c_0_773,plain,
lhs_atom76,
c_0_608,
[final] ).
cnf(c_0_774,plain,
lhs_atom75,
c_0_609,
[final] ).
cnf(c_0_775,plain,
lhs_atom74,
c_0_610,
[final] ).
cnf(c_0_776,plain,
lhs_atom73,
c_0_611,
[final] ).
cnf(c_0_777,plain,
lhs_atom72,
c_0_612,
[final] ).
cnf(c_0_778,plain,
lhs_atom71,
c_0_613,
[final] ).
cnf(c_0_779,plain,
lhs_atom70,
c_0_614,
[final] ).
cnf(c_0_780,plain,
lhs_atom69,
c_0_615,
[final] ).
cnf(c_0_781,plain,
lhs_atom68,
c_0_616,
[final] ).
cnf(c_0_782,plain,
lhs_atom67,
c_0_617,
[final] ).
cnf(c_0_783,plain,
lhs_atom66,
c_0_618,
[final] ).
cnf(c_0_784,plain,
lhs_atom65,
c_0_619,
[final] ).
cnf(c_0_785,plain,
lhs_atom64,
c_0_620,
[final] ).
cnf(c_0_786,plain,
lhs_atom63,
c_0_621,
[final] ).
cnf(c_0_787,plain,
lhs_atom62,
c_0_622,
[final] ).
cnf(c_0_788,plain,
lhs_atom61,
c_0_623,
[final] ).
cnf(c_0_789,plain,
lhs_atom60,
c_0_624,
[final] ).
cnf(c_0_790,plain,
lhs_atom59,
c_0_625,
[final] ).
cnf(c_0_791,plain,
lhs_atom58,
c_0_626,
[final] ).
cnf(c_0_792,plain,
lhs_atom57,
c_0_627,
[final] ).
cnf(c_0_793,plain,
lhs_atom56,
c_0_628,
[final] ).
cnf(c_0_794,plain,
lhs_atom55,
c_0_629,
[final] ).
cnf(c_0_795,plain,
lhs_atom54,
c_0_630,
[final] ).
cnf(c_0_796,plain,
lhs_atom53,
c_0_631,
[final] ).
cnf(c_0_797,plain,
lhs_atom52,
c_0_632,
[final] ).
cnf(c_0_798,plain,
lhs_atom51,
c_0_633,
[final] ).
cnf(c_0_799,plain,
lhs_atom50,
c_0_634,
[final] ).
cnf(c_0_800,plain,
lhs_atom49,
c_0_635,
[final] ).
cnf(c_0_801,plain,
lhs_atom48,
c_0_636,
[final] ).
cnf(c_0_802,plain,
lhs_atom47,
c_0_637,
[final] ).
cnf(c_0_803,plain,
lhs_atom46,
c_0_638,
[final] ).
cnf(c_0_804,plain,
lhs_atom45,
c_0_639,
[final] ).
cnf(c_0_805,plain,
lhs_atom44,
c_0_640,
[final] ).
cnf(c_0_806,plain,
lhs_atom43,
c_0_641,
[final] ).
cnf(c_0_807,plain,
lhs_atom42,
c_0_642,
[final] ).
cnf(c_0_808,plain,
lhs_atom41,
c_0_643,
[final] ).
cnf(c_0_809,plain,
lhs_atom40,
c_0_644,
[final] ).
cnf(c_0_810,plain,
lhs_atom39,
c_0_645,
[final] ).
cnf(c_0_811,plain,
lhs_atom38,
c_0_646,
[final] ).
cnf(c_0_812,plain,
lhs_atom37,
c_0_647,
[final] ).
cnf(c_0_813,plain,
lhs_atom36,
c_0_648,
[final] ).
cnf(c_0_814,plain,
lhs_atom35,
c_0_649,
[final] ).
cnf(c_0_815,plain,
lhs_atom33,
c_0_650,
[final] ).
cnf(c_0_816,plain,
lhs_atom32,
c_0_651,
[final] ).
cnf(c_0_817,plain,
lhs_atom30,
c_0_652,
[final] ).
cnf(c_0_818,plain,
lhs_atom27,
c_0_653,
[final] ).
cnf(c_0_819,plain,
lhs_atom21,
c_0_654,
[final] ).
cnf(c_0_820,plain,
lhs_atom18,
c_0_655,
[final] ).
cnf(c_0_821,plain,
lhs_atom17,
c_0_656,
[final] ).
cnf(c_0_822,plain,
lhs_atom12,
c_0_657,
[final] ).
cnf(c_0_823,plain,
lhs_atom11,
c_0_658,
[final] ).
cnf(c_0_824,plain,
lhs_atom2,
c_0_659,
[final] ).
% End CNF derivation
cnf(c_0_660_0,axiom,
hAPP(hAPP(c_Power_Opower_Opower(X2,X1,X5),X4),c_Suc(X3)) = hAPP(hAPP(X1,X4),hAPP(hAPP(c_Power_Opower_Opower(X2,X1,X5),X4),X3)),
inference(unfold_definition,[status(thm)],[c_0_660,def_lhs_atom6]) ).
cnf(c_0_661_0,axiom,
hAPP(hAPP(c_Power_Opower_Opower(X2,X1,X4),X3),c_HOL_Ozero__class_Ozero(tc_nat)) = X2,
inference(unfold_definition,[status(thm)],[c_0_661,def_lhs_atom15]) ).
cnf(c_0_662_0,axiom,
hAPP(c_Polynomial_Opoly(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1(X3,X2),tc_Complex_Ocomplex),X1) = hAPP(c_Polynomial_Opoly(X2,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),X3),X1)),
inference(unfold_definition,[status(thm)],[c_0_662,def_lhs_atom31]) ).
cnf(c_0_663_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1)),
inference(unfold_definition,[status(thm)],[c_0_663,def_lhs_atom23]) ).
cnf(c_0_664_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1)),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3)),
inference(unfold_definition,[status(thm)],[c_0_664,def_lhs_atom22]) ).
cnf(c_0_665_0,axiom,
hBOOL(c_fequal(X1,X1,X2)),
inference(unfold_definition,[status(thm)],[c_0_665,def_lhs_atom165]) ).
cnf(c_0_666_0,axiom,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1(X2,X1),tc_Complex_Ocomplex) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_666,def_lhs_atom28]) ).
cnf(c_0_667_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),
inference(unfold_definition,[status(thm)],[c_0_667,def_lhs_atom5]) ).
cnf(c_0_668_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_Suc(X1)) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1)),
inference(unfold_definition,[status(thm)],[c_0_668,def_lhs_atom4]) ).
cnf(c_0_669_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X2)),X1) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1)),
inference(unfold_definition,[status(thm)],[c_0_669,def_lhs_atom3]) ).
cnf(c_0_670_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X2)),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_Suc(X1)),
inference(unfold_definition,[status(thm)],[c_0_670,def_lhs_atom1]) ).
cnf(c_0_671_0,axiom,
hAPP(c_Polynomial_Opoly(v_q____,tc_Complex_Ocomplex),X1) = hAPP(c_Polynomial_Opoly(v_pa____,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),v_c____),X1)),
inference(unfold_definition,[status(thm)],[c_0_671,def_lhs_atom34]) ).
cnf(c_0_672_0,axiom,
c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(c_Polynomial_Opoly(v_pa____,tc_Complex_Ocomplex),v_c____),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(hAPP(c_Polynomial_Opoly(v_pa____,tc_Complex_Ocomplex),X1),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_672,def_lhs_atom29]) ).
cnf(c_0_673_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1) = X1,
inference(unfold_definition,[status(thm)],[c_0_673,def_lhs_atom26]) ).
cnf(c_0_674_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)) = X1,
inference(unfold_definition,[status(thm)],[c_0_674,def_lhs_atom25]) ).
cnf(c_0_675_0,axiom,
X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)),
inference(unfold_definition,[status(thm)],[c_0_675,def_lhs_atom24]) ).
cnf(c_0_676_0,axiom,
c_Suc(X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),
inference(unfold_definition,[status(thm)],[c_0_676,def_lhs_atom20]) ).
cnf(c_0_677_0,axiom,
c_Suc(X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X1),
inference(unfold_definition,[status(thm)],[c_0_677,def_lhs_atom19]) ).
cnf(c_0_678_0,axiom,
c_lessequals(X1,X1,tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_678,def_lhs_atom16]) ).
cnf(c_0_679_0,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_679,def_lhs_atom14]) ).
cnf(c_0_680_0,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_680,def_lhs_atom13]) ).
cnf(c_0_681_0,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
inference(unfold_definition,[status(thm)],[c_0_681,def_lhs_atom10]) ).
cnf(c_0_682_0,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
inference(unfold_definition,[status(thm)],[c_0_682,def_lhs_atom9]) ).
cnf(c_0_683_0,axiom,
X1 != c_Suc(X1),
inference(unfold_definition,[status(thm)],[c_0_683,def_lhs_atom8]) ).
cnf(c_0_684_0,axiom,
c_Suc(X1) != X1,
inference(unfold_definition,[status(thm)],[c_0_684,def_lhs_atom7]) ).
cnf(c_0_685_0,axiom,
class_HOL_Ozero(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_685,def_lhs_atom164]) ).
cnf(c_0_686_0,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_686,def_lhs_atom163]) ).
cnf(c_0_687_0,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_687,def_lhs_atom162]) ).
cnf(c_0_688_0,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_688,def_lhs_atom161]) ).
cnf(c_0_689_0,axiom,
class_Nat_Osemiring__char__0(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_689,def_lhs_atom160]) ).
cnf(c_0_690_0,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_690,def_lhs_atom159]) ).
cnf(c_0_691_0,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_691,def_lhs_atom158]) ).
cnf(c_0_692_0,axiom,
class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_692,def_lhs_atom157]) ).
cnf(c_0_693_0,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_693,def_lhs_atom156]) ).
cnf(c_0_694_0,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_694,def_lhs_atom155]) ).
cnf(c_0_695_0,axiom,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_695,def_lhs_atom154]) ).
cnf(c_0_696_0,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_696,def_lhs_atom153]) ).
cnf(c_0_697_0,axiom,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_697,def_lhs_atom152]) ).
cnf(c_0_698_0,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_698,def_lhs_atom151]) ).
cnf(c_0_699_0,axiom,
class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_699,def_lhs_atom150]) ).
cnf(c_0_700_0,axiom,
class_Ring__and__Field_Osemiring__1(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_700,def_lhs_atom149]) ).
cnf(c_0_701_0,axiom,
class_OrderedGroup_Osemigroup__add(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_701,def_lhs_atom148]) ).
cnf(c_0_702_0,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_702,def_lhs_atom147]) ).
cnf(c_0_703_0,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_703,def_lhs_atom146]) ).
cnf(c_0_704_0,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_704,def_lhs_atom145]) ).
cnf(c_0_705_0,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_705,def_lhs_atom144]) ).
cnf(c_0_706_0,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_706,def_lhs_atom143]) ).
cnf(c_0_707_0,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_707,def_lhs_atom142]) ).
cnf(c_0_708_0,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_708,def_lhs_atom141]) ).
cnf(c_0_709_0,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_709,def_lhs_atom140]) ).
cnf(c_0_710_0,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_710,def_lhs_atom139]) ).
cnf(c_0_711_0,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_711,def_lhs_atom138]) ).
cnf(c_0_712_0,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_712,def_lhs_atom137]) ).
cnf(c_0_713_0,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_713,def_lhs_atom136]) ).
cnf(c_0_714_0,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_714,def_lhs_atom135]) ).
cnf(c_0_715_0,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_715,def_lhs_atom134]) ).
cnf(c_0_716_0,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_716,def_lhs_atom133]) ).
cnf(c_0_717_0,axiom,
class_HOL_Ozero(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_717,def_lhs_atom132]) ).
cnf(c_0_718_0,axiom,
class_Power_Opower(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_718,def_lhs_atom131]) ).
cnf(c_0_719_0,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_719,def_lhs_atom130]) ).
cnf(c_0_720_0,axiom,
class_Int_Oring__char__0(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_720,def_lhs_atom129]) ).
cnf(c_0_721_0,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_721,def_lhs_atom128]) ).
cnf(c_0_722_0,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_722,def_lhs_atom127]) ).
cnf(c_0_723_0,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_723,def_lhs_atom126]) ).
cnf(c_0_724_0,axiom,
class_Nat_Osemiring__char__0(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_724,def_lhs_atom125]) ).
cnf(c_0_725_0,axiom,
class_Ring__and__Field_Oidom(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_725,def_lhs_atom124]) ).
cnf(c_0_726_0,axiom,
class_Ring__and__Field_Oring(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_726,def_lhs_atom123]) ).
cnf(c_0_727_0,axiom,
class_Ring__and__Field_Oring__1(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_727,def_lhs_atom122]) ).
cnf(c_0_728_0,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_728,def_lhs_atom121]) ).
cnf(c_0_729_0,axiom,
class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_729,def_lhs_atom120]) ).
cnf(c_0_730_0,axiom,
class_Ring__and__Field_Osemiring(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_730,def_lhs_atom119]) ).
cnf(c_0_731_0,axiom,
class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_731,def_lhs_atom118]) ).
cnf(c_0_732_0,axiom,
class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_732,def_lhs_atom117]) ).
cnf(c_0_733_0,axiom,
class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_733,def_lhs_atom116]) ).
cnf(c_0_734_0,axiom,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_734,def_lhs_atom115]) ).
cnf(c_0_735_0,axiom,
class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_735,def_lhs_atom114]) ).
cnf(c_0_736_0,axiom,
class_Ring__and__Field_Osemiring__0(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_736,def_lhs_atom113]) ).
cnf(c_0_737_0,axiom,
class_Ring__and__Field_Osemiring__1(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_737,def_lhs_atom112]) ).
cnf(c_0_738_0,axiom,
class_OrderedGroup_Osemigroup__add(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_738,def_lhs_atom111]) ).
cnf(c_0_739_0,axiom,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_739,def_lhs_atom110]) ).
cnf(c_0_740_0,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_740,def_lhs_atom109]) ).
cnf(c_0_741_0,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_741,def_lhs_atom108]) ).
cnf(c_0_742_0,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_742,def_lhs_atom107]) ).
cnf(c_0_743_0,axiom,
class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_743,def_lhs_atom106]) ).
cnf(c_0_744_0,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_744,def_lhs_atom105]) ).
cnf(c_0_745_0,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_745,def_lhs_atom104]) ).
cnf(c_0_746_0,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_746,def_lhs_atom103]) ).
cnf(c_0_747_0,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_747,def_lhs_atom102]) ).
cnf(c_0_748_0,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_748,def_lhs_atom101]) ).
cnf(c_0_749_0,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_749,def_lhs_atom100]) ).
cnf(c_0_750_0,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_750,def_lhs_atom99]) ).
cnf(c_0_751_0,axiom,
class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_751,def_lhs_atom98]) ).
cnf(c_0_752_0,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_752,def_lhs_atom97]) ).
cnf(c_0_753_0,axiom,
class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_753,def_lhs_atom96]) ).
cnf(c_0_754_0,axiom,
class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_754,def_lhs_atom95]) ).
cnf(c_0_755_0,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_755,def_lhs_atom94]) ).
cnf(c_0_756_0,axiom,
class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_756,def_lhs_atom93]) ).
cnf(c_0_757_0,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_757,def_lhs_atom92]) ).
cnf(c_0_758_0,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_758,def_lhs_atom91]) ).
cnf(c_0_759_0,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_759,def_lhs_atom90]) ).
cnf(c_0_760_0,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_760,def_lhs_atom89]) ).
cnf(c_0_761_0,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_761,def_lhs_atom88]) ).
cnf(c_0_762_0,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_762,def_lhs_atom87]) ).
cnf(c_0_763_0,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_763,def_lhs_atom86]) ).
cnf(c_0_764_0,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_764,def_lhs_atom85]) ).
cnf(c_0_765_0,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_765,def_lhs_atom84]) ).
cnf(c_0_766_0,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_766,def_lhs_atom83]) ).
cnf(c_0_767_0,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_767,def_lhs_atom82]) ).
cnf(c_0_768_0,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_768,def_lhs_atom81]) ).
cnf(c_0_769_0,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_769,def_lhs_atom80]) ).
cnf(c_0_770_0,axiom,
class_HOL_Ozero(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_770,def_lhs_atom79]) ).
cnf(c_0_771_0,axiom,
class_Power_Opower(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_771,def_lhs_atom78]) ).
cnf(c_0_772_0,axiom,
class_Orderings_Oorder(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_772,def_lhs_atom77]) ).
cnf(c_0_773_0,axiom,
class_Orderings_Olinorder(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_773,def_lhs_atom76]) ).
cnf(c_0_774_0,axiom,
class_Orderings_Opreorder(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_774,def_lhs_atom75]) ).
cnf(c_0_775_0,axiom,
class_Nat_Osemiring__char__0(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_775,def_lhs_atom74]) ).
cnf(c_0_776_0,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_776,def_lhs_atom73]) ).
cnf(c_0_777_0,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_777,def_lhs_atom72]) ).
cnf(c_0_778_0,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_778,def_lhs_atom71]) ).
cnf(c_0_779_0,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_779,def_lhs_atom70]) ).
cnf(c_0_780_0,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_780,def_lhs_atom69]) ).
cnf(c_0_781_0,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_781,def_lhs_atom68]) ).
cnf(c_0_782_0,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_782,def_lhs_atom67]) ).
cnf(c_0_783_0,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_783,def_lhs_atom66]) ).
cnf(c_0_784_0,axiom,
class_OrderedGroup_Osemigroup__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_784,def_lhs_atom65]) ).
cnf(c_0_785_0,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_785,def_lhs_atom64]) ).
cnf(c_0_786_0,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_786,def_lhs_atom63]) ).
cnf(c_0_787_0,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_787,def_lhs_atom62]) ).
cnf(c_0_788_0,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_788,def_lhs_atom61]) ).
cnf(c_0_789_0,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_789,def_lhs_atom60]) ).
cnf(c_0_790_0,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_790,def_lhs_atom59]) ).
cnf(c_0_791_0,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_791,def_lhs_atom58]) ).
cnf(c_0_792_0,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_792,def_lhs_atom57]) ).
cnf(c_0_793_0,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_793,def_lhs_atom56]) ).
cnf(c_0_794_0,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_794,def_lhs_atom55]) ).
cnf(c_0_795_0,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_795,def_lhs_atom54]) ).
cnf(c_0_796_0,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_796,def_lhs_atom53]) ).
cnf(c_0_797_0,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_797,def_lhs_atom52]) ).
cnf(c_0_798_0,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_798,def_lhs_atom51]) ).
cnf(c_0_799_0,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_799,def_lhs_atom50]) ).
cnf(c_0_800_0,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_800,def_lhs_atom49]) ).
cnf(c_0_801_0,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_801,def_lhs_atom48]) ).
cnf(c_0_802_0,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_802,def_lhs_atom47]) ).
cnf(c_0_803_0,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_803,def_lhs_atom46]) ).
cnf(c_0_804_0,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_804,def_lhs_atom45]) ).
cnf(c_0_805_0,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_805,def_lhs_atom44]) ).
cnf(c_0_806_0,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_806,def_lhs_atom43]) ).
cnf(c_0_807_0,axiom,
class_Ring__and__Field_Ocomm__ring(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_807,def_lhs_atom42]) ).
cnf(c_0_808_0,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_808,def_lhs_atom41]) ).
cnf(c_0_809_0,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
inference(unfold_definition,[status(thm)],[c_0_809,def_lhs_atom40]) ).
cnf(c_0_810_0,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_810,def_lhs_atom39]) ).
cnf(c_0_811_0,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_811,def_lhs_atom38]) ).
cnf(c_0_812_0,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_812,def_lhs_atom37]) ).
cnf(c_0_813_0,axiom,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(v_q____,tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_813,def_lhs_atom36]) ).
cnf(c_0_814_0,axiom,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(v_pa____,tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_814,def_lhs_atom35]) ).
cnf(c_0_815_0,axiom,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_q____,tc_Complex_Ocomplex) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_pa____,tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_815,def_lhs_atom33]) ).
cnf(c_0_816_0,axiom,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_816,def_lhs_atom32]) ).
cnf(c_0_817_0,axiom,
v_n____ = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_pa____,tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_817,def_lhs_atom30]) ).
cnf(c_0_818_0,axiom,
hAPP(c_Polynomial_Opoly(v_pa____,tc_Complex_Ocomplex),v_c____) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(unfold_definition,[status(thm)],[c_0_818,def_lhs_atom27]) ).
cnf(c_0_819_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_819,def_lhs_atom21]) ).
cnf(c_0_820_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(unfold_definition,[status(thm)],[c_0_820,def_lhs_atom18]) ).
cnf(c_0_821_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(unfold_definition,[status(thm)],[c_0_821,def_lhs_atom17]) ).
cnf(c_0_822_0,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)),
inference(unfold_definition,[status(thm)],[c_0_822,def_lhs_atom12]) ).
cnf(c_0_823_0,axiom,
c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(unfold_definition,[status(thm)],[c_0_823,def_lhs_atom11]) ).
cnf(c_0_824_0,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
inference(unfold_definition,[status(thm)],[c_0_824,def_lhs_atom2]) ).
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0_001,axiom,
! [X13,X6,X10,X12,X20,X3] :
( ~ class_HOL_Ozero(X20)
| c_Polynomial_Opoly__rec(X13,X10,c_Polynomial_OpCons(X12,X6,X20),X3,X20) = hAPP(hAPP(hAPP(X10,X12),X6),c_HOL_OIf(c_fequal(X6,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X20)),tc_Polynomial_Opoly(X20)),X13,c_Polynomial_Opoly__rec(X13,X10,X6,X3,X20),X3)) ),
file('<stdin>',cls_poly__rec_Osimps_0) ).
fof(c_0_1_002,axiom,
! [X13,X6,X10,X12,X20,X3] :
( ~ class_HOL_Ozero(X20)
| hAPP(hAPP(hAPP(X10,c_HOL_Ozero__class_Ozero(X20)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X20))),X13) != X13
| c_Polynomial_Opoly__rec(X13,X10,c_Polynomial_OpCons(X12,X6,X20),X3,X20) = hAPP(hAPP(hAPP(X10,X12),X6),c_Polynomial_Opoly__rec(X13,X10,X6,X3,X20)) ),
file('<stdin>',cls_poly__rec__pCons_0) ).
fof(c_0_2_003,axiom,
! [X15,X9,X7,X3] :
( ~ class_OrderedGroup_Osemigroup__add(X3)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),X9),X15,X3,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X9,X15,X3,X3)) ),
file('<stdin>',cls_foldl__assoc_0) ).
fof(c_0_3_004,axiom,
! [X15,X7,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3),X15,X3,X3)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X7,X15,X3,X3) ),
file('<stdin>',cls_foldl__absorb0_0) ).
fof(c_0_4_005,axiom,
! [X14,X11,X12,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X3),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11)),X14) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X3),X3),X12),X14)),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X3),X3),X11),X14)) ),
file('<stdin>',cls_comm__monoid__add_Opower__mult__distrib_0) ).
fof(c_0_5_006,axiom,
! [X14,X22,X12,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X3),X3),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X14)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X3),X3),X12),X22)),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X3),X3),X12),X14)) ),
file('<stdin>',cls_comm__monoid__add_Opower__add_0) ).
fof(c_0_6_007,axiom,
! [X13,X6] :
( ~ class_Ring__and__Field_Oidom(t_a)
| hAPP(c_Polynomial_Opoly(X6,t_a),X13) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(t_a),hAPP(c_Polynomial_Opoly(X6,t_a),c_HOL_Ozero__class_Ozero(t_a))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X13),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1(X6))),hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__2(X6),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__3(X6),t_a),t_a),X13)))
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X6,t_a),t_a,t_a) ),
file('<stdin>',cls_poly__decompose_3) ).
fof(c_0_7_008,axiom,
! [X14,X12,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X3),X3),X12),X14)),X12) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X3),X3),X12),X14)) ),
file('<stdin>',cls_comm__monoid__add_Opower__commutes_0) ).
fof(c_0_8_009,axiom,
! [X23,X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Osemiring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X23)),X16)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11)),X23)),X16) ),
file('<stdin>',cls_combine__common__factor_0) ).
fof(c_0_9_010,axiom,
! [X14,X12,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X3),X3),X12),c_Suc(X14)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X3),X3),X12),X14)),X12) ),
file('<stdin>',cls_comm__monoid__add_Opower__Suc2_0) ).
fof(c_0_10_011,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3))),X3) ),
file('<stdin>',cls_sum__squares__gt__zero__iff_0) ).
fof(c_0_11_012,axiom,
! [X13,X10,X20,X3] :
( ~ class_HOL_Ozero(X20)
| hAPP(hAPP(hAPP(X10,c_HOL_Ozero__class_Ozero(X20)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X20))),X13) != X13
| c_Polynomial_Opoly__rec(X13,X10,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X20)),X3,X20) = X13 ),
file('<stdin>',cls_poly__rec__0_0) ).
fof(c_0_12_013,axiom,
! [X9,X7,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| X9 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X7)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X9)),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_sum__squares__le__zero__iff_1) ).
fof(c_0_13_014,axiom,
! [X9,X7,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| X7 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X7)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X9)),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_sum__squares__le__zero__iff_0) ).
fof(c_0_14_015,axiom,
! [X9,X7,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X7)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X9)),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_not__sum__squares__lt__zero_0) ).
fof(c_0_15_016,axiom,
! [X6,X21,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(X12,X6,X3),X21,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X21,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X6,X21,X3),X3)),c_Polynomial_OpCons(X12,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X6,X21,X3),X3)) ),
file('<stdin>',cls_offset__poly__pCons_0) ).
fof(c_0_16_017,axiom,
! [X18,X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X18)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X18)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X16))
| X16 = X18
| X12 = X11 ),
file('<stdin>',cls_class__ringb_Onoteq__reduce_0) ).
fof(c_0_17_018,axiom,
! [X13,X9,X7,X24,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X24),X9)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X13)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X24),X13)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X9))
| X9 = X13
| X24 = X7 ),
file('<stdin>',cls_class__ringb_Oadd__mul__solve_0) ).
fof(c_0_18_019,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3))),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_sum__squares__le__zero__iff_2) ).
fof(c_0_19_020,axiom,
! [X14,X12,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X3),X3),X12),c_Suc(X14)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X3),X3),X12),X14)) ),
file('<stdin>',cls_comm__monoid__add_Opower__Suc_0) ).
fof(c_0_20_021,axiom,
! [X30,X31,X32,X33,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X33),X32)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X31),X30)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X31),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X33),X32)),X30)) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I15_J_0) ).
fof(c_0_21_022,axiom,
! [X9,X7,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X7)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X9)),X3)
| X9 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_sum__squares__gt__zero__iff_2) ).
fof(c_0_22_023,axiom,
! [X9,X7,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X7)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X9)),X3)
| X7 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_sum__squares__gt__zero__iff_1) ).
fof(c_0_23_024,axiom,
! [X9,X7,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X7)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X9)),X3) ),
file('<stdin>',cls_sum__squares__ge__zero_0) ).
fof(c_0_24_025,axiom,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oring__1(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ouminus__class_Ouminus(X12,X3)),X14) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X3),X3)),X14)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14)) ),
file('<stdin>',cls_power__minus_0) ).
fof(c_0_25_026,axiom,
! [X13,X9,X7,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X9)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X13)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X13)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X9)) ),
file('<stdin>',cls_class__ringb_Oadd__mul__solve_1) ).
fof(c_0_26_027,axiom,
! [X7,X18,X16,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X16)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X18)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X18)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X16)) ),
file('<stdin>',cls_class__ringb_Onoteq__reduce_1) ).
fof(c_0_27_028,axiom,
! [X30,X31,X32,X33,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X33),X32)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X31),X30)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X33),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X32),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X31),X30))) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I14_J_0) ).
fof(c_0_28_029,axiom,
! [X30,X31,X32,X33,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X33),X32)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X31),X30)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X33),X31)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X32),X30)) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I13_J_0) ).
fof(c_0_29_030,axiom,
! [X18,X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X18)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X18)) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I20_J_0) ).
fof(c_0_30_031,axiom,
! [X8,X6,X11,X12,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X3)),c_Polynomial_OpCons(X12,X6,X3)),c_Polynomial_OpCons(X11,X8,X3)) = c_Polynomial_OpCons(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X3)),X6),X8),X3) ),
file('<stdin>',cls_add__pCons_0) ).
fof(c_0_31_032,axiom,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14),X3)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
file('<stdin>',cls_power__Suc__less_0) ).
fof(c_0_32_033,axiom,
! [X6,X16,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X16,X6,X3)),c_Polynomial_OpCons(X12,X6,X3)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| X6 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_offset__poly__eq__0__lemma_0) ).
fof(c_0_33_034,axiom,
! [X8,X6,X14,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(c_Polynomial_Ocoeff(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X3)),X6),X8),X3),X14) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(c_Polynomial_Ocoeff(X6,X3),X14)),hAPP(c_Polynomial_Ocoeff(X8,X3),X14)) ),
file('<stdin>',cls_coeff__add_0) ).
fof(c_0_34_035,axiom,
! [X7,X8,X6,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| hAPP(c_Polynomial_Opoly(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X3)),X6),X8),X3),X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(c_Polynomial_Opoly(X6,X3),X7)),hAPP(c_Polynomial_Opoly(X8,X3),X7)) ),
file('<stdin>',cls_poly__add_0) ).
fof(c_0_35_036,axiom,
! [X18,X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Opordered__semiring(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X18),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_lessequals(X16,X18,X3)
| ~ c_lessequals(X12,X11,X3) ),
file('<stdin>',cls_mult__mono_0) ).
fof(c_0_36_037,axiom,
! [X18,X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Opordered__semiring(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X18),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3)
| ~ c_lessequals(X16,X18,X3)
| ~ c_lessequals(X12,X11,X3) ),
file('<stdin>',cls_mult__mono_H_0) ).
fof(c_0_37_038,axiom,
! [X18,X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X18),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3)
| ~ c_HOL_Oord__class_Oless(X16,X18,X3)
| ~ c_HOL_Oord__class_Oless(X12,X11,X3) ),
file('<stdin>',cls_mult__strict__mono_H_0) ).
fof(c_0_38_039,axiom,
! [X18,X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X18),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_HOL_Oord__class_Oless(X16,X18,X3)
| ~ c_HOL_Oord__class_Oless(X12,X11,X3) ),
file('<stdin>',cls_mult__strict__mono_0) ).
fof(c_0_39_040,axiom,
! [X18,X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X18),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X12,X3)
| ~ c_HOL_Oord__class_Oless(X16,X18,X3)
| ~ c_lessequals(X12,X11,X3) ),
file('<stdin>',cls_mult__le__less__imp__less_0) ).
fof(c_0_40_041,axiom,
! [X18,X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X18),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3)
| ~ c_lessequals(X16,X18,X3)
| ~ c_HOL_Oord__class_Oless(X12,X11,X3) ),
file('<stdin>',cls_mult__less__le__imp__less_0) ).
fof(c_0_41_042,axiom,
! [X6] :
( ~ class_Ring__and__Field_Oidom(t_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__3(X6),t_a)),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1(X6))),c_HOL_Oone__class_Oone(tc_nat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X6,t_a)
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X6,t_a),t_a,t_a) ),
file('<stdin>',cls_poly__decompose_2) ).
fof(c_0_42_043,axiom,
! [X14,X11,X12,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11)),X14) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X11),X14)) ),
file('<stdin>',cls_power__mult__distrib_0) ).
fof(c_0_43_044,axiom,
! [X9,X7,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X9)),X8) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X7),X8)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X8)) ),
file('<stdin>',cls_class__semiring_Opwr__mul_0) ).
fof(c_0_44_045,axiom,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11)),X16) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X16)) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I8_J_0) ).
fof(c_0_45_046,axiom,
! [X36,X9,X7,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),X9)),X36) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X36)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X36)) ),
file('<stdin>',cls_mult__left_Oadd_0) ).
fof(c_0_46_047,axiom,
! [X11,X35,X12,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X35)),X11) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X35),X11)) ),
file('<stdin>',cls_mult_Oadd__left_0) ).
fof(c_0_47_048,axiom,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11)),X16) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X16)) ),
file('<stdin>',cls_comm__semiring__class_Odistrib_0) ).
fof(c_0_48_049,axiom,
! [X22,X11,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X22)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X22)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11)),X22) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I1_J_0) ).
fof(c_0_49_050,axiom,
! [X8,X6,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(X12,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X3)),X6),X8),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X12,X6,X3)),c_Polynomial_Osmult(X12,X8,X3)) ),
file('<stdin>',cls_smult__add__right_0) ).
fof(c_0_50_051,axiom,
! [X14,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(X12,X11,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),c_Suc(X14)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X11),c_Suc(X14)),X3) ),
file('<stdin>',cls_power__le__imp__le__base_0) ).
fof(c_0_51_052,axiom,
! [X9,X7,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X7)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X9)) != c_HOL_Ozero__class_Ozero(X3)
| X7 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_sum__squares__eq__zero__iff_0) ).
fof(c_0_52_053,axiom,
! [X9,X7,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X7)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X9)) != c_HOL_Ozero__class_Ozero(X3)
| X9 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_sum__squares__eq__zero__iff_1) ).
fof(c_0_53_054,axiom,
! [X7,X6,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X12,X6,X3),X3),X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),hAPP(c_Polynomial_Opoly(X6,X3),X7))) ),
file('<stdin>',cls_poly__pCons_0) ).
fof(c_0_54_055,axiom,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14)),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X12,X3) ),
file('<stdin>',cls_power__less__power__Suc_0) ).
fof(c_0_55_056,axiom,
! [X14,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X12,X11,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X11),X14),X3) ),
file('<stdin>',cls_power__less__imp__less__base_0) ).
fof(c_0_56_057,axiom,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(X12,X11,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X16),X3) ),
file('<stdin>',cls_mult__less__imp__less__right_0) ).
fof(c_0_57_058,axiom,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(X12,X11,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3) ),
file('<stdin>',cls_mult__less__imp__less__left_0) ).
fof(c_0_58_059,axiom,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semiring(X3)
| c_HOL_Oord__class_Oless(X12,X11,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X16),X3) ),
file('<stdin>',cls_mult__right__less__imp__less_0) ).
fof(c_0_59_060,axiom,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semiring(X3)
| c_HOL_Oord__class_Oless(X12,X11,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3) ),
file('<stdin>',cls_mult__left__less__imp__less_0) ).
fof(c_0_60_061,axiom,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_lessequals(X12,X11,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X16),X3) ),
file('<stdin>',cls_mult__right__le__imp__le_0) ).
fof(c_0_61_062,axiom,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_lessequals(X12,X11,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3) ),
file('<stdin>',cls_mult__left__le__imp__le_0) ).
fof(c_0_62_063,axiom,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X12,X11,X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X16,X3) ),
file('<stdin>',cls_mult__le__cancel__left__pos_0) ).
fof(c_0_63_064,axiom,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X11,X12,X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3)
| ~ c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__le__cancel__left__neg_0) ).
fof(c_0_64_065,axiom,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X12,X11,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X16,X3) ),
file('<stdin>',cls_mult__less__cancel__left__pos_0) ).
fof(c_0_65_066,axiom,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X11,X12,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3)
| ~ c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__less__cancel__left__neg_0) ).
fof(c_0_66_067,axiom,
! [X14,X11,X12,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X3)),c_Polynomial_Omonom(X12,X14,X3)),c_Polynomial_Omonom(X11,X14,X3)) = c_Polynomial_Omonom(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11),X14,X3) ),
file('<stdin>',cls_add__monom_0) ).
fof(c_0_67_068,axiom,
! [X6,X11,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11),X6,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X12,X6,X3)),c_Polynomial_Osmult(X11,X6,X3)) ),
file('<stdin>',cls_smult__add__left_0) ).
fof(c_0_68_069,axiom,
! [X22,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X22)),X22) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),c_HOL_Oone__class_Oone(X3))),X22) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I2_J_0) ).
fof(c_0_69_070,axiom,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3) ),
file('<stdin>',cls_mult__less__cancel__left__disj_0) ).
fof(c_0_70_071,axiom,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X16),X3) ),
file('<stdin>',cls_mult__less__cancel__right__disj_0) ).
fof(c_0_71_072,axiom,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X11,X12,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3) ),
file('<stdin>',cls_mult__less__cancel__left__disj_1) ).
fof(c_0_72_073,axiom,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X12,X11,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3) ),
file('<stdin>',cls_mult__less__cancel__left__disj_2) ).
fof(c_0_73_074,axiom,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X11,X12,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X16),X3) ),
file('<stdin>',cls_mult__less__cancel__right__disj_1) ).
fof(c_0_74_075,axiom,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X12,X11,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X16),X3) ),
file('<stdin>',cls_mult__less__cancel__right__disj_2) ).
fof(c_0_75_076,axiom,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X11,X12,X3)
| c_HOL_Oord__class_Oless(X12,X11,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3) ),
file('<stdin>',cls_mult__less__cancel__left__disj_3) ).
fof(c_0_76_077,axiom,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X11,X12,X3)
| c_HOL_Oord__class_Oless(X12,X11,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X16),X3) ),
file('<stdin>',cls_mult__less__cancel__right__disj_3) ).
fof(c_0_77_078,axiom,
! [X31,X32,X33,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X33),X32)),X31) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X33),X31)),X32) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I16_J_0) ).
fof(c_0_78_079,axiom,
! [X9,X34,X7,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X34),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),X9)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X34),X7)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X34),X9)) ),
file('<stdin>',cls_mult__right_Oadd_0) ).
fof(c_0_79_080,axiom,
! [X37,X11,X12,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X37)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X37)) ),
file('<stdin>',cls_mult_Oadd__right_0) ).
fof(c_0_80_081,axiom,
! [X13,X9,X7,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X13)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X9)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X13)) ),
file('<stdin>',cls_class__semiring_Omul__d_0) ).
fof(c_0_81_082,axiom,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11)),X16) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16)),X11) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I23_J_0) ).
fof(c_0_82_083,axiom,
! [X7,X8,X6,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X7),X6)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X7),X8)) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X8)) ),
file('<stdin>',cls_class__semiring_Omul__pwr_0) ).
fof(c_0_83_084,axiom,
! [X14,X22,X12,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X14)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X22)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14)) ),
file('<stdin>',cls_power__add_0) ).
fof(c_0_84_085,axiom,
! [X7,X19,X18,X16,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X16)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X18))
| X16 = X18
| X19 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
fof(c_0_85_086,axiom,
! [X18,X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X12,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X18),X3)
| ~ c_lessequals(X16,X18,X3)
| ~ c_lessequals(X12,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X16),X3) ),
file('<stdin>',cls_le__add__right__mono_0) ).
fof(c_0_86_087,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3))) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_sum__squares__eq__zero__iff_2) ).
fof(c_0_87_088,axiom,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14)),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X12,X3) ),
file('<stdin>',cls_power__gt1__lemma_0) ).
fof(c_0_88_089,axiom,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_lessequals(X12,X11,X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X16),X3) ),
file('<stdin>',cls_add__le__cancel__right_0) ).
fof(c_0_89_090,axiom,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_lessequals(X12,X11,X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X11),X3) ),
file('<stdin>',cls_add__le__cancel__left_0) ).
fof(c_0_90_091,axiom,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(X12,X11,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X11),X3) ),
file('<stdin>',cls_add__less__cancel__left_0) ).
fof(c_0_91_092,axiom,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(X12,X11,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X16),X3) ),
file('<stdin>',cls_add__less__cancel__right_0) ).
fof(c_0_92_093,axiom,
! [X9,X7,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X7),X7,X3)
| ~ c_lessequals(X9,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X7,X3) ),
file('<stdin>',cls_mult__left__le__one__le_0) ).
fof(c_0_93_094,axiom,
! [X9,X7,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X9),X7,X3)
| ~ c_lessequals(X9,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X7,X3) ),
file('<stdin>',cls_mult__right__le__one__le_0) ).
fof(c_0_94_095,axiom,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X16),X3)
| ~ c_lessequals(X16,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X11,X12,X3) ),
file('<stdin>',cls_mult__right__mono__neg_0) ).
fof(c_0_95_096,axiom,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3)
| ~ c_lessequals(X16,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X11,X12,X3) ),
file('<stdin>',cls_mult__left__mono__neg_0) ).
fof(c_0_96_097,axiom,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Omult__mono(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X16),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_lessequals(X12,X11,X3) ),
file('<stdin>',cls_mult__right__mono_0) ).
fof(c_0_97_098,axiom,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Omult__mono(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_lessequals(X12,X11,X3) ),
file('<stdin>',cls_mult__left__mono_0) ).
fof(c_0_98_099,axiom,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Omult__mono1(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_lessequals(X12,X11,X3) ),
file('<stdin>',cls_mult__mono1_0) ).
fof(c_0_99_100,axiom,
! [X14,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X11),X14),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3)
| ~ c_lessequals(X12,X11,X3) ),
file('<stdin>',cls_power__mono_0) ).
fof(c_0_100_101,axiom,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3)
| ~ c_lessequals(X12,X11,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X16,X3) ),
file('<stdin>',cls_mult__le__cancel__left__pos_1) ).
fof(c_0_101_102,axiom,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3)
| ~ c_lessequals(X11,X12,X3)
| ~ c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__le__cancel__left__neg_1) ).
fof(c_0_102_103,axiom,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_HOL_Oord__class_Oless(X12,X11,X3) ),
file('<stdin>',cls_mult__strict__left__mono__comm_0) ).
fof(c_0_103_104,axiom,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X16),X3)
| ~ c_HOL_Oord__class_Oless(X11,X12,X3)
| ~ c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__less__cancel__right__disj_5) ).
fof(c_0_104_105,axiom,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X16),X3)
| ~ c_HOL_Oord__class_Oless(X12,X11,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X16,X3) ),
file('<stdin>',cls_mult__less__cancel__right__disj_4) ).
fof(c_0_105_106,axiom,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X16),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_HOL_Oord__class_Oless(X12,X11,X3) ),
file('<stdin>',cls_mult__strict__right__mono_0) ).
fof(c_0_106_107,axiom,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X16),X3)
| ~ c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X11,X12,X3) ),
file('<stdin>',cls_mult__strict__right__mono__neg_0) ).
fof(c_0_107_108,axiom,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3)
| ~ c_HOL_Oord__class_Oless(X11,X12,X3)
| ~ c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__less__cancel__left__disj_5) ).
fof(c_0_108_109,axiom,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3)
| ~ c_HOL_Oord__class_Oless(X12,X11,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X16,X3) ),
file('<stdin>',cls_mult__less__cancel__left__disj_4) ).
fof(c_0_109_110,axiom,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_HOL_Oord__class_Oless(X12,X11,X3) ),
file('<stdin>',cls_mult__strict__left__mono_0) ).
fof(c_0_110_111,axiom,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3)
| ~ c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X11,X12,X3) ),
file('<stdin>',cls_mult__strict__left__mono__neg_0) ).
fof(c_0_111_112,axiom,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3)
| ~ c_HOL_Oord__class_Oless(X12,X11,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X16,X3) ),
file('<stdin>',cls_mult__less__cancel__left__pos_1) ).
fof(c_0_112_113,axiom,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3)
| ~ c_HOL_Oord__class_Oless(X11,X12,X3)
| ~ c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__less__cancel__left__neg_1) ).
fof(c_0_113_114,axiom,
( ~ class_HOL_Ozero(t_a)
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_p,t_a) = c_HOL_OIf(c_fequal(v_p,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),tc_Polynomial_Opoly(t_a)),c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_Polynomial_Odegree(v_p,t_a)),tc_nat) ),
file('<stdin>',cls_psize__def__raw_0) ).
fof(c_0_114_115,axiom,
! [X22,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X22),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X22)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),c_HOL_Oone__class_Oone(X3))),X22) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I3_J_0) ).
fof(c_0_115_116,axiom,
! [X18,X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X18),X3)
| ~ c_lessequals(X16,X18,X3)
| ~ c_lessequals(X12,X11,X3) ),
file('<stdin>',cls_add__mono_0) ).
fof(c_0_116_117,axiom,
! [X18,X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X18),X3)
| ~ c_HOL_Oord__class_Oless(X16,X18,X3)
| ~ c_HOL_Oord__class_Oless(X12,X11,X3) ),
file('<stdin>',cls_add__strict__mono_0) ).
fof(c_0_117_118,axiom,
! [X18,X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X18),X3)
| ~ c_lessequals(X16,X18,X3)
| ~ c_HOL_Oord__class_Oless(X12,X11,X3) ),
file('<stdin>',cls_add__less__le__mono_0) ).
fof(c_0_118_119,axiom,
! [X18,X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X18),X3)
| ~ c_HOL_Oord__class_Oless(X16,X18,X3)
| ~ c_lessequals(X12,X11,X3) ),
file('<stdin>',cls_add__le__less__mono_0) ).
fof(c_0_119_120,axiom,
! [X6,X11,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(X12,c_Polynomial_OpCons(X11,X6,X3),X3) = c_Polynomial_OpCons(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),c_Polynomial_Osmult(X12,X6,X3),X3) ),
file('<stdin>',cls_smult__pCons_0) ).
fof(c_0_120_121,axiom,
! [X19,X8,X6,X16,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X3)),X6),c_Polynomial_Osmult(X16,X8,X3)) != c_Polynomial_OpCons(X19,X8,X3)
| X19 = hAPP(c_Polynomial_Opoly(X6,X3),X16) ),
file('<stdin>',cls_synthetic__div__unique_0) ).
fof(c_0_121_122,axiom,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X12,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X12),X3) ),
file('<stdin>',cls_zero__less__mult__pos2_0) ).
fof(c_0_122_123,axiom,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X12,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),X3) ),
file('<stdin>',cls_zero__less__mult__pos_0) ).
fof(c_0_123_124,axiom,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11)),X16) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X16)) ),
file('<stdin>',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
fof(c_0_124_125,axiom,
! [X31,X32,X33,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X33),X32)),X31) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X33),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X32),X31)) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I17_J_0) ).
fof(c_0_125_126,axiom,
! [X30,X31,X33,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X33),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X31),X30)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X33),X31)),X30) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I18_J_0) ).
fof(c_0_126_127,axiom,
! [X13,X9,X7,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X13)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X9)),X13) ),
file('<stdin>',cls_class__semiring_Omul__a_0) ).
fof(c_0_127_128,axiom,
! [X14,X12,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14)),X12) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14)) ),
file('<stdin>',cls_power__commutes_0) ).
fof(c_0_128_129,axiom,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11)),X16) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X16)) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I21_J_0) ).
fof(c_0_129_130,axiom,
! [X18,X16,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X18)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16)),X18) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I25_J_0) ).
fof(c_0_130_131,axiom,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Oab__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11)),X16) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X16)) ),
file('<stdin>',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
fof(c_0_131_132,axiom,
! [X13,X9,X7,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X13)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),X9)),X13) ),
file('<stdin>',cls_class__semiring_Oadd__a_0) ).
fof(c_0_132_133,axiom,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11)),X16) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X16)) ),
file('<stdin>',cls_comm__monoid__add_Omult__assoc_0) ).
fof(c_0_133_134,axiom,
! [X7,X14,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(c_Polynomial_Opoly(c_Polynomial_Omonom(X12,X14,X3),X3),X7) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X7),X14)) ),
file('<stdin>',cls_poly__monom_0) ).
fof(c_0_134_135,axiom,
! [X7,X6,X21,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| hAPP(c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X6,X21,X3),X3),X7) = hAPP(c_Polynomial_Opoly(X6,X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X7)) ),
file('<stdin>',cls_poly__offset__poly_0) ).
fof(c_0_135_136,axiom,
! [X6,X14,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| hAPP(c_Polynomial_Ocoeff(c_Polynomial_Osmult(X12,X6,X3),X3),X14) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),hAPP(c_Polynomial_Ocoeff(X6,X3),X14)) ),
file('<stdin>',cls_coeff__smult_0) ).
fof(c_0_136_137,axiom,
! [X7,X6,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| hAPP(c_Polynomial_Opoly(c_Polynomial_Osmult(X12,X6,X3),X3),X7) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),hAPP(c_Polynomial_Opoly(X6,X3),X7)) ),
file('<stdin>',cls_poly__smult_0) ).
fof(c_0_137_138,axiom,
! [X22,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X22),X22) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oone__class_Oone(X3)),c_HOL_Oone__class_Oone(X3))),X22) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I4_J_0) ).
fof(c_0_138_139,axiom,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X12,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),X3) ),
file('<stdin>',cls_zero__le__mult__iff_0) ).
fof(c_0_139_140,axiom,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),X3) ),
file('<stdin>',cls_zero__le__mult__iff_1) ).
fof(c_0_140_141,axiom,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X12,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),X3) ),
file('<stdin>',cls_zero__le__mult__iff_2) ).
fof(c_0_141_142,axiom,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),X3) ),
file('<stdin>',cls_zero__le__mult__iff_3) ).
fof(c_0_142_143,axiom,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| c_lessequals(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__le__0__iff_3) ).
fof(c_0_143_144,axiom,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X12,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__le__0__iff_2) ).
fof(c_0_144_145,axiom,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__le__0__iff_1) ).
fof(c_0_145_146,axiom,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X12,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__le__0__iff_0) ).
fof(c_0_146_147,axiom,
! [X13,X9,X7,X17,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X13)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X17)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),X13) = X17 ),
file('<stdin>',cls_add__cancel__21_0) ).
fof(c_0_147_148,axiom,
! [X14,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),c_Suc(X14)) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X11),c_Suc(X14))
| X12 = X11
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
file('<stdin>',cls_power__inject__base_0) ).
fof(c_0_148_149,axiom,
! [X7,X8,X6,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| hAPP(c_Polynomial_Opoly(c_Polynomial_Opcompose(X6,X8,X3),X3),X7) = hAPP(c_Polynomial_Opoly(X6,X3),hAPP(c_Polynomial_Opoly(X8,X3),X7)) ),
file('<stdin>',cls_poly__pcompose_0) ).
fof(c_0_149_150,axiom,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),c_Suc(X14)),c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
file('<stdin>',cls_power__Suc__less__one_0) ).
fof(c_0_150_151,axiom,
! [X14,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| X14 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3)),X14),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_zero__less__power__eq_2) ).
fof(c_0_151_152,axiom,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),X3)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X12,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__nonpos__nonpos_0) ).
fof(c_0_152_153,axiom,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),X3)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X12,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_split__mult__pos__le_1) ).
fof(c_0_153_154,axiom,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
file('<stdin>',cls_split__mult__pos__le_0) ).
fof(c_0_154_155,axiom,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
file('<stdin>',cls_zero__le__mult__iff_4) ).
fof(c_0_155_156,axiom,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),X3)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X12,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_zero__le__mult__iff_5) ).
fof(c_0_156_157,axiom,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
file('<stdin>',cls_mult__nonneg__nonneg_0) ).
fof(c_0_157_158,axiom,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
file('<stdin>',cls_mult__le__0__iff_4) ).
fof(c_0_158_159,axiom,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_lessequals(X12,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__le__0__iff_5) ).
fof(c_0_159_160,axiom,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
file('<stdin>',cls_split__mult__neg__le_0) ).
fof(c_0_160_161,axiom,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_lessequals(X12,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_split__mult__neg__le_1) ).
fof(c_0_161_162,axiom,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
file('<stdin>',cls_mult__nonneg__nonpos_0) ).
fof(c_0_162_163,axiom,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_lessequals(X12,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__nonpos__nonneg_0) ).
fof(c_0_163_164,axiom,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X12),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
file('<stdin>',cls_mult__nonneg__nonpos2_0) ).
fof(c_0_164_165,axiom,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
file('<stdin>',cls_add__nonneg__pos_0) ).
fof(c_0_165_166,axiom,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
file('<stdin>',cls_add__pos__nonneg_0) ).
fof(c_0_166_167,axiom,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X12),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
file('<stdin>',cls_mult__pos__neg2_0) ).
fof(c_0_167_168,axiom,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
file('<stdin>',cls_mult__pos__neg_0) ).
fof(c_0_168_169,axiom,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__neg__pos_0) ).
fof(c_0_169_170,axiom,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X12,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_add__nonpos__neg_0) ).
fof(c_0_170_171,axiom,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_add__neg__nonpos_0) ).
fof(c_0_171_172,axiom,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
file('<stdin>',cls_mult__pos__pos_0) ).
fof(c_0_172_173,axiom,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),X3)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__neg__neg_0) ).
fof(c_0_173_174,axiom,
! [X14,X22,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X22),X14),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X14,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X22,X3) ),
file('<stdin>',cls_less__1__mult_0) ).
fof(c_0_174_175,axiom,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_add__neg__neg_0) ).
fof(c_0_175_176,axiom,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
file('<stdin>',cls_add__nonneg__nonneg_0) ).
fof(c_0_176_177,axiom,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
file('<stdin>',cls_add__pos__pos_0) ).
fof(c_0_177_178,axiom,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X12,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_add__nonpos__nonpos_0) ).
fof(c_0_178_179,axiom,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oord__class_Oless(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16),X3)
| ~ c_lessequals(X11,X16,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
file('<stdin>',cls_add__strict__increasing_0) ).
fof(c_0_179_180,axiom,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oord__class_Oless(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16),X3)
| ~ c_HOL_Oord__class_Oless(X11,X16,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
file('<stdin>',cls_add__strict__increasing2_0) ).
fof(c_0_180_181,axiom,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_lessequals(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16),X3)
| ~ c_lessequals(X11,X16,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
file('<stdin>',cls_add__increasing_0) ).
fof(c_0_181_182,axiom,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_lessequals(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16),X3)
| ~ c_lessequals(X11,X12,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X16,X3) ),
file('<stdin>',cls_add__increasing2_0) ).
fof(c_0_182_183,axiom,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X16),X3)
| ~ c_lessequals(X12,X11,X3) ),
file('<stdin>',cls_add__le__cancel__right_1) ).
fof(c_0_183_184,axiom,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X11),X3)
| ~ c_lessequals(X12,X11,X3) ),
file('<stdin>',cls_add__le__cancel__left_1) ).
fof(c_0_184_185,axiom,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X16),X3)
| ~ c_lessequals(X12,X11,X3) ),
file('<stdin>',cls_add__right__mono_0) ).
fof(c_0_185_186,axiom,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X11),X3)
| ~ c_lessequals(X12,X11,X3) ),
file('<stdin>',cls_add__left__mono_0) ).
fof(c_0_186_187,axiom,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X11),X3)
| ~ c_HOL_Oord__class_Oless(X12,X11,X3) ),
file('<stdin>',cls_add__less__cancel__left_1) ).
fof(c_0_187_188,axiom,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X11),X3)
| ~ c_HOL_Oord__class_Oless(X12,X11,X3) ),
file('<stdin>',cls_add__strict__left__mono_0) ).
fof(c_0_188_189,axiom,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X16),X3)
| ~ c_HOL_Oord__class_Oless(X12,X11,X3) ),
file('<stdin>',cls_add__less__cancel__right_1) ).
fof(c_0_189_190,axiom,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X16),X3)
| ~ c_HOL_Oord__class_Oless(X12,X11,X3) ),
file('<stdin>',cls_add__strict__right__mono_0) ).
fof(c_0_190_191,axiom,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16),X3)
| ~ c_HOL_Oord__class_Oless(X11,X16,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
file('<stdin>',cls_pos__add__strict_0) ).
fof(c_0_191_192,axiom,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(X12,c_HOL_Ouminus__class_Ouminus(X11,X3),X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_le__eq__neg_1) ).
fof(c_0_192_193,axiom,
! [X7,X14,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| X7 = c_HOL_Ozero__class_Ozero(X3)
| c_lessequals(X7,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X7),X14),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_power__le__zero__eq_3) ).
fof(c_0_193_194,axiom,
! [X14,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X3),X3),c_HOL_Ozero__class_Ozero(X3)),X14) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_comm__monoid__add_Opower__one_0) ).
fof(c_0_194_195,axiom,
! [X14,X11,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(X12,c_Polynomial_Omonom(X11,X14,X3),X3) = c_Polynomial_Omonom(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),X14,X3) ),
file('<stdin>',cls_smult__monom_0) ).
fof(c_0_195_196,axiom,
! [X6,X11,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(X12,c_Polynomial_Osmult(X11,X6,X3),X3) = c_Polynomial_Osmult(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),X6,X3) ),
file('<stdin>',cls_smult__smult_0) ).
fof(c_0_196_197,axiom,
! [X7,X14,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X7),X14),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_power__less__zero__eq_1) ).
fof(c_0_197_198,axiom,
! [X12,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X12),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_even__less__0__iff_0) ).
fof(c_0_198_199,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X12),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_double__add__less__zero__iff__single__less__zero_0) ).
fof(c_0_199_200,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X12,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X12),X3) ),
file('<stdin>',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
fof(c_0_200_201,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X12),X3) ),
file('<stdin>',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
fof(c_0_201_202,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(X12,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X12),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
fof(c_0_202_203,axiom,
! [X7,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X7),X8)),X7) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X7),c_Suc(X8)) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I28_J_0) ).
fof(c_0_203_204,axiom,
! [X14,X12,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),c_Suc(X14)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14)),X12) ),
file('<stdin>',cls_power__Suc2_0) ).
fof(c_0_204_205,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X3),X3),X12),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_comm__monoid__add_Opower__0_0) ).
fof(c_0_205_206,axiom,
! [X30,X31,X33,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X33),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X31),X30)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X31),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X33),X30)) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I19_J_0) ).
fof(c_0_206_207,axiom,
! [X18,X16,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X18)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X18)) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I22_J_0) ).
fof(c_0_207_208,axiom,
! [X13,X9,X7,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X13)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),X13)) ),
file('<stdin>',cls_add__cancel__21_1) ).
fof(c_0_208_209,axiom,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X16)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16)) ),
file('<stdin>',cls_comm__monoid__add_Omult__left__commute_0) ).
fof(c_0_209_210,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X3),X3),X12),c_HOL_Oone__class_Oone(tc_nat)) = X12 ),
file('<stdin>',cls_comm__monoid__add_Opower__one__right_0) ).
fof(c_0_210_211,axiom,
! [X6,X14,X12,X3] :
( ~ class_HOL_Ozero(X3)
| hAPP(c_Polynomial_Ocoeff(c_Polynomial_OpCons(X12,X6,X3),X3),c_Suc(X14)) = hAPP(c_Polynomial_Ocoeff(X6,X3),X14) ),
file('<stdin>',cls_coeff__pCons__Suc_0) ).
fof(c_0_211_212,axiom,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X12,c_HOL_Ouminus__class_Ouminus(X11,X3),X3) ),
file('<stdin>',cls_le__eq__neg_0) ).
fof(c_0_212_213,axiom,
! [X9,X7,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),X9) != c_HOL_Ozero__class_Ozero(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X7,X3)
| X7 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_add__nonneg__eq__0__iff_0) ).
fof(c_0_213_214,axiom,
! [X9,X7,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),X9) != c_HOL_Ozero__class_Ozero(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X7,X3)
| X9 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_add__nonneg__eq__0__iff_1) ).
fof(c_0_214_215,axiom,
! [X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3)) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_add__nonneg__eq__0__iff_2) ).
fof(c_0_215_216,axiom,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),c_Suc(X14)),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X12,X3) ),
file('<stdin>',cls_power__gt1_0) ).
fof(c_0_216_217,axiom,
! [X21,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(X12,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3),X21,X3) = c_Polynomial_OpCons(X12,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3) ),
file('<stdin>',cls_offset__poly__single_0) ).
fof(c_0_217_218,axiom,
! [X7,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X7),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_power__le__zero__eq_0) ).
fof(c_0_218_219,axiom,
! [X14,X22,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X22) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X12,X3)
| X22 = X14 ),
file('<stdin>',cls_power__inject__exp_0) ).
fof(c_0_219_220,axiom,
! [X14,X22,X12,X3] :
( ~ class_HOL_Ozero(X3)
| hAPP(c_Polynomial_Ocoeff(c_Polynomial_Omonom(X12,X22,X3),X3),X14) = c_HOL_Ozero__class_Ozero(X3)
| X22 = X14 ),
file('<stdin>',cls_coeff__monom_1) ).
fof(c_0_220_221,axiom,
! [X13,X9,X7,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X13)) != X9
| X7 = c_HOL_Ouminus__class_Ouminus(X13,X3) ),
file('<stdin>',cls_add__cancel__end_0) ).
fof(c_0_221_222,axiom,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ouminus__class_Ouminus(X12,X3)),X11)) = X11 ),
file('<stdin>',cls_add__minus__cancel_0) ).
fof(c_0_222_223,axiom,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
file('<stdin>',cls_zero__le__power__iff_1) ).
fof(c_0_223_224,axiom,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
file('<stdin>',cls_zero__le__power_0) ).
fof(c_0_224_225,axiom,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_HOL_Oone__class_Oone(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14),X3)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X3),X12,X3) ),
file('<stdin>',cls_one__le__power_0) ).
fof(c_0_225_226,axiom,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
file('<stdin>',cls_zero__less__power_0) ).
fof(c_0_226_227,axiom,
! [X12,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X12),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_even__less__0__iff_1) ).
fof(c_0_227_228,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X12),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_double__add__less__zero__iff__single__less__zero_1) ).
fof(c_0_228_229,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X12),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
file('<stdin>',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
fof(c_0_229_230,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X12),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
file('<stdin>',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
fof(c_0_230_231,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X12),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X12,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
fof(c_0_231_232,axiom,
! [X6,X12,X3] :
( ~ class_HOL_Ozero(X3)
| hAPP(c_Polynomial_Ocoeff(c_Polynomial_OpCons(X12,X6,X3),X3),c_HOL_Ozero__class_Ozero(tc_nat)) = X12 ),
file('<stdin>',cls_coeff__pCons__0_0) ).
fof(c_0_232_233,axiom,
! [X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X12),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_not__square__less__zero_0) ).
fof(c_0_233_234,axiom,
! [X7,X12,X3] :
( ~ class_HOL_Ozero(X3)
| hAPP(c_Polynomial_Ocoeff(c_Polynomial_Omonom(X12,X7,X3),X3),X7) = X12 ),
file('<stdin>',cls_coeff__monom_0) ).
fof(c_0_234_235,axiom,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ouminus__class_Ouminus(X11,X3)),c_HOL_Ouminus__class_Ouminus(X12,X3)) ),
file('<stdin>',cls_minus__add_0) ).
fof(c_0_235_236,axiom,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ouminus__class_Ouminus(X12,X3)),c_HOL_Ouminus__class_Ouminus(X11,X3)) ),
file('<stdin>',cls_minus__add__distrib_0) ).
fof(c_0_236_237,axiom,
! [X14,X22,X3] :
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X14),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Nat_Osemiring__1__class_Oof__nat(X22,X3)),c_Nat_Osemiring__1__class_Oof__nat(X14,X3)) ),
file('<stdin>',cls_of__nat__add_0) ).
fof(c_0_237_238,axiom,
! [X14,X12,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Omonom(X12,c_Suc(X14),X3) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X3),c_Polynomial_Omonom(X12,X14,X3),X3) ),
file('<stdin>',cls_monom__Suc_0) ).
fof(c_0_238_239,axiom,
! [X13,X9,X7,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X7,X13,X3)
| ~ c_HOL_Oord__class_Oless(X9,X13,X3)
| ~ c_lessequals(X7,X9,X3) ),
file('<stdin>',cls_order__le__less__trans_0) ).
fof(c_0_239_240,axiom,
! [X13,X9,X7,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X7,X13,X3)
| ~ c_lessequals(X9,X13,X3)
| ~ c_HOL_Oord__class_Oless(X7,X9,X3) ),
file('<stdin>',cls_order__less__le__trans_0) ).
fof(c_0_240_241,axiom,
! [X13,X9,X7,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X7,X13,X3)
| ~ c_lessequals(X9,X13,X3)
| ~ c_lessequals(X7,X9,X3) ),
file('<stdin>',cls_order__trans_0) ).
fof(c_0_241_242,axiom,
! [X13,X9,X7,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X13,X7,X3)
| ~ c_HOL_Oord__class_Oless(X13,X9,X3)
| ~ c_lessequals(X9,X7,X3) ),
file('<stdin>',cls_xt1_I8_J_0) ).
fof(c_0_242_243,axiom,
! [X13,X9,X7,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X13,X7,X3)
| ~ c_lessequals(X13,X9,X3)
| ~ c_HOL_Oord__class_Oless(X9,X7,X3) ),
file('<stdin>',cls_xt1_I7_J_0) ).
fof(c_0_243_244,axiom,
! [X13,X9,X7,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X13,X7,X3)
| ~ c_lessequals(X13,X9,X3)
| ~ c_lessequals(X9,X7,X3) ),
file('<stdin>',cls_xt1_I6_J_0) ).
fof(c_0_244_245,axiom,
! [X13,X9,X7,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X13,X7,X3)
| ~ c_HOL_Oord__class_Oless(X13,X9,X3)
| ~ c_HOL_Oord__class_Oless(X9,X7,X3) ),
file('<stdin>',cls_xt1_I10_J_0) ).
fof(c_0_245_246,axiom,
! [X13,X9,X7,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X7,X13,X3)
| ~ c_HOL_Oord__class_Oless(X9,X13,X3)
| ~ c_HOL_Oord__class_Oless(X7,X9,X3) ),
file('<stdin>',cls_order__less__trans_0) ).
fof(c_0_246_247,axiom,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X12,X11,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X11,X3),c_HOL_Ouminus__class_Ouminus(X12,X3),X3) ),
file('<stdin>',cls_neg__less__iff__less_0) ).
fof(c_0_247_248,axiom,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X12,X11,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X11,X3),c_HOL_Ouminus__class_Ouminus(X12,X3),X3) ),
file('<stdin>',cls_neg__le__iff__le_0) ).
fof(c_0_248_249,axiom,
! [X11,X12,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ouminus__class_Ouminus(X12,X3)),X11) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),X3) ),
file('<stdin>',cls_mult_Ominus__left_0) ).
fof(c_0_249_250,axiom,
! [X9,X7,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ouminus__class_Ouminus(X7,X3)),X9) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X9),X3) ),
file('<stdin>',cls_mult__left_Ominus_0) ).
fof(c_0_250_251,axiom,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ouminus__class_Ouminus(X12,X3)),X11) ),
file('<stdin>',cls_minus__mult__left_0) ).
fof(c_0_251_252,axiom,
! [X25,X26,X27] :
( c_lessequals(X27,X25,tc_RealDef_Oreal)
| ~ c_lessequals(X26,X25,tc_RealDef_Oreal)
| ~ c_lessequals(X27,X26,tc_RealDef_Oreal) ),
file('<stdin>',cls_real__le__trans_0) ).
fof(c_0_252_253,axiom,
! [X7,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X7),X8)) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X7),c_Suc(X8)) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I27_J_0) ).
fof(c_0_253_254,axiom,
! [X7,X14,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X7),c_Suc(X14)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X7),X14)) ),
file('<stdin>',cls_class__semiring_Opwr__Suc_0) ).
fof(c_0_254_255,axiom,
! [X14,X12,X3] :
( ~ class_Power_Opower(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),c_Suc(X14)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14)) ),
file('<stdin>',cls_power__Suc_0) ).
fof(c_0_255_256,axiom,
! [X7,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X7),c_Suc(X8)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X7),X8)) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I35_J_0) ).
fof(c_0_256_257,axiom,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X12,X3),X11,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X11,X3),X12,X3) ),
file('<stdin>',cls_minus__less__iff_1) ).
fof(c_0_257_258,axiom,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X11,X3),X12,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X12,X3),X11,X3) ),
file('<stdin>',cls_minus__less__iff_0) ).
fof(c_0_258_259,axiom,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X12,c_HOL_Ouminus__class_Ouminus(X11,X3),X3)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ouminus__class_Ouminus(X12,X3),X3) ),
file('<stdin>',cls_less__minus__iff_1) ).
fof(c_0_259_260,axiom,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X11,c_HOL_Ouminus__class_Ouminus(X12,X3),X3)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Ouminus__class_Ouminus(X11,X3),X3) ),
file('<stdin>',cls_less__minus__iff_0) ).
fof(c_0_260_261,axiom,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X12,X3),X11,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X11,X3),X12,X3) ),
file('<stdin>',cls_minus__le__iff_1) ).
fof(c_0_261_262,axiom,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X11,X3),X12,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X12,X3),X11,X3) ),
file('<stdin>',cls_minus__le__iff_0) ).
fof(c_0_262_263,axiom,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X12,c_HOL_Ouminus__class_Ouminus(X11,X3),X3)
| ~ c_lessequals(X11,c_HOL_Ouminus__class_Ouminus(X12,X3),X3) ),
file('<stdin>',cls_le__minus__iff_1) ).
fof(c_0_263_264,axiom,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X11,c_HOL_Ouminus__class_Ouminus(X12,X3),X3)
| ~ c_lessequals(X12,c_HOL_Ouminus__class_Ouminus(X11,X3),X3) ),
file('<stdin>',cls_le__minus__iff_0) ).
fof(c_0_264_265,axiom,
! [X13,X9,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ouminus__class_Ouminus(X13,X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X13)) = X9 ),
file('<stdin>',cls_add__cancel__end_1) ).
fof(c_0_265_266,axiom,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ouminus__class_Ouminus(X12,X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11)) = X11 ),
file('<stdin>',cls_minus__add__cancel_0) ).
fof(c_0_266_267,axiom,
! [X9,X7,X3] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X9)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X9) ),
file('<stdin>',cls_mult__left__idem_0) ).
fof(c_0_267_268,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oone__class_Oone(X3)),c_HOL_Oone__class_Oone(X3)),X3) ),
file('<stdin>',cls_zero__less__two_0) ).
fof(c_0_268_269,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X12,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ouminus__class_Ouminus(X12,X3),X3) ),
file('<stdin>',cls_neg__0__le__iff__le_0) ).
fof(c_0_269_270,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X12,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_neg__le__0__iff__le_0) ).
fof(c_0_270_271,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ouminus__class_Ouminus(X12,X3),X3) ),
file('<stdin>',cls_neg__0__less__iff__less_0) ).
fof(c_0_271_272,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X12,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X12,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_neg__less__0__iff__less_0) ).
fof(c_0_272_273,axiom,
! [X9,X7,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X7,X9,X3)
| c_lessequals(X9,X7,X3)
| ~ c_lessequals(X7,X9,X3) ),
file('<stdin>',cls_less__le__not__le_2) ).
fof(c_0_273_274,axiom,
! [X11,X12,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),c_HOL_Ouminus__class_Ouminus(X11,X3)) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),X3) ),
file('<stdin>',cls_mult_Ominus__right_0) ).
fof(c_0_274_275,axiom,
! [X34,X7,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X34),c_HOL_Ouminus__class_Ouminus(X7,X3)) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X34),X7),X3) ),
file('<stdin>',cls_mult__right_Ominus_0) ).
fof(c_0_275_276,axiom,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),c_HOL_Ouminus__class_Ouminus(X11,X3)) ),
file('<stdin>',cls_minus__mult__right_0) ).
fof(c_0_276_277,axiom,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X11,X3),c_HOL_Ouminus__class_Ouminus(X12,X3),X3)
| ~ c_HOL_Oord__class_Oless(X12,X11,X3) ),
file('<stdin>',cls_neg__less__iff__less_1) ).
fof(c_0_277_278,axiom,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X11,X3),c_HOL_Ouminus__class_Ouminus(X12,X3),X3)
| ~ c_lessequals(X12,X11,X3) ),
file('<stdin>',cls_le__imp__neg__le_0) ).
fof(c_0_278_279,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(X12,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X12,c_HOL_Ouminus__class_Ouminus(X12,X3),X3) ),
file('<stdin>',cls_le__minus__self__iff_0) ).
fof(c_0_279_280,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X12,X3),X12,X3) ),
file('<stdin>',cls_minus__le__self__iff_0) ).
fof(c_0_280_281,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_lessequals(X12,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X12,c_HOL_Ouminus__class_Ouminus(X12,X3),X3) ),
file('<stdin>',cls_less__eq__neg__nonpos_0) ).
fof(c_0_281_282,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X12,X3),X12,X3) ),
file('<stdin>',cls_neg__less__eq__nonneg_0) ).
fof(c_0_282_283,axiom,
! [X12,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Ouminus__class_Ouminus(X12,X3),X3) ),
file('<stdin>',cls_less__minus__self__iff_0) ).
fof(c_0_283_284,axiom,
! [X6,X16,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(X16,X6,X3) != c_Polynomial_OpCons(X12,X6,X3)
| X6 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_synthetic__div__unique__lemma_0) ).
fof(c_0_284_285,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ouminus__class_Ouminus(X12,X3),X3)
| ~ c_lessequals(X12,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_neg__0__le__iff__le_1) ).
fof(c_0_285_286,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X12,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
file('<stdin>',cls_neg__le__0__iff__le_1) ).
fof(c_0_286_287,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ouminus__class_Ouminus(X12,X3),X3)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_neg__0__less__iff__less_1) ).
fof(c_0_287_288,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X12,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
file('<stdin>',cls_neg__less__0__iff__less_1) ).
fof(c_0_288_289,axiom,
! [X11,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ouminus__class_Ouminus(X11,X3)),c_HOL_Ouminus__class_Ouminus(X11,X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X11) ),
file('<stdin>',cls_square__eq__iff_1) ).
fof(c_0_289_290,axiom,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ouminus__class_Ouminus(X12,X3)),c_HOL_Ouminus__class_Ouminus(X11,X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11) ),
file('<stdin>',cls_minus__mult__minus_0) ).
fof(c_0_290_291,axiom,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ouminus__class_Ouminus(X12,X3)),X11) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),c_HOL_Ouminus__class_Ouminus(X11,X3)) ),
file('<stdin>',cls_minus__mult__commute_0) ).
fof(c_0_291_292,axiom,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X12) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X11)
| X12 = c_HOL_Ouminus__class_Ouminus(X11,X3)
| X12 = X11 ),
file('<stdin>',cls_square__eq__iff_0) ).
fof(c_0_292_293,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(X12,c_HOL_Ouminus__class_Ouminus(X12,X3),X3)
| ~ c_lessequals(X12,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_le__minus__self__iff_1) ).
fof(c_0_293_294,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X12,X3),X12,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
file('<stdin>',cls_minus__le__self__iff_1) ).
fof(c_0_294_295,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_lessequals(X12,c_HOL_Ouminus__class_Ouminus(X12,X3),X3)
| ~ c_lessequals(X12,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_less__eq__neg__nonpos_1) ).
fof(c_0_295_296,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X12,X3),X12,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
file('<stdin>',cls_neg__less__eq__nonneg_1) ).
fof(c_0_296_297,axiom,
! [X12,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X12,c_HOL_Ouminus__class_Ouminus(X12,X3),X3)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_less__minus__self__iff_1) ).
fof(c_0_297_298,axiom,
! [X9,X7,X3] :
( ~ class_Orderings_Oorder(X3)
| X7 = X9
| ~ c_lessequals(X7,X9,X3)
| ~ c_lessequals(X9,X7,X3) ),
file('<stdin>',cls_order__antisym__conv_0) ).
fof(c_0_298_299,axiom,
! [X9,X7,X3] :
( ~ class_Orderings_Oorder(X3)
| X7 = X9
| ~ c_lessequals(X9,X7,X3)
| ~ c_lessequals(X7,X9,X3) ),
file('<stdin>',cls_order__eq__iff_2) ).
fof(c_0_299_300,axiom,
! [X9,X7,X3] :
( ~ class_Orderings_Oorder(X3)
| X7 = X9
| ~ c_lessequals(X9,X7,X3)
| ~ c_lessequals(X7,X9,X3) ),
file('<stdin>',cls_order__antisym_0) ).
fof(c_0_300_301,axiom,
! [X8,X6,X11,X12,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_OpCons(X12,X6,X3) != c_Polynomial_OpCons(X11,X8,X3)
| X12 = X11 ),
file('<stdin>',cls_pCons__eq__iff_0) ).
fof(c_0_301_302,axiom,
! [X8,X6,X11,X12,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_OpCons(X12,X6,X3) != c_Polynomial_OpCons(X11,X8,X3)
| X6 = X8 ),
file('<stdin>',cls_pCons__eq__iff_1) ).
fof(c_0_302_303,axiom,
! [X14,X11,X12,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Omonom(X12,X14,X3) != c_Polynomial_Omonom(X11,X14,X3)
| X12 = X11 ),
file('<stdin>',cls_monom__eq__iff_0) ).
fof(c_0_303_304,axiom,
! [X13,X9,X7,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),X9) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),X13)
| X9 = X13 ),
file('<stdin>',cls_class__ringb_Oadd__cancel_0) ).
fof(c_0_304_305,axiom,
! [X11,X12,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X11,X12,X3)
| ~ c_HOL_Oord__class_Oless(X12,X11,X3) ),
file('<stdin>',cls_order__less__asym_H_0) ).
fof(c_0_305_306,axiom,
! [X9,X7,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X9,X7,X3)
| ~ c_HOL_Oord__class_Oless(X7,X9,X3) ),
file('<stdin>',cls_order__less__asym_0) ).
fof(c_0_306_307,axiom,
! [X9,X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X7,X9,X3)
| ~ c_HOL_Oord__class_Oless(X9,X7,X3) ),
file('<stdin>',cls_not__less__iff__gr__or__eq_1) ).
fof(c_0_307_308,axiom,
! [X11,X12,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X12,X11,X3)
| ~ c_HOL_Oord__class_Oless(X11,X12,X3) ),
file('<stdin>',cls_xt1_I9_J_0) ).
fof(c_0_308_309,axiom,
! [X9,X7,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X9,X7,X3)
| ~ c_HOL_Oord__class_Oless(X7,X9,X3) ),
file('<stdin>',cls_less__le__not__le_1) ).
fof(c_0_309_310,axiom,
! [X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X7,X7,X3)
| ~ c_HOL_Oord__class_Oless(X7,X7,X3) ),
file('<stdin>',cls_linorder__antisym__conv2_1) ).
fof(c_0_310_311,axiom,
! [X9,X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X7,X9,X3)
| ~ c_lessequals(X9,X7,X3) ),
file('<stdin>',cls_linorder__not__less_1) ).
fof(c_0_311_312,axiom,
! [X9,X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X7,X9,X3)
| ~ c_HOL_Oord__class_Oless(X9,X7,X3) ),
file('<stdin>',cls_linorder__not__le_1) ).
fof(c_0_312_313,axiom,
! [X6,X12,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Polynomial_Oorder(X12,X6,X3) != c_HOL_Ozero__class_Ozero(tc_nat)
| X6 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| hAPP(c_Polynomial_Opoly(X6,X3),X12) != c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_order__root_0) ).
fof(c_0_313_314,axiom,
! [X1,X2,X3] :
( X2 = X1
| ~ hBOOL(c_fequal(X2,X1,X3)) ),
file('<stdin>',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(c_0_314_315,axiom,
! [X7,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X7),c_HOL_Ozero__class_Ozero(tc_nat)),X3) ),
file('<stdin>',cls_zero__less__power__eq_3) ).
fof(c_0_315_316,axiom,
! [X12,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X12,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),c_HOL_Oone__class_Oone(X3)),X3) ),
file('<stdin>',cls_less__add__one_0) ).
fof(c_0_316_317,axiom,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16)
| X11 = X16 ),
file('<stdin>',cls_add__imp__eq_0) ).
fof(c_0_317_318,axiom,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16)
| X11 = X16 ),
file('<stdin>',cls_add__left__cancel_0) ).
fof(c_0_318_319,axiom,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X12) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X12)
| X11 = X16 ),
file('<stdin>',cls_add__right__cancel_0) ).
fof(c_0_319_320,axiom,
! [X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X12),X3) ),
file('<stdin>',cls_zero__le__square_0) ).
fof(c_0_320_321,axiom,
! [X13,X24] :
( X13 = X24
| ~ c_lessequals(X24,X13,tc_RealDef_Oreal)
| ~ c_lessequals(X13,X24,tc_RealDef_Oreal) ),
file('<stdin>',cls_real__le__antisym_0) ).
fof(c_0_321_322,axiom,
! [X6,X12,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Odegree(c_Polynomial_OpCons(X12,X6,X3),X3) = c_Suc(c_Polynomial_Odegree(X6,X3))
| X6 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_degree__pCons__eq_0) ).
fof(c_0_322_323,axiom,
! [X12,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Odegree(c_Polynomial_OpCons(X12,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3),X3) = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_degree__pCons__0_0) ).
fof(c_0_323_324,axiom,
! [X11,X12,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X11,X12,X3)
| X12 = X11
| ~ c_lessequals(X11,X12,X3) ),
file('<stdin>',cls_xt1_I11_J_0) ).
fof(c_0_324_325,axiom,
! [X11,X12,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X11,X12,X3)
| ~ c_lessequals(X11,X12,X3)
| X12 = X11 ),
file('<stdin>',cls_xt1_I12_J_0) ).
fof(c_0_325_326,axiom,
! [X9,X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| X7 = X9
| c_HOL_Oord__class_Oless(X7,X9,X3)
| ~ c_lessequals(X7,X9,X3) ),
file('<stdin>',cls_linorder__antisym__conv2_0) ).
fof(c_0_326_327,axiom,
! [X9,X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| X7 = X9
| ~ c_lessequals(X7,X9,X3)
| c_HOL_Oord__class_Oless(X7,X9,X3) ),
file('<stdin>',cls_linorder__antisym__conv1_0) ).
fof(c_0_327_328,axiom,
! [X11,X12,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X12,X11,X3)
| ~ c_lessequals(X12,X11,X3)
| X12 = X11 ),
file('<stdin>',cls_order__neq__le__trans_0) ).
fof(c_0_328_329,axiom,
! [X11,X12,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X12,X11,X3)
| X12 = X11
| ~ c_lessequals(X12,X11,X3) ),
file('<stdin>',cls_order__le__neq__trans_0) ).
fof(c_0_329_330,axiom,
! [X9,X7,X3] :
( ~ class_Orderings_Oorder(X3)
| X7 = X9
| c_HOL_Oord__class_Oless(X7,X9,X3)
| ~ c_lessequals(X7,X9,X3) ),
file('<stdin>',cls_order__le__less_0) ).
fof(c_0_330_331,axiom,
! [X9,X7,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X7,X9,X3)
| X7 = X9
| ~ c_lessequals(X7,X9,X3) ),
file('<stdin>',cls_order__less__le_2) ).
fof(c_0_331_332,axiom,
! [X3] :
( ~ class_HOL_Ozero(X3)
| hAPP(c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3),c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3)) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_leading__coeff__0__iff_1) ).
fof(c_0_332_333,axiom,
! [X7,X3] :
( ~ class_Int_Onumber__ring(X3)
| c_HOL_Ouminus__class_Ouminus(X7,X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X3),X3)),X7) ),
file('<stdin>',cls_class__ring_Oneg__mul_0) ).
fof(c_0_333_334,axiom,
! [X9,X7,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X7,X9,X3)
| ~ c_HOL_Oord__class_Oless(X7,X9,X3) ),
file('<stdin>',cls_order__le__less_1) ).
fof(c_0_334_335,axiom,
! [X9,X7,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X7,X9,X3)
| ~ c_HOL_Oord__class_Oless(X7,X9,X3) ),
file('<stdin>',cls_order__less__imp__le_0) ).
fof(c_0_335_336,axiom,
! [X6,X12,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Polynomial_Odegree(c_Polynomial_Osmult(X12,X6,X3),X3) = c_Polynomial_Odegree(X6,X3)
| X12 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_degree__smult__eq_1) ).
fof(c_0_336_337,axiom,
! [X14,X22,X25] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X25) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X25)
| X22 = X14 ),
file('<stdin>',cls_nat__add__right__cancel_0) ).
fof(c_0_337_338,axiom,
! [X14,X22,X25] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X22) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X14)
| X22 = X14 ),
file('<stdin>',cls_nat__add__left__cancel_0) ).
fof(c_0_338_339,axiom,
! [X13,X9,X7] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X9) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X13)
| X9 = X13 ),
file('<stdin>',cls_natgb_Oadd__cancel_0) ).
fof(c_0_339_340,axiom,
! [X22,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X22,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_of__nat__less__0__iff_0) ).
fof(c_0_340_341,axiom,
! [X6,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Polynomial_Odegree(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X3),X6,X3),X3) = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_degree__smult__eq_0) ).
fof(c_0_341_342,axiom,
! [X6,X21,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X6,X21,X3),X3) = c_Polynomial_Odegree(X6,X3) ),
file('<stdin>',cls_degree__offset__poly_0) ).
fof(c_0_342_343,axiom,
! [X12,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Omonom(X12,c_HOL_Ozero__class_Ozero(tc_nat),X3) = c_Polynomial_OpCons(X12,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3) ),
file('<stdin>',cls_monom__0_0) ).
fof(c_0_343_344,axiom,
! [X14,X12,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Odegree(c_Polynomial_Omonom(X12,X14,X3),X3) = X14
| X12 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_degree__monom__eq_0) ).
fof(c_0_344_345,axiom,
! [X6,X3] :
( ~ class_HOL_Ozero(X3)
| hAPP(c_Polynomial_Ocoeff(X6,X3),c_Polynomial_Odegree(X6,X3)) != c_HOL_Ozero__class_Ozero(X3)
| X6 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_leading__coeff__0__iff_0) ).
fof(c_0_345_346,axiom,
! [X6,X12,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Polynomial_Osmult(X12,X6,X3) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| X6 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| X12 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_smult__eq__0__iff_0) ).
fof(c_0_346_347,axiom,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Ozero__neq__one(X3)
| ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| ~ class_Ring__and__Field_Omult__zero(X3)
| ~ class_Power_Opower(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14) != c_HOL_Ozero__class_Ozero(X3)
| X12 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_power__eq__0__iff_0) ).
fof(c_0_347_348,axiom,
! [X12,X3] :
( ~ class_Ring__and__Field_Ozero__neq__one(X3)
| ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| ~ class_Ring__and__Field_Omult__zero(X3)
| ~ class_Power_Opower(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_power__eq__0__iff_1) ).
fof(c_0_348_349,axiom,
! [X8,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X3)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))),X8) = X8 ),
file('<stdin>',cls_add__poly__code_I1_J_0) ).
fof(c_0_349_350,axiom,
! [X6,X21,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X6,X21,X3) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| X6 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_offset__poly__eq__0__iff_0) ).
fof(c_0_350_351,axiom,
! [X6,X12,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_OpCons(X12,X6,X3) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| X6 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_pCons__eq__0__iff_1) ).
fof(c_0_351_352,axiom,
! [X9,X7,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X9,X7,X3)
| c_HOL_Oord__class_Oless(X7,X9,X3)
| X7 = X9 ),
file('<stdin>',cls_linorder__neqE__ordered__idom_0) ).
fof(c_0_352_353,axiom,
! [X9,X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| X7 = X9
| c_HOL_Oord__class_Oless(X9,X7,X3)
| c_HOL_Oord__class_Oless(X7,X9,X3) ),
file('<stdin>',cls_not__less__iff__gr__or__eq_0) ).
fof(c_0_353_354,axiom,
! [X9,X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| X7 = X9
| c_HOL_Oord__class_Oless(X7,X9,X3)
| c_HOL_Oord__class_Oless(X9,X7,X3) ),
file('<stdin>',cls_linorder__antisym__conv3_0) ).
fof(c_0_354_355,axiom,
! [X9,X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X9,X7,X3)
| X7 = X9
| c_HOL_Oord__class_Oless(X7,X9,X3) ),
file('<stdin>',cls_linorder__less__linear_0) ).
fof(c_0_355_356,axiom,
! [X9,X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X9,X7,X3)
| c_HOL_Oord__class_Oless(X7,X9,X3)
| X7 = X9 ),
file('<stdin>',cls_linorder__neqE_0) ).
fof(c_0_356_357,axiom,
! [X22,X3] :
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X22),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oone__class_Oone(X3)),c_Nat_Osemiring__1__class_Oof__nat(X22,X3)) ),
file('<stdin>',cls_of__nat__Suc_0) ).
fof(c_0_357_358,axiom,
! [X9,X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X9,X7,X3)
| c_lessequals(X7,X9,X3) ),
file('<stdin>',cls_linorder__linear_0) ).
fof(c_0_358_359,axiom,
! [X9,X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X7,X9,X3)
| c_lessequals(X9,X7,X3) ),
file('<stdin>',cls_not__leE_0) ).
fof(c_0_359_360,axiom,
! [X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X7,X7,X3)
| c_lessequals(X7,X7,X3) ),
file('<stdin>',cls_linorder__antisym__conv1_1) ).
fof(c_0_360_361,axiom,
! [X9,X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X9,X7,X3)
| c_HOL_Oord__class_Oless(X7,X9,X3) ),
file('<stdin>',cls_linorder__not__less_0) ).
fof(c_0_361_362,axiom,
! [X9,X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X9,X7,X3)
| c_lessequals(X7,X9,X3) ),
file('<stdin>',cls_linorder__not__le_0) ).
fof(c_0_362_363,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ouminus__class_Ouminus(X12,X3)),X12) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_left__minus_0) ).
fof(c_0_363_364,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ouminus__class_Ouminus(X12,X3)),X12) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_ab__left__minus_0) ).
fof(c_0_364_365,axiom,
! [X11,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ouminus__class_Ouminus(X11,X3)),X11) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_eq__neg__iff__add__eq__0_0) ).
fof(c_0_365_366,axiom,
! [X14,X12,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Omonom(X12,X14,X3) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| X12 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_monom__eq__0__iff_0) ).
fof(c_0_366_367,axiom,
! [X6,X12,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_OpCons(X12,X6,X3) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| X12 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_pCons__eq__0__iff_0) ).
fof(c_0_367_368,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_not__one__less__zero_0) ).
fof(c_0_368_369,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_not__one__le__zero_0) ).
fof(c_0_369_370,axiom,
! [X9,X7,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X9) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X7) ),
file('<stdin>',cls_class__semiring_Omul__c_0) ).
fof(c_0_370_371,axiom,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X12) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I7_J_0) ).
fof(c_0_371_372,axiom,
! [X16,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X12) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I24_J_0) ).
fof(c_0_372_373,axiom,
! [X9,X7,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),X9) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X7) ),
file('<stdin>',cls_class__semiring_Oadd__c_0) ).
fof(c_0_373_374,axiom,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X12) ),
file('<stdin>',cls_comm__monoid__add_Omult__commute_0) ).
fof(c_0_374_375,axiom,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11) != c_HOL_Ozero__class_Ozero(X3)
| c_HOL_Ouminus__class_Ouminus(X12,X3) = X11 ),
file('<stdin>',cls_minus__unique_0) ).
fof(c_0_375_376,axiom,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11) != c_HOL_Ozero__class_Ozero(X3)
| X12 = c_HOL_Ouminus__class_Ouminus(X11,X3) ),
file('<stdin>',cls_eq__neg__iff__add__eq__0_1) ).
fof(c_0_376_377,axiom,
! [X9,X7,X10] :
( hAPP(X10,X7) = hAPP(X10,X9)
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X10,t_a,t_b) ),
file('<stdin>',cls_constant__def_0) ).
fof(c_0_377_378,axiom,
! [X6,X12,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| hAPP(c_Polynomial_Opoly(X6,X3),X12) = c_HOL_Ozero__class_Ozero(X3)
| c_Polynomial_Oorder(X12,X6,X3) = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_order__root_2) ).
fof(c_0_378_379,axiom,
! [X13,X24] :
( c_lessequals(X24,X13,tc_RealDef_Oreal)
| c_lessequals(X13,X24,tc_RealDef_Oreal) ),
file('<stdin>',cls_real__le__linear_0) ).
fof(c_0_379_380,axiom,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11) != c_HOL_Ozero__class_Ozero(X3)
| X11 = c_HOL_Ozero__class_Ozero(X3)
| X12 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mult__eq__0__iff_0) ).
fof(c_0_380_381,axiom,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11) != c_HOL_Ozero__class_Ozero(X3)
| X11 = c_HOL_Ozero__class_Ozero(X3)
| X12 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_no__zero__divisors_0) ).
fof(c_0_381_382,axiom,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11) != c_HOL_Ozero__class_Ozero(X3)
| X12 = c_HOL_Ozero__class_Ozero(X3)
| X11 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_no__zero__divirors__neq0_0) ).
fof(c_0_382_383,axiom,
! [X7,X12,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| X7 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),X12)
| X12 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_class__ringb_Oadd__r0__iff_0) ).
fof(c_0_383_384,axiom,
! [X6,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X3)),X6),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))) = X6 ),
file('<stdin>',cls_add__poly__code_I2_J_0) ).
fof(c_0_384_385,axiom,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14) != c_HOL_Ozero__class_Ozero(X3)
| X12 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_field__power__not__zero_0) ).
fof(c_0_385_386,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X12) != c_HOL_Ozero__class_Ozero(X3)
| X12 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_double__eq__0__iff_0) ).
fof(c_0_386_387,axiom,
! [X14,X3] :
( ~ class_Ring__and__Field_Ozero__neq__one(X3)
| ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| ~ class_Ring__and__Field_Omult__zero(X3)
| ~ class_Power_Opower(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3)),X14) = c_HOL_Ozero__class_Ozero(X3)
| X14 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_power__eq__0__iff_2) ).
fof(c_0_387_388,axiom,
! [X14,X22] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X14) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X14 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X22 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('<stdin>',cls_add__is__1_1) ).
fof(c_0_388_389,axiom,
! [X14,X22] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X14)
| X14 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X22 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('<stdin>',cls_one__is__add_1) ).
fof(c_0_389_390,axiom,
! [X6,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Oring__char__0(X3)
| c_Polynomial_Opoly(X6,X3) != c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3)
| X6 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_poly__zero_0) ).
fof(c_0_390_391,axiom,
! [X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_pCons__0__0_0) ).
fof(c_0_391_392,axiom,
! [X14,X22] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X14)
| X14 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X14 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_one__is__add_3) ).
fof(c_0_392_393,axiom,
! [X14,X22] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X14)
| X22 = c_HOL_Ozero__class_Ozero(tc_nat)
| X22 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('<stdin>',cls_one__is__add_0) ).
fof(c_0_393_394,axiom,
! [X14,X22] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X14) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X22 = c_HOL_Ozero__class_Ozero(tc_nat)
| X22 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('<stdin>',cls_add__is__1_0) ).
fof(c_0_394_395,axiom,
! [X14,X22] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X14) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X14 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X14 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_add__is__1_3) ).
fof(c_0_395_396,axiom,
( hAPP(c_Polynomial_Opoly(v_pa____,tc_Complex_Ocomplex),v_c____) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(v_pa____,tc_Complex_Ocomplex),v_sko__unknown__thm__rrS__1(v_pa____)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('<stdin>',cls_calculation_0) ).
fof(c_0_396_397,axiom,
! [X22,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X22,X3),X3) ),
file('<stdin>',cls_zero__le__imp__of__nat_0) ).
fof(c_0_397_398,axiom,
! [X14,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X14,X3),X3) ),
file('<stdin>',cls_of__nat__0__le__iff_0) ).
fof(c_0_398_399,axiom,
! [X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X7,X7,X3) ),
file('<stdin>',cls_linorder__neq__iff_1) ).
fof(c_0_399_400,axiom,
! [X7,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X7,X7,X3) ),
file('<stdin>',cls_order__less__le_1) ).
fof(c_0_400_401,axiom,
! [X7,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X7,X7,X3) ),
file('<stdin>',cls_order__less__irrefl_0) ).
fof(c_0_401_402,axiom,
! [X14,X22] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X14) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X22 = c_HOL_Ozero__class_Ozero(tc_nat)
| X14 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_add__is__1_2) ).
fof(c_0_402_403,axiom,
! [X14,X22] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X14)
| X22 = c_HOL_Ozero__class_Ozero(tc_nat)
| X14 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_one__is__add_2) ).
fof(c_0_403_404,axiom,
! [X12,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Polynomial_Osmult(X12,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_smult__eq__0__iff_2) ).
fof(c_0_404_405,axiom,
! [X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(X12,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_smult__0__right_0) ).
fof(c_0_405_406,axiom,
! [X21,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X21,X3) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_offset__poly__0_0) ).
fof(c_0_406_407,axiom,
! [X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Opcompose(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X8,X3) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_pcompose__0_0) ).
fof(c_0_407_408,axiom,
! [X6] :
( ~ class_Ring__and__Field_Oidom(t_a)
| v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1(X6) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X6,t_a),t_a,t_a) ),
file('<stdin>',cls_poly__decompose_1) ).
fof(c_0_408_409,axiom,
! [X6] :
( ~ class_Ring__and__Field_Oidom(t_a)
| v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__2(X6) != c_HOL_Ozero__class_Ozero(t_a)
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X6,t_a),t_a,t_a) ),
file('<stdin>',cls_poly__decompose_0) ).
fof(c_0_409_410,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),c_HOL_Ouminus__class_Ouminus(X12,X3)) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_right__minus_0) ).
fof(c_0_410_411,axiom,
! [X14,X3] :
( ~ class_Ring__and__Field_Osemiring__0(X3)
| ~ class_Power_Opower(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3)),c_Suc(X14)) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_power__0__Suc_0) ).
fof(c_0_411_412,axiom,
! [X14,X3] :
( ~ class_HOL_Ozero(X3)
| hAPP(c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3),X14) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_coeff__0_0) ).
fof(c_0_412_413,axiom,
! [X12,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| hAPP(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3),X12) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_order__root_1) ).
fof(c_0_413_414,axiom,
! [X7,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| hAPP(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3),X7) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_poly__0_0) ).
fof(c_0_414_415,axiom,
! [X14,X3] :
( ~ class_Ring__and__Field_Osemiring__0(X3)
| ~ class_Power_Opower(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3)),X14) = c_HOL_Ozero__class_Ozero(X3)
| X14 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_power__0__left_1) ).
fof(c_0_415_416,axiom,
! [X3] :
( ~ class_Ring__and__Field_Osemiring__0(X3)
| ~ class_Power_Opower(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(X3) ),
file('<stdin>',cls_power__0__left_0) ).
fof(c_0_416_417,axiom,
! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3)) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_double__eq__0__iff_1) ).
fof(c_0_417_418,axiom,
! [X14,X22] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X14) != c_HOL_Ozero__class_Ozero(tc_nat)
| X22 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_add__is__0_0) ).
fof(c_0_418_419,axiom,
! [X14,X22] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X14) != c_HOL_Ozero__class_Ozero(tc_nat)
| X14 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_add__is__0_1) ).
fof(c_0_419_420,axiom,
! [X7,X12] :
( X7 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X12)
| X12 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_natgb_Oadd__r0__iff_0) ).
fof(c_0_420_421,axiom,
! [X14,X22] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X14) != X22
| X14 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_add__eq__self__zero_0) ).
fof(c_0_421_422,axiom,
! [X3] :
( ~ class_Power_Opower(X3)
| c_Power_Opower__class_Opower(X3) = c_Power_Opower_Opower(c_HOL_Oone__class_Oone(X3),c_HOL_Otimes__class_Otimes(X3),X3) ),
file('<stdin>',cls_power__power__power_0) ).
fof(c_0_422_423,axiom,
! [X14,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(X3),X14,X3) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_monom__eq__0_0) ).
fof(c_0_423_424,axiom,
! [X6,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X3),X6,X3) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_smult__eq__0__iff_1) ).
fof(c_0_424_425,axiom,
! [X6,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X3),X6,X3) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_smult__0__left_0) ).
fof(c_0_425_426,axiom,
! [X14,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Oone__class_Oone(X3)),X14) = c_HOL_Oone__class_Oone(X3) ),
file('<stdin>',cls_power__one_0) ).
fof(c_0_426_427,axiom,
! [X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),X12) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I9_J_0) ).
fof(c_0_427_428,axiom,
! [X9,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),X9) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mult__left_Ozero_0) ).
fof(c_0_428_429,axiom,
! [X11,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),X11) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mult_Ozero__left_0) ).
fof(c_0_429_430,axiom,
! [X7,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),X7) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_class__semiring_Omul__0_0) ).
fof(c_0_430_431,axiom,
! [X12,X3] :
( ~ class_Ring__and__Field_Omult__zero(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),X12) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mult__zero__left_0) ).
fof(c_0_431_432,axiom,
! [X11,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),X11) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mult__eq__0__iff_1) ).
fof(c_0_432_433,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oone__class_Oone(X3),X3) ),
file('<stdin>',cls_zero__le__one_0) ).
fof(c_0_433_434,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oone__class_Oone(X3),X3) ),
file('<stdin>',cls_zero__less__one_0) ).
fof(c_0_434_435,axiom,
! [X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_OrderedGroup_Ocomm__monoid__add__axioms(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X3),X3) ),
file('<stdin>',cls_comm__monoid__add__class_Oaxioms_0) ).
fof(c_0_435_436,axiom,
! [X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| c_OrderedGroup_Omonoid__add__axioms(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X3),X3) ),
file('<stdin>',cls_monoid__add__class_Oaxioms_0) ).
fof(c_0_436_437,axiom,
! [X7,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| X7 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),c_HOL_Ozero__class_Ozero(X3)) ),
file('<stdin>',cls_class__ringb_Oadd__r0__iff_1) ).
fof(c_0_437_438,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Oone__class_Oone(X3)),X12) = X12 ),
file('<stdin>',cls_mult__1__left_0) ).
fof(c_0_438_439,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Oone__class_Oone(X3)),X12) = X12 ),
file('<stdin>',cls_mult__1_0) ).
fof(c_0_439_440,axiom,
! [X7,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Oone__class_Oone(X3)),X7) = X7 ),
file('<stdin>',cls_class__semiring_Omul__1_0) ).
fof(c_0_440_441,axiom,
! [X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Oone__class_Oone(X3)),X12) = X12 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I11_J_0) ).
fof(c_0_441_442,axiom,
! [X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X12) = X12 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I5_J_0) ).
fof(c_0_442_443,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X12) = X12 ),
file('<stdin>',cls_comm__monoid__add_Omult__1_0) ).
fof(c_0_443_444,axiom,
! [X7,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X7) = X7 ),
file('<stdin>',cls_class__semiring_Oadd__0_0) ).
fof(c_0_444_445,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X12) = X12 ),
file('<stdin>',cls_add__0__left_0) ).
fof(c_0_445_446,axiom,
! [X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),c_HOL_Ozero__class_Ozero(X3)) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I10_J_0) ).
fof(c_0_446_447,axiom,
! [X12,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),c_HOL_Ozero__class_Ozero(X3)) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mult_Ozero__right_0) ).
fof(c_0_447_448,axiom,
! [X7,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),c_HOL_Ozero__class_Ozero(X3)) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mult__right_Ozero_0) ).
fof(c_0_448_449,axiom,
! [X12,X3] :
( ~ class_Ring__and__Field_Omult__zero(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),c_HOL_Ozero__class_Ozero(X3)) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mult__zero__right_0) ).
fof(c_0_449_450,axiom,
! [X12,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),c_HOL_Ozero__class_Ozero(X3)) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mult__eq__0__iff_2) ).
fof(c_0_450_451,axiom,
! [X6,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Polynomial_Osmult(c_HOL_Oone__class_Oone(X3),X6,X3) = X6 ),
file('<stdin>',cls_smult__1__left_0) ).
fof(c_0_451_452,axiom,
! [X7,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X7),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(X3) ),
file('<stdin>',cls_class__semiring_Opwr__0_0) ).
fof(c_0_452_453,axiom,
! [X12,X3] :
( ~ class_Power_Opower(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(X3) ),
file('<stdin>',cls_power__0_0) ).
fof(c_0_453_454,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),c_HOL_Oone__class_Oone(X3)) = X12 ),
file('<stdin>',cls_mult__1__right_0) ).
fof(c_0_454_455,axiom,
! [X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),c_HOL_Oone__class_Oone(X3)) = X12 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I12_J_0) ).
fof(c_0_455_456,axiom,
! [X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),c_HOL_Ozero__class_Ozero(X3)) = X12 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(c_0_456_457,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),c_HOL_Ozero__class_Ozero(X3)) = X12 ),
file('<stdin>',cls_comm__monoid__add_Omult__1__right_0) ).
fof(c_0_457_458,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),c_HOL_Ozero__class_Ozero(X3)) = X12 ),
file('<stdin>',cls_monoid__add__class_Oadd__0__right_0) ).
fof(c_0_458_459,axiom,
! [X7,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X7),c_HOL_Oone__class_Oone(tc_nat)) = X7 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I33_J_0) ).
fof(c_0_459_460,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),c_HOL_Oone__class_Oone(tc_nat)) = X12 ),
file('<stdin>',cls_power__one__right_0) ).
fof(c_0_460_461,axiom,
! [X6,X3] :
( ~ class_HOL_Ozero(X3)
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X6,X3) = c_Suc(c_Polynomial_Odegree(X6,X3))
| X6 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_psize__def_1) ).
fof(c_0_461_462,axiom,
! [X7,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X7,X7,X3) ),
file('<stdin>',cls_order__eq__refl_0) ).
fof(c_0_462_463,axiom,
! [X7,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X7,X7,X3) ),
file('<stdin>',cls_order__eq__iff_0) ).
fof(c_0_463_464,axiom,
! [X7,X3] :
( ~ class_RealVector_Oreal__normed__vector(X3)
| c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(X7,X3),X3) = c_RealVector_Onorm__class_Onorm(X7,X3) ),
file('<stdin>',cls_norm__minus__cancel_0) ).
fof(c_0_464_465,axiom,
! [X8,X6,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Oring__char__0(X3)
| c_Polynomial_Opoly(X6,X3) != c_Polynomial_Opoly(X8,X3)
| X6 = X8 ),
file('<stdin>',cls_poly__eq__iff_0) ).
fof(c_0_465_466,axiom,
! [X7,X3] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X7) = X7 ),
file('<stdin>',cls_mult__idem_0) ).
fof(c_0_466_467,axiom,
! [X13,X6] :
( ~ class_Ring__and__Field_Oidom(t_a)
| v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2(X6) != c_HOL_Ozero__class_Ozero(t_a)
| hAPP(c_Polynomial_Opoly(X6,t_a),X13) = c_HOL_Ozero__class_Ozero(t_a)
| X13 = c_HOL_Ozero__class_Ozero(t_a) ),
file('<stdin>',cls_poly__decompose__lemma_0) ).
fof(c_0_467_468,axiom,
! [X9,X7,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Ocoeff(X7,X3) != c_Polynomial_Ocoeff(X9,X3)
| X7 = X9 ),
file('<stdin>',cls_coeff__inject_0) ).
fof(c_0_468_469,axiom,
! [X9,X7,X3] :
( ~ class_Lattices_Oboolean__algebra(X3)
| c_HOL_Ouminus__class_Ouminus(X7,X3) != c_HOL_Ouminus__class_Ouminus(X9,X3)
| X7 = X9 ),
file('<stdin>',cls_compl__eq__compl__iff_0) ).
fof(c_0_469_470,axiom,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(X12,X3) != c_HOL_Ouminus__class_Ouminus(X11,X3)
| X12 = X11 ),
file('<stdin>',cls_neg__equal__iff__equal_0) ).
fof(c_0_470_471,axiom,
! [X14,X22,X3] :
( ~ class_Nat_Osemiring__char__0(X3)
| c_Nat_Osemiring__1__class_Oof__nat(X22,X3) != c_Nat_Osemiring__1__class_Oof__nat(X14,X3)
| X22 = X14 ),
file('<stdin>',cls_of__nat__eq__iff_0) ).
fof(c_0_471_472,axiom,
! [X11,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X11,X3),X3) = X11 ),
file('<stdin>',cls_minus__equation__iff_1) ).
fof(c_0_472_473,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| X12 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X12,X3),X3) ),
file('<stdin>',cls_equation__minus__iff_1) ).
fof(c_0_473_474,axiom,
! [X11,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| X11 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X11,X3),X3) ),
file('<stdin>',cls_equation__minus__iff_0) ).
fof(c_0_474_475,axiom,
! [X7,X3] :
( ~ class_Lattices_Oboolean__algebra(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X7,X3),X3) = X7 ),
file('<stdin>',cls_double__compl_0) ).
fof(c_0_475_476,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X12,X3),X3) = X12 ),
file('<stdin>',cls_minus__minus_0) ).
fof(c_0_476_477,axiom,
! [X6,X3] :
( ~ class_HOL_Ozero(X3)
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X6,X3) != c_HOL_Ozero__class_Ozero(tc_nat)
| X6 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_psize__eq__0__iff_0) ).
fof(c_0_477_478,axiom,
! [X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3) = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_degree__0_0) ).
fof(c_0_478_479,axiom,
! [X3] :
( ~ class_HOL_Ozero(X3)
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3) = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_psize__def_0) ).
fof(c_0_479_480,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(X12,X3) != c_HOL_Ozero__class_Ozero(X3)
| X12 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_neg__equal__0__iff__equal_0) ).
fof(c_0_480_481,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Ouminus__class_Ouminus(X12,X3)
| c_HOL_Ozero__class_Ozero(X3) = X12 ),
file('<stdin>',cls_neg__0__equal__iff__equal_0) ).
fof(c_0_481_482,axiom,
! [X5,X4] :
( class_Lattices_Oboolean__algebra(tc_fun(X5,X4))
| ~ class_Lattices_Oboolean__algebra(X4) ),
file('<stdin>',clsarity_fun__Lattices_Oboolean__algebra) ).
fof(c_0_482_483,axiom,
! [X5,X4] :
( class_Orderings_Opreorder(tc_fun(X5,X4))
| ~ class_Orderings_Opreorder(X4) ),
file('<stdin>',clsarity_fun__Orderings_Opreorder) ).
fof(c_0_483_484,axiom,
! [X5,X4] :
( class_Orderings_Oorder(tc_fun(X5,X4))
| ~ class_Orderings_Oorder(X4) ),
file('<stdin>',clsarity_fun__Orderings_Oorder) ).
fof(c_0_484_485,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_HOL_Ouminus__class_Ouminus(X12,X3) != X12
| X12 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_neg__equal__zero_0) ).
fof(c_0_485_486,axiom,
! [X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_neg__0__equal__iff__equal_1) ).
fof(c_0_486_487,axiom,
! [X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_minus__zero_0) ).
fof(c_0_487_488,axiom,
! [X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_neg__equal__zero_1) ).
fof(c_0_488_489,axiom,
! [X3] :
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X3) = c_HOL_Oone__class_Oone(X3) ),
file('<stdin>',cls_of__nat__1_0) ).
fof(c_0_489_490,axiom,
! [X3] :
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_of__nat__0_0) ).
fof(c_0_490_491,axiom,
! [X3] :
( ~ class_Ring__and__Field_Ozero__neq__one(X3)
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Oone__class_Oone(X3) ),
file('<stdin>',cls_zero__neq__one_0) ).
fof(c_0_491_492,axiom,
! [X3] :
( ~ class_Ring__and__Field_Ozero__neq__one(X3)
| c_HOL_Oone__class_Oone(X3) != c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_one__neq__zero_0) ).
fof(c_0_492_493,axiom,
! [X4] :
( class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X4))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__comm__monoid__add) ).
fof(c_0_493_494,axiom,
! [X4] :
( class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ocomm__ring__1(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1) ).
fof(c_0_494_495,axiom,
! [X4] :
( class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ocomm__ring(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring) ).
fof(c_0_495_496,axiom,
! [X4] :
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(c_0_496_497,axiom,
! [X4] :
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(c_0_497_498,axiom,
! [X4] :
( class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(c_0_498_499,axiom,
! [X4] :
( class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__cancel__semiring) ).
fof(c_0_499_500,axiom,
! [X4] :
( class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oidom(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1__no__zero__divisors) ).
fof(c_0_500_501,axiom,
! [X4] :
( class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring__strict) ).
fof(c_0_501_502,axiom,
! [X4] :
( class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(c_0_502_503,axiom,
! [X4] :
( class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__comm__monoid__add) ).
fof(c_0_503_504,axiom,
! [X4] :
( class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oidom(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors) ).
fof(c_0_504_505,axiom,
! [X4] :
( class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X4))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(c_0_505_506,axiom,
! [X4] :
( class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict) ).
fof(c_0_506_507,axiom,
! [X4] :
( class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add) ).
fof(c_0_507_508,axiom,
! [X4] :
( class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Oordered__ab__group__add) ).
fof(c_0_508_509,axiom,
! [X4] :
( class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X4))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add) ).
fof(c_0_509_510,axiom,
! [X4] :
( class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__semiring) ).
fof(c_0_510_511,axiom,
! [X4] :
( class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring) ).
fof(c_0_511_512,axiom,
! [X4] :
( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oidom(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors) ).
fof(c_0_512_513,axiom,
! [X4] :
( class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semidom) ).
fof(c_0_513_514,axiom,
! [X4] :
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1) ).
fof(c_0_514_515,axiom,
! [X4] :
( class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0) ).
fof(c_0_515_516,axiom,
! [X4] :
( class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult) ).
fof(c_0_516_517,axiom,
! [X4] :
( class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult) ).
fof(c_0_517_518,axiom,
! [X4] :
( class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add) ).
fof(c_0_518_519,axiom,
! [X4] :
( class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring) ).
fof(c_0_519_520,axiom,
! [X4] :
( class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring) ).
fof(c_0_520_521,axiom,
! [X4] :
( class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__add) ).
fof(c_0_521_522,axiom,
! [X4] :
( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one) ).
fof(c_0_522_523,axiom,
! [X4] :
( class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__idom) ).
fof(c_0_523_524,axiom,
! [X4] :
( class_OrderedGroup_Osemigroup__add(tc_Polynomial_Opoly(X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Osemigroup__add) ).
fof(c_0_524_525,axiom,
! [X4] :
( class_Ring__and__Field_Osemiring__1(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring__1) ).
fof(c_0_525_526,axiom,
! [X4] :
( class_Ring__and__Field_Osemiring__0(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring__0) ).
fof(c_0_526_527,axiom,
! [X4] :
( class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono1) ).
fof(c_0_527_528,axiom,
! [X4] :
( class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X4))
| ~ class_OrderedGroup_Oab__group__add(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Oab__group__add) ).
fof(c_0_528_529,axiom,
! [X4] :
( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero) ).
fof(c_0_529_530,axiom,
! [X4] :
( class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono) ).
fof(c_0_530_531,axiom,
! [X4] :
( class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__mult) ).
fof(c_0_531_532,axiom,
! [X4] :
( class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring) ).
fof(c_0_532_533,axiom,
! [X4] :
( class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add) ).
fof(c_0_533_534,axiom,
! [X4] :
( class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X4))
| ~ class_OrderedGroup_Oab__group__add(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add) ).
fof(c_0_534_535,axiom,
! [X4] :
( class_Ring__and__Field_Oring__1(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ocomm__ring__1(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1) ).
fof(c_0_535_536,axiom,
! [X4] :
( class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ocomm__ring(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Oring) ).
fof(c_0_536_537,axiom,
! [X4] :
( class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oidom(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Oidom) ).
fof(c_0_537_538,axiom,
! [X4] :
( class_Nat_Osemiring__char__0(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__Nat_Osemiring__char__0) ).
fof(c_0_538_539,axiom,
! [X4] :
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__Orderings_Opreorder) ).
fof(c_0_539_540,axiom,
! [X4] :
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__Orderings_Olinorder) ).
fof(c_0_540_541,axiom,
! [X4] :
( class_Orderings_Oorder(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__Orderings_Oorder) ).
fof(c_0_541_542,axiom,
! [X4] :
( class_Int_Oring__char__0(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__Int_Oring__char__0) ).
fof(c_0_542_543,axiom,
! [X4] :
( class_Int_Onumber__ring(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ocomm__ring__1(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__Int_Onumber__ring) ).
fof(c_0_543_544,axiom,
! [X4] :
( class_Power_Opower(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__Power_Opower) ).
fof(c_0_544_545,axiom,
! [X4] :
( class_HOL_Ozero(tc_Polynomial_Opoly(X4))
| ~ class_HOL_Ozero(X4) ),
file('<stdin>',clsarity_Polynomial__Opoly__HOL_Ozero) ).
fof(c_0_545_546,axiom,
! [X28,X29] :
( c_Suc(X29) != c_Suc(X28)
| X29 = X28 ),
file('<stdin>',cls_nat_Oinject_0) ).
fof(c_0_546_547,axiom,
! [X9,X7] :
( c_Suc(X7) != c_Suc(X9)
| X7 = X9 ),
file('<stdin>',cls_Suc__inject_0) ).
fof(c_0_547_548,plain,
! [X13,X6,X10,X12,X20,X3] :
( ~ class_HOL_Ozero(X20)
| c_Polynomial_Opoly__rec(X13,X10,c_Polynomial_OpCons(X12,X6,X20),X3,X20) = hAPP(hAPP(hAPP(X10,X12),X6),c_HOL_OIf(c_fequal(X6,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X20)),tc_Polynomial_Opoly(X20)),X13,c_Polynomial_Opoly__rec(X13,X10,X6,X3,X20),X3)) ),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_548_549,plain,
! [X13,X6,X10,X12,X20,X3] :
( ~ class_HOL_Ozero(X20)
| hAPP(hAPP(hAPP(X10,c_HOL_Ozero__class_Ozero(X20)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X20))),X13) != X13
| c_Polynomial_Opoly__rec(X13,X10,c_Polynomial_OpCons(X12,X6,X20),X3,X20) = hAPP(hAPP(hAPP(X10,X12),X6),c_Polynomial_Opoly__rec(X13,X10,X6,X3,X20)) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_549_550,plain,
! [X15,X9,X7,X3] :
( ~ class_OrderedGroup_Osemigroup__add(X3)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),X9),X15,X3,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X9,X15,X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_550_551,plain,
! [X15,X7,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3),X15,X3,X3)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X7,X15,X3,X3) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_551_552,plain,
! [X14,X11,X12,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X3),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11)),X14) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X3),X3),X12),X14)),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X3),X3),X11),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_552_553,plain,
! [X14,X22,X12,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X3),X3),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X14)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X3),X3),X12),X22)),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X3),X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_553_554,plain,
! [X13,X6] :
( ~ class_Ring__and__Field_Oidom(t_a)
| hAPP(c_Polynomial_Opoly(X6,t_a),X13) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(t_a),hAPP(c_Polynomial_Opoly(X6,t_a),c_HOL_Ozero__class_Ozero(t_a))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X13),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1(X6))),hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__2(X6),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__3(X6),t_a),t_a),X13)))
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X6,t_a),t_a,t_a) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_554_555,plain,
! [X14,X12,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X3),X3),X12),X14)),X12) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X3),X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_555_556,plain,
! [X23,X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Osemiring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X23)),X16)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11)),X23)),X16) ),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_556_557,plain,
! [X14,X12,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X3),X3),X12),c_Suc(X14)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X3),X3),X12),X14)),X12) ),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_557_558,plain,
! [X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3))),X3) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_558_559,plain,
! [X13,X10,X20,X3] :
( ~ class_HOL_Ozero(X20)
| hAPP(hAPP(hAPP(X10,c_HOL_Ozero__class_Ozero(X20)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X20))),X13) != X13
| c_Polynomial_Opoly__rec(X13,X10,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X20)),X3,X20) = X13 ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_559_560,plain,
! [X9,X7,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| X9 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X7)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X9)),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_560_561,plain,
! [X9,X7,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| X7 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X7)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X9)),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_561_562,plain,
! [X9,X7,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X7)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X9)),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_562_563,plain,
! [X6,X21,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(X12,X6,X3),X21,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X21,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X6,X21,X3),X3)),c_Polynomial_OpCons(X12,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X6,X21,X3),X3)) ),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_563_564,plain,
! [X18,X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X18)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X18)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X16))
| X16 = X18
| X12 = X11 ),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_564_565,plain,
! [X13,X9,X7,X24,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X24),X9)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X13)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X24),X13)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X9))
| X9 = X13
| X24 = X7 ),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_565_566,plain,
! [X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3))),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_566_567,plain,
! [X14,X12,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X3),X3),X12),c_Suc(X14)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X3),X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_567_568,plain,
! [X30,X31,X32,X33,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X33),X32)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X31),X30)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X31),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X33),X32)),X30)) ),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
fof(c_0_568_569,plain,
! [X9,X7,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X7)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X9)),X3)
| X9 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_569_570,plain,
! [X9,X7,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X7)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X9)),X3)
| X7 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_570_571,plain,
! [X9,X7,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X7)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X9)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_23]) ).
fof(c_0_571_572,plain,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oring__1(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ouminus__class_Ouminus(X12,X3)),X14) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X3),X3)),X14)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_572_573,plain,
! [X13,X9,X7,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X9)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X13)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X13)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_573_574,plain,
! [X7,X18,X16,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X16)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X18)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X18)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X16)) ),
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_574_575,plain,
! [X30,X31,X32,X33,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X33),X32)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X31),X30)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X33),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X32),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X31),X30))) ),
inference(fof_simplification,[status(thm)],[c_0_27]) ).
fof(c_0_575_576,plain,
! [X30,X31,X32,X33,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X33),X32)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X31),X30)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X33),X31)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X32),X30)) ),
inference(fof_simplification,[status(thm)],[c_0_28]) ).
fof(c_0_576_577,plain,
! [X18,X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X18)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X18)) ),
inference(fof_simplification,[status(thm)],[c_0_29]) ).
fof(c_0_577_578,plain,
! [X8,X6,X11,X12,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X3)),c_Polynomial_OpCons(X12,X6,X3)),c_Polynomial_OpCons(X11,X8,X3)) = c_Polynomial_OpCons(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X3)),X6),X8),X3) ),
inference(fof_simplification,[status(thm)],[c_0_30]) ).
fof(c_0_578_579,plain,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14),X3)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_579_580,plain,
! [X6,X16,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X16,X6,X3)),c_Polynomial_OpCons(X12,X6,X3)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| X6 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_580_581,plain,
! [X8,X6,X14,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(c_Polynomial_Ocoeff(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X3)),X6),X8),X3),X14) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(c_Polynomial_Ocoeff(X6,X3),X14)),hAPP(c_Polynomial_Ocoeff(X8,X3),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_581_582,plain,
! [X7,X8,X6,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| hAPP(c_Polynomial_Opoly(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X3)),X6),X8),X3),X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(c_Polynomial_Opoly(X6,X3),X7)),hAPP(c_Polynomial_Opoly(X8,X3),X7)) ),
inference(fof_simplification,[status(thm)],[c_0_34]) ).
fof(c_0_582_583,plain,
! [X18,X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Opordered__semiring(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X18),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_lessequals(X16,X18,X3)
| ~ c_lessequals(X12,X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_583_584,plain,
! [X18,X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Opordered__semiring(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X18),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3)
| ~ c_lessequals(X16,X18,X3)
| ~ c_lessequals(X12,X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_36]) ).
fof(c_0_584_585,plain,
! [X18,X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X18),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3)
| ~ c_HOL_Oord__class_Oless(X16,X18,X3)
| ~ c_HOL_Oord__class_Oless(X12,X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_37]) ).
fof(c_0_585_586,plain,
! [X18,X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X18),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_HOL_Oord__class_Oless(X16,X18,X3)
| ~ c_HOL_Oord__class_Oless(X12,X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_38]) ).
fof(c_0_586_587,plain,
! [X18,X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X18),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X12,X3)
| ~ c_HOL_Oord__class_Oless(X16,X18,X3)
| ~ c_lessequals(X12,X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_39]) ).
fof(c_0_587_588,plain,
! [X18,X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X18),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3)
| ~ c_lessequals(X16,X18,X3)
| ~ c_HOL_Oord__class_Oless(X12,X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_588_589,plain,
! [X6] :
( ~ class_Ring__and__Field_Oidom(t_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__3(X6),t_a)),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1(X6))),c_HOL_Oone__class_Oone(tc_nat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X6,t_a)
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X6,t_a),t_a,t_a) ),
inference(fof_simplification,[status(thm)],[c_0_41]) ).
fof(c_0_589_590,plain,
! [X14,X11,X12,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11)),X14) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X11),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_42]) ).
fof(c_0_590_591,plain,
! [X9,X7,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X9)),X8) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X7),X8)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_43]) ).
fof(c_0_591_592,plain,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11)),X16) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X16)) ),
inference(fof_simplification,[status(thm)],[c_0_44]) ).
fof(c_0_592_593,plain,
! [X36,X9,X7,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),X9)),X36) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X36)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X36)) ),
inference(fof_simplification,[status(thm)],[c_0_45]) ).
fof(c_0_593_594,plain,
! [X11,X35,X12,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X35)),X11) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X35),X11)) ),
inference(fof_simplification,[status(thm)],[c_0_46]) ).
fof(c_0_594_595,plain,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11)),X16) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X16)) ),
inference(fof_simplification,[status(thm)],[c_0_47]) ).
fof(c_0_595_596,plain,
! [X22,X11,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X22)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X22)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11)),X22) ),
inference(fof_simplification,[status(thm)],[c_0_48]) ).
fof(c_0_596_597,plain,
! [X8,X6,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(X12,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X3)),X6),X8),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X12,X6,X3)),c_Polynomial_Osmult(X12,X8,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_49]) ).
fof(c_0_597_598,plain,
! [X14,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(X12,X11,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),c_Suc(X14)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X11),c_Suc(X14)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_50]) ).
fof(c_0_598_599,plain,
! [X9,X7,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X7)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X9)) != c_HOL_Ozero__class_Ozero(X3)
| X7 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_51]) ).
fof(c_0_599_600,plain,
! [X9,X7,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X7)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X9)) != c_HOL_Ozero__class_Ozero(X3)
| X9 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_52]) ).
fof(c_0_600_601,plain,
! [X7,X6,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X12,X6,X3),X3),X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),hAPP(c_Polynomial_Opoly(X6,X3),X7))) ),
inference(fof_simplification,[status(thm)],[c_0_53]) ).
fof(c_0_601_602,plain,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14)),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_54]) ).
fof(c_0_602_603,plain,
! [X14,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X12,X11,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X11),X14),X3) ),
inference(fof_simplification,[status(thm)],[c_0_55]) ).
fof(c_0_603_604,plain,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(X12,X11,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X16),X3) ),
inference(fof_simplification,[status(thm)],[c_0_56]) ).
fof(c_0_604_605,plain,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(X12,X11,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3) ),
inference(fof_simplification,[status(thm)],[c_0_57]) ).
fof(c_0_605_606,plain,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semiring(X3)
| c_HOL_Oord__class_Oless(X12,X11,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X16),X3) ),
inference(fof_simplification,[status(thm)],[c_0_58]) ).
fof(c_0_606_607,plain,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semiring(X3)
| c_HOL_Oord__class_Oless(X12,X11,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3) ),
inference(fof_simplification,[status(thm)],[c_0_59]) ).
fof(c_0_607_608,plain,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_lessequals(X12,X11,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X16),X3) ),
inference(fof_simplification,[status(thm)],[c_0_60]) ).
fof(c_0_608_609,plain,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_lessequals(X12,X11,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3) ),
inference(fof_simplification,[status(thm)],[c_0_61]) ).
fof(c_0_609_610,plain,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X12,X11,X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_62]) ).
fof(c_0_610_611,plain,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X11,X12,X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3)
| ~ c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_63]) ).
fof(c_0_611_612,plain,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X12,X11,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_64]) ).
fof(c_0_612_613,plain,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X11,X12,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3)
| ~ c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_65]) ).
fof(c_0_613_614,plain,
! [X14,X11,X12,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X3)),c_Polynomial_Omonom(X12,X14,X3)),c_Polynomial_Omonom(X11,X14,X3)) = c_Polynomial_Omonom(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11),X14,X3) ),
inference(fof_simplification,[status(thm)],[c_0_66]) ).
fof(c_0_614_615,plain,
! [X6,X11,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11),X6,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X12,X6,X3)),c_Polynomial_Osmult(X11,X6,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_67]) ).
fof(c_0_615_616,plain,
! [X22,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X22)),X22) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),c_HOL_Oone__class_Oone(X3))),X22) ),
inference(fof_simplification,[status(thm)],[c_0_68]) ).
fof(c_0_616_617,plain,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3) ),
inference(fof_simplification,[status(thm)],[c_0_69]) ).
fof(c_0_617_618,plain,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X16),X3) ),
inference(fof_simplification,[status(thm)],[c_0_70]) ).
fof(c_0_618_619,plain,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X11,X12,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3) ),
inference(fof_simplification,[status(thm)],[c_0_71]) ).
fof(c_0_619_620,plain,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X12,X11,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3) ),
inference(fof_simplification,[status(thm)],[c_0_72]) ).
fof(c_0_620_621,plain,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X11,X12,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X16),X3) ),
inference(fof_simplification,[status(thm)],[c_0_73]) ).
fof(c_0_621_622,plain,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X12,X11,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X16),X3) ),
inference(fof_simplification,[status(thm)],[c_0_74]) ).
fof(c_0_622_623,plain,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X11,X12,X3)
| c_HOL_Oord__class_Oless(X12,X11,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3) ),
inference(fof_simplification,[status(thm)],[c_0_75]) ).
fof(c_0_623_624,plain,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X11,X12,X3)
| c_HOL_Oord__class_Oless(X12,X11,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X16),X3) ),
inference(fof_simplification,[status(thm)],[c_0_76]) ).
fof(c_0_624_625,plain,
! [X31,X32,X33,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X33),X32)),X31) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X33),X31)),X32) ),
inference(fof_simplification,[status(thm)],[c_0_77]) ).
fof(c_0_625_626,plain,
! [X9,X34,X7,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X34),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),X9)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X34),X7)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X34),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_78]) ).
fof(c_0_626_627,plain,
! [X37,X11,X12,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X37)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X37)) ),
inference(fof_simplification,[status(thm)],[c_0_79]) ).
fof(c_0_627_628,plain,
! [X13,X9,X7,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X13)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X9)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_80]) ).
fof(c_0_628_629,plain,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11)),X16) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16)),X11) ),
inference(fof_simplification,[status(thm)],[c_0_81]) ).
fof(c_0_629_630,plain,
! [X7,X8,X6,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X7),X6)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X7),X8)) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_82]) ).
fof(c_0_630_631,plain,
! [X14,X22,X12,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X14)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X22)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_83]) ).
fof(c_0_631_632,plain,
! [X7,X19,X18,X16,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X16)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X18))
| X16 = X18
| X19 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_84]) ).
fof(c_0_632_633,plain,
! [X18,X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X12,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X18),X3)
| ~ c_lessequals(X16,X18,X3)
| ~ c_lessequals(X12,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X16),X3) ),
inference(fof_simplification,[status(thm)],[c_0_85]) ).
fof(c_0_633_634,plain,
! [X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3))) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_86]) ).
fof(c_0_634_635,plain,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14)),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_87]) ).
fof(c_0_635_636,plain,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_lessequals(X12,X11,X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X16),X3) ),
inference(fof_simplification,[status(thm)],[c_0_88]) ).
fof(c_0_636_637,plain,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_lessequals(X12,X11,X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X11),X3) ),
inference(fof_simplification,[status(thm)],[c_0_89]) ).
fof(c_0_637_638,plain,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(X12,X11,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X11),X3) ),
inference(fof_simplification,[status(thm)],[c_0_90]) ).
fof(c_0_638_639,plain,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(X12,X11,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X16),X3) ),
inference(fof_simplification,[status(thm)],[c_0_91]) ).
fof(c_0_639_640,plain,
! [X9,X7,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X7),X7,X3)
| ~ c_lessequals(X9,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_92]) ).
fof(c_0_640_641,plain,
! [X9,X7,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X9),X7,X3)
| ~ c_lessequals(X9,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_93]) ).
fof(c_0_641_642,plain,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X16),X3)
| ~ c_lessequals(X16,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X11,X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_94]) ).
fof(c_0_642_643,plain,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3)
| ~ c_lessequals(X16,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X11,X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_95]) ).
fof(c_0_643_644,plain,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Omult__mono(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X16),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_lessequals(X12,X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_96]) ).
fof(c_0_644_645,plain,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Omult__mono(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_lessequals(X12,X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_97]) ).
fof(c_0_645_646,plain,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Omult__mono1(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_lessequals(X12,X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_98]) ).
fof(c_0_646_647,plain,
! [X14,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X11),X14),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3)
| ~ c_lessequals(X12,X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_99]) ).
fof(c_0_647_648,plain,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3)
| ~ c_lessequals(X12,X11,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_100]) ).
fof(c_0_648_649,plain,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3)
| ~ c_lessequals(X11,X12,X3)
| ~ c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_101]) ).
fof(c_0_649_650,plain,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_HOL_Oord__class_Oless(X12,X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_102]) ).
fof(c_0_650_651,plain,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X16),X3)
| ~ c_HOL_Oord__class_Oless(X11,X12,X3)
| ~ c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_103]) ).
fof(c_0_651_652,plain,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X16),X3)
| ~ c_HOL_Oord__class_Oless(X12,X11,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_104]) ).
fof(c_0_652_653,plain,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X16),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_HOL_Oord__class_Oless(X12,X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_105]) ).
fof(c_0_653_654,plain,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X16),X3)
| ~ c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X11,X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_106]) ).
fof(c_0_654_655,plain,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3)
| ~ c_HOL_Oord__class_Oless(X11,X12,X3)
| ~ c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_107]) ).
fof(c_0_655_656,plain,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3)
| ~ c_HOL_Oord__class_Oless(X12,X11,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_108]) ).
fof(c_0_656_657,plain,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X16,X3)
| ~ c_HOL_Oord__class_Oless(X12,X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_109]) ).
fof(c_0_657_658,plain,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3)
| ~ c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X11,X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_110]) ).
fof(c_0_658_659,plain,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3)
| ~ c_HOL_Oord__class_Oless(X12,X11,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_111]) ).
fof(c_0_659_660,plain,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X16),X11),X3)
| ~ c_HOL_Oord__class_Oless(X11,X12,X3)
| ~ c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_112]) ).
fof(c_0_660_661,plain,
( ~ class_HOL_Ozero(t_a)
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_p,t_a) = c_HOL_OIf(c_fequal(v_p,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),tc_Polynomial_Opoly(t_a)),c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_Polynomial_Odegree(v_p,t_a)),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_113]) ).
fof(c_0_661_662,plain,
! [X22,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X22),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X22)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),c_HOL_Oone__class_Oone(X3))),X22) ),
inference(fof_simplification,[status(thm)],[c_0_114]) ).
fof(c_0_662_663,plain,
! [X18,X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X18),X3)
| ~ c_lessequals(X16,X18,X3)
| ~ c_lessequals(X12,X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_115]) ).
fof(c_0_663_664,plain,
! [X18,X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X18),X3)
| ~ c_HOL_Oord__class_Oless(X16,X18,X3)
| ~ c_HOL_Oord__class_Oless(X12,X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_116]) ).
fof(c_0_664_665,plain,
! [X18,X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X18),X3)
| ~ c_lessequals(X16,X18,X3)
| ~ c_HOL_Oord__class_Oless(X12,X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_117]) ).
fof(c_0_665_666,plain,
! [X18,X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X18),X3)
| ~ c_HOL_Oord__class_Oless(X16,X18,X3)
| ~ c_lessequals(X12,X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_118]) ).
fof(c_0_666_667,plain,
! [X6,X11,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(X12,c_Polynomial_OpCons(X11,X6,X3),X3) = c_Polynomial_OpCons(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),c_Polynomial_Osmult(X12,X6,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_119]) ).
fof(c_0_667_668,plain,
! [X19,X8,X6,X16,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X3)),X6),c_Polynomial_Osmult(X16,X8,X3)) != c_Polynomial_OpCons(X19,X8,X3)
| X19 = hAPP(c_Polynomial_Opoly(X6,X3),X16) ),
inference(fof_simplification,[status(thm)],[c_0_120]) ).
fof(c_0_668_669,plain,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X12,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X12),X3) ),
inference(fof_simplification,[status(thm)],[c_0_121]) ).
fof(c_0_669_670,plain,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X12,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),X3) ),
inference(fof_simplification,[status(thm)],[c_0_122]) ).
fof(c_0_670_671,plain,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11)),X16) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X16)) ),
inference(fof_simplification,[status(thm)],[c_0_123]) ).
fof(c_0_671_672,plain,
! [X31,X32,X33,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X33),X32)),X31) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X33),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X32),X31)) ),
inference(fof_simplification,[status(thm)],[c_0_124]) ).
fof(c_0_672_673,plain,
! [X30,X31,X33,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X33),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X31),X30)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X33),X31)),X30) ),
inference(fof_simplification,[status(thm)],[c_0_125]) ).
fof(c_0_673_674,plain,
! [X13,X9,X7,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X13)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X9)),X13) ),
inference(fof_simplification,[status(thm)],[c_0_126]) ).
fof(c_0_674_675,plain,
! [X14,X12,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14)),X12) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_127]) ).
fof(c_0_675_676,plain,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11)),X16) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X16)) ),
inference(fof_simplification,[status(thm)],[c_0_128]) ).
fof(c_0_676_677,plain,
! [X18,X16,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X18)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16)),X18) ),
inference(fof_simplification,[status(thm)],[c_0_129]) ).
fof(c_0_677_678,plain,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Oab__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11)),X16) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X16)) ),
inference(fof_simplification,[status(thm)],[c_0_130]) ).
fof(c_0_678_679,plain,
! [X13,X9,X7,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X13)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),X9)),X13) ),
inference(fof_simplification,[status(thm)],[c_0_131]) ).
fof(c_0_679_680,plain,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11)),X16) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X16)) ),
inference(fof_simplification,[status(thm)],[c_0_132]) ).
fof(c_0_680_681,plain,
! [X7,X14,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(c_Polynomial_Opoly(c_Polynomial_Omonom(X12,X14,X3),X3),X7) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X7),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_133]) ).
fof(c_0_681_682,plain,
! [X7,X6,X21,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| hAPP(c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X6,X21,X3),X3),X7) = hAPP(c_Polynomial_Opoly(X6,X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X7)) ),
inference(fof_simplification,[status(thm)],[c_0_134]) ).
fof(c_0_682_683,plain,
! [X6,X14,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| hAPP(c_Polynomial_Ocoeff(c_Polynomial_Osmult(X12,X6,X3),X3),X14) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),hAPP(c_Polynomial_Ocoeff(X6,X3),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_135]) ).
fof(c_0_683_684,plain,
! [X7,X6,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| hAPP(c_Polynomial_Opoly(c_Polynomial_Osmult(X12,X6,X3),X3),X7) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),hAPP(c_Polynomial_Opoly(X6,X3),X7)) ),
inference(fof_simplification,[status(thm)],[c_0_136]) ).
fof(c_0_684_685,plain,
! [X22,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X22),X22) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oone__class_Oone(X3)),c_HOL_Oone__class_Oone(X3))),X22) ),
inference(fof_simplification,[status(thm)],[c_0_137]) ).
fof(c_0_685_686,plain,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X12,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),X3) ),
inference(fof_simplification,[status(thm)],[c_0_138]) ).
fof(c_0_686_687,plain,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),X3) ),
inference(fof_simplification,[status(thm)],[c_0_139]) ).
fof(c_0_687_688,plain,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X12,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),X3) ),
inference(fof_simplification,[status(thm)],[c_0_140]) ).
fof(c_0_688_689,plain,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),X3) ),
inference(fof_simplification,[status(thm)],[c_0_141]) ).
fof(c_0_689_690,plain,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| c_lessequals(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_142]) ).
fof(c_0_690_691,plain,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X12,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_143]) ).
fof(c_0_691_692,plain,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_144]) ).
fof(c_0_692_693,plain,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X12,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_145]) ).
fof(c_0_693_694,plain,
! [X13,X9,X7,X17,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X13)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X17)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),X13) = X17 ),
inference(fof_simplification,[status(thm)],[c_0_146]) ).
fof(c_0_694_695,plain,
! [X14,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),c_Suc(X14)) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X11),c_Suc(X14))
| X12 = X11
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_147]) ).
fof(c_0_695_696,plain,
! [X7,X8,X6,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| hAPP(c_Polynomial_Opoly(c_Polynomial_Opcompose(X6,X8,X3),X3),X7) = hAPP(c_Polynomial_Opoly(X6,X3),hAPP(c_Polynomial_Opoly(X8,X3),X7)) ),
inference(fof_simplification,[status(thm)],[c_0_148]) ).
fof(c_0_696_697,plain,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),c_Suc(X14)),c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_149]) ).
fof(c_0_697_698,plain,
! [X14,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| X14 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3)),X14),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_150]) ).
fof(c_0_698_699,plain,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),X3)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X12,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_151]) ).
fof(c_0_699_700,plain,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),X3)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X12,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_152]) ).
fof(c_0_700_701,plain,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_153]) ).
fof(c_0_701_702,plain,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_154]) ).
fof(c_0_702_703,plain,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),X3)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X12,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_155]) ).
fof(c_0_703_704,plain,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_156]) ).
fof(c_0_704_705,plain,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_157]) ).
fof(c_0_705_706,plain,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_lessequals(X12,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_158]) ).
fof(c_0_706_707,plain,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_159]) ).
fof(c_0_707_708,plain,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_lessequals(X12,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_160]) ).
fof(c_0_708_709,plain,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_161]) ).
fof(c_0_709_710,plain,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_lessequals(X12,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_162]) ).
fof(c_0_710_711,plain,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X12),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_163]) ).
fof(c_0_711_712,plain,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_164]) ).
fof(c_0_712_713,plain,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_165]) ).
fof(c_0_713_714,plain,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X12),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_166]) ).
fof(c_0_714_715,plain,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_167]) ).
fof(c_0_715_716,plain,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_168]) ).
fof(c_0_716_717,plain,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X12,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_169]) ).
fof(c_0_717_718,plain,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_170]) ).
fof(c_0_718_719,plain,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_171]) ).
fof(c_0_719_720,plain,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),X3)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_172]) ).
fof(c_0_720_721,plain,
! [X14,X22,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X22),X14),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X14,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X22,X3) ),
inference(fof_simplification,[status(thm)],[c_0_173]) ).
fof(c_0_721_722,plain,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_174]) ).
fof(c_0_722_723,plain,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_175]) ).
fof(c_0_723_724,plain,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_176]) ).
fof(c_0_724_725,plain,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X12,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_177]) ).
fof(c_0_725_726,plain,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oord__class_Oless(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16),X3)
| ~ c_lessequals(X11,X16,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_178]) ).
fof(c_0_726_727,plain,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oord__class_Oless(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16),X3)
| ~ c_HOL_Oord__class_Oless(X11,X16,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_179]) ).
fof(c_0_727_728,plain,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_lessequals(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16),X3)
| ~ c_lessequals(X11,X16,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_180]) ).
fof(c_0_728_729,plain,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_lessequals(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16),X3)
| ~ c_lessequals(X11,X12,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_181]) ).
fof(c_0_729_730,plain,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X16),X3)
| ~ c_lessequals(X12,X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_182]) ).
fof(c_0_730_731,plain,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X11),X3)
| ~ c_lessequals(X12,X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_183]) ).
fof(c_0_731_732,plain,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X16),X3)
| ~ c_lessequals(X12,X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_184]) ).
fof(c_0_732_733,plain,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X11),X3)
| ~ c_lessequals(X12,X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_185]) ).
fof(c_0_733_734,plain,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X11),X3)
| ~ c_HOL_Oord__class_Oless(X12,X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_186]) ).
fof(c_0_734_735,plain,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X11),X3)
| ~ c_HOL_Oord__class_Oless(X12,X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_187]) ).
fof(c_0_735_736,plain,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X16),X3)
| ~ c_HOL_Oord__class_Oless(X12,X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_188]) ).
fof(c_0_736_737,plain,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X16),X3)
| ~ c_HOL_Oord__class_Oless(X12,X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_189]) ).
fof(c_0_737_738,plain,
! [X16,X11,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16),X3)
| ~ c_HOL_Oord__class_Oless(X11,X16,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_190]) ).
fof(c_0_738_739,plain,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(X12,c_HOL_Ouminus__class_Ouminus(X11,X3),X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_191]) ).
fof(c_0_739_740,plain,
! [X7,X14,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| X7 = c_HOL_Ozero__class_Ozero(X3)
| c_lessequals(X7,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X7),X14),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_192]) ).
fof(c_0_740_741,plain,
! [X14,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X3),X3),c_HOL_Ozero__class_Ozero(X3)),X14) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_193]) ).
fof(c_0_741_742,plain,
! [X14,X11,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(X12,c_Polynomial_Omonom(X11,X14,X3),X3) = c_Polynomial_Omonom(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),X14,X3) ),
inference(fof_simplification,[status(thm)],[c_0_194]) ).
fof(c_0_742_743,plain,
! [X6,X11,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(X12,c_Polynomial_Osmult(X11,X6,X3),X3) = c_Polynomial_Osmult(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_195]) ).
fof(c_0_743_744,plain,
! [X7,X14,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X7),X14),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_196]) ).
fof(c_0_744_745,plain,
! [X12,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X12),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_197]) ).
fof(c_0_745_746,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X12),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_198]) ).
fof(c_0_746_747,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X12,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X12),X3) ),
inference(fof_simplification,[status(thm)],[c_0_199]) ).
fof(c_0_747_748,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X12),X3) ),
inference(fof_simplification,[status(thm)],[c_0_200]) ).
fof(c_0_748_749,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(X12,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X12),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_201]) ).
fof(c_0_749_750,plain,
! [X7,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X7),X8)),X7) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X7),c_Suc(X8)) ),
inference(fof_simplification,[status(thm)],[c_0_202]) ).
fof(c_0_750_751,plain,
! [X14,X12,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),c_Suc(X14)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14)),X12) ),
inference(fof_simplification,[status(thm)],[c_0_203]) ).
fof(c_0_751_752,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X3),X3),X12),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_204]) ).
fof(c_0_752_753,plain,
! [X30,X31,X33,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X33),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X31),X30)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X31),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X33),X30)) ),
inference(fof_simplification,[status(thm)],[c_0_205]) ).
fof(c_0_753_754,plain,
! [X18,X16,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X18)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X18)) ),
inference(fof_simplification,[status(thm)],[c_0_206]) ).
fof(c_0_754_755,plain,
! [X13,X9,X7,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X13)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_207]) ).
fof(c_0_755_756,plain,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X16)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16)) ),
inference(fof_simplification,[status(thm)],[c_0_208]) ).
fof(c_0_756_757,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X3),X3),X12),c_HOL_Oone__class_Oone(tc_nat)) = X12 ),
inference(fof_simplification,[status(thm)],[c_0_209]) ).
fof(c_0_757_758,plain,
! [X6,X14,X12,X3] :
( ~ class_HOL_Ozero(X3)
| hAPP(c_Polynomial_Ocoeff(c_Polynomial_OpCons(X12,X6,X3),X3),c_Suc(X14)) = hAPP(c_Polynomial_Ocoeff(X6,X3),X14) ),
inference(fof_simplification,[status(thm)],[c_0_210]) ).
fof(c_0_758_759,plain,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X12,c_HOL_Ouminus__class_Ouminus(X11,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_211]) ).
fof(c_0_759_760,plain,
! [X9,X7,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),X9) != c_HOL_Ozero__class_Ozero(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X7,X3)
| X7 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_212]) ).
fof(c_0_760_761,plain,
! [X9,X7,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),X9) != c_HOL_Ozero__class_Ozero(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X7,X3)
| X9 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_213]) ).
fof(c_0_761_762,plain,
! [X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3)) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_214]) ).
fof(c_0_762_763,plain,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),c_Suc(X14)),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_215]) ).
fof(c_0_763_764,plain,
! [X21,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(X12,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3),X21,X3) = c_Polynomial_OpCons(X12,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_216]) ).
fof(c_0_764_765,plain,
! [X7,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X7),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_217]) ).
fof(c_0_765_766,plain,
! [X14,X22,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X22) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X12,X3)
| X22 = X14 ),
inference(fof_simplification,[status(thm)],[c_0_218]) ).
fof(c_0_766_767,plain,
! [X14,X22,X12,X3] :
( ~ class_HOL_Ozero(X3)
| hAPP(c_Polynomial_Ocoeff(c_Polynomial_Omonom(X12,X22,X3),X3),X14) = c_HOL_Ozero__class_Ozero(X3)
| X22 = X14 ),
inference(fof_simplification,[status(thm)],[c_0_219]) ).
fof(c_0_767_768,plain,
! [X13,X9,X7,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X13)) != X9
| X7 = c_HOL_Ouminus__class_Ouminus(X13,X3) ),
inference(fof_simplification,[status(thm)],[c_0_220]) ).
fof(c_0_768_769,plain,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ouminus__class_Ouminus(X12,X3)),X11)) = X11 ),
inference(fof_simplification,[status(thm)],[c_0_221]) ).
fof(c_0_769_770,plain,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_222]) ).
fof(c_0_770_771,plain,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_223]) ).
fof(c_0_771_772,plain,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_HOL_Oone__class_Oone(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14),X3)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X3),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_224]) ).
fof(c_0_772_773,plain,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_225]) ).
fof(c_0_773_774,plain,
! [X12,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X12),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_226]) ).
fof(c_0_774_775,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X12),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_227]) ).
fof(c_0_775_776,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X12),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_228]) ).
fof(c_0_776_777,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X12),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_229]) ).
fof(c_0_777_778,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X12),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X12,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_230]) ).
fof(c_0_778_779,plain,
! [X6,X12,X3] :
( ~ class_HOL_Ozero(X3)
| hAPP(c_Polynomial_Ocoeff(c_Polynomial_OpCons(X12,X6,X3),X3),c_HOL_Ozero__class_Ozero(tc_nat)) = X12 ),
inference(fof_simplification,[status(thm)],[c_0_231]) ).
fof(c_0_779_780,plain,
! [X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X12),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_232]) ).
fof(c_0_780_781,plain,
! [X7,X12,X3] :
( ~ class_HOL_Ozero(X3)
| hAPP(c_Polynomial_Ocoeff(c_Polynomial_Omonom(X12,X7,X3),X3),X7) = X12 ),
inference(fof_simplification,[status(thm)],[c_0_233]) ).
fof(c_0_781_782,plain,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ouminus__class_Ouminus(X11,X3)),c_HOL_Ouminus__class_Ouminus(X12,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_234]) ).
fof(c_0_782_783,plain,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ouminus__class_Ouminus(X12,X3)),c_HOL_Ouminus__class_Ouminus(X11,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_235]) ).
fof(c_0_783_784,plain,
! [X14,X22,X3] :
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X14),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Nat_Osemiring__1__class_Oof__nat(X22,X3)),c_Nat_Osemiring__1__class_Oof__nat(X14,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_236]) ).
fof(c_0_784_785,plain,
! [X14,X12,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Omonom(X12,c_Suc(X14),X3) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X3),c_Polynomial_Omonom(X12,X14,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_237]) ).
fof(c_0_785_786,plain,
! [X13,X9,X7,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X7,X13,X3)
| ~ c_HOL_Oord__class_Oless(X9,X13,X3)
| ~ c_lessequals(X7,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_238]) ).
fof(c_0_786_787,plain,
! [X13,X9,X7,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X7,X13,X3)
| ~ c_lessequals(X9,X13,X3)
| ~ c_HOL_Oord__class_Oless(X7,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_239]) ).
fof(c_0_787_788,plain,
! [X13,X9,X7,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X7,X13,X3)
| ~ c_lessequals(X9,X13,X3)
| ~ c_lessequals(X7,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_240]) ).
fof(c_0_788_789,plain,
! [X13,X9,X7,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X13,X7,X3)
| ~ c_HOL_Oord__class_Oless(X13,X9,X3)
| ~ c_lessequals(X9,X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_241]) ).
fof(c_0_789_790,plain,
! [X13,X9,X7,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X13,X7,X3)
| ~ c_lessequals(X13,X9,X3)
| ~ c_HOL_Oord__class_Oless(X9,X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_242]) ).
fof(c_0_790_791,plain,
! [X13,X9,X7,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X13,X7,X3)
| ~ c_lessequals(X13,X9,X3)
| ~ c_lessequals(X9,X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_243]) ).
fof(c_0_791_792,plain,
! [X13,X9,X7,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X13,X7,X3)
| ~ c_HOL_Oord__class_Oless(X13,X9,X3)
| ~ c_HOL_Oord__class_Oless(X9,X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_244]) ).
fof(c_0_792_793,plain,
! [X13,X9,X7,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X7,X13,X3)
| ~ c_HOL_Oord__class_Oless(X9,X13,X3)
| ~ c_HOL_Oord__class_Oless(X7,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_245]) ).
fof(c_0_793_794,plain,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X12,X11,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X11,X3),c_HOL_Ouminus__class_Ouminus(X12,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_246]) ).
fof(c_0_794_795,plain,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X12,X11,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X11,X3),c_HOL_Ouminus__class_Ouminus(X12,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_247]) ).
fof(c_0_795_796,plain,
! [X11,X12,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ouminus__class_Ouminus(X12,X3)),X11) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),X3) ),
inference(fof_simplification,[status(thm)],[c_0_248]) ).
fof(c_0_796_797,plain,
! [X9,X7,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ouminus__class_Ouminus(X7,X3)),X9) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X9),X3) ),
inference(fof_simplification,[status(thm)],[c_0_249]) ).
fof(c_0_797_798,plain,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ouminus__class_Ouminus(X12,X3)),X11) ),
inference(fof_simplification,[status(thm)],[c_0_250]) ).
fof(c_0_798_799,plain,
! [X25,X26,X27] :
( c_lessequals(X27,X25,tc_RealDef_Oreal)
| ~ c_lessequals(X26,X25,tc_RealDef_Oreal)
| ~ c_lessequals(X27,X26,tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[c_0_251]) ).
fof(c_0_799_800,plain,
! [X7,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X7),X8)) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X7),c_Suc(X8)) ),
inference(fof_simplification,[status(thm)],[c_0_252]) ).
fof(c_0_800_801,plain,
! [X7,X14,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X7),c_Suc(X14)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X7),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_253]) ).
fof(c_0_801_802,plain,
! [X14,X12,X3] :
( ~ class_Power_Opower(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),c_Suc(X14)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_254]) ).
fof(c_0_802_803,plain,
! [X7,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X7),c_Suc(X8)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X7),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_255]) ).
fof(c_0_803_804,plain,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X12,X3),X11,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X11,X3),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_256]) ).
fof(c_0_804_805,plain,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X11,X3),X12,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X12,X3),X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_257]) ).
fof(c_0_805_806,plain,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X12,c_HOL_Ouminus__class_Ouminus(X11,X3),X3)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ouminus__class_Ouminus(X12,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_258]) ).
fof(c_0_806_807,plain,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X11,c_HOL_Ouminus__class_Ouminus(X12,X3),X3)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Ouminus__class_Ouminus(X11,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_259]) ).
fof(c_0_807_808,plain,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X12,X3),X11,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X11,X3),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_260]) ).
fof(c_0_808_809,plain,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X11,X3),X12,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X12,X3),X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_261]) ).
fof(c_0_809_810,plain,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X12,c_HOL_Ouminus__class_Ouminus(X11,X3),X3)
| ~ c_lessequals(X11,c_HOL_Ouminus__class_Ouminus(X12,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_262]) ).
fof(c_0_810_811,plain,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X11,c_HOL_Ouminus__class_Ouminus(X12,X3),X3)
| ~ c_lessequals(X12,c_HOL_Ouminus__class_Ouminus(X11,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_263]) ).
fof(c_0_811_812,plain,
! [X13,X9,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ouminus__class_Ouminus(X13,X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X13)) = X9 ),
inference(fof_simplification,[status(thm)],[c_0_264]) ).
fof(c_0_812_813,plain,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ouminus__class_Ouminus(X12,X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11)) = X11 ),
inference(fof_simplification,[status(thm)],[c_0_265]) ).
fof(c_0_813_814,plain,
! [X9,X7,X3] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X9)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X9) ),
inference(fof_simplification,[status(thm)],[c_0_266]) ).
fof(c_0_814_815,plain,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oone__class_Oone(X3)),c_HOL_Oone__class_Oone(X3)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_267]) ).
fof(c_0_815_816,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X12,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ouminus__class_Ouminus(X12,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_268]) ).
fof(c_0_816_817,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X12,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_269]) ).
fof(c_0_817_818,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ouminus__class_Ouminus(X12,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_270]) ).
fof(c_0_818_819,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X12,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X12,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_271]) ).
fof(c_0_819_820,plain,
! [X9,X7,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X7,X9,X3)
| c_lessequals(X9,X7,X3)
| ~ c_lessequals(X7,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_272]) ).
fof(c_0_820_821,plain,
! [X11,X12,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),c_HOL_Ouminus__class_Ouminus(X11,X3)) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),X3) ),
inference(fof_simplification,[status(thm)],[c_0_273]) ).
fof(c_0_821_822,plain,
! [X34,X7,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X34),c_HOL_Ouminus__class_Ouminus(X7,X3)) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X34),X7),X3) ),
inference(fof_simplification,[status(thm)],[c_0_274]) ).
fof(c_0_822_823,plain,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),c_HOL_Ouminus__class_Ouminus(X11,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_275]) ).
fof(c_0_823_824,plain,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X11,X3),c_HOL_Ouminus__class_Ouminus(X12,X3),X3)
| ~ c_HOL_Oord__class_Oless(X12,X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_276]) ).
fof(c_0_824_825,plain,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X11,X3),c_HOL_Ouminus__class_Ouminus(X12,X3),X3)
| ~ c_lessequals(X12,X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_277]) ).
fof(c_0_825,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(X12,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X12,c_HOL_Ouminus__class_Ouminus(X12,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_278]) ).
fof(c_0_826,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X12,X3),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_279]) ).
fof(c_0_827,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_lessequals(X12,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X12,c_HOL_Ouminus__class_Ouminus(X12,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_280]) ).
fof(c_0_828,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X12,X3),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_281]) ).
fof(c_0_829,plain,
! [X12,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Ouminus__class_Ouminus(X12,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_282]) ).
fof(c_0_830,plain,
! [X6,X16,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(X16,X6,X3) != c_Polynomial_OpCons(X12,X6,X3)
| X6 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_283]) ).
fof(c_0_831,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ouminus__class_Ouminus(X12,X3),X3)
| ~ c_lessequals(X12,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_284]) ).
fof(c_0_832,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X12,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_285]) ).
fof(c_0_833,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ouminus__class_Ouminus(X12,X3),X3)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_286]) ).
fof(c_0_834,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X12,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_287]) ).
fof(c_0_835,plain,
! [X11,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ouminus__class_Ouminus(X11,X3)),c_HOL_Ouminus__class_Ouminus(X11,X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X11) ),
inference(fof_simplification,[status(thm)],[c_0_288]) ).
fof(c_0_836,plain,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ouminus__class_Ouminus(X12,X3)),c_HOL_Ouminus__class_Ouminus(X11,X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11) ),
inference(fof_simplification,[status(thm)],[c_0_289]) ).
fof(c_0_837,plain,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ouminus__class_Ouminus(X12,X3)),X11) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),c_HOL_Ouminus__class_Ouminus(X11,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_290]) ).
fof(c_0_838,plain,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X12) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X11)
| X12 = c_HOL_Ouminus__class_Ouminus(X11,X3)
| X12 = X11 ),
inference(fof_simplification,[status(thm)],[c_0_291]) ).
fof(c_0_839,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(X12,c_HOL_Ouminus__class_Ouminus(X12,X3),X3)
| ~ c_lessequals(X12,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_292]) ).
fof(c_0_840,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X12,X3),X12,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_293]) ).
fof(c_0_841,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_lessequals(X12,c_HOL_Ouminus__class_Ouminus(X12,X3),X3)
| ~ c_lessequals(X12,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_294]) ).
fof(c_0_842,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X12,X3),X12,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_295]) ).
fof(c_0_843,plain,
! [X12,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X12,c_HOL_Ouminus__class_Ouminus(X12,X3),X3)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_296]) ).
fof(c_0_844,plain,
! [X9,X7,X3] :
( ~ class_Orderings_Oorder(X3)
| X7 = X9
| ~ c_lessequals(X7,X9,X3)
| ~ c_lessequals(X9,X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_297]) ).
fof(c_0_845,plain,
! [X9,X7,X3] :
( ~ class_Orderings_Oorder(X3)
| X7 = X9
| ~ c_lessequals(X9,X7,X3)
| ~ c_lessequals(X7,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_298]) ).
fof(c_0_846,plain,
! [X9,X7,X3] :
( ~ class_Orderings_Oorder(X3)
| X7 = X9
| ~ c_lessequals(X9,X7,X3)
| ~ c_lessequals(X7,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_299]) ).
fof(c_0_847,plain,
! [X8,X6,X11,X12,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_OpCons(X12,X6,X3) != c_Polynomial_OpCons(X11,X8,X3)
| X12 = X11 ),
inference(fof_simplification,[status(thm)],[c_0_300]) ).
fof(c_0_848,plain,
! [X8,X6,X11,X12,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_OpCons(X12,X6,X3) != c_Polynomial_OpCons(X11,X8,X3)
| X6 = X8 ),
inference(fof_simplification,[status(thm)],[c_0_301]) ).
fof(c_0_849,plain,
! [X14,X11,X12,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Omonom(X12,X14,X3) != c_Polynomial_Omonom(X11,X14,X3)
| X12 = X11 ),
inference(fof_simplification,[status(thm)],[c_0_302]) ).
fof(c_0_850,plain,
! [X13,X9,X7,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),X9) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),X13)
| X9 = X13 ),
inference(fof_simplification,[status(thm)],[c_0_303]) ).
fof(c_0_851,plain,
! [X11,X12,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X11,X12,X3)
| ~ c_HOL_Oord__class_Oless(X12,X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_304]) ).
fof(c_0_852,plain,
! [X9,X7,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X9,X7,X3)
| ~ c_HOL_Oord__class_Oless(X7,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_305]) ).
fof(c_0_853,plain,
! [X9,X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X7,X9,X3)
| ~ c_HOL_Oord__class_Oless(X9,X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_306]) ).
fof(c_0_854,plain,
! [X11,X12,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X12,X11,X3)
| ~ c_HOL_Oord__class_Oless(X11,X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_307]) ).
fof(c_0_855,plain,
! [X9,X7,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X9,X7,X3)
| ~ c_HOL_Oord__class_Oless(X7,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_308]) ).
fof(c_0_856,plain,
! [X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X7,X7,X3)
| ~ c_HOL_Oord__class_Oless(X7,X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_309]) ).
fof(c_0_857,plain,
! [X9,X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X7,X9,X3)
| ~ c_lessequals(X9,X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_310]) ).
fof(c_0_858,plain,
! [X9,X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X7,X9,X3)
| ~ c_HOL_Oord__class_Oless(X9,X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_311]) ).
fof(c_0_859,plain,
! [X6,X12,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Polynomial_Oorder(X12,X6,X3) != c_HOL_Ozero__class_Ozero(tc_nat)
| X6 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| hAPP(c_Polynomial_Opoly(X6,X3),X12) != c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_312]) ).
fof(c_0_860,plain,
! [X1,X2,X3] :
( X2 = X1
| ~ hBOOL(c_fequal(X2,X1,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_313]) ).
fof(c_0_861,plain,
! [X7,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X7),c_HOL_Ozero__class_Ozero(tc_nat)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_314]) ).
fof(c_0_862,plain,
! [X12,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X12,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),c_HOL_Oone__class_Oone(X3)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_315]) ).
fof(c_0_863,plain,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16)
| X11 = X16 ),
inference(fof_simplification,[status(thm)],[c_0_316]) ).
fof(c_0_864,plain,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16)
| X11 = X16 ),
inference(fof_simplification,[status(thm)],[c_0_317]) ).
fof(c_0_865,plain,
! [X16,X11,X12,X3] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X12) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X12)
| X11 = X16 ),
inference(fof_simplification,[status(thm)],[c_0_318]) ).
fof(c_0_866,plain,
! [X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X12),X3) ),
inference(fof_simplification,[status(thm)],[c_0_319]) ).
fof(c_0_867,plain,
! [X13,X24] :
( X13 = X24
| ~ c_lessequals(X24,X13,tc_RealDef_Oreal)
| ~ c_lessequals(X13,X24,tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[c_0_320]) ).
fof(c_0_868,plain,
! [X6,X12,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Odegree(c_Polynomial_OpCons(X12,X6,X3),X3) = c_Suc(c_Polynomial_Odegree(X6,X3))
| X6 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_321]) ).
fof(c_0_869,plain,
! [X12,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Odegree(c_Polynomial_OpCons(X12,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3),X3) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_322]) ).
fof(c_0_870,plain,
! [X11,X12,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X11,X12,X3)
| X12 = X11
| ~ c_lessequals(X11,X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_323]) ).
fof(c_0_871,plain,
! [X11,X12,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X11,X12,X3)
| ~ c_lessequals(X11,X12,X3)
| X12 = X11 ),
inference(fof_simplification,[status(thm)],[c_0_324]) ).
fof(c_0_872,plain,
! [X9,X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| X7 = X9
| c_HOL_Oord__class_Oless(X7,X9,X3)
| ~ c_lessequals(X7,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_325]) ).
fof(c_0_873,plain,
! [X9,X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| X7 = X9
| ~ c_lessequals(X7,X9,X3)
| c_HOL_Oord__class_Oless(X7,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_326]) ).
fof(c_0_874,plain,
! [X11,X12,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X12,X11,X3)
| ~ c_lessequals(X12,X11,X3)
| X12 = X11 ),
inference(fof_simplification,[status(thm)],[c_0_327]) ).
fof(c_0_875,plain,
! [X11,X12,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X12,X11,X3)
| X12 = X11
| ~ c_lessequals(X12,X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_328]) ).
fof(c_0_876,plain,
! [X9,X7,X3] :
( ~ class_Orderings_Oorder(X3)
| X7 = X9
| c_HOL_Oord__class_Oless(X7,X9,X3)
| ~ c_lessequals(X7,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_329]) ).
fof(c_0_877,plain,
! [X9,X7,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X7,X9,X3)
| X7 = X9
| ~ c_lessequals(X7,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_330]) ).
fof(c_0_878,plain,
! [X3] :
( ~ class_HOL_Ozero(X3)
| hAPP(c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3),c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3)) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_331]) ).
fof(c_0_879,plain,
! [X7,X3] :
( ~ class_Int_Onumber__ring(X3)
| c_HOL_Ouminus__class_Ouminus(X7,X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X3),X3)),X7) ),
inference(fof_simplification,[status(thm)],[c_0_332]) ).
fof(c_0_880,plain,
! [X9,X7,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X7,X9,X3)
| ~ c_HOL_Oord__class_Oless(X7,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_333]) ).
fof(c_0_881,plain,
! [X9,X7,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X7,X9,X3)
| ~ c_HOL_Oord__class_Oless(X7,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_334]) ).
fof(c_0_882,plain,
! [X6,X12,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Polynomial_Odegree(c_Polynomial_Osmult(X12,X6,X3),X3) = c_Polynomial_Odegree(X6,X3)
| X12 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_335]) ).
fof(c_0_883,axiom,
! [X14,X22,X25] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X25) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X25)
| X22 = X14 ),
c_0_336 ).
fof(c_0_884,axiom,
! [X14,X22,X25] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X22) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X14)
| X22 = X14 ),
c_0_337 ).
fof(c_0_885,axiom,
! [X13,X9,X7] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X9) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X13)
| X9 = X13 ),
c_0_338 ).
fof(c_0_886,plain,
! [X22,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X22,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_339]) ).
fof(c_0_887,plain,
! [X6,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Polynomial_Odegree(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X3),X6,X3),X3) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_340]) ).
fof(c_0_888,plain,
! [X6,X21,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X6,X21,X3),X3) = c_Polynomial_Odegree(X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_341]) ).
fof(c_0_889,plain,
! [X12,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Omonom(X12,c_HOL_Ozero__class_Ozero(tc_nat),X3) = c_Polynomial_OpCons(X12,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_342]) ).
fof(c_0_890,plain,
! [X14,X12,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Odegree(c_Polynomial_Omonom(X12,X14,X3),X3) = X14
| X12 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_343]) ).
fof(c_0_891,plain,
! [X6,X3] :
( ~ class_HOL_Ozero(X3)
| hAPP(c_Polynomial_Ocoeff(X6,X3),c_Polynomial_Odegree(X6,X3)) != c_HOL_Ozero__class_Ozero(X3)
| X6 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_344]) ).
fof(c_0_892,plain,
! [X6,X12,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Polynomial_Osmult(X12,X6,X3) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| X6 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| X12 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_345]) ).
fof(c_0_893,plain,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Ozero__neq__one(X3)
| ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| ~ class_Ring__and__Field_Omult__zero(X3)
| ~ class_Power_Opower(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14) != c_HOL_Ozero__class_Ozero(X3)
| X12 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_346]) ).
fof(c_0_894,plain,
! [X12,X3] :
( ~ class_Ring__and__Field_Ozero__neq__one(X3)
| ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| ~ class_Ring__and__Field_Omult__zero(X3)
| ~ class_Power_Opower(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_347]) ).
fof(c_0_895,plain,
! [X8,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X3)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))),X8) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_348]) ).
fof(c_0_896,plain,
! [X6,X21,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X6,X21,X3) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| X6 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_349]) ).
fof(c_0_897,plain,
! [X6,X12,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_OpCons(X12,X6,X3) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| X6 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_350]) ).
fof(c_0_898,plain,
! [X9,X7,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X9,X7,X3)
| c_HOL_Oord__class_Oless(X7,X9,X3)
| X7 = X9 ),
inference(fof_simplification,[status(thm)],[c_0_351]) ).
fof(c_0_899,plain,
! [X9,X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| X7 = X9
| c_HOL_Oord__class_Oless(X9,X7,X3)
| c_HOL_Oord__class_Oless(X7,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_352]) ).
fof(c_0_900,plain,
! [X9,X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| X7 = X9
| c_HOL_Oord__class_Oless(X7,X9,X3)
| c_HOL_Oord__class_Oless(X9,X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_353]) ).
fof(c_0_901,plain,
! [X9,X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X9,X7,X3)
| X7 = X9
| c_HOL_Oord__class_Oless(X7,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_354]) ).
fof(c_0_902,plain,
! [X9,X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X9,X7,X3)
| c_HOL_Oord__class_Oless(X7,X9,X3)
| X7 = X9 ),
inference(fof_simplification,[status(thm)],[c_0_355]) ).
fof(c_0_903,plain,
! [X22,X3] :
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X22),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oone__class_Oone(X3)),c_Nat_Osemiring__1__class_Oof__nat(X22,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_356]) ).
fof(c_0_904,plain,
! [X9,X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X9,X7,X3)
| c_lessequals(X7,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_357]) ).
fof(c_0_905,plain,
! [X9,X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X7,X9,X3)
| c_lessequals(X9,X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_358]) ).
fof(c_0_906,plain,
! [X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X7,X7,X3)
| c_lessequals(X7,X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_359]) ).
fof(c_0_907,plain,
! [X9,X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X9,X7,X3)
| c_HOL_Oord__class_Oless(X7,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_360]) ).
fof(c_0_908,plain,
! [X9,X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X9,X7,X3)
| c_lessequals(X7,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_361]) ).
fof(c_0_909,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ouminus__class_Ouminus(X12,X3)),X12) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_362]) ).
fof(c_0_910,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ouminus__class_Ouminus(X12,X3)),X12) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_363]) ).
fof(c_0_911,plain,
! [X11,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ouminus__class_Ouminus(X11,X3)),X11) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_364]) ).
fof(c_0_912,plain,
! [X14,X12,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Omonom(X12,X14,X3) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| X12 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_365]) ).
fof(c_0_913,plain,
! [X6,X12,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_OpCons(X12,X6,X3) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| X12 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_366]) ).
fof(c_0_914,plain,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_367]) ).
fof(c_0_915,plain,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_368]) ).
fof(c_0_916,plain,
! [X9,X7,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X9) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X7) ),
inference(fof_simplification,[status(thm)],[c_0_369]) ).
fof(c_0_917,plain,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X11),X12) ),
inference(fof_simplification,[status(thm)],[c_0_370]) ).
fof(c_0_918,plain,
! [X16,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X16) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X12) ),
inference(fof_simplification,[status(thm)],[c_0_371]) ).
fof(c_0_919,plain,
! [X9,X7,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),X9) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X7) ),
inference(fof_simplification,[status(thm)],[c_0_372]) ).
fof(c_0_920,plain,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X12) ),
inference(fof_simplification,[status(thm)],[c_0_373]) ).
fof(c_0_921,plain,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11) != c_HOL_Ozero__class_Ozero(X3)
| c_HOL_Ouminus__class_Ouminus(X12,X3) = X11 ),
inference(fof_simplification,[status(thm)],[c_0_374]) ).
fof(c_0_922,plain,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X11) != c_HOL_Ozero__class_Ozero(X3)
| X12 = c_HOL_Ouminus__class_Ouminus(X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_375]) ).
fof(c_0_923,plain,
! [X9,X7,X10] :
( hAPP(X10,X7) = hAPP(X10,X9)
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X10,t_a,t_b) ),
inference(fof_simplification,[status(thm)],[c_0_376]) ).
fof(c_0_924,plain,
! [X6,X12,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| hAPP(c_Polynomial_Opoly(X6,X3),X12) = c_HOL_Ozero__class_Ozero(X3)
| c_Polynomial_Oorder(X12,X6,X3) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_377]) ).
fof(c_0_925,axiom,
! [X13,X24] :
( c_lessequals(X24,X13,tc_RealDef_Oreal)
| c_lessequals(X13,X24,tc_RealDef_Oreal) ),
c_0_378 ).
fof(c_0_926,plain,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11) != c_HOL_Ozero__class_Ozero(X3)
| X11 = c_HOL_Ozero__class_Ozero(X3)
| X12 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_379]) ).
fof(c_0_927,plain,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11) != c_HOL_Ozero__class_Ozero(X3)
| X11 = c_HOL_Ozero__class_Ozero(X3)
| X12 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_380]) ).
fof(c_0_928,plain,
! [X11,X12,X3] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X11) != c_HOL_Ozero__class_Ozero(X3)
| X12 = c_HOL_Ozero__class_Ozero(X3)
| X11 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_381]) ).
fof(c_0_929,plain,
! [X7,X12,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| X7 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),X12)
| X12 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_382]) ).
fof(c_0_930,plain,
! [X6,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X3)),X6),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))) = X6 ),
inference(fof_simplification,[status(thm)],[c_0_383]) ).
fof(c_0_931,plain,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),X14) != c_HOL_Ozero__class_Ozero(X3)
| X12 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_384]) ).
fof(c_0_932,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X12) != c_HOL_Ozero__class_Ozero(X3)
| X12 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_385]) ).
fof(c_0_933,plain,
! [X14,X3] :
( ~ class_Ring__and__Field_Ozero__neq__one(X3)
| ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| ~ class_Ring__and__Field_Omult__zero(X3)
| ~ class_Power_Opower(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3)),X14) = c_HOL_Ozero__class_Ozero(X3)
| X14 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_386]) ).
fof(c_0_934,axiom,
! [X14,X22] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X14) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X14 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X22 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_387 ).
fof(c_0_935,axiom,
! [X14,X22] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X14)
| X14 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X22 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_388 ).
fof(c_0_936,plain,
! [X6,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Oring__char__0(X3)
| c_Polynomial_Opoly(X6,X3) != c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3)
| X6 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_389]) ).
fof(c_0_937,plain,
! [X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_390]) ).
fof(c_0_938,axiom,
! [X14,X22] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X14)
| X14 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X14 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_391 ).
fof(c_0_939,axiom,
! [X14,X22] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X14)
| X22 = c_HOL_Ozero__class_Ozero(tc_nat)
| X22 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_392 ).
fof(c_0_940,axiom,
! [X14,X22] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X14) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X22 = c_HOL_Ozero__class_Ozero(tc_nat)
| X22 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_393 ).
fof(c_0_941,axiom,
! [X14,X22] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X14) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X14 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X14 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_394 ).
fof(c_0_942,axiom,
( hAPP(c_Polynomial_Opoly(v_pa____,tc_Complex_Ocomplex),v_c____) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(v_pa____,tc_Complex_Ocomplex),v_sko__unknown__thm__rrS__1(v_pa____)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
c_0_395 ).
fof(c_0_943,plain,
! [X22,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X22,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_396]) ).
fof(c_0_944,plain,
! [X14,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X14,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_397]) ).
fof(c_0_945,plain,
! [X7,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X7,X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_398]) ).
fof(c_0_946,plain,
! [X7,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X7,X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_399]) ).
fof(c_0_947,plain,
! [X7,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X7,X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_400]) ).
fof(c_0_948,axiom,
! [X14,X22] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X14) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X22 = c_HOL_Ozero__class_Ozero(tc_nat)
| X14 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_401 ).
fof(c_0_949,axiom,
! [X14,X22] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X14)
| X22 = c_HOL_Ozero__class_Ozero(tc_nat)
| X14 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_402 ).
fof(c_0_950,plain,
! [X12,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Polynomial_Osmult(X12,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_403]) ).
fof(c_0_951,plain,
! [X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(X12,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_404]) ).
fof(c_0_952,plain,
! [X21,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X21,X3) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_405]) ).
fof(c_0_953,plain,
! [X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Opcompose(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X8,X3) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_406]) ).
fof(c_0_954,plain,
! [X6] :
( ~ class_Ring__and__Field_Oidom(t_a)
| v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1(X6) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X6,t_a),t_a,t_a) ),
inference(fof_simplification,[status(thm)],[c_0_407]) ).
fof(c_0_955,plain,
! [X6] :
( ~ class_Ring__and__Field_Oidom(t_a)
| v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__2(X6) != c_HOL_Ozero__class_Ozero(t_a)
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X6,t_a),t_a,t_a) ),
inference(fof_simplification,[status(thm)],[c_0_408]) ).
fof(c_0_956,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),c_HOL_Ouminus__class_Ouminus(X12,X3)) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_409]) ).
fof(c_0_957,plain,
! [X14,X3] :
( ~ class_Ring__and__Field_Osemiring__0(X3)
| ~ class_Power_Opower(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3)),c_Suc(X14)) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_410]) ).
fof(c_0_958,plain,
! [X14,X3] :
( ~ class_HOL_Ozero(X3)
| hAPP(c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3),X14) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_411]) ).
fof(c_0_959,plain,
! [X12,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| hAPP(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3),X12) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_412]) ).
fof(c_0_960,plain,
! [X7,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| hAPP(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3),X7) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_413]) ).
fof(c_0_961,plain,
! [X14,X3] :
( ~ class_Ring__and__Field_Osemiring__0(X3)
| ~ class_Power_Opower(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3)),X14) = c_HOL_Ozero__class_Ozero(X3)
| X14 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_414]) ).
fof(c_0_962,plain,
! [X3] :
( ~ class_Ring__and__Field_Osemiring__0(X3)
| ~ class_Power_Opower(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(X3) ),
inference(fof_simplification,[status(thm)],[c_0_415]) ).
fof(c_0_963,plain,
! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3)) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_416]) ).
fof(c_0_964,axiom,
! [X14,X22] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X14) != c_HOL_Ozero__class_Ozero(tc_nat)
| X22 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_417 ).
fof(c_0_965,axiom,
! [X14,X22] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X14) != c_HOL_Ozero__class_Ozero(tc_nat)
| X14 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_418 ).
fof(c_0_966,axiom,
! [X7,X12] :
( X7 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X12)
| X12 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_419 ).
fof(c_0_967,axiom,
! [X14,X22] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X14) != X22
| X14 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_420 ).
fof(c_0_968,plain,
! [X3] :
( ~ class_Power_Opower(X3)
| c_Power_Opower__class_Opower(X3) = c_Power_Opower_Opower(c_HOL_Oone__class_Oone(X3),c_HOL_Otimes__class_Otimes(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_421]) ).
fof(c_0_969,plain,
! [X14,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(X3),X14,X3) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_422]) ).
fof(c_0_970,plain,
! [X6,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X3),X6,X3) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_423]) ).
fof(c_0_971,plain,
! [X6,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X3),X6,X3) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_424]) ).
fof(c_0_972,plain,
! [X14,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Oone__class_Oone(X3)),X14) = c_HOL_Oone__class_Oone(X3) ),
inference(fof_simplification,[status(thm)],[c_0_425]) ).
fof(c_0_973,plain,
! [X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),X12) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_426]) ).
fof(c_0_974,plain,
! [X9,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),X9) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_427]) ).
fof(c_0_975,plain,
! [X11,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),X11) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_428]) ).
fof(c_0_976,plain,
! [X7,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),X7) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_429]) ).
fof(c_0_977,plain,
! [X12,X3] :
( ~ class_Ring__and__Field_Omult__zero(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),X12) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_430]) ).
fof(c_0_978,plain,
! [X11,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),X11) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_431]) ).
fof(c_0_979,plain,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oone__class_Oone(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_432]) ).
fof(c_0_980,plain,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oone__class_Oone(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_433]) ).
fof(c_0_981,plain,
! [X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_OrderedGroup_Ocomm__monoid__add__axioms(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_434]) ).
fof(c_0_982,plain,
! [X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| c_OrderedGroup_Omonoid__add__axioms(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_435]) ).
fof(c_0_983,plain,
! [X7,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| X7 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X7),c_HOL_Ozero__class_Ozero(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_436]) ).
fof(c_0_984,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Oone__class_Oone(X3)),X12) = X12 ),
inference(fof_simplification,[status(thm)],[c_0_437]) ).
fof(c_0_985,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Oone__class_Oone(X3)),X12) = X12 ),
inference(fof_simplification,[status(thm)],[c_0_438]) ).
fof(c_0_986,plain,
! [X7,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Oone__class_Oone(X3)),X7) = X7 ),
inference(fof_simplification,[status(thm)],[c_0_439]) ).
fof(c_0_987,plain,
! [X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Oone__class_Oone(X3)),X12) = X12 ),
inference(fof_simplification,[status(thm)],[c_0_440]) ).
fof(c_0_988,plain,
! [X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X12) = X12 ),
inference(fof_simplification,[status(thm)],[c_0_441]) ).
fof(c_0_989,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X12) = X12 ),
inference(fof_simplification,[status(thm)],[c_0_442]) ).
fof(c_0_990,plain,
! [X7,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X7) = X7 ),
inference(fof_simplification,[status(thm)],[c_0_443]) ).
fof(c_0_991,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X12) = X12 ),
inference(fof_simplification,[status(thm)],[c_0_444]) ).
fof(c_0_992,plain,
! [X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),c_HOL_Ozero__class_Ozero(X3)) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_445]) ).
fof(c_0_993,plain,
! [X12,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),c_HOL_Ozero__class_Ozero(X3)) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_446]) ).
fof(c_0_994,plain,
! [X7,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),c_HOL_Ozero__class_Ozero(X3)) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_447]) ).
fof(c_0_995,plain,
! [X12,X3] :
( ~ class_Ring__and__Field_Omult__zero(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),c_HOL_Ozero__class_Ozero(X3)) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_448]) ).
fof(c_0_996,plain,
! [X12,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),c_HOL_Ozero__class_Ozero(X3)) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_449]) ).
fof(c_0_997,plain,
! [X6,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Polynomial_Osmult(c_HOL_Oone__class_Oone(X3),X6,X3) = X6 ),
inference(fof_simplification,[status(thm)],[c_0_450]) ).
fof(c_0_998,plain,
! [X7,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X7),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(X3) ),
inference(fof_simplification,[status(thm)],[c_0_451]) ).
fof(c_0_999,plain,
! [X12,X3] :
( ~ class_Power_Opower(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(X3) ),
inference(fof_simplification,[status(thm)],[c_0_452]) ).
fof(c_0_1000,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),c_HOL_Oone__class_Oone(X3)) = X12 ),
inference(fof_simplification,[status(thm)],[c_0_453]) ).
fof(c_0_1001,plain,
! [X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),c_HOL_Oone__class_Oone(X3)) = X12 ),
inference(fof_simplification,[status(thm)],[c_0_454]) ).
fof(c_0_1002,plain,
! [X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),c_HOL_Ozero__class_Ozero(X3)) = X12 ),
inference(fof_simplification,[status(thm)],[c_0_455]) ).
fof(c_0_1003,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),c_HOL_Ozero__class_Ozero(X3)) = X12 ),
inference(fof_simplification,[status(thm)],[c_0_456]) ).
fof(c_0_1004,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),c_HOL_Ozero__class_Ozero(X3)) = X12 ),
inference(fof_simplification,[status(thm)],[c_0_457]) ).
fof(c_0_1005,plain,
! [X7,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X7),c_HOL_Oone__class_Oone(tc_nat)) = X7 ),
inference(fof_simplification,[status(thm)],[c_0_458]) ).
fof(c_0_1006,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X12),c_HOL_Oone__class_Oone(tc_nat)) = X12 ),
inference(fof_simplification,[status(thm)],[c_0_459]) ).
fof(c_0_1007,plain,
! [X6,X3] :
( ~ class_HOL_Ozero(X3)
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X6,X3) = c_Suc(c_Polynomial_Odegree(X6,X3))
| X6 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_460]) ).
fof(c_0_1008,plain,
! [X7,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X7,X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_461]) ).
fof(c_0_1009,plain,
! [X7,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X7,X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_462]) ).
fof(c_0_1010,plain,
! [X7,X3] :
( ~ class_RealVector_Oreal__normed__vector(X3)
| c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(X7,X3),X3) = c_RealVector_Onorm__class_Onorm(X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_463]) ).
fof(c_0_1011,plain,
! [X8,X6,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Oring__char__0(X3)
| c_Polynomial_Opoly(X6,X3) != c_Polynomial_Opoly(X8,X3)
| X6 = X8 ),
inference(fof_simplification,[status(thm)],[c_0_464]) ).
fof(c_0_1012,plain,
! [X7,X3] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X7),X7) = X7 ),
inference(fof_simplification,[status(thm)],[c_0_465]) ).
fof(c_0_1013,plain,
! [X13,X6] :
( ~ class_Ring__and__Field_Oidom(t_a)
| v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2(X6) != c_HOL_Ozero__class_Ozero(t_a)
| hAPP(c_Polynomial_Opoly(X6,t_a),X13) = c_HOL_Ozero__class_Ozero(t_a)
| X13 = c_HOL_Ozero__class_Ozero(t_a) ),
inference(fof_simplification,[status(thm)],[c_0_466]) ).
fof(c_0_1014,plain,
! [X9,X7,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Ocoeff(X7,X3) != c_Polynomial_Ocoeff(X9,X3)
| X7 = X9 ),
inference(fof_simplification,[status(thm)],[c_0_467]) ).
fof(c_0_1015,plain,
! [X9,X7,X3] :
( ~ class_Lattices_Oboolean__algebra(X3)
| c_HOL_Ouminus__class_Ouminus(X7,X3) != c_HOL_Ouminus__class_Ouminus(X9,X3)
| X7 = X9 ),
inference(fof_simplification,[status(thm)],[c_0_468]) ).
fof(c_0_1016,plain,
! [X11,X12,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(X12,X3) != c_HOL_Ouminus__class_Ouminus(X11,X3)
| X12 = X11 ),
inference(fof_simplification,[status(thm)],[c_0_469]) ).
fof(c_0_1017,plain,
! [X14,X22,X3] :
( ~ class_Nat_Osemiring__char__0(X3)
| c_Nat_Osemiring__1__class_Oof__nat(X22,X3) != c_Nat_Osemiring__1__class_Oof__nat(X14,X3)
| X22 = X14 ),
inference(fof_simplification,[status(thm)],[c_0_470]) ).
fof(c_0_1018,plain,
! [X11,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X11,X3),X3) = X11 ),
inference(fof_simplification,[status(thm)],[c_0_471]) ).
fof(c_0_1019,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| X12 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X12,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_472]) ).
fof(c_0_1020,plain,
! [X11,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| X11 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X11,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_473]) ).
fof(c_0_1021,plain,
! [X7,X3] :
( ~ class_Lattices_Oboolean__algebra(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X7,X3),X3) = X7 ),
inference(fof_simplification,[status(thm)],[c_0_474]) ).
fof(c_0_1022,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X12,X3),X3) = X12 ),
inference(fof_simplification,[status(thm)],[c_0_475]) ).
fof(c_0_1023,plain,
! [X6,X3] :
( ~ class_HOL_Ozero(X3)
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X6,X3) != c_HOL_Ozero__class_Ozero(tc_nat)
| X6 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_476]) ).
fof(c_0_1024,plain,
! [X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_477]) ).
fof(c_0_1025,plain,
! [X3] :
( ~ class_HOL_Ozero(X3)
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_478]) ).
fof(c_0_1026,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(X12,X3) != c_HOL_Ozero__class_Ozero(X3)
| X12 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_479]) ).
fof(c_0_1027,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Ouminus__class_Ouminus(X12,X3)
| c_HOL_Ozero__class_Ozero(X3) = X12 ),
inference(fof_simplification,[status(thm)],[c_0_480]) ).
fof(c_0_1028,plain,
! [X5,X4] :
( class_Lattices_Oboolean__algebra(tc_fun(X5,X4))
| ~ class_Lattices_Oboolean__algebra(X4) ),
inference(fof_simplification,[status(thm)],[c_0_481]) ).
fof(c_0_1029,plain,
! [X5,X4] :
( class_Orderings_Opreorder(tc_fun(X5,X4))
| ~ class_Orderings_Opreorder(X4) ),
inference(fof_simplification,[status(thm)],[c_0_482]) ).
fof(c_0_1030,plain,
! [X5,X4] :
( class_Orderings_Oorder(tc_fun(X5,X4))
| ~ class_Orderings_Oorder(X4) ),
inference(fof_simplification,[status(thm)],[c_0_483]) ).
fof(c_0_1031,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_HOL_Ouminus__class_Ouminus(X12,X3) != X12
| X12 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_484]) ).
fof(c_0_1032,plain,
! [X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_485]) ).
fof(c_0_1033,plain,
! [X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_486]) ).
fof(c_0_1034,plain,
! [X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_487]) ).
fof(c_0_1035,plain,
! [X3] :
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X3) = c_HOL_Oone__class_Oone(X3) ),
inference(fof_simplification,[status(thm)],[c_0_488]) ).
fof(c_0_1036,plain,
! [X3] :
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_489]) ).
fof(c_0_1037,plain,
! [X3] :
( ~ class_Ring__and__Field_Ozero__neq__one(X3)
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Oone__class_Oone(X3) ),
inference(fof_simplification,[status(thm)],[c_0_490]) ).
fof(c_0_1038,plain,
! [X3] :
( ~ class_Ring__and__Field_Ozero__neq__one(X3)
| c_HOL_Oone__class_Oone(X3) != c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_491]) ).
fof(c_0_1039,plain,
! [X4] :
( class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X4))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X4) ),
inference(fof_simplification,[status(thm)],[c_0_492]) ).
fof(c_0_1040,plain,
! [X4] :
( class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ocomm__ring__1(X4) ),
inference(fof_simplification,[status(thm)],[c_0_493]) ).
fof(c_0_1041,plain,
! [X4] :
( class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ocomm__ring(X4) ),
inference(fof_simplification,[status(thm)],[c_0_494]) ).
fof(c_0_1042,plain,
! [X4] :
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
inference(fof_simplification,[status(thm)],[c_0_495]) ).
fof(c_0_1043,plain,
! [X4] :
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
inference(fof_simplification,[status(thm)],[c_0_496]) ).
fof(c_0_1044,plain,
! [X4] :
( class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
inference(fof_simplification,[status(thm)],[c_0_497]) ).
fof(c_0_1045,plain,
! [X4] :
( class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
inference(fof_simplification,[status(thm)],[c_0_498]) ).
fof(c_0_1046,plain,
! [X4] :
( class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oidom(X4) ),
inference(fof_simplification,[status(thm)],[c_0_499]) ).
fof(c_0_1047,plain,
! [X4] :
( class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
inference(fof_simplification,[status(thm)],[c_0_500]) ).
fof(c_0_1048,plain,
! [X4] :
( class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
inference(fof_simplification,[status(thm)],[c_0_501]) ).
fof(c_0_1049,plain,
! [X4] :
( class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
inference(fof_simplification,[status(thm)],[c_0_502]) ).
fof(c_0_1050,plain,
! [X4] :
( class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oidom(X4) ),
inference(fof_simplification,[status(thm)],[c_0_503]) ).
fof(c_0_1051,plain,
! [X4] :
( class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X4))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X4) ),
inference(fof_simplification,[status(thm)],[c_0_504]) ).
fof(c_0_1052,plain,
! [X4] :
( class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
inference(fof_simplification,[status(thm)],[c_0_505]) ).
fof(c_0_1053,plain,
! [X4] :
( class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
inference(fof_simplification,[status(thm)],[c_0_506]) ).
fof(c_0_1054,plain,
! [X4] :
( class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
inference(fof_simplification,[status(thm)],[c_0_507]) ).
fof(c_0_1055,plain,
! [X4] :
( class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X4))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X4) ),
inference(fof_simplification,[status(thm)],[c_0_508]) ).
fof(c_0_1056,plain,
! [X4] :
( class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
inference(fof_simplification,[status(thm)],[c_0_509]) ).
fof(c_0_1057,plain,
! [X4] :
( class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
inference(fof_simplification,[status(thm)],[c_0_510]) ).
fof(c_0_1058,plain,
! [X4] :
( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oidom(X4) ),
inference(fof_simplification,[status(thm)],[c_0_511]) ).
fof(c_0_1059,plain,
! [X4] :
( class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
inference(fof_simplification,[status(thm)],[c_0_512]) ).
fof(c_0_1060,plain,
! [X4] :
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(fof_simplification,[status(thm)],[c_0_513]) ).
fof(c_0_1061,plain,
! [X4] :
( class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
inference(fof_simplification,[status(thm)],[c_0_514]) ).
fof(c_0_1062,plain,
! [X4] :
( class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
inference(fof_simplification,[status(thm)],[c_0_515]) ).
fof(c_0_1063,plain,
! [X4] :
( class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(fof_simplification,[status(thm)],[c_0_516]) ).
fof(c_0_1064,plain,
! [X4] :
( class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
inference(fof_simplification,[status(thm)],[c_0_517]) ).
fof(c_0_1065,plain,
! [X4] :
( class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
inference(fof_simplification,[status(thm)],[c_0_518]) ).
fof(c_0_1066,plain,
! [X4] :
( class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
inference(fof_simplification,[status(thm)],[c_0_519]) ).
fof(c_0_1067,plain,
! [X4] :
( class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
inference(fof_simplification,[status(thm)],[c_0_520]) ).
fof(c_0_1068,plain,
! [X4] :
( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(fof_simplification,[status(thm)],[c_0_521]) ).
fof(c_0_1069,plain,
! [X4] :
( class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
inference(fof_simplification,[status(thm)],[c_0_522]) ).
fof(c_0_1070,plain,
! [X4] :
( class_OrderedGroup_Osemigroup__add(tc_Polynomial_Opoly(X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
inference(fof_simplification,[status(thm)],[c_0_523]) ).
fof(c_0_1071,plain,
! [X4] :
( class_Ring__and__Field_Osemiring__1(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(fof_simplification,[status(thm)],[c_0_524]) ).
fof(c_0_1072,plain,
! [X4] :
( class_Ring__and__Field_Osemiring__0(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
inference(fof_simplification,[status(thm)],[c_0_525]) ).
fof(c_0_1073,plain,
! [X4] :
( class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
inference(fof_simplification,[status(thm)],[c_0_526]) ).
fof(c_0_1074,plain,
! [X4] :
( class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X4))
| ~ class_OrderedGroup_Oab__group__add(X4) ),
inference(fof_simplification,[status(thm)],[c_0_527]) ).
fof(c_0_1075,plain,
! [X4] :
( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
inference(fof_simplification,[status(thm)],[c_0_528]) ).
fof(c_0_1076,plain,
! [X4] :
( class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
inference(fof_simplification,[status(thm)],[c_0_529]) ).
fof(c_0_1077,plain,
! [X4] :
( class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(fof_simplification,[status(thm)],[c_0_530]) ).
fof(c_0_1078,plain,
! [X4] :
( class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
inference(fof_simplification,[status(thm)],[c_0_531]) ).
fof(c_0_1079,plain,
! [X4] :
( class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
inference(fof_simplification,[status(thm)],[c_0_532]) ).
fof(c_0_1080,plain,
! [X4] :
( class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X4))
| ~ class_OrderedGroup_Oab__group__add(X4) ),
inference(fof_simplification,[status(thm)],[c_0_533]) ).
fof(c_0_1081,plain,
! [X4] :
( class_Ring__and__Field_Oring__1(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ocomm__ring__1(X4) ),
inference(fof_simplification,[status(thm)],[c_0_534]) ).
fof(c_0_1082,plain,
! [X4] :
( class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ocomm__ring(X4) ),
inference(fof_simplification,[status(thm)],[c_0_535]) ).
fof(c_0_1083,plain,
! [X4] :
( class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oidom(X4) ),
inference(fof_simplification,[status(thm)],[c_0_536]) ).
fof(c_0_1084,plain,
! [X4] :
( class_Nat_Osemiring__char__0(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
inference(fof_simplification,[status(thm)],[c_0_537]) ).
fof(c_0_1085,plain,
! [X4] :
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
inference(fof_simplification,[status(thm)],[c_0_538]) ).
fof(c_0_1086,plain,
! [X4] :
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
inference(fof_simplification,[status(thm)],[c_0_539]) ).
fof(c_0_1087,plain,
! [X4] :
( class_Orderings_Oorder(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
inference(fof_simplification,[status(thm)],[c_0_540]) ).
fof(c_0_1088,plain,
! [X4] :
( class_Int_Oring__char__0(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Oordered__idom(X4) ),
inference(fof_simplification,[status(thm)],[c_0_541]) ).
fof(c_0_1089,plain,
! [X4] :
( class_Int_Onumber__ring(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ocomm__ring__1(X4) ),
inference(fof_simplification,[status(thm)],[c_0_542]) ).
fof(c_0_1090,plain,
! [X4] :
( class_Power_Opower(tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(fof_simplification,[status(thm)],[c_0_543]) ).
fof(c_0_1091,plain,
! [X4] :
( class_HOL_Ozero(tc_Polynomial_Opoly(X4))
| ~ class_HOL_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_544]) ).
fof(c_0_1092,axiom,
! [X28,X29] :
( c_Suc(X29) != c_Suc(X28)
| X29 = X28 ),
c_0_545 ).
fof(c_0_1093,axiom,
! [X9,X7] :
( c_Suc(X7) != c_Suc(X9)
| X7 = X9 ),
c_0_546 ).
fof(c_0_1094,plain,
! [X21,X22,X23,X24,X25,X26] :
( ~ class_HOL_Ozero(X25)
| c_Polynomial_Opoly__rec(X21,X23,c_Polynomial_OpCons(X24,X22,X25),X26,X25) = hAPP(hAPP(hAPP(X23,X24),X22),c_HOL_OIf(c_fequal(X22,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X25)),tc_Polynomial_Opoly(X25)),X21,c_Polynomial_Opoly__rec(X21,X23,X22,X26,X25),X26)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_547])])]) ).
fof(c_0_1095,plain,
! [X21,X22,X23,X24,X25,X26] :
( ~ class_HOL_Ozero(X25)
| hAPP(hAPP(hAPP(X23,c_HOL_Ozero__class_Ozero(X25)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X25))),X21) != X21
| c_Polynomial_Opoly__rec(X21,X23,c_Polynomial_OpCons(X24,X22,X25),X26,X25) = hAPP(hAPP(hAPP(X23,X24),X22),c_Polynomial_Opoly__rec(X21,X23,X22,X26,X25)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_548])])]) ).
fof(c_0_1096,plain,
! [X16,X17,X18,X19] :
( ~ class_OrderedGroup_Osemigroup__add(X19)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X19),X18),X17),X16,X19,X19) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X19),X18),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X19),X17,X16,X19,X19)) ),
inference(variable_rename,[status(thm)],[c_0_549]) ).
fof(c_0_1097,plain,
! [X16,X17,X18] :
( ~ class_OrderedGroup_Omonoid__add(X18)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X18),X17),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X18),c_HOL_Ozero__class_Ozero(X18),X16,X18,X18)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X18),X17,X16,X18,X18) ),
inference(variable_rename,[status(thm)],[c_0_550]) ).
fof(c_0_1098,plain,
! [X15,X16,X17,X18] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X18)
| hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X18),c_HOL_Oplus__class_Oplus(X18),X18),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X18),X17),X16)),X15) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X18),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X18),c_HOL_Oplus__class_Oplus(X18),X18),X17),X15)),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X18),c_HOL_Oplus__class_Oplus(X18),X18),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_551]) ).
fof(c_0_1099,plain,
! [X23,X24,X25,X26] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X26)
| hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X26),c_HOL_Oplus__class_Oplus(X26),X26),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X23)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X26),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X26),c_HOL_Oplus__class_Oplus(X26),X26),X25),X24)),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X26),c_HOL_Oplus__class_Oplus(X26),X26),X25),X23)) ),
inference(variable_rename,[status(thm)],[c_0_552]) ).
fof(c_0_1100,plain,
! [X14,X15] :
( ~ class_Ring__and__Field_Oidom(t_a)
| hAPP(c_Polynomial_Opoly(X15,t_a),X14) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(t_a),hAPP(c_Polynomial_Opoly(X15,t_a),c_HOL_Ozero__class_Ozero(t_a))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X14),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1(X15))),hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__2(X15),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__3(X15),t_a),t_a),X14)))
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X15,t_a),t_a,t_a) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_553])])]) ).
fof(c_0_1101,plain,
! [X15,X16,X17] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X17)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X17),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X17),c_HOL_Oplus__class_Oplus(X17),X17),X16),X15)),X16) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X17),X16),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X17),c_HOL_Oplus__class_Oplus(X17),X17),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_554]) ).
fof(c_0_1102,plain,
! [X24,X25,X26,X27,X28] :
( ~ class_Ring__and__Field_Osemiring(X28)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X28),X27),X24)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X28),X26),X24)),X25)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X28),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X27),X26)),X24)),X25) ),
inference(variable_rename,[status(thm)],[c_0_555]) ).
fof(c_0_1103,plain,
! [X15,X16,X17] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X17)
| hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X17),c_HOL_Oplus__class_Oplus(X17),X17),X16),c_Suc(X15)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X17),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X17),c_HOL_Oplus__class_Oplus(X17),X17),X16),X15)),X16) ),
inference(variable_rename,[status(thm)],[c_0_556]) ).
fof(c_0_1104,plain,
! [X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),c_HOL_Ozero__class_Ozero(X4)),c_HOL_Ozero__class_Ozero(X4))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),c_HOL_Ozero__class_Ozero(X4)),c_HOL_Ozero__class_Ozero(X4))),X4) ),
inference(variable_rename,[status(thm)],[c_0_557]) ).
fof(c_0_1105,plain,
! [X21,X22,X23,X24] :
( ~ class_HOL_Ozero(X23)
| hAPP(hAPP(hAPP(X22,c_HOL_Ozero__class_Ozero(X23)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X23))),X21) != X21
| c_Polynomial_Opoly__rec(X21,X22,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X23)),X24,X23) = X21 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_558])])]) ).
fof(c_0_1106,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| X10 = c_HOL_Ozero__class_Ozero(X12)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X12),X11),X11)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X12),X10),X10)),c_HOL_Ozero__class_Ozero(X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_559]) ).
fof(c_0_1107,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| X11 = c_HOL_Ozero__class_Ozero(X12)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X12),X11),X11)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X12),X10),X10)),c_HOL_Ozero__class_Ozero(X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_560]) ).
fof(c_0_1108,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X12),X11),X11)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X12),X10),X10)),c_HOL_Ozero__class_Ozero(X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_561]) ).
fof(c_0_1109,plain,
! [X22,X23,X24,X25] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X25)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(X24,X22,X25),X23,X25) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X25)),c_Polynomial_Osmult(X23,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X22,X23,X25),X25)),c_Polynomial_OpCons(X24,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X22,X23,X25),X25)) ),
inference(variable_rename,[status(thm)],[c_0_562]) ).
fof(c_0_1110,plain,
! [X19,X20,X21,X22,X23] :
( ~ class_Ring__and__Field_Oidom(X23)
| ~ class_Int_Onumber__ring(X23)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X23),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X23),X22),X20)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X23),X21),X19)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X23),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X23),X22),X19)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X23),X21),X20))
| X20 = X19
| X22 = X21 ),
inference(variable_rename,[status(thm)],[c_0_563]) ).
fof(c_0_1111,plain,
! [X25,X26,X27,X28,X29] :
( ~ class_Ring__and__Field_Oidom(X29)
| ~ class_Int_Onumber__ring(X29)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X29),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X29),X28),X26)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X29),X27),X25)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X29),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X29),X28),X25)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X29),X27),X26))
| X26 = X25
| X28 = X27 ),
inference(variable_rename,[status(thm)],[c_0_564]) ).
fof(c_0_1112,plain,
! [X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),c_HOL_Ozero__class_Ozero(X4)),c_HOL_Ozero__class_Ozero(X4))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),c_HOL_Ozero__class_Ozero(X4)),c_HOL_Ozero__class_Ozero(X4))),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(variable_rename,[status(thm)],[c_0_565]) ).
fof(c_0_1113,plain,
! [X15,X16,X17] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X17)
| hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X17),c_HOL_Oplus__class_Oplus(X17),X17),X16),c_Suc(X15)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X17),X16),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X17),c_HOL_Oplus__class_Oplus(X17),X17),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_566]) ).
fof(c_0_1114,plain,
! [X34,X35,X36,X37,X38] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X38)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X38),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X38),X37),X36)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X38),X35),X34)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X38),X35),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X38),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X38),X37),X36)),X34)) ),
inference(variable_rename,[status(thm)],[c_0_567]) ).
fof(c_0_1115,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X12),X11),X11)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X12),X10),X10)),X12)
| X10 = c_HOL_Ozero__class_Ozero(X12) ),
inference(variable_rename,[status(thm)],[c_0_568]) ).
fof(c_0_1116,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X12),X11),X11)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X12),X10),X10)),X12)
| X11 = c_HOL_Ozero__class_Ozero(X12) ),
inference(variable_rename,[status(thm)],[c_0_569]) ).
fof(c_0_1117,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| c_lessequals(c_HOL_Ozero__class_Ozero(X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X12),X11),X11)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X12),X10),X10)),X12) ),
inference(variable_rename,[status(thm)],[c_0_570]) ).
fof(c_0_1118,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Oring__1(X17)
| hAPP(hAPP(c_Power_Opower__class_Opower(X17),c_HOL_Ouminus__class_Ouminus(X16,X17)),X15) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X17),hAPP(hAPP(c_Power_Opower__class_Opower(X17),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X17),X17)),X15)),hAPP(hAPP(c_Power_Opower__class_Opower(X17),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_571]) ).
fof(c_0_1119,plain,
! [X14,X15,X16,X17] :
( ~ class_Ring__and__Field_Oidom(X17)
| ~ class_Int_Onumber__ring(X17)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X17),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X17),X16),X15)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X17),X16),X14)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X17),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X17),X16),X14)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X17),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_572]) ).
fof(c_0_1120,plain,
! [X19,X20,X21,X22] :
( ~ class_Ring__and__Field_Oidom(X22)
| ~ class_Int_Onumber__ring(X22)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X22),X19),X21)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X22),X19),X20)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X22),X19),X20)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X22),X19),X21)) ),
inference(variable_rename,[status(thm)],[c_0_573]) ).
fof(c_0_1121,plain,
! [X34,X35,X36,X37,X38] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X38)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X38),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X38),X37),X36)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X38),X35),X34)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X38),X37),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X38),X36),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X38),X35),X34))) ),
inference(variable_rename,[status(thm)],[c_0_574]) ).
fof(c_0_1122,plain,
! [X34,X35,X36,X37,X38] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X38)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X38),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X38),X37),X36)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X38),X35),X34)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X38),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X38),X37),X35)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X38),X36),X34)) ),
inference(variable_rename,[status(thm)],[c_0_575]) ).
fof(c_0_1123,plain,
! [X19,X20,X21,X22,X23] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X23)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X23),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X23),X22),X21)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X23),X20),X19)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X23),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X23),X22),X20)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X23),X21),X19)) ),
inference(variable_rename,[status(thm)],[c_0_576]) ).
fof(c_0_1124,plain,
! [X13,X14,X15,X16,X17] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X17)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X17)),c_Polynomial_OpCons(X16,X14,X17)),c_Polynomial_OpCons(X15,X13,X17)) = c_Polynomial_OpCons(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X17),X16),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X17)),X14),X13),X17) ),
inference(variable_rename,[status(thm)],[c_0_577]) ).
fof(c_0_1125,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Oordered__semidom(X17)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X17),X16),hAPP(hAPP(c_Power_Opower__class_Opower(X17),X16),X15)),hAPP(hAPP(c_Power_Opower__class_Opower(X17),X16),X15),X17)
| ~ c_HOL_Oord__class_Oless(X16,c_HOL_Oone__class_Oone(X17),X17)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X17),X16,X17) ),
inference(variable_rename,[status(thm)],[c_0_578]) ).
fof(c_0_1126,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X20)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X20)),c_Polynomial_Osmult(X18,X17,X20)),c_Polynomial_OpCons(X19,X17,X20)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X20))
| X17 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X20)) ),
inference(variable_rename,[status(thm)],[c_0_579]) ).
fof(c_0_1127,plain,
! [X15,X16,X17,X18] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X18)
| hAPP(c_Polynomial_Ocoeff(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X18)),X16),X15),X18),X17) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X18),hAPP(c_Polynomial_Ocoeff(X16,X18),X17)),hAPP(c_Polynomial_Ocoeff(X15,X18),X17)) ),
inference(variable_rename,[status(thm)],[c_0_580]) ).
fof(c_0_1128,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X12)
| hAPP(c_Polynomial_Opoly(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X12)),X11),X10),X12),X9) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X12),hAPP(c_Polynomial_Opoly(X11,X12),X9)),hAPP(c_Polynomial_Opoly(X10,X12),X9)) ),
inference(variable_rename,[status(thm)],[c_0_581]) ).
fof(c_0_1129,plain,
! [X19,X20,X21,X22,X23] :
( ~ class_Ring__and__Field_Opordered__semiring(X23)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X23),X22),X20),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X23),X21),X19),X23)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X23),X20,X23)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X23),X21,X23)
| ~ c_lessequals(X20,X19,X23)
| ~ c_lessequals(X22,X21,X23) ),
inference(variable_rename,[status(thm)],[c_0_582]) ).
fof(c_0_1130,plain,
! [X19,X20,X21,X22,X23] :
( ~ class_Ring__and__Field_Opordered__semiring(X23)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X23),X22),X20),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X23),X21),X19),X23)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X23),X20,X23)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X23),X22,X23)
| ~ c_lessequals(X20,X19,X23)
| ~ c_lessequals(X22,X21,X23) ),
inference(variable_rename,[status(thm)],[c_0_583]) ).
fof(c_0_1131,plain,
! [X19,X20,X21,X22,X23] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X23)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X23),X22),X20),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X23),X21),X19),X23)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X23),X20,X23)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X23),X22,X23)
| ~ c_HOL_Oord__class_Oless(X20,X19,X23)
| ~ c_HOL_Oord__class_Oless(X22,X21,X23) ),
inference(variable_rename,[status(thm)],[c_0_584]) ).
fof(c_0_1132,plain,
! [X19,X20,X21,X22,X23] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X23)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X23),X22),X20),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X23),X21),X19),X23)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X23),X20,X23)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X23),X21,X23)
| ~ c_HOL_Oord__class_Oless(X20,X19,X23)
| ~ c_HOL_Oord__class_Oless(X22,X21,X23) ),
inference(variable_rename,[status(thm)],[c_0_585]) ).
fof(c_0_1133,plain,
! [X19,X20,X21,X22,X23] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X23)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X23),X22),X20),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X23),X21),X19),X23)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X23),X20,X23)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X23),X22,X23)
| ~ c_HOL_Oord__class_Oless(X20,X19,X23)
| ~ c_lessequals(X22,X21,X23) ),
inference(variable_rename,[status(thm)],[c_0_586]) ).
fof(c_0_1134,plain,
! [X19,X20,X21,X22,X23] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X23)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X23),X22),X20),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X23),X21),X19),X23)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X23),X20,X23)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X23),X22,X23)
| ~ c_lessequals(X20,X19,X23)
| ~ c_HOL_Oord__class_Oless(X22,X21,X23) ),
inference(variable_rename,[status(thm)],[c_0_587]) ).
fof(c_0_1135,plain,
! [X7] :
( ~ class_Ring__and__Field_Oidom(t_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__3(X7),t_a)),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1(X7))),c_HOL_Oone__class_Oone(tc_nat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X7,t_a)
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X7,t_a),t_a,t_a) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_588])])]) ).
fof(c_0_1136,plain,
! [X15,X16,X17,X18] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X18)
| hAPP(hAPP(c_Power_Opower__class_Opower(X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X18),X17),X16)),X15) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X18),hAPP(hAPP(c_Power_Opower__class_Opower(X18),X17),X15)),hAPP(hAPP(c_Power_Opower__class_Opower(X18),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_589]) ).
fof(c_0_1137,plain,
! [X10,X11,X12,X13] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X13)
| hAPP(hAPP(c_Power_Opower__class_Opower(X13),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X13),X11),X10)),X12) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X13),hAPP(hAPP(c_Power_Opower__class_Opower(X13),X11),X12)),hAPP(hAPP(c_Power_Opower__class_Opower(X13),X10),X12)) ),
inference(variable_rename,[status(thm)],[c_0_590]) ).
fof(c_0_1138,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X20)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X19),X18)),X17) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X19),X17)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X18),X17)) ),
inference(variable_rename,[status(thm)],[c_0_591]) ).
fof(c_0_1139,plain,
! [X37,X38,X39,X40] :
( ~ class_RealVector_Oreal__normed__algebra(X40)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X40),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X40),X39),X38)),X37) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X40),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X40),X39),X37)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X40),X38),X37)) ),
inference(variable_rename,[status(thm)],[c_0_592]) ).
fof(c_0_1140,plain,
! [X36,X37,X38,X39] :
( ~ class_RealVector_Oreal__normed__algebra(X39)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X39),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X39),X38),X37)),X36) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X39),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X39),X38),X36)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X39),X37),X36)) ),
inference(variable_rename,[status(thm)],[c_0_593]) ).
fof(c_0_1141,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Ocomm__semiring(X20)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X19),X18)),X17) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X19),X17)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X18),X17)) ),
inference(variable_rename,[status(thm)],[c_0_594]) ).
fof(c_0_1142,plain,
! [X23,X24,X25,X26] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X26)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X26),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X26),X25),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X26),X24),X23)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X26),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X26),X25),X24)),X23) ),
inference(variable_rename,[status(thm)],[c_0_595]) ).
fof(c_0_1143,plain,
! [X13,X14,X15,X16] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X16)
| c_Polynomial_Osmult(X15,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X16)),X14),X13),X16) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X16)),c_Polynomial_Osmult(X15,X14,X16)),c_Polynomial_Osmult(X15,X13,X16)) ),
inference(variable_rename,[status(thm)],[c_0_596]) ).
fof(c_0_1144,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Oordered__semidom(X18)
| c_lessequals(X17,X16,X18)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X16,X18)
| ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X18),X17),c_Suc(X15)),hAPP(hAPP(c_Power_Opower__class_Opower(X18),X16),c_Suc(X15)),X18) ),
inference(variable_rename,[status(thm)],[c_0_597]) ).
fof(c_0_1145,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X12),X11),X11)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X12),X10),X10)) != c_HOL_Ozero__class_Ozero(X12)
| X11 = c_HOL_Ozero__class_Ozero(X12) ),
inference(variable_rename,[status(thm)],[c_0_598]) ).
fof(c_0_1146,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X12),X11),X11)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X12),X10),X10)) != c_HOL_Ozero__class_Ozero(X12)
| X10 = c_HOL_Ozero__class_Ozero(X12) ),
inference(variable_rename,[status(thm)],[c_0_599]) ).
fof(c_0_1147,plain,
! [X13,X14,X15,X16] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X16)
| hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X15,X14,X16),X16),X13) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X16),X15),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X16),X13),hAPP(c_Polynomial_Opoly(X14,X16),X13))) ),
inference(variable_rename,[status(thm)],[c_0_600]) ).
fof(c_0_1148,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Oordered__semidom(X17)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X17),X16),X15),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X17),X16),hAPP(hAPP(c_Power_Opower__class_Opower(X17),X16),X15)),X17)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X17),X16,X17) ),
inference(variable_rename,[status(thm)],[c_0_601]) ).
fof(c_0_1149,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Oordered__semidom(X18)
| c_HOL_Oord__class_Oless(X17,X16,X18)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X16,X18)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X18),X17),X15),hAPP(hAPP(c_Power_Opower__class_Opower(X18),X16),X15),X18) ),
inference(variable_rename,[status(thm)],[c_0_602]) ).
fof(c_0_1150,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X20)
| c_HOL_Oord__class_Oless(X19,X18,X20)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X20),X17,X20)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X19),X17),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X18),X17),X20) ),
inference(variable_rename,[status(thm)],[c_0_603]) ).
fof(c_0_1151,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X20)
| c_HOL_Oord__class_Oless(X19,X18,X20)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X20),X17,X20)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X18),X20) ),
inference(variable_rename,[status(thm)],[c_0_604]) ).
fof(c_0_1152,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Oordered__semiring(X20)
| c_HOL_Oord__class_Oless(X19,X18,X20)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X20),X17,X20)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X19),X17),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X18),X17),X20) ),
inference(variable_rename,[status(thm)],[c_0_605]) ).
fof(c_0_1153,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Oordered__semiring(X20)
| c_HOL_Oord__class_Oless(X19,X18,X20)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X20),X17,X20)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X18),X20) ),
inference(variable_rename,[status(thm)],[c_0_606]) ).
fof(c_0_1154,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X20)
| c_lessequals(X19,X18,X20)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X20),X17,X20)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X19),X17),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X18),X17),X20) ),
inference(variable_rename,[status(thm)],[c_0_607]) ).
fof(c_0_1155,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X20)
| c_lessequals(X19,X18,X20)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X20),X17,X20)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X18),X20) ),
inference(variable_rename,[status(thm)],[c_0_608]) ).
fof(c_0_1156,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X20)
| c_lessequals(X19,X18,X20)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X18),X20)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X20),X17,X20) ),
inference(variable_rename,[status(thm)],[c_0_609]) ).
fof(c_0_1157,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X20)
| c_lessequals(X18,X19,X20)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X18),X20)
| ~ c_HOL_Oord__class_Oless(X17,c_HOL_Ozero__class_Ozero(X20),X20) ),
inference(variable_rename,[status(thm)],[c_0_610]) ).
fof(c_0_1158,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X20)
| c_HOL_Oord__class_Oless(X19,X18,X20)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X18),X20)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X20),X17,X20) ),
inference(variable_rename,[status(thm)],[c_0_611]) ).
fof(c_0_1159,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X20)
| c_HOL_Oord__class_Oless(X18,X19,X20)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X18),X20)
| ~ c_HOL_Oord__class_Oless(X17,c_HOL_Ozero__class_Ozero(X20),X20) ),
inference(variable_rename,[status(thm)],[c_0_612]) ).
fof(c_0_1160,plain,
! [X15,X16,X17,X18] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X18)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X18)),c_Polynomial_Omonom(X17,X15,X18)),c_Polynomial_Omonom(X16,X15,X18)) = c_Polynomial_Omonom(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X18),X17),X16),X15,X18) ),
inference(variable_rename,[status(thm)],[c_0_613]) ).
fof(c_0_1161,plain,
! [X13,X14,X15,X16] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X16)
| c_Polynomial_Osmult(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X16),X15),X14),X13,X16) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X16)),c_Polynomial_Osmult(X15,X13,X16)),c_Polynomial_Osmult(X14,X13,X16)) ),
inference(variable_rename,[status(thm)],[c_0_614]) ).
fof(c_0_1162,plain,
! [X23,X24,X25] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X25)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X25),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X25),X24),X23)),X23) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X25),X24),c_HOL_Oone__class_Oone(X25))),X23) ),
inference(variable_rename,[status(thm)],[c_0_615]) ).
fof(c_0_1163,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X20)
| c_HOL_Oord__class_Oless(X17,c_HOL_Ozero__class_Ozero(X20),X20)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X20),X17,X20)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X18),X20) ),
inference(variable_rename,[status(thm)],[c_0_616]) ).
fof(c_0_1164,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X20)
| c_HOL_Oord__class_Oless(X17,c_HOL_Ozero__class_Ozero(X20),X20)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X20),X17,X20)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X19),X17),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X18),X17),X20) ),
inference(variable_rename,[status(thm)],[c_0_617]) ).
fof(c_0_1165,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X20)
| c_HOL_Oord__class_Oless(X18,X19,X20)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X20),X17,X20)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X18),X20) ),
inference(variable_rename,[status(thm)],[c_0_618]) ).
fof(c_0_1166,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X20)
| c_HOL_Oord__class_Oless(X17,c_HOL_Ozero__class_Ozero(X20),X20)
| c_HOL_Oord__class_Oless(X19,X18,X20)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X18),X20) ),
inference(variable_rename,[status(thm)],[c_0_619]) ).
fof(c_0_1167,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X20)
| c_HOL_Oord__class_Oless(X18,X19,X20)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X20),X17,X20)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X19),X17),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X18),X17),X20) ),
inference(variable_rename,[status(thm)],[c_0_620]) ).
fof(c_0_1168,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X20)
| c_HOL_Oord__class_Oless(X17,c_HOL_Ozero__class_Ozero(X20),X20)
| c_HOL_Oord__class_Oless(X19,X18,X20)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X19),X17),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X18),X17),X20) ),
inference(variable_rename,[status(thm)],[c_0_621]) ).
fof(c_0_1169,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X20)
| c_HOL_Oord__class_Oless(X18,X19,X20)
| c_HOL_Oord__class_Oless(X19,X18,X20)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X18),X20) ),
inference(variable_rename,[status(thm)],[c_0_622]) ).
fof(c_0_1170,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X20)
| c_HOL_Oord__class_Oless(X18,X19,X20)
| c_HOL_Oord__class_Oless(X19,X18,X20)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X19),X17),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X18),X17),X20) ),
inference(variable_rename,[status(thm)],[c_0_623]) ).
fof(c_0_1171,plain,
! [X34,X35,X36,X37] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X37)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X37),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X37),X36),X35)),X34) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X37),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X37),X36),X34)),X35) ),
inference(variable_rename,[status(thm)],[c_0_624]) ).
fof(c_0_1172,plain,
! [X35,X36,X37,X38] :
( ~ class_RealVector_Oreal__normed__algebra(X38)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X38),X36),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X38),X37),X35)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X38),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X38),X36),X37)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X38),X36),X35)) ),
inference(variable_rename,[status(thm)],[c_0_625]) ).
fof(c_0_1173,plain,
! [X38,X39,X40,X41] :
( ~ class_RealVector_Oreal__normed__algebra(X41)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X41),X40),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X39),X38)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X41),X40),X39)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X41),X40),X38)) ),
inference(variable_rename,[status(thm)],[c_0_626]) ).
fof(c_0_1174,plain,
! [X14,X15,X16,X17] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X17)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X17),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X17),X15),X14)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X17),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X17),X16),X15)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X17),X16),X14)) ),
inference(variable_rename,[status(thm)],[c_0_627]) ).
fof(c_0_1175,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X20)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X19),X18)),X17) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X19),X17)),X18) ),
inference(variable_rename,[status(thm)],[c_0_628]) ).
fof(c_0_1176,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X12)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X12),hAPP(hAPP(c_Power_Opower__class_Opower(X12),X9),X11)),hAPP(hAPP(c_Power_Opower__class_Opower(X12),X9),X10)) = hAPP(hAPP(c_Power_Opower__class_Opower(X12),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X10)) ),
inference(variable_rename,[status(thm)],[c_0_629]) ).
fof(c_0_1177,plain,
! [X23,X24,X25,X26] :
( ~ class_OrderedGroup_Omonoid__mult(X26)
| hAPP(hAPP(c_Power_Opower__class_Opower(X26),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X23)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X26),hAPP(hAPP(c_Power_Opower__class_Opower(X26),X25),X24)),hAPP(hAPP(c_Power_Opower__class_Opower(X26),X25),X23)) ),
inference(variable_rename,[status(thm)],[c_0_630]) ).
fof(c_0_1178,plain,
! [X20,X21,X22,X23,X24] :
( ~ class_Ring__and__Field_Oidom(X24)
| ~ class_Int_Onumber__ring(X24)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X24),X20),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X24),X21),X23)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X24),X20),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X24),X21),X22))
| X23 = X22
| X21 = c_HOL_Ozero__class_Ozero(X24) ),
inference(variable_rename,[status(thm)],[c_0_631]) ).
fof(c_0_1179,plain,
! [X19,X20,X21,X22,X23] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X23)
| c_lessequals(X22,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X23),X21),X19),X23)
| ~ c_lessequals(X20,X19,X23)
| ~ c_lessequals(X22,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X23),X21),X20),X23) ),
inference(variable_rename,[status(thm)],[c_0_632]) ).
fof(c_0_1180,plain,
! [X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),c_HOL_Ozero__class_Ozero(X4)),c_HOL_Ozero__class_Ozero(X4))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),c_HOL_Ozero__class_Ozero(X4)),c_HOL_Ozero__class_Ozero(X4))) = c_HOL_Ozero__class_Ozero(X4) ),
inference(variable_rename,[status(thm)],[c_0_633]) ).
fof(c_0_1181,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Oordered__semidom(X17)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X17),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X17),X16),hAPP(hAPP(c_Power_Opower__class_Opower(X17),X16),X15)),X17)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X17),X16,X17) ),
inference(variable_rename,[status(thm)],[c_0_634]) ).
fof(c_0_1182,plain,
! [X17,X18,X19,X20] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X20)
| c_lessequals(X19,X18,X20)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X19),X17),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X18),X17),X20) ),
inference(variable_rename,[status(thm)],[c_0_635]) ).
fof(c_0_1183,plain,
! [X17,X18,X19,X20] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X20)
| c_lessequals(X19,X18,X20)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X17),X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X17),X18),X20) ),
inference(variable_rename,[status(thm)],[c_0_636]) ).
fof(c_0_1184,plain,
! [X17,X18,X19,X20] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X20)
| c_HOL_Oord__class_Oless(X19,X18,X20)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X17),X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X17),X18),X20) ),
inference(variable_rename,[status(thm)],[c_0_637]) ).
fof(c_0_1185,plain,
! [X17,X18,X19,X20] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X20)
| c_HOL_Oord__class_Oless(X19,X18,X20)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X19),X17),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X18),X17),X20) ),
inference(variable_rename,[status(thm)],[c_0_638]) ).
fof(c_0_1186,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__idom(X12)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X12),X10),X11),X11,X12)
| ~ c_lessequals(X10,c_HOL_Oone__class_Oone(X12),X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X10,X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_639]) ).
fof(c_0_1187,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__idom(X12)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X12),X11),X10),X11,X12)
| ~ c_lessequals(X10,c_HOL_Oone__class_Oone(X12),X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X10,X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_640]) ).
fof(c_0_1188,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Opordered__ring(X20)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X19),X17),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X18),X17),X20)
| ~ c_lessequals(X17,c_HOL_Ozero__class_Ozero(X20),X20)
| ~ c_lessequals(X18,X19,X20) ),
inference(variable_rename,[status(thm)],[c_0_641]) ).
fof(c_0_1189,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Opordered__ring(X20)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X18),X20)
| ~ c_lessequals(X17,c_HOL_Ozero__class_Ozero(X20),X20)
| ~ c_lessequals(X18,X19,X20) ),
inference(variable_rename,[status(thm)],[c_0_642]) ).
fof(c_0_1190,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Omult__mono(X20)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X19),X17),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X18),X17),X20)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X20),X17,X20)
| ~ c_lessequals(X19,X18,X20) ),
inference(variable_rename,[status(thm)],[c_0_643]) ).
fof(c_0_1191,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Omult__mono(X20)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X18),X20)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X20),X17,X20)
| ~ c_lessequals(X19,X18,X20) ),
inference(variable_rename,[status(thm)],[c_0_644]) ).
fof(c_0_1192,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Omult__mono1(X20)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X18),X20)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X20),X17,X20)
| ~ c_lessequals(X19,X18,X20) ),
inference(variable_rename,[status(thm)],[c_0_645]) ).
fof(c_0_1193,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Oordered__semidom(X18)
| c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X18),X17),X15),hAPP(hAPP(c_Power_Opower__class_Opower(X18),X16),X15),X18)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18)
| ~ c_lessequals(X17,X16,X18) ),
inference(variable_rename,[status(thm)],[c_0_646]) ).
fof(c_0_1194,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X20)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X18),X20)
| ~ c_lessequals(X19,X18,X20)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X20),X17,X20) ),
inference(variable_rename,[status(thm)],[c_0_647]) ).
fof(c_0_1195,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X20)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X18),X20)
| ~ c_lessequals(X18,X19,X20)
| ~ c_HOL_Oord__class_Oless(X17,c_HOL_Ozero__class_Ozero(X20),X20) ),
inference(variable_rename,[status(thm)],[c_0_648]) ).
fof(c_0_1196,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X20)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X18),X20)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X20),X17,X20)
| ~ c_HOL_Oord__class_Oless(X19,X18,X20) ),
inference(variable_rename,[status(thm)],[c_0_649]) ).
fof(c_0_1197,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X20)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X19),X17),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X18),X17),X20)
| ~ c_HOL_Oord__class_Oless(X18,X19,X20)
| ~ c_HOL_Oord__class_Oless(X17,c_HOL_Ozero__class_Ozero(X20),X20) ),
inference(variable_rename,[status(thm)],[c_0_650]) ).
fof(c_0_1198,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X20)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X19),X17),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X18),X17),X20)
| ~ c_HOL_Oord__class_Oless(X19,X18,X20)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X20),X17,X20) ),
inference(variable_rename,[status(thm)],[c_0_651]) ).
fof(c_0_1199,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X20)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X19),X17),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X18),X17),X20)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X20),X17,X20)
| ~ c_HOL_Oord__class_Oless(X19,X18,X20) ),
inference(variable_rename,[status(thm)],[c_0_652]) ).
fof(c_0_1200,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X20)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X19),X17),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X18),X17),X20)
| ~ c_HOL_Oord__class_Oless(X17,c_HOL_Ozero__class_Ozero(X20),X20)
| ~ c_HOL_Oord__class_Oless(X18,X19,X20) ),
inference(variable_rename,[status(thm)],[c_0_653]) ).
fof(c_0_1201,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X20)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X18),X20)
| ~ c_HOL_Oord__class_Oless(X18,X19,X20)
| ~ c_HOL_Oord__class_Oless(X17,c_HOL_Ozero__class_Ozero(X20),X20) ),
inference(variable_rename,[status(thm)],[c_0_654]) ).
fof(c_0_1202,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X20)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X18),X20)
| ~ c_HOL_Oord__class_Oless(X19,X18,X20)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X20),X17,X20) ),
inference(variable_rename,[status(thm)],[c_0_655]) ).
fof(c_0_1203,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X20)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X18),X20)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X20),X17,X20)
| ~ c_HOL_Oord__class_Oless(X19,X18,X20) ),
inference(variable_rename,[status(thm)],[c_0_656]) ).
fof(c_0_1204,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X20)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X18),X20)
| ~ c_HOL_Oord__class_Oless(X17,c_HOL_Ozero__class_Ozero(X20),X20)
| ~ c_HOL_Oord__class_Oless(X18,X19,X20) ),
inference(variable_rename,[status(thm)],[c_0_657]) ).
fof(c_0_1205,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X20)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X18),X20)
| ~ c_HOL_Oord__class_Oless(X19,X18,X20)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X20),X17,X20) ),
inference(variable_rename,[status(thm)],[c_0_658]) ).
fof(c_0_1206,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X20)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X17),X18),X20)
| ~ c_HOL_Oord__class_Oless(X18,X19,X20)
| ~ c_HOL_Oord__class_Oless(X17,c_HOL_Ozero__class_Ozero(X20),X20) ),
inference(variable_rename,[status(thm)],[c_0_659]) ).
fof(c_0_1207,plain,
( ~ class_HOL_Ozero(t_a)
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_p,t_a) = c_HOL_OIf(c_fequal(v_p,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),tc_Polynomial_Opoly(t_a)),c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_Polynomial_Odegree(v_p,t_a)),tc_nat) ),
c_0_660 ).
fof(c_0_1208,plain,
! [X23,X24,X25] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X25)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X25),X23),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X25),X24),X23)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X25),X24),c_HOL_Oone__class_Oone(X25))),X23) ),
inference(variable_rename,[status(thm)],[c_0_661]) ).
fof(c_0_1209,plain,
! [X19,X20,X21,X22,X23] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X23)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X23),X22),X20),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X23),X21),X19),X23)
| ~ c_lessequals(X20,X19,X23)
| ~ c_lessequals(X22,X21,X23) ),
inference(variable_rename,[status(thm)],[c_0_662]) ).
fof(c_0_1210,plain,
! [X19,X20,X21,X22,X23] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X23)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X23),X22),X20),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X23),X21),X19),X23)
| ~ c_HOL_Oord__class_Oless(X20,X19,X23)
| ~ c_HOL_Oord__class_Oless(X22,X21,X23) ),
inference(variable_rename,[status(thm)],[c_0_663]) ).
fof(c_0_1211,plain,
! [X19,X20,X21,X22,X23] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X23)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X23),X22),X20),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X23),X21),X19),X23)
| ~ c_lessequals(X20,X19,X23)
| ~ c_HOL_Oord__class_Oless(X22,X21,X23) ),
inference(variable_rename,[status(thm)],[c_0_664]) ).
fof(c_0_1212,plain,
! [X19,X20,X21,X22,X23] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X23)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X23),X22),X20),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X23),X21),X19),X23)
| ~ c_HOL_Oord__class_Oless(X20,X19,X23)
| ~ c_lessequals(X22,X21,X23) ),
inference(variable_rename,[status(thm)],[c_0_665]) ).
fof(c_0_1213,plain,
! [X13,X14,X15,X16] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X16)
| c_Polynomial_Osmult(X15,c_Polynomial_OpCons(X14,X13,X16),X16) = c_Polynomial_OpCons(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X16),X15),X14),c_Polynomial_Osmult(X15,X13,X16),X16) ),
inference(variable_rename,[status(thm)],[c_0_666]) ).
fof(c_0_1214,plain,
! [X20,X21,X22,X23,X24] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X24)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X24)),X22),c_Polynomial_Osmult(X23,X21,X24)) != c_Polynomial_OpCons(X20,X21,X24)
| X20 = hAPP(c_Polynomial_Opoly(X22,X24),X23) ),
inference(variable_rename,[status(thm)],[c_0_667]) ).
fof(c_0_1215,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X15)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X15),X13,X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X15),X14,X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X15),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X13),X14),X15) ),
inference(variable_rename,[status(thm)],[c_0_668]) ).
fof(c_0_1216,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X15)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X15),X13,X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X15),X14,X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X15),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X14),X13),X15) ),
inference(variable_rename,[status(thm)],[c_0_669]) ).
fof(c_0_1217,plain,
! [X17,X18,X19,X20] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X20)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X19),X18)),X17) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X18),X17)) ),
inference(variable_rename,[status(thm)],[c_0_670]) ).
fof(c_0_1218,plain,
! [X34,X35,X36,X37] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X37)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X37),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X37),X36),X35)),X34) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X37),X36),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X37),X35),X34)) ),
inference(variable_rename,[status(thm)],[c_0_671]) ).
fof(c_0_1219,plain,
! [X34,X35,X36,X37] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X37)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X37),X36),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X37),X35),X34)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X37),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X37),X36),X35)),X34) ),
inference(variable_rename,[status(thm)],[c_0_672]) ).
fof(c_0_1220,plain,
! [X14,X15,X16,X17] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X17)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X17),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X17),X15),X14)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X17),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X17),X16),X15)),X14) ),
inference(variable_rename,[status(thm)],[c_0_673]) ).
fof(c_0_1221,plain,
! [X15,X16,X17] :
( ~ class_OrderedGroup_Omonoid__mult(X17)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X17),hAPP(hAPP(c_Power_Opower__class_Opower(X17),X16),X15)),X16) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X17),X16),hAPP(hAPP(c_Power_Opower__class_Opower(X17),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_674]) ).
fof(c_0_1222,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X20)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X19),X18)),X17) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X18),X17)) ),
inference(variable_rename,[status(thm)],[c_0_675]) ).
fof(c_0_1223,plain,
! [X19,X20,X21,X22] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X22)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),X21),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),X20),X19)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),X21),X20)),X19) ),
inference(variable_rename,[status(thm)],[c_0_676]) ).
fof(c_0_1224,plain,
! [X17,X18,X19,X20] :
( ~ class_OrderedGroup_Oab__semigroup__add(X20)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X19),X18)),X17) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X18),X17)) ),
inference(variable_rename,[status(thm)],[c_0_677]) ).
fof(c_0_1225,plain,
! [X14,X15,X16,X17] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X17)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X17),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X17),X15),X14)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X17),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X17),X16),X15)),X14) ),
inference(variable_rename,[status(thm)],[c_0_678]) ).
fof(c_0_1226,plain,
! [X17,X18,X19,X20] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X20)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X19),X18)),X17) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X18),X17)) ),
inference(variable_rename,[status(thm)],[c_0_679]) ).
fof(c_0_1227,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
| hAPP(c_Polynomial_Opoly(c_Polynomial_Omonom(X17,X16,X18),X18),X15) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X18),X17),hAPP(hAPP(c_Power_Opower__class_Opower(X18),X15),X16)) ),
inference(variable_rename,[status(thm)],[c_0_680]) ).
fof(c_0_1228,plain,
! [X22,X23,X24,X25] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X25)
| hAPP(c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X23,X24,X25),X25),X22) = hAPP(c_Polynomial_Opoly(X23,X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X25),X24),X22)) ),
inference(variable_rename,[status(thm)],[c_0_681]) ).
fof(c_0_1229,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X18)
| hAPP(c_Polynomial_Ocoeff(c_Polynomial_Osmult(X17,X15,X18),X18),X16) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X18),X17),hAPP(c_Polynomial_Ocoeff(X15,X18),X16)) ),
inference(variable_rename,[status(thm)],[c_0_682]) ).
fof(c_0_1230,plain,
! [X13,X14,X15,X16] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X16)
| hAPP(c_Polynomial_Opoly(c_Polynomial_Osmult(X15,X14,X16),X16),X13) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X16),X15),hAPP(c_Polynomial_Opoly(X14,X16),X13)) ),
inference(variable_rename,[status(thm)],[c_0_683]) ).
fof(c_0_1231,plain,
! [X23,X24] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X24)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X24),X23),X23) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X24),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X24),c_HOL_Oone__class_Oone(X24)),c_HOL_Oone__class_Oone(X24))),X23) ),
inference(variable_rename,[status(thm)],[c_0_684]) ).
fof(c_0_1232,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X15)
| c_lessequals(X14,c_HOL_Ozero__class_Ozero(X15),X15)
| c_lessequals(c_HOL_Ozero__class_Ozero(X15),X14,X15)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X15),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X14),X13),X15) ),
inference(variable_rename,[status(thm)],[c_0_685]) ).
fof(c_0_1233,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X15)
| c_lessequals(X13,c_HOL_Ozero__class_Ozero(X15),X15)
| c_lessequals(c_HOL_Ozero__class_Ozero(X15),X14,X15)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X15),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X14),X13),X15) ),
inference(variable_rename,[status(thm)],[c_0_686]) ).
fof(c_0_1234,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X15)
| c_lessequals(X14,c_HOL_Ozero__class_Ozero(X15),X15)
| c_lessequals(c_HOL_Ozero__class_Ozero(X15),X13,X15)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X15),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X14),X13),X15) ),
inference(variable_rename,[status(thm)],[c_0_687]) ).
fof(c_0_1235,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X15)
| c_lessequals(X13,c_HOL_Ozero__class_Ozero(X15),X15)
| c_lessequals(c_HOL_Ozero__class_Ozero(X15),X13,X15)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X15),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X14),X13),X15) ),
inference(variable_rename,[status(thm)],[c_0_688]) ).
fof(c_0_1236,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X15)
| c_lessequals(c_HOL_Ozero__class_Ozero(X15),X13,X15)
| c_lessequals(X13,c_HOL_Ozero__class_Ozero(X15),X15)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X14),X13),c_HOL_Ozero__class_Ozero(X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_689]) ).
fof(c_0_1237,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X15)
| c_lessequals(X14,c_HOL_Ozero__class_Ozero(X15),X15)
| c_lessequals(X13,c_HOL_Ozero__class_Ozero(X15),X15)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X14),X13),c_HOL_Ozero__class_Ozero(X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_690]) ).
fof(c_0_1238,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X15)
| c_lessequals(c_HOL_Ozero__class_Ozero(X15),X13,X15)
| c_lessequals(c_HOL_Ozero__class_Ozero(X15),X14,X15)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X14),X13),c_HOL_Ozero__class_Ozero(X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_691]) ).
fof(c_0_1239,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X15)
| c_lessequals(X14,c_HOL_Ozero__class_Ozero(X15),X15)
| c_lessequals(c_HOL_Ozero__class_Ozero(X15),X14,X15)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X14),X13),c_HOL_Ozero__class_Ozero(X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_692]) ).
fof(c_0_1240,plain,
! [X18,X19,X20,X21,X22] :
( ~ class_OrderedGroup_Oab__group__add(X22)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),X20),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),X19),X18)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),X19),X21)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),X20),X18) = X21 ),
inference(variable_rename,[status(thm)],[c_0_693]) ).
fof(c_0_1241,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Oordered__semidom(X18)
| hAPP(hAPP(c_Power_Opower__class_Opower(X18),X17),c_Suc(X15)) != hAPP(hAPP(c_Power_Opower__class_Opower(X18),X16),c_Suc(X15))
| X17 = X16
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X16,X18)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18) ),
inference(variable_rename,[status(thm)],[c_0_694]) ).
fof(c_0_1242,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X12)
| hAPP(c_Polynomial_Opoly(c_Polynomial_Opcompose(X11,X10,X12),X12),X9) = hAPP(c_Polynomial_Opoly(X11,X12),hAPP(c_Polynomial_Opoly(X10,X12),X9)) ),
inference(variable_rename,[status(thm)],[c_0_695]) ).
fof(c_0_1243,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Oordered__semidom(X17)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X17),X16),c_Suc(X15)),c_HOL_Oone__class_Oone(X17),X17)
| ~ c_HOL_Oord__class_Oless(X16,c_HOL_Oone__class_Oone(X17),X17)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X17),X16,X17) ),
inference(variable_rename,[status(thm)],[c_0_696]) ).
fof(c_0_1244,plain,
! [X15,X16] :
( ~ class_Ring__and__Field_Oordered__idom(X16)
| X15 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X16),hAPP(hAPP(c_Power_Opower__class_Opower(X16),c_HOL_Ozero__class_Ozero(X16)),X15),X16)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X16),c_HOL_Ozero__class_Ozero(X16),X16) ),
inference(variable_rename,[status(thm)],[c_0_697]) ).
fof(c_0_1245,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Opordered__ring(X15)
| c_lessequals(c_HOL_Ozero__class_Ozero(X15),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X14),X13),X15)
| ~ c_lessequals(X13,c_HOL_Ozero__class_Ozero(X15),X15)
| ~ c_lessequals(X14,c_HOL_Ozero__class_Ozero(X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_698]) ).
fof(c_0_1246,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Opordered__ring(X15)
| c_lessequals(c_HOL_Ozero__class_Ozero(X15),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X14),X13),X15)
| ~ c_lessequals(X13,c_HOL_Ozero__class_Ozero(X15),X15)
| ~ c_lessequals(X14,c_HOL_Ozero__class_Ozero(X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_699]) ).
fof(c_0_1247,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Opordered__ring(X15)
| c_lessequals(c_HOL_Ozero__class_Ozero(X15),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X14),X13),X15)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X15),X13,X15)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X15),X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_700]) ).
fof(c_0_1248,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X15)
| c_lessequals(c_HOL_Ozero__class_Ozero(X15),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X14),X13),X15)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X15),X13,X15)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X15),X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_701]) ).
fof(c_0_1249,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X15)
| c_lessequals(c_HOL_Ozero__class_Ozero(X15),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X14),X13),X15)
| ~ c_lessequals(X13,c_HOL_Ozero__class_Ozero(X15),X15)
| ~ c_lessequals(X14,c_HOL_Ozero__class_Ozero(X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_702]) ).
fof(c_0_1250,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X15)
| c_lessequals(c_HOL_Ozero__class_Ozero(X15),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X14),X13),X15)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X15),X13,X15)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X15),X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_703]) ).
fof(c_0_1251,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X15)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X14),X13),c_HOL_Ozero__class_Ozero(X15),X15)
| ~ c_lessequals(X13,c_HOL_Ozero__class_Ozero(X15),X15)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X15),X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_704]) ).
fof(c_0_1252,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X15)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X14),X13),c_HOL_Ozero__class_Ozero(X15),X15)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X15),X13,X15)
| ~ c_lessequals(X14,c_HOL_Ozero__class_Ozero(X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_705]) ).
fof(c_0_1253,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X15)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X14),X13),c_HOL_Ozero__class_Ozero(X15),X15)
| ~ c_lessequals(X13,c_HOL_Ozero__class_Ozero(X15),X15)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X15),X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_706]) ).
fof(c_0_1254,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X15)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X14),X13),c_HOL_Ozero__class_Ozero(X15),X15)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X15),X13,X15)
| ~ c_lessequals(X14,c_HOL_Ozero__class_Ozero(X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_707]) ).
fof(c_0_1255,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X15)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X14),X13),c_HOL_Ozero__class_Ozero(X15),X15)
| ~ c_lessequals(X13,c_HOL_Ozero__class_Ozero(X15),X15)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X15),X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_708]) ).
fof(c_0_1256,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X15)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X14),X13),c_HOL_Ozero__class_Ozero(X15),X15)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X15),X13,X15)
| ~ c_lessequals(X14,c_HOL_Ozero__class_Ozero(X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_709]) ).
fof(c_0_1257,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X15)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X13),X14),c_HOL_Ozero__class_Ozero(X15),X15)
| ~ c_lessequals(X13,c_HOL_Ozero__class_Ozero(X15),X15)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X15),X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_710]) ).
fof(c_0_1258,plain,
! [X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X15)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X13),X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X15),X13,X15)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X15),X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_711]) ).
fof(c_0_1259,plain,
! [X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X15)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X13),X15)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X15),X13,X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X15),X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_712]) ).
fof(c_0_1260,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X15)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X13),X14),c_HOL_Ozero__class_Ozero(X15),X15)
| ~ c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X15),X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X15),X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_713]) ).
fof(c_0_1261,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X15)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X14),X13),c_HOL_Ozero__class_Ozero(X15),X15)
| ~ c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X15),X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X15),X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_714]) ).
fof(c_0_1262,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X15)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X14),X13),c_HOL_Ozero__class_Ozero(X15),X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X15),X13,X15)
| ~ c_HOL_Oord__class_Oless(X14,c_HOL_Ozero__class_Ozero(X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_715]) ).
fof(c_0_1263,plain,
! [X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X15)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X13),c_HOL_Ozero__class_Ozero(X15),X15)
| ~ c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X15),X15)
| ~ c_lessequals(X14,c_HOL_Ozero__class_Ozero(X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_716]) ).
fof(c_0_1264,plain,
! [X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X15)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X13),c_HOL_Ozero__class_Ozero(X15),X15)
| ~ c_lessequals(X13,c_HOL_Ozero__class_Ozero(X15),X15)
| ~ c_HOL_Oord__class_Oless(X14,c_HOL_Ozero__class_Ozero(X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_717]) ).
fof(c_0_1265,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X15)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X15),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X14),X13),X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X15),X13,X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X15),X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_718]) ).
fof(c_0_1266,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X15)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X15),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X14),X13),X15)
| ~ c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X15),X15)
| ~ c_HOL_Oord__class_Oless(X14,c_HOL_Ozero__class_Ozero(X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_719]) ).
fof(c_0_1267,plain,
! [X23,X24,X25] :
( ~ class_Ring__and__Field_Oordered__semidom(X25)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X25),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X25),X24),X23),X25)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X25),X23,X25)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X25),X24,X25) ),
inference(variable_rename,[status(thm)],[c_0_720]) ).
fof(c_0_1268,plain,
! [X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X15)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X13),c_HOL_Ozero__class_Ozero(X15),X15)
| ~ c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X15),X15)
| ~ c_HOL_Oord__class_Oless(X14,c_HOL_Ozero__class_Ozero(X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_721]) ).
fof(c_0_1269,plain,
! [X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X15)
| c_lessequals(c_HOL_Ozero__class_Ozero(X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X13),X15)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X15),X13,X15)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X15),X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_722]) ).
fof(c_0_1270,plain,
! [X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X15)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X13),X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X15),X13,X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X15),X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_723]) ).
fof(c_0_1271,plain,
! [X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X15)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X13),c_HOL_Ozero__class_Ozero(X15),X15)
| ~ c_lessequals(X13,c_HOL_Ozero__class_Ozero(X15),X15)
| ~ c_lessequals(X14,c_HOL_Ozero__class_Ozero(X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_724]) ).
fof(c_0_1272,plain,
! [X17,X18,X19,X20] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X20)
| ~ class_OrderedGroup_Ocomm__monoid__add(X20)
| c_HOL_Oord__class_Oless(X18,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X19),X17),X20)
| ~ c_lessequals(X18,X17,X20)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X20),X19,X20) ),
inference(variable_rename,[status(thm)],[c_0_725]) ).
fof(c_0_1273,plain,
! [X17,X18,X19,X20] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X20)
| ~ class_OrderedGroup_Ocomm__monoid__add(X20)
| c_HOL_Oord__class_Oless(X18,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X19),X17),X20)
| ~ c_HOL_Oord__class_Oless(X18,X17,X20)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X20),X19,X20) ),
inference(variable_rename,[status(thm)],[c_0_726]) ).
fof(c_0_1274,plain,
! [X17,X18,X19,X20] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X20)
| ~ class_OrderedGroup_Ocomm__monoid__add(X20)
| c_lessequals(X18,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X19),X17),X20)
| ~ c_lessequals(X18,X17,X20)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X20),X19,X20) ),
inference(variable_rename,[status(thm)],[c_0_727]) ).
fof(c_0_1275,plain,
! [X17,X18,X19,X20] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X20)
| ~ class_OrderedGroup_Ocomm__monoid__add(X20)
| c_lessequals(X18,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X19),X17),X20)
| ~ c_lessequals(X18,X19,X20)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X20),X17,X20) ),
inference(variable_rename,[status(thm)],[c_0_728]) ).
fof(c_0_1276,plain,
! [X17,X18,X19,X20] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X20)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X19),X17),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X18),X17),X20)
| ~ c_lessequals(X19,X18,X20) ),
inference(variable_rename,[status(thm)],[c_0_729]) ).
fof(c_0_1277,plain,
! [X17,X18,X19,X20] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X20)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X17),X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X17),X18),X20)
| ~ c_lessequals(X19,X18,X20) ),
inference(variable_rename,[status(thm)],[c_0_730]) ).
fof(c_0_1278,plain,
! [X17,X18,X19,X20] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X20)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X19),X17),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X18),X17),X20)
| ~ c_lessequals(X19,X18,X20) ),
inference(variable_rename,[status(thm)],[c_0_731]) ).
fof(c_0_1279,plain,
! [X17,X18,X19,X20] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X20)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X17),X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X17),X18),X20)
| ~ c_lessequals(X19,X18,X20) ),
inference(variable_rename,[status(thm)],[c_0_732]) ).
fof(c_0_1280,plain,
! [X17,X18,X19,X20] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X20)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X17),X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X17),X18),X20)
| ~ c_HOL_Oord__class_Oless(X19,X18,X20) ),
inference(variable_rename,[status(thm)],[c_0_733]) ).
fof(c_0_1281,plain,
! [X17,X18,X19,X20] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X20)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X17),X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X17),X18),X20)
| ~ c_HOL_Oord__class_Oless(X19,X18,X20) ),
inference(variable_rename,[status(thm)],[c_0_734]) ).
fof(c_0_1282,plain,
! [X17,X18,X19,X20] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X20)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X19),X17),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X18),X17),X20)
| ~ c_HOL_Oord__class_Oless(X19,X18,X20) ),
inference(variable_rename,[status(thm)],[c_0_735]) ).
fof(c_0_1283,plain,
! [X17,X18,X19,X20] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X20)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X19),X17),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X18),X17),X20)
| ~ c_HOL_Oord__class_Oless(X19,X18,X20) ),
inference(variable_rename,[status(thm)],[c_0_736]) ).
fof(c_0_1284,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Oordered__semidom(X20)
| c_HOL_Oord__class_Oless(X18,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X19),X17),X20)
| ~ c_HOL_Oord__class_Oless(X18,X17,X20)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X20),X19,X20) ),
inference(variable_rename,[status(thm)],[c_0_737]) ).
fof(c_0_1285,plain,
! [X13,X14,X15] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X15)
| c_lessequals(X14,c_HOL_Ouminus__class_Ouminus(X13,X15),X15)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X13),c_HOL_Ozero__class_Ozero(X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_738]) ).
fof(c_0_1286,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Oordered__idom(X17)
| X15 = c_HOL_Ozero__class_Ozero(X17)
| c_lessequals(X15,c_HOL_Ozero__class_Ozero(X17),X17)
| ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X17),X15),X16),c_HOL_Ozero__class_Ozero(X17),X17) ),
inference(variable_rename,[status(thm)],[c_0_739]) ).
fof(c_0_1287,plain,
! [X15,X16] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X16)
| hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X16),c_HOL_Oplus__class_Oplus(X16),X16),c_HOL_Ozero__class_Ozero(X16)),X15) = c_HOL_Ozero__class_Ozero(X16) ),
inference(variable_rename,[status(thm)],[c_0_740]) ).
fof(c_0_1288,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X18)
| c_Polynomial_Osmult(X17,c_Polynomial_Omonom(X16,X15,X18),X18) = c_Polynomial_Omonom(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X18),X17),X16),X15,X18) ),
inference(variable_rename,[status(thm)],[c_0_741]) ).
fof(c_0_1289,plain,
! [X13,X14,X15,X16] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X16)
| c_Polynomial_Osmult(X15,c_Polynomial_Osmult(X14,X13,X16),X16) = c_Polynomial_Osmult(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X16),X15),X14),X13,X16) ),
inference(variable_rename,[status(thm)],[c_0_742]) ).
fof(c_0_1290,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Oordered__idom(X17)
| c_HOL_Oord__class_Oless(X15,c_HOL_Ozero__class_Ozero(X17),X17)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X17),X15),X16),c_HOL_Ozero__class_Ozero(X17),X17) ),
inference(variable_rename,[status(thm)],[c_0_743]) ).
fof(c_0_1291,plain,
! [X13,X14] :
( ~ class_Ring__and__Field_Oordered__idom(X14)
| c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X14),X14)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X14),X13),X13),c_HOL_Ozero__class_Ozero(X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_744]) ).
fof(c_0_1292,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X14)
| c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X14),X14)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X14),X13),X13),c_HOL_Ozero__class_Ozero(X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_745]) ).
fof(c_0_1293,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X14)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X14),X13,X14)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X14),X13),X13),X14) ),
inference(variable_rename,[status(thm)],[c_0_746]) ).
fof(c_0_1294,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X14)
| c_lessequals(c_HOL_Ozero__class_Ozero(X14),X13,X14)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X14),X13),X13),X14) ),
inference(variable_rename,[status(thm)],[c_0_747]) ).
fof(c_0_1295,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X14)
| c_lessequals(X13,c_HOL_Ozero__class_Ozero(X14),X14)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X14),X13),X13),c_HOL_Ozero__class_Ozero(X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_748]) ).
fof(c_0_1296,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X11)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X11),hAPP(hAPP(c_Power_Opower__class_Opower(X11),X9),X10)),X9) = hAPP(hAPP(c_Power_Opower__class_Opower(X11),X9),c_Suc(X10)) ),
inference(variable_rename,[status(thm)],[c_0_749]) ).
fof(c_0_1297,plain,
! [X15,X16,X17] :
( ~ class_OrderedGroup_Omonoid__mult(X17)
| hAPP(hAPP(c_Power_Opower__class_Opower(X17),X16),c_Suc(X15)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X17),hAPP(hAPP(c_Power_Opower__class_Opower(X17),X16),X15)),X16) ),
inference(variable_rename,[status(thm)],[c_0_750]) ).
fof(c_0_1298,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X14)
| hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X14),c_HOL_Oplus__class_Oplus(X14),X14),X13),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(X14) ),
inference(variable_rename,[status(thm)],[c_0_751]) ).
fof(c_0_1299,plain,
! [X34,X35,X36,X37] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X37)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X37),X36),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X37),X35),X34)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X37),X35),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X37),X36),X34)) ),
inference(variable_rename,[status(thm)],[c_0_752]) ).
fof(c_0_1300,plain,
! [X19,X20,X21,X22] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X22)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),X21),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),X20),X19)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),X20),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),X21),X19)) ),
inference(variable_rename,[status(thm)],[c_0_753]) ).
fof(c_0_1301,plain,
! [X14,X15,X16,X17] :
( ~ class_OrderedGroup_Oab__group__add(X17)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X17),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X17),X15),X14)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X17),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X17),X16),X14)) ),
inference(variable_rename,[status(thm)],[c_0_754]) ).
fof(c_0_1302,plain,
! [X17,X18,X19,X20] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X20)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X18),X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X18),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X19),X17)) ),
inference(variable_rename,[status(thm)],[c_0_755]) ).
fof(c_0_1303,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X14)
| hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X14),c_HOL_Oplus__class_Oplus(X14),X14),X13),c_HOL_Oone__class_Oone(tc_nat)) = X13 ),
inference(variable_rename,[status(thm)],[c_0_756]) ).
fof(c_0_1304,plain,
! [X15,X16,X17,X18] :
( ~ class_HOL_Ozero(X18)
| hAPP(c_Polynomial_Ocoeff(c_Polynomial_OpCons(X17,X15,X18),X18),c_Suc(X16)) = hAPP(c_Polynomial_Ocoeff(X15,X18),X16) ),
inference(variable_rename,[status(thm)],[c_0_757]) ).
fof(c_0_1305,plain,
! [X13,X14,X15] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X15)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X13),c_HOL_Ozero__class_Ozero(X15),X15)
| ~ c_lessequals(X14,c_HOL_Ouminus__class_Ouminus(X13,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_758]) ).
fof(c_0_1306,plain,
! [X10,X11,X12] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X12)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X12),X11),X10) != c_HOL_Ozero__class_Ozero(X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X10,X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X11,X12)
| X11 = c_HOL_Ozero__class_Ozero(X12) ),
inference(variable_rename,[status(thm)],[c_0_759]) ).
fof(c_0_1307,plain,
! [X10,X11,X12] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X12)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X12),X11),X10) != c_HOL_Ozero__class_Ozero(X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X10,X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X11,X12)
| X10 = c_HOL_Ozero__class_Ozero(X12) ),
inference(variable_rename,[status(thm)],[c_0_760]) ).
fof(c_0_1308,plain,
! [X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_HOL_Ozero__class_Ozero(X4)),c_HOL_Ozero__class_Ozero(X4)) = c_HOL_Ozero__class_Ozero(X4) ),
inference(variable_rename,[status(thm)],[c_0_761]) ).
fof(c_0_1309,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Oordered__semidom(X17)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X17),hAPP(hAPP(c_Power_Opower__class_Opower(X17),X16),c_Suc(X15)),X17)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X17),X16,X17) ),
inference(variable_rename,[status(thm)],[c_0_762]) ).
fof(c_0_1310,plain,
! [X22,X23,X24] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X24)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(X23,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X24)),X24),X22,X24) = c_Polynomial_OpCons(X23,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X24)),X24) ),
inference(variable_rename,[status(thm)],[c_0_763]) ).
fof(c_0_1311,plain,
! [X8,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X9)
| ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(X9),X9) ),
inference(variable_rename,[status(thm)],[c_0_764]) ).
fof(c_0_1312,plain,
! [X23,X24,X25,X26] :
( ~ class_Ring__and__Field_Oordered__semidom(X26)
| hAPP(hAPP(c_Power_Opower__class_Opower(X26),X25),X24) != hAPP(hAPP(c_Power_Opower__class_Opower(X26),X25),X23)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X26),X25,X26)
| X24 = X23 ),
inference(variable_rename,[status(thm)],[c_0_765]) ).
fof(c_0_1313,plain,
! [X23,X24,X25,X26] :
( ~ class_HOL_Ozero(X26)
| hAPP(c_Polynomial_Ocoeff(c_Polynomial_Omonom(X25,X24,X26),X26),X23) = c_HOL_Ozero__class_Ozero(X26)
| X24 = X23 ),
inference(variable_rename,[status(thm)],[c_0_766]) ).
fof(c_0_1314,plain,
! [X14,X15,X16,X17] :
( ~ class_OrderedGroup_Oab__group__add(X17)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X17),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X17),X15),X14)) != X15
| X16 = c_HOL_Ouminus__class_Ouminus(X14,X17) ),
inference(variable_rename,[status(thm)],[c_0_767]) ).
fof(c_0_1315,plain,
! [X13,X14,X15] :
( ~ class_OrderedGroup_Ogroup__add(X15)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),c_HOL_Ouminus__class_Ouminus(X14,X15)),X13)) = X13 ),
inference(variable_rename,[status(thm)],[c_0_768]) ).
fof(c_0_1316,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Oordered__idom(X17)
| c_lessequals(c_HOL_Ozero__class_Ozero(X17),hAPP(hAPP(c_Power_Opower__class_Opower(X17),X16),X15),X17)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X17),X16,X17) ),
inference(variable_rename,[status(thm)],[c_0_769]) ).
fof(c_0_1317,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Oordered__semidom(X17)
| c_lessequals(c_HOL_Ozero__class_Ozero(X17),hAPP(hAPP(c_Power_Opower__class_Opower(X17),X16),X15),X17)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X17),X16,X17) ),
inference(variable_rename,[status(thm)],[c_0_770]) ).
fof(c_0_1318,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Oordered__semidom(X17)
| c_lessequals(c_HOL_Oone__class_Oone(X17),hAPP(hAPP(c_Power_Opower__class_Opower(X17),X16),X15),X17)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X17),X16,X17) ),
inference(variable_rename,[status(thm)],[c_0_771]) ).
fof(c_0_1319,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Oordered__semidom(X17)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X17),hAPP(hAPP(c_Power_Opower__class_Opower(X17),X16),X15),X17)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X17),X16,X17) ),
inference(variable_rename,[status(thm)],[c_0_772]) ).
fof(c_0_1320,plain,
! [X13,X14] :
( ~ class_Ring__and__Field_Oordered__idom(X14)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X14),X13),X13),c_HOL_Ozero__class_Ozero(X14),X14)
| ~ c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_773]) ).
fof(c_0_1321,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X14)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X14),X13),X13),c_HOL_Ozero__class_Ozero(X14),X14)
| ~ c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_774]) ).
fof(c_0_1322,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X14)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X14),X13),X13),X14)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X14),X13,X14) ),
inference(variable_rename,[status(thm)],[c_0_775]) ).
fof(c_0_1323,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X14)
| c_lessequals(c_HOL_Ozero__class_Ozero(X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X14),X13),X13),X14)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X14),X13,X14) ),
inference(variable_rename,[status(thm)],[c_0_776]) ).
fof(c_0_1324,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X14)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X14),X13),X13),c_HOL_Ozero__class_Ozero(X14),X14)
| ~ c_lessequals(X13,c_HOL_Ozero__class_Ozero(X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_777]) ).
fof(c_0_1325,plain,
! [X13,X14,X15] :
( ~ class_HOL_Ozero(X15)
| hAPP(c_Polynomial_Ocoeff(c_Polynomial_OpCons(X14,X13,X15),X15),c_HOL_Ozero__class_Ozero(tc_nat)) = X14 ),
inference(variable_rename,[status(thm)],[c_0_778]) ).
fof(c_0_1326,plain,
! [X13,X14] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X14)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X14),X13),X13),c_HOL_Ozero__class_Ozero(X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_779]) ).
fof(c_0_1327,plain,
! [X13,X14,X15] :
( ~ class_HOL_Ozero(X15)
| hAPP(c_Polynomial_Ocoeff(c_Polynomial_Omonom(X14,X13,X15),X15),X13) = X14 ),
inference(variable_rename,[status(thm)],[c_0_780]) ).
fof(c_0_1328,plain,
! [X13,X14,X15] :
( ~ class_OrderedGroup_Ogroup__add(X15)
| c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X13),X15) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),c_HOL_Ouminus__class_Ouminus(X13,X15)),c_HOL_Ouminus__class_Ouminus(X14,X15)) ),
inference(variable_rename,[status(thm)],[c_0_781]) ).
fof(c_0_1329,plain,
! [X13,X14,X15] :
( ~ class_OrderedGroup_Oab__group__add(X15)
| c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X13),X15) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),c_HOL_Ouminus__class_Ouminus(X14,X15)),c_HOL_Ouminus__class_Ouminus(X13,X15)) ),
inference(variable_rename,[status(thm)],[c_0_782]) ).
fof(c_0_1330,plain,
! [X23,X24,X25] :
( ~ class_Ring__and__Field_Osemiring__1(X25)
| c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X23),X25) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X25),c_Nat_Osemiring__1__class_Oof__nat(X24,X25)),c_Nat_Osemiring__1__class_Oof__nat(X23,X25)) ),
inference(variable_rename,[status(thm)],[c_0_783]) ).
fof(c_0_1331,plain,
! [X15,X16,X17] :
( ~ class_HOL_Ozero(X17)
| c_Polynomial_Omonom(X16,c_Suc(X15),X17) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X17),c_Polynomial_Omonom(X16,X15,X17),X17) ),
inference(variable_rename,[status(thm)],[c_0_784]) ).
fof(c_0_1332,plain,
! [X14,X15,X16,X17] :
( ~ class_Orderings_Opreorder(X17)
| c_HOL_Oord__class_Oless(X16,X14,X17)
| ~ c_HOL_Oord__class_Oless(X15,X14,X17)
| ~ c_lessequals(X16,X15,X17) ),
inference(variable_rename,[status(thm)],[c_0_785]) ).
fof(c_0_1333,plain,
! [X14,X15,X16,X17] :
( ~ class_Orderings_Opreorder(X17)
| c_HOL_Oord__class_Oless(X16,X14,X17)
| ~ c_lessequals(X15,X14,X17)
| ~ c_HOL_Oord__class_Oless(X16,X15,X17) ),
inference(variable_rename,[status(thm)],[c_0_786]) ).
fof(c_0_1334,plain,
! [X14,X15,X16,X17] :
( ~ class_Orderings_Opreorder(X17)
| c_lessequals(X16,X14,X17)
| ~ c_lessequals(X15,X14,X17)
| ~ c_lessequals(X16,X15,X17) ),
inference(variable_rename,[status(thm)],[c_0_787]) ).
fof(c_0_1335,plain,
! [X14,X15,X16,X17] :
( ~ class_Orderings_Oorder(X17)
| c_HOL_Oord__class_Oless(X14,X16,X17)
| ~ c_HOL_Oord__class_Oless(X14,X15,X17)
| ~ c_lessequals(X15,X16,X17) ),
inference(variable_rename,[status(thm)],[c_0_788]) ).
fof(c_0_1336,plain,
! [X14,X15,X16,X17] :
( ~ class_Orderings_Oorder(X17)
| c_HOL_Oord__class_Oless(X14,X16,X17)
| ~ c_lessequals(X14,X15,X17)
| ~ c_HOL_Oord__class_Oless(X15,X16,X17) ),
inference(variable_rename,[status(thm)],[c_0_789]) ).
fof(c_0_1337,plain,
! [X14,X15,X16,X17] :
( ~ class_Orderings_Oorder(X17)
| c_lessequals(X14,X16,X17)
| ~ c_lessequals(X14,X15,X17)
| ~ c_lessequals(X15,X16,X17) ),
inference(variable_rename,[status(thm)],[c_0_790]) ).
fof(c_0_1338,plain,
! [X14,X15,X16,X17] :
( ~ class_Orderings_Oorder(X17)
| c_HOL_Oord__class_Oless(X14,X16,X17)
| ~ c_HOL_Oord__class_Oless(X14,X15,X17)
| ~ c_HOL_Oord__class_Oless(X15,X16,X17) ),
inference(variable_rename,[status(thm)],[c_0_791]) ).
fof(c_0_1339,plain,
! [X14,X15,X16,X17] :
( ~ class_Orderings_Opreorder(X17)
| c_HOL_Oord__class_Oless(X16,X14,X17)
| ~ c_HOL_Oord__class_Oless(X15,X14,X17)
| ~ c_HOL_Oord__class_Oless(X16,X15,X17) ),
inference(variable_rename,[status(thm)],[c_0_792]) ).
fof(c_0_1340,plain,
! [X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X15)
| c_HOL_Oord__class_Oless(X14,X13,X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X13,X15),c_HOL_Ouminus__class_Ouminus(X14,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_793]) ).
fof(c_0_1341,plain,
! [X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X15)
| c_lessequals(X14,X13,X15)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X13,X15),c_HOL_Ouminus__class_Ouminus(X14,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_794]) ).
fof(c_0_1342,plain,
! [X13,X14,X15] :
( ~ class_RealVector_Oreal__normed__algebra(X15)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),c_HOL_Ouminus__class_Ouminus(X14,X15)),X13) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X14),X13),X15) ),
inference(variable_rename,[status(thm)],[c_0_795]) ).
fof(c_0_1343,plain,
! [X10,X11,X12] :
( ~ class_RealVector_Oreal__normed__algebra(X12)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X12),c_HOL_Ouminus__class_Ouminus(X11,X12)),X10) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X12),X11),X10),X12) ),
inference(variable_rename,[status(thm)],[c_0_796]) ).
fof(c_0_1344,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Oring(X15)
| c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X14),X13),X15) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),c_HOL_Ouminus__class_Ouminus(X14,X15)),X13) ),
inference(variable_rename,[status(thm)],[c_0_797]) ).
fof(c_0_1345,plain,
! [X28,X29,X30] :
( c_lessequals(X30,X28,tc_RealDef_Oreal)
| ~ c_lessequals(X29,X28,tc_RealDef_Oreal)
| ~ c_lessequals(X30,X29,tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[c_0_798]) ).
fof(c_0_1346,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X11)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X11),X9),hAPP(hAPP(c_Power_Opower__class_Opower(X11),X9),X10)) = hAPP(hAPP(c_Power_Opower__class_Opower(X11),X9),c_Suc(X10)) ),
inference(variable_rename,[status(thm)],[c_0_799]) ).
fof(c_0_1347,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X17)
| hAPP(hAPP(c_Power_Opower__class_Opower(X17),X15),c_Suc(X16)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X17),X15),hAPP(hAPP(c_Power_Opower__class_Opower(X17),X15),X16)) ),
inference(variable_rename,[status(thm)],[c_0_800]) ).
fof(c_0_1348,plain,
! [X15,X16,X17] :
( ~ class_Power_Opower(X17)
| hAPP(hAPP(c_Power_Opower__class_Opower(X17),X16),c_Suc(X15)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X17),X16),hAPP(hAPP(c_Power_Opower__class_Opower(X17),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_801]) ).
fof(c_0_1349,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X11)
| hAPP(hAPP(c_Power_Opower__class_Opower(X11),X9),c_Suc(X10)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X11),X9),hAPP(hAPP(c_Power_Opower__class_Opower(X11),X9),X10)) ),
inference(variable_rename,[status(thm)],[c_0_802]) ).
fof(c_0_1350,plain,
! [X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X15)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X14,X15),X13,X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X13,X15),X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_803]) ).
fof(c_0_1351,plain,
! [X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X15)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X13,X15),X14,X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X14,X15),X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_804]) ).
fof(c_0_1352,plain,
! [X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X15)
| c_HOL_Oord__class_Oless(X14,c_HOL_Ouminus__class_Ouminus(X13,X15),X15)
| ~ c_HOL_Oord__class_Oless(X13,c_HOL_Ouminus__class_Ouminus(X14,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_805]) ).
fof(c_0_1353,plain,
! [X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X15)
| c_HOL_Oord__class_Oless(X13,c_HOL_Ouminus__class_Ouminus(X14,X15),X15)
| ~ c_HOL_Oord__class_Oless(X14,c_HOL_Ouminus__class_Ouminus(X13,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_806]) ).
fof(c_0_1354,plain,
! [X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X15)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X14,X15),X13,X15)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X13,X15),X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_807]) ).
fof(c_0_1355,plain,
! [X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X15)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X13,X15),X14,X15)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X14,X15),X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_808]) ).
fof(c_0_1356,plain,
! [X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X15)
| c_lessequals(X14,c_HOL_Ouminus__class_Ouminus(X13,X15),X15)
| ~ c_lessequals(X13,c_HOL_Ouminus__class_Ouminus(X14,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_809]) ).
fof(c_0_1357,plain,
! [X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X15)
| c_lessequals(X13,c_HOL_Ouminus__class_Ouminus(X14,X15),X15)
| ~ c_lessequals(X14,c_HOL_Ouminus__class_Ouminus(X13,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_810]) ).
fof(c_0_1358,plain,
! [X14,X15,X16] :
( ~ class_OrderedGroup_Oab__group__add(X16)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X16),c_HOL_Ouminus__class_Ouminus(X14,X16)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X16),X15),X14)) = X15 ),
inference(variable_rename,[status(thm)],[c_0_811]) ).
fof(c_0_1359,plain,
! [X13,X14,X15] :
( ~ class_OrderedGroup_Ogroup__add(X15)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),c_HOL_Ouminus__class_Ouminus(X14,X15)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X13)) = X13 ),
inference(variable_rename,[status(thm)],[c_0_812]) ).
fof(c_0_1360,plain,
! [X10,X11,X12] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X12)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X12),X11),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X12),X11),X10)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X12),X11),X10) ),
inference(variable_rename,[status(thm)],[c_0_813]) ).
fof(c_0_1361,plain,
! [X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_HOL_Oone__class_Oone(X4)),c_HOL_Oone__class_Oone(X4)),X4) ),
inference(variable_rename,[status(thm)],[c_0_814]) ).
fof(c_0_1362,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X14)
| c_lessequals(X13,c_HOL_Ozero__class_Ozero(X14),X14)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X14),c_HOL_Ouminus__class_Ouminus(X13,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_815]) ).
fof(c_0_1363,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X14)
| c_lessequals(c_HOL_Ozero__class_Ozero(X14),X13,X14)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X13,X14),c_HOL_Ozero__class_Ozero(X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_816]) ).
fof(c_0_1364,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X14)
| c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X14),X14)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X14),c_HOL_Ouminus__class_Ouminus(X13,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_817]) ).
fof(c_0_1365,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X14)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X14),X13,X14)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X13,X14),c_HOL_Ozero__class_Ozero(X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_818]) ).
fof(c_0_1366,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Opreorder(X12)
| c_HOL_Oord__class_Oless(X11,X10,X12)
| c_lessequals(X10,X11,X12)
| ~ c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_819]) ).
fof(c_0_1367,plain,
! [X13,X14,X15] :
( ~ class_RealVector_Oreal__normed__algebra(X15)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X14),c_HOL_Ouminus__class_Ouminus(X13,X15)) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X14),X13),X15) ),
inference(variable_rename,[status(thm)],[c_0_820]) ).
fof(c_0_1368,plain,
! [X35,X36,X37] :
( ~ class_RealVector_Oreal__normed__algebra(X37)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X37),X35),c_HOL_Ouminus__class_Ouminus(X36,X37)) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X37),X35),X36),X37) ),
inference(variable_rename,[status(thm)],[c_0_821]) ).
fof(c_0_1369,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Oring(X15)
| c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X14),X13),X15) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X14),c_HOL_Ouminus__class_Ouminus(X13,X15)) ),
inference(variable_rename,[status(thm)],[c_0_822]) ).
fof(c_0_1370,plain,
! [X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X15)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X13,X15),c_HOL_Ouminus__class_Ouminus(X14,X15),X15)
| ~ c_HOL_Oord__class_Oless(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_823]) ).
fof(c_0_1371,plain,
! [X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X15)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X13,X15),c_HOL_Ouminus__class_Ouminus(X14,X15),X15)
| ~ c_lessequals(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_824]) ).
fof(c_0_1372,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X14)
| c_lessequals(X13,c_HOL_Ozero__class_Ozero(X14),X14)
| ~ c_lessequals(X13,c_HOL_Ouminus__class_Ouminus(X13,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_825]) ).
fof(c_0_1373,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X14)
| c_lessequals(c_HOL_Ozero__class_Ozero(X14),X13,X14)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X13,X14),X13,X14) ),
inference(variable_rename,[status(thm)],[c_0_826]) ).
fof(c_0_1374,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X14)
| c_lessequals(X13,c_HOL_Ozero__class_Ozero(X14),X14)
| ~ c_lessequals(X13,c_HOL_Ouminus__class_Ouminus(X13,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_827]) ).
fof(c_0_1375,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X14)
| c_lessequals(c_HOL_Ozero__class_Ozero(X14),X13,X14)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X13,X14),X13,X14) ),
inference(variable_rename,[status(thm)],[c_0_828]) ).
fof(c_0_1376,plain,
! [X13,X14] :
( ~ class_Ring__and__Field_Oordered__idom(X14)
| c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X14),X14)
| ~ c_HOL_Oord__class_Oless(X13,c_HOL_Ouminus__class_Ouminus(X13,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_829]) ).
fof(c_0_1377,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X20)
| c_Polynomial_Osmult(X18,X17,X20) != c_Polynomial_OpCons(X19,X17,X20)
| X17 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X20)) ),
inference(variable_rename,[status(thm)],[c_0_830]) ).
fof(c_0_1378,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X14)
| c_lessequals(c_HOL_Ozero__class_Ozero(X14),c_HOL_Ouminus__class_Ouminus(X13,X14),X14)
| ~ c_lessequals(X13,c_HOL_Ozero__class_Ozero(X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_831]) ).
fof(c_0_1379,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X14)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X13,X14),c_HOL_Ozero__class_Ozero(X14),X14)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X14),X13,X14) ),
inference(variable_rename,[status(thm)],[c_0_832]) ).
fof(c_0_1380,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X14)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X14),c_HOL_Ouminus__class_Ouminus(X13,X14),X14)
| ~ c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_833]) ).
fof(c_0_1381,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X14)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X13,X14),c_HOL_Ozero__class_Ozero(X14),X14)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X14),X13,X14) ),
inference(variable_rename,[status(thm)],[c_0_834]) ).
fof(c_0_1382,plain,
! [X12,X13] :
( ~ class_Ring__and__Field_Oidom(X13)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X13),c_HOL_Ouminus__class_Ouminus(X12,X13)),c_HOL_Ouminus__class_Ouminus(X12,X13)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X13),X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_835]) ).
fof(c_0_1383,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Oring(X15)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),c_HOL_Ouminus__class_Ouminus(X14,X15)),c_HOL_Ouminus__class_Ouminus(X13,X15)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X14),X13) ),
inference(variable_rename,[status(thm)],[c_0_836]) ).
fof(c_0_1384,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Oring(X15)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),c_HOL_Ouminus__class_Ouminus(X14,X15)),X13) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X14),c_HOL_Ouminus__class_Ouminus(X13,X15)) ),
inference(variable_rename,[status(thm)],[c_0_837]) ).
fof(c_0_1385,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Oidom(X15)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X14),X14) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X13),X13)
| X14 = c_HOL_Ouminus__class_Ouminus(X13,X15)
| X14 = X13 ),
inference(variable_rename,[status(thm)],[c_0_838]) ).
fof(c_0_1386,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X14)
| c_lessequals(X13,c_HOL_Ouminus__class_Ouminus(X13,X14),X14)
| ~ c_lessequals(X13,c_HOL_Ozero__class_Ozero(X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_839]) ).
fof(c_0_1387,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X14)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X13,X14),X13,X14)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X14),X13,X14) ),
inference(variable_rename,[status(thm)],[c_0_840]) ).
fof(c_0_1388,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X14)
| c_lessequals(X13,c_HOL_Ouminus__class_Ouminus(X13,X14),X14)
| ~ c_lessequals(X13,c_HOL_Ozero__class_Ozero(X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_841]) ).
fof(c_0_1389,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X14)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X13,X14),X13,X14)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X14),X13,X14) ),
inference(variable_rename,[status(thm)],[c_0_842]) ).
fof(c_0_1390,plain,
! [X13,X14] :
( ~ class_Ring__and__Field_Oordered__idom(X14)
| c_HOL_Oord__class_Oless(X13,c_HOL_Ouminus__class_Ouminus(X13,X14),X14)
| ~ c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_843]) ).
fof(c_0_1391,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Oorder(X12)
| X11 = X10
| ~ c_lessequals(X11,X10,X12)
| ~ c_lessequals(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_844]) ).
fof(c_0_1392,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Oorder(X12)
| X11 = X10
| ~ c_lessequals(X10,X11,X12)
| ~ c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_845]) ).
fof(c_0_1393,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Oorder(X12)
| X11 = X10
| ~ c_lessequals(X10,X11,X12)
| ~ c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_846]) ).
fof(c_0_1394,plain,
! [X13,X14,X15,X16,X17] :
( ~ class_HOL_Ozero(X17)
| c_Polynomial_OpCons(X16,X14,X17) != c_Polynomial_OpCons(X15,X13,X17)
| X16 = X15 ),
inference(variable_rename,[status(thm)],[c_0_847]) ).
fof(c_0_1395,plain,
! [X13,X14,X15,X16,X17] :
( ~ class_HOL_Ozero(X17)
| c_Polynomial_OpCons(X16,X14,X17) != c_Polynomial_OpCons(X15,X13,X17)
| X14 = X13 ),
inference(variable_rename,[status(thm)],[c_0_848]) ).
fof(c_0_1396,plain,
! [X15,X16,X17,X18] :
( ~ class_HOL_Ozero(X18)
| c_Polynomial_Omonom(X17,X15,X18) != c_Polynomial_Omonom(X16,X15,X18)
| X17 = X16 ),
inference(variable_rename,[status(thm)],[c_0_849]) ).
fof(c_0_1397,plain,
! [X14,X15,X16,X17] :
( ~ class_Ring__and__Field_Oidom(X17)
| ~ class_Int_Onumber__ring(X17)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X17),X16),X15) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X17),X16),X14)
| X15 = X14 ),
inference(variable_rename,[status(thm)],[c_0_850]) ).
fof(c_0_1398,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Opreorder(X15)
| ~ c_HOL_Oord__class_Oless(X13,X14,X15)
| ~ c_HOL_Oord__class_Oless(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_851]) ).
fof(c_0_1399,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Opreorder(X12)
| ~ c_HOL_Oord__class_Oless(X10,X11,X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_852]) ).
fof(c_0_1400,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12)
| ~ c_HOL_Oord__class_Oless(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_853]) ).
fof(c_0_1401,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Oorder(X15)
| ~ c_HOL_Oord__class_Oless(X14,X13,X15)
| ~ c_HOL_Oord__class_Oless(X13,X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_854]) ).
fof(c_0_1402,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Opreorder(X12)
| ~ c_lessequals(X10,X11,X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_855]) ).
fof(c_0_1403,plain,
! [X8,X9] :
( ~ class_Orderings_Olinorder(X9)
| ~ c_lessequals(X8,X8,X9)
| ~ c_HOL_Oord__class_Oless(X8,X8,X9) ),
inference(variable_rename,[status(thm)],[c_0_856]) ).
fof(c_0_1404,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12)
| ~ c_lessequals(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_857]) ).
fof(c_0_1405,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| ~ c_lessequals(X11,X10,X12)
| ~ c_HOL_Oord__class_Oless(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_858]) ).
fof(c_0_1406,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Oidom(X15)
| c_Polynomial_Oorder(X14,X13,X15) != c_HOL_Ozero__class_Ozero(tc_nat)
| X13 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X15))
| hAPP(c_Polynomial_Opoly(X13,X15),X14) != c_HOL_Ozero__class_Ozero(X15) ),
inference(variable_rename,[status(thm)],[c_0_859]) ).
fof(c_0_1407,plain,
! [X4,X5,X6] :
( X5 = X4
| ~ hBOOL(c_fequal(X5,X4,X6)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_860])])]) ).
fof(c_0_1408,plain,
! [X8,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X9)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X9),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),c_HOL_Ozero__class_Ozero(tc_nat)),X9) ),
inference(variable_rename,[status(thm)],[c_0_861]) ).
fof(c_0_1409,plain,
! [X13,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X14)
| c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X14),X13),c_HOL_Oone__class_Oone(X14)),X14) ),
inference(variable_rename,[status(thm)],[c_0_862]) ).
fof(c_0_1410,plain,
! [X17,X18,X19,X20] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X20)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X19),X18) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X19),X17)
| X18 = X17 ),
inference(variable_rename,[status(thm)],[c_0_863]) ).
fof(c_0_1411,plain,
! [X17,X18,X19,X20] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X20)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X19),X18) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X19),X17)
| X18 = X17 ),
inference(variable_rename,[status(thm)],[c_0_864]) ).
fof(c_0_1412,plain,
! [X17,X18,X19,X20] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X20)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X18),X19) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X17),X19)
| X18 = X17 ),
inference(variable_rename,[status(thm)],[c_0_865]) ).
fof(c_0_1413,plain,
! [X13,X14] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X14)
| c_lessequals(c_HOL_Ozero__class_Ozero(X14),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X14),X13),X13),X14) ),
inference(variable_rename,[status(thm)],[c_0_866]) ).
fof(c_0_1414,plain,
! [X25,X26] :
( X25 = X26
| ~ c_lessequals(X26,X25,tc_RealDef_Oreal)
| ~ c_lessequals(X25,X26,tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[c_0_867]) ).
fof(c_0_1415,plain,
! [X13,X14,X15] :
( ~ class_HOL_Ozero(X15)
| c_Polynomial_Odegree(c_Polynomial_OpCons(X14,X13,X15),X15) = c_Suc(c_Polynomial_Odegree(X13,X15))
| X13 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X15)) ),
inference(variable_rename,[status(thm)],[c_0_868]) ).
fof(c_0_1416,plain,
! [X13,X14] :
( ~ class_HOL_Ozero(X14)
| c_Polynomial_Odegree(c_Polynomial_OpCons(X13,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X14)),X14),X14) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_869]) ).
fof(c_0_1417,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Oorder(X15)
| c_HOL_Oord__class_Oless(X13,X14,X15)
| X14 = X13
| ~ c_lessequals(X13,X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_870]) ).
fof(c_0_1418,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Oorder(X15)
| c_HOL_Oord__class_Oless(X13,X14,X15)
| ~ c_lessequals(X13,X14,X15)
| X14 = X13 ),
inference(variable_rename,[status(thm)],[c_0_871]) ).
fof(c_0_1419,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| X11 = X10
| c_HOL_Oord__class_Oless(X11,X10,X12)
| ~ c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_872]) ).
fof(c_0_1420,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| X11 = X10
| ~ c_lessequals(X11,X10,X12)
| c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_873]) ).
fof(c_0_1421,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Oorder(X15)
| c_HOL_Oord__class_Oless(X14,X13,X15)
| ~ c_lessequals(X14,X13,X15)
| X14 = X13 ),
inference(variable_rename,[status(thm)],[c_0_874]) ).
fof(c_0_1422,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Oorder(X15)
| c_HOL_Oord__class_Oless(X14,X13,X15)
| X14 = X13
| ~ c_lessequals(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_875]) ).
fof(c_0_1423,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Oorder(X12)
| X11 = X10
| c_HOL_Oord__class_Oless(X11,X10,X12)
| ~ c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_876]) ).
fof(c_0_1424,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Oorder(X12)
| c_HOL_Oord__class_Oless(X11,X10,X12)
| X11 = X10
| ~ c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_877]) ).
fof(c_0_1425,plain,
! [X4] :
( ~ class_HOL_Ozero(X4)
| hAPP(c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4),c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4)) = c_HOL_Ozero__class_Ozero(X4) ),
inference(variable_rename,[status(thm)],[c_0_878]) ).
fof(c_0_1426,plain,
! [X8,X9] :
( ~ class_Int_Onumber__ring(X9)
| c_HOL_Ouminus__class_Ouminus(X8,X9) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X9),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X9),X9)),X8) ),
inference(variable_rename,[status(thm)],[c_0_879]) ).
fof(c_0_1427,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Oorder(X12)
| c_lessequals(X11,X10,X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_880]) ).
fof(c_0_1428,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Opreorder(X12)
| c_lessequals(X11,X10,X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_881]) ).
fof(c_0_1429,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Oidom(X15)
| c_Polynomial_Odegree(c_Polynomial_Osmult(X14,X13,X15),X15) = c_Polynomial_Odegree(X13,X15)
| X14 = c_HOL_Ozero__class_Ozero(X15) ),
inference(variable_rename,[status(thm)],[c_0_882]) ).
fof(c_0_1430,plain,
! [X26,X27,X28] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X27),X28) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X26),X28)
| X27 = X26 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_883])])]) ).
fof(c_0_1431,plain,
! [X26,X27,X28] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X28),X27) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X28),X26)
| X27 = X26 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_884])])]) ).
fof(c_0_1432,plain,
! [X14,X15,X16] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X15) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X14)
| X15 = X14 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_885])])]) ).
fof(c_0_1433,plain,
! [X23,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X24)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X23,X24),c_HOL_Ozero__class_Ozero(X24),X24) ),
inference(variable_rename,[status(thm)],[c_0_886]) ).
fof(c_0_1434,plain,
! [X7,X8] :
( ~ class_Ring__and__Field_Oidom(X8)
| c_Polynomial_Odegree(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X8),X7,X8),X8) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_887]) ).
fof(c_0_1435,plain,
! [X22,X23,X24] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X24)
| c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X22,X23,X24),X24) = c_Polynomial_Odegree(X22,X24) ),
inference(variable_rename,[status(thm)],[c_0_888]) ).
fof(c_0_1436,plain,
! [X13,X14] :
( ~ class_HOL_Ozero(X14)
| c_Polynomial_Omonom(X13,c_HOL_Ozero__class_Ozero(tc_nat),X14) = c_Polynomial_OpCons(X13,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X14)),X14) ),
inference(variable_rename,[status(thm)],[c_0_889]) ).
fof(c_0_1437,plain,
! [X15,X16,X17] :
( ~ class_HOL_Ozero(X17)
| c_Polynomial_Odegree(c_Polynomial_Omonom(X16,X15,X17),X17) = X15
| X16 = c_HOL_Ozero__class_Ozero(X17) ),
inference(variable_rename,[status(thm)],[c_0_890]) ).
fof(c_0_1438,plain,
! [X7,X8] :
( ~ class_HOL_Ozero(X8)
| hAPP(c_Polynomial_Ocoeff(X7,X8),c_Polynomial_Odegree(X7,X8)) != c_HOL_Ozero__class_Ozero(X8)
| X7 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ),
inference(variable_rename,[status(thm)],[c_0_891]) ).
fof(c_0_1439,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Oidom(X15)
| c_Polynomial_Osmult(X14,X13,X15) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X15))
| X13 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X15))
| X14 = c_HOL_Ozero__class_Ozero(X15) ),
inference(variable_rename,[status(thm)],[c_0_892]) ).
fof(c_0_1440,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Ozero__neq__one(X17)
| ~ class_Ring__and__Field_Ono__zero__divisors(X17)
| ~ class_Ring__and__Field_Omult__zero(X17)
| ~ class_Power_Opower(X17)
| hAPP(hAPP(c_Power_Opower__class_Opower(X17),X16),X15) != c_HOL_Ozero__class_Ozero(X17)
| X16 = c_HOL_Ozero__class_Ozero(X17) ),
inference(variable_rename,[status(thm)],[c_0_893]) ).
fof(c_0_1441,plain,
! [X13,X14] :
( ~ class_Ring__and__Field_Ozero__neq__one(X14)
| ~ class_Ring__and__Field_Ono__zero__divisors(X14)
| ~ class_Ring__and__Field_Omult__zero(X14)
| ~ class_Power_Opower(X14)
| hAPP(hAPP(c_Power_Opower__class_Opower(X14),X13),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(X14) ),
inference(variable_rename,[status(thm)],[c_0_894]) ).
fof(c_0_1442,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X10)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X10)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))),X9) = X9 ),
inference(variable_rename,[status(thm)],[c_0_895]) ).
fof(c_0_1443,plain,
! [X22,X23,X24] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X24)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X22,X23,X24) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X24))
| X22 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X24)) ),
inference(variable_rename,[status(thm)],[c_0_896]) ).
fof(c_0_1444,plain,
! [X13,X14,X15] :
( ~ class_HOL_Ozero(X15)
| c_Polynomial_OpCons(X14,X13,X15) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X15))
| X13 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X15)) ),
inference(variable_rename,[status(thm)],[c_0_897]) ).
fof(c_0_1445,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__idom(X12)
| c_HOL_Oord__class_Oless(X10,X11,X12)
| c_HOL_Oord__class_Oless(X11,X10,X12)
| X11 = X10 ),
inference(variable_rename,[status(thm)],[c_0_898]) ).
fof(c_0_1446,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| X11 = X10
| c_HOL_Oord__class_Oless(X10,X11,X12)
| c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_899]) ).
fof(c_0_1447,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| X11 = X10
| c_HOL_Oord__class_Oless(X11,X10,X12)
| c_HOL_Oord__class_Oless(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_900]) ).
fof(c_0_1448,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| c_HOL_Oord__class_Oless(X10,X11,X12)
| X11 = X10
| c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_901]) ).
fof(c_0_1449,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| c_HOL_Oord__class_Oless(X10,X11,X12)
| c_HOL_Oord__class_Oless(X11,X10,X12)
| X11 = X10 ),
inference(variable_rename,[status(thm)],[c_0_902]) ).
fof(c_0_1450,plain,
! [X23,X24] :
( ~ class_Ring__and__Field_Osemiring__1(X24)
| c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X23),X24) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X24),c_HOL_Oone__class_Oone(X24)),c_Nat_Osemiring__1__class_Oof__nat(X23,X24)) ),
inference(variable_rename,[status(thm)],[c_0_903]) ).
fof(c_0_1451,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| c_lessequals(X10,X11,X12)
| c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_904]) ).
fof(c_0_1452,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| c_HOL_Oord__class_Oless(X11,X10,X12)
| c_lessequals(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_905]) ).
fof(c_0_1453,plain,
! [X8,X9] :
( ~ class_Orderings_Olinorder(X9)
| c_HOL_Oord__class_Oless(X8,X8,X9)
| c_lessequals(X8,X8,X9) ),
inference(variable_rename,[status(thm)],[c_0_906]) ).
fof(c_0_1454,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| c_lessequals(X10,X11,X12)
| c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_907]) ).
fof(c_0_1455,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| c_HOL_Oord__class_Oless(X10,X11,X12)
| c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_908]) ).
fof(c_0_1456,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Ogroup__add(X14)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X14),c_HOL_Ouminus__class_Ouminus(X13,X14)),X13) = c_HOL_Ozero__class_Ozero(X14) ),
inference(variable_rename,[status(thm)],[c_0_909]) ).
fof(c_0_1457,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Oab__group__add(X14)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X14),c_HOL_Ouminus__class_Ouminus(X13,X14)),X13) = c_HOL_Ozero__class_Ozero(X14) ),
inference(variable_rename,[status(thm)],[c_0_910]) ).
fof(c_0_1458,plain,
! [X12,X13] :
( ~ class_OrderedGroup_Ogroup__add(X13)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),c_HOL_Ouminus__class_Ouminus(X12,X13)),X12) = c_HOL_Ozero__class_Ozero(X13) ),
inference(variable_rename,[status(thm)],[c_0_911]) ).
fof(c_0_1459,plain,
! [X15,X16,X17] :
( ~ class_HOL_Ozero(X17)
| c_Polynomial_Omonom(X16,X15,X17) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X17))
| X16 = c_HOL_Ozero__class_Ozero(X17) ),
inference(variable_rename,[status(thm)],[c_0_912]) ).
fof(c_0_1460,plain,
! [X13,X14,X15] :
( ~ class_HOL_Ozero(X15)
| c_Polynomial_OpCons(X14,X13,X15) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X15))
| X14 = c_HOL_Ozero__class_Ozero(X15) ),
inference(variable_rename,[status(thm)],[c_0_913]) ).
fof(c_0_1461,plain,
! [X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(variable_rename,[status(thm)],[c_0_914]) ).
fof(c_0_1462,plain,
! [X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(variable_rename,[status(thm)],[c_0_915]) ).
fof(c_0_1463,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X12)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X12),X11),X10) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X12),X10),X11) ),
inference(variable_rename,[status(thm)],[c_0_916]) ).
fof(c_0_1464,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X15)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X14),X13) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X13),X14) ),
inference(variable_rename,[status(thm)],[c_0_917]) ).
fof(c_0_1465,plain,
! [X17,X18,X19] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X19)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X19),X18),X17) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X19),X17),X18) ),
inference(variable_rename,[status(thm)],[c_0_918]) ).
fof(c_0_1466,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X12)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X12),X11),X10) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X12),X10),X11) ),
inference(variable_rename,[status(thm)],[c_0_919]) ).
fof(c_0_1467,plain,
! [X13,X14,X15] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X15)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X13) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X13),X14) ),
inference(variable_rename,[status(thm)],[c_0_920]) ).
fof(c_0_1468,plain,
! [X13,X14,X15] :
( ~ class_OrderedGroup_Ogroup__add(X15)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X13) != c_HOL_Ozero__class_Ozero(X15)
| c_HOL_Ouminus__class_Ouminus(X14,X15) = X13 ),
inference(variable_rename,[status(thm)],[c_0_921]) ).
fof(c_0_1469,plain,
! [X13,X14,X15] :
( ~ class_OrderedGroup_Ogroup__add(X15)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X13) != c_HOL_Ozero__class_Ozero(X15)
| X14 = c_HOL_Ouminus__class_Ouminus(X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_922]) ).
fof(c_0_1470,plain,
! [X11,X12,X13] :
( hAPP(X13,X12) = hAPP(X13,X11)
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X13,t_a,t_b) ),
inference(variable_rename,[status(thm)],[c_0_923]) ).
fof(c_0_1471,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Oidom(X15)
| hAPP(c_Polynomial_Opoly(X13,X15),X14) = c_HOL_Ozero__class_Ozero(X15)
| c_Polynomial_Oorder(X14,X13,X15) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_924]) ).
fof(c_0_1472,plain,
! [X25,X26] :
( c_lessequals(X26,X25,tc_RealDef_Oreal)
| c_lessequals(X25,X26,tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[c_0_925]) ).
fof(c_0_1473,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X15)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X14),X13) != c_HOL_Ozero__class_Ozero(X15)
| X13 = c_HOL_Ozero__class_Ozero(X15)
| X14 = c_HOL_Ozero__class_Ozero(X15) ),
inference(variable_rename,[status(thm)],[c_0_926]) ).
fof(c_0_1474,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X15)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X14),X13) != c_HOL_Ozero__class_Ozero(X15)
| X13 = c_HOL_Ozero__class_Ozero(X15)
| X14 = c_HOL_Ozero__class_Ozero(X15) ),
inference(variable_rename,[status(thm)],[c_0_927]) ).
fof(c_0_1475,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X15)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X14),X13) != c_HOL_Ozero__class_Ozero(X15)
| X14 = c_HOL_Ozero__class_Ozero(X15)
| X13 = c_HOL_Ozero__class_Ozero(X15) ),
inference(variable_rename,[status(thm)],[c_0_928]) ).
fof(c_0_1476,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Oidom(X15)
| ~ class_Int_Onumber__ring(X15)
| X13 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X13),X14)
| X14 = c_HOL_Ozero__class_Ozero(X15) ),
inference(variable_rename,[status(thm)],[c_0_929]) ).
fof(c_0_1477,plain,
! [X7,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X8)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X8)),X7),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))) = X7 ),
inference(variable_rename,[status(thm)],[c_0_930]) ).
fof(c_0_1478,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X17)
| hAPP(hAPP(c_Power_Opower__class_Opower(X17),X16),X15) != c_HOL_Ozero__class_Ozero(X17)
| X16 = c_HOL_Ozero__class_Ozero(X17) ),
inference(variable_rename,[status(thm)],[c_0_931]) ).
fof(c_0_1479,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X14)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X14),X13),X13) != c_HOL_Ozero__class_Ozero(X14)
| X13 = c_HOL_Ozero__class_Ozero(X14) ),
inference(variable_rename,[status(thm)],[c_0_932]) ).
fof(c_0_1480,plain,
! [X15,X16] :
( ~ class_Ring__and__Field_Ozero__neq__one(X16)
| ~ class_Ring__and__Field_Ono__zero__divisors(X16)
| ~ class_Ring__and__Field_Omult__zero(X16)
| ~ class_Power_Opower(X16)
| hAPP(hAPP(c_Power_Opower__class_Opower(X16),c_HOL_Ozero__class_Ozero(X16)),X15) = c_HOL_Ozero__class_Ozero(X16)
| X15 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_933]) ).
fof(c_0_1481,plain,
! [X23,X24] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X23) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X23 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X24 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(variable_rename,[status(thm)],[c_0_934]) ).
fof(c_0_1482,plain,
! [X23,X24] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X23)
| X23 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X24 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(variable_rename,[status(thm)],[c_0_935]) ).
fof(c_0_1483,plain,
! [X7,X8] :
( ~ class_Ring__and__Field_Oidom(X8)
| ~ class_Int_Oring__char__0(X8)
| c_Polynomial_Opoly(X7,X8) != c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)),X8)
| X7 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ),
inference(variable_rename,[status(thm)],[c_0_936]) ).
fof(c_0_1484,plain,
! [X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
inference(variable_rename,[status(thm)],[c_0_937]) ).
fof(c_0_1485,plain,
! [X23,X24] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X23)
| X23 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X23 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_938])])]) ).
fof(c_0_1486,plain,
! [X23,X24] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X23)
| X24 = c_HOL_Ozero__class_Ozero(tc_nat)
| X24 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(variable_rename,[status(thm)],[c_0_939]) ).
fof(c_0_1487,plain,
! [X23,X24] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X23) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X24 = c_HOL_Ozero__class_Ozero(tc_nat)
| X24 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(variable_rename,[status(thm)],[c_0_940]) ).
fof(c_0_1488,plain,
! [X23,X24] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X23) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X23 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X23 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_941])])]) ).
fof(c_0_1489,axiom,
( hAPP(c_Polynomial_Opoly(v_pa____,tc_Complex_Ocomplex),v_c____) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(v_pa____,tc_Complex_Ocomplex),v_sko__unknown__thm__rrS__1(v_pa____)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
c_0_942 ).
fof(c_0_1490,plain,
! [X23,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X24)
| c_lessequals(c_HOL_Ozero__class_Ozero(X24),c_Nat_Osemiring__1__class_Oof__nat(X23,X24),X24) ),
inference(variable_rename,[status(thm)],[c_0_943]) ).
fof(c_0_1491,plain,
! [X15,X16] :
( ~ class_Ring__and__Field_Oordered__semidom(X16)
| c_lessequals(c_HOL_Ozero__class_Ozero(X16),c_Nat_Osemiring__1__class_Oof__nat(X15,X16),X16) ),
inference(variable_rename,[status(thm)],[c_0_944]) ).
fof(c_0_1492,plain,
! [X8,X9] :
( ~ class_Orderings_Olinorder(X9)
| ~ c_HOL_Oord__class_Oless(X8,X8,X9) ),
inference(variable_rename,[status(thm)],[c_0_945]) ).
fof(c_0_1493,plain,
! [X8,X9] :
( ~ class_Orderings_Oorder(X9)
| ~ c_HOL_Oord__class_Oless(X8,X8,X9) ),
inference(variable_rename,[status(thm)],[c_0_946]) ).
fof(c_0_1494,plain,
! [X8,X9] :
( ~ class_Orderings_Opreorder(X9)
| ~ c_HOL_Oord__class_Oless(X8,X8,X9) ),
inference(variable_rename,[status(thm)],[c_0_947]) ).
fof(c_0_1495,plain,
! [X23,X24] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X23) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X24 = c_HOL_Ozero__class_Ozero(tc_nat)
| X23 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_948]) ).
fof(c_0_1496,plain,
! [X23,X24] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X23)
| X24 = c_HOL_Ozero__class_Ozero(tc_nat)
| X23 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_949]) ).
fof(c_0_1497,plain,
! [X13,X14] :
( ~ class_Ring__and__Field_Oidom(X14)
| c_Polynomial_Osmult(X13,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X14)),X14) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X14)) ),
inference(variable_rename,[status(thm)],[c_0_950]) ).
fof(c_0_1498,plain,
! [X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X14)
| c_Polynomial_Osmult(X13,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X14)),X14) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X14)) ),
inference(variable_rename,[status(thm)],[c_0_951]) ).
fof(c_0_1499,plain,
! [X22,X23] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X23)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X23)),X22,X23) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X23)) ),
inference(variable_rename,[status(thm)],[c_0_952]) ).
fof(c_0_1500,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X10)
| c_Polynomial_Opcompose(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)),X9,X10) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ),
inference(variable_rename,[status(thm)],[c_0_953]) ).
fof(c_0_1501,plain,
! [X7] :
( ~ class_Ring__and__Field_Oidom(t_a)
| v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1(X7) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X7,t_a),t_a,t_a) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_954])])]) ).
fof(c_0_1502,plain,
! [X7] :
( ~ class_Ring__and__Field_Oidom(t_a)
| v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__2(X7) != c_HOL_Ozero__class_Ozero(t_a)
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X7,t_a),t_a,t_a) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_955])])]) ).
fof(c_0_1503,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Ogroup__add(X14)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X14),X13),c_HOL_Ouminus__class_Ouminus(X13,X14)) = c_HOL_Ozero__class_Ozero(X14) ),
inference(variable_rename,[status(thm)],[c_0_956]) ).
fof(c_0_1504,plain,
! [X15,X16] :
( ~ class_Ring__and__Field_Osemiring__0(X16)
| ~ class_Power_Opower(X16)
| hAPP(hAPP(c_Power_Opower__class_Opower(X16),c_HOL_Ozero__class_Ozero(X16)),c_Suc(X15)) = c_HOL_Ozero__class_Ozero(X16) ),
inference(variable_rename,[status(thm)],[c_0_957]) ).
fof(c_0_1505,plain,
! [X15,X16] :
( ~ class_HOL_Ozero(X16)
| hAPP(c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X16)),X16),X15) = c_HOL_Ozero__class_Ozero(X16) ),
inference(variable_rename,[status(thm)],[c_0_958]) ).
fof(c_0_1506,plain,
! [X13,X14] :
( ~ class_Ring__and__Field_Oidom(X14)
| hAPP(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X14)),X14),X13) = c_HOL_Ozero__class_Ozero(X14) ),
inference(variable_rename,[status(thm)],[c_0_959]) ).
fof(c_0_1507,plain,
! [X8,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X9)
| hAPP(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)),X9),X8) = c_HOL_Ozero__class_Ozero(X9) ),
inference(variable_rename,[status(thm)],[c_0_960]) ).
fof(c_0_1508,plain,
! [X15,X16] :
( ~ class_Ring__and__Field_Osemiring__0(X16)
| ~ class_Power_Opower(X16)
| hAPP(hAPP(c_Power_Opower__class_Opower(X16),c_HOL_Ozero__class_Ozero(X16)),X15) = c_HOL_Ozero__class_Ozero(X16)
| X15 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_961]) ).
fof(c_0_1509,plain,
! [X4] :
( ~ class_Ring__and__Field_Osemiring__0(X4)
| ~ class_Power_Opower(X4)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4),c_HOL_Ozero__class_Ozero(X4)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(X4) ),
inference(variable_rename,[status(thm)],[c_0_962]) ).
fof(c_0_1510,plain,
! [X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_HOL_Ozero__class_Ozero(X4)),c_HOL_Ozero__class_Ozero(X4)) = c_HOL_Ozero__class_Ozero(X4) ),
inference(variable_rename,[status(thm)],[c_0_963]) ).
fof(c_0_1511,plain,
! [X23,X24] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X23) != c_HOL_Ozero__class_Ozero(tc_nat)
| X24 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_964]) ).
fof(c_0_1512,plain,
! [X23,X24] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X23) != c_HOL_Ozero__class_Ozero(tc_nat)
| X23 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_965])])]) ).
fof(c_0_1513,plain,
! [X13,X14] :
( X13 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X14)
| X14 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_966]) ).
fof(c_0_1514,plain,
! [X23,X24] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X23) != X24
| X23 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_967])])]) ).
fof(c_0_1515,plain,
! [X4] :
( ~ class_Power_Opower(X4)
| c_Power_Opower__class_Opower(X4) = c_Power_Opower_Opower(c_HOL_Oone__class_Oone(X4),c_HOL_Otimes__class_Otimes(X4),X4) ),
inference(variable_rename,[status(thm)],[c_0_968]) ).
fof(c_0_1516,plain,
! [X15,X16] :
( ~ class_HOL_Ozero(X16)
| c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(X16),X15,X16) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X16)) ),
inference(variable_rename,[status(thm)],[c_0_969]) ).
fof(c_0_1517,plain,
! [X7,X8] :
( ~ class_Ring__and__Field_Oidom(X8)
| c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X8),X7,X8) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ),
inference(variable_rename,[status(thm)],[c_0_970]) ).
fof(c_0_1518,plain,
! [X7,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X8)
| c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X8),X7,X8) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ),
inference(variable_rename,[status(thm)],[c_0_971]) ).
fof(c_0_1519,plain,
! [X15,X16] :
( ~ class_OrderedGroup_Omonoid__mult(X16)
| hAPP(hAPP(c_Power_Opower__class_Opower(X16),c_HOL_Oone__class_Oone(X16)),X15) = c_HOL_Oone__class_Oone(X16) ),
inference(variable_rename,[status(thm)],[c_0_972]) ).
fof(c_0_1520,plain,
! [X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X14)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X14),c_HOL_Ozero__class_Ozero(X14)),X13) = c_HOL_Ozero__class_Ozero(X14) ),
inference(variable_rename,[status(thm)],[c_0_973]) ).
fof(c_0_1521,plain,
! [X10,X11] :
( ~ class_RealVector_Oreal__normed__algebra(X11)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X11),c_HOL_Ozero__class_Ozero(X11)),X10) = c_HOL_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[c_0_974]) ).
fof(c_0_1522,plain,
! [X12,X13] :
( ~ class_RealVector_Oreal__normed__algebra(X13)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X13),c_HOL_Ozero__class_Ozero(X13)),X12) = c_HOL_Ozero__class_Ozero(X13) ),
inference(variable_rename,[status(thm)],[c_0_975]) ).
fof(c_0_1523,plain,
! [X8,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X9)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X9),c_HOL_Ozero__class_Ozero(X9)),X8) = c_HOL_Ozero__class_Ozero(X9) ),
inference(variable_rename,[status(thm)],[c_0_976]) ).
fof(c_0_1524,plain,
! [X13,X14] :
( ~ class_Ring__and__Field_Omult__zero(X14)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X14),c_HOL_Ozero__class_Ozero(X14)),X13) = c_HOL_Ozero__class_Ozero(X14) ),
inference(variable_rename,[status(thm)],[c_0_977]) ).
fof(c_0_1525,plain,
! [X12,X13] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X13)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X13),c_HOL_Ozero__class_Ozero(X13)),X12) = c_HOL_Ozero__class_Ozero(X13) ),
inference(variable_rename,[status(thm)],[c_0_978]) ).
fof(c_0_1526,plain,
! [X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oone__class_Oone(X4),X4) ),
inference(variable_rename,[status(thm)],[c_0_979]) ).
fof(c_0_1527,plain,
! [X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oone__class_Oone(X4),X4) ),
inference(variable_rename,[status(thm)],[c_0_980]) ).
fof(c_0_1528,plain,
! [X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_OrderedGroup_Ocomm__monoid__add__axioms(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(X4),X4) ),
inference(variable_rename,[status(thm)],[c_0_981]) ).
fof(c_0_1529,plain,
! [X4] :
( ~ class_OrderedGroup_Omonoid__add(X4)
| c_OrderedGroup_Omonoid__add__axioms(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(X4),X4) ),
inference(variable_rename,[status(thm)],[c_0_982]) ).
fof(c_0_1530,plain,
! [X8,X9] :
( ~ class_Ring__and__Field_Oidom(X9)
| ~ class_Int_Onumber__ring(X9)
| X8 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X8),c_HOL_Ozero__class_Ozero(X9)) ),
inference(variable_rename,[status(thm)],[c_0_983]) ).
fof(c_0_1531,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Omonoid__mult(X14)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X14),c_HOL_Oone__class_Oone(X14)),X13) = X13 ),
inference(variable_rename,[status(thm)],[c_0_984]) ).
fof(c_0_1532,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X14)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X14),c_HOL_Oone__class_Oone(X14)),X13) = X13 ),
inference(variable_rename,[status(thm)],[c_0_985]) ).
fof(c_0_1533,plain,
! [X8,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X9)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X9),c_HOL_Oone__class_Oone(X9)),X8) = X8 ),
inference(variable_rename,[status(thm)],[c_0_986]) ).
fof(c_0_1534,plain,
! [X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X14)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X14),c_HOL_Oone__class_Oone(X14)),X13) = X13 ),
inference(variable_rename,[status(thm)],[c_0_987]) ).
fof(c_0_1535,plain,
! [X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X14)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X14),c_HOL_Ozero__class_Ozero(X14)),X13) = X13 ),
inference(variable_rename,[status(thm)],[c_0_988]) ).
fof(c_0_1536,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X14)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X14),c_HOL_Ozero__class_Ozero(X14)),X13) = X13 ),
inference(variable_rename,[status(thm)],[c_0_989]) ).
fof(c_0_1537,plain,
! [X8,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),c_HOL_Ozero__class_Ozero(X9)),X8) = X8 ),
inference(variable_rename,[status(thm)],[c_0_990]) ).
fof(c_0_1538,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Omonoid__add(X14)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X14),c_HOL_Ozero__class_Ozero(X14)),X13) = X13 ),
inference(variable_rename,[status(thm)],[c_0_991]) ).
fof(c_0_1539,plain,
! [X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X14)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X14),X13),c_HOL_Ozero__class_Ozero(X14)) = c_HOL_Ozero__class_Ozero(X14) ),
inference(variable_rename,[status(thm)],[c_0_992]) ).
fof(c_0_1540,plain,
! [X13,X14] :
( ~ class_RealVector_Oreal__normed__algebra(X14)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X14),X13),c_HOL_Ozero__class_Ozero(X14)) = c_HOL_Ozero__class_Ozero(X14) ),
inference(variable_rename,[status(thm)],[c_0_993]) ).
fof(c_0_1541,plain,
! [X8,X9] :
( ~ class_RealVector_Oreal__normed__algebra(X9)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X9),X8),c_HOL_Ozero__class_Ozero(X9)) = c_HOL_Ozero__class_Ozero(X9) ),
inference(variable_rename,[status(thm)],[c_0_994]) ).
fof(c_0_1542,plain,
! [X13,X14] :
( ~ class_Ring__and__Field_Omult__zero(X14)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X14),X13),c_HOL_Ozero__class_Ozero(X14)) = c_HOL_Ozero__class_Ozero(X14) ),
inference(variable_rename,[status(thm)],[c_0_995]) ).
fof(c_0_1543,plain,
! [X13,X14] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X14)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X14),X13),c_HOL_Ozero__class_Ozero(X14)) = c_HOL_Ozero__class_Ozero(X14) ),
inference(variable_rename,[status(thm)],[c_0_996]) ).
fof(c_0_1544,plain,
! [X7,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X8)
| c_Polynomial_Osmult(c_HOL_Oone__class_Oone(X8),X7,X8) = X7 ),
inference(variable_rename,[status(thm)],[c_0_997]) ).
fof(c_0_1545,plain,
! [X8,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X9)
| hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(X9) ),
inference(variable_rename,[status(thm)],[c_0_998]) ).
fof(c_0_1546,plain,
! [X13,X14] :
( ~ class_Power_Opower(X14)
| hAPP(hAPP(c_Power_Opower__class_Opower(X14),X13),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(X14) ),
inference(variable_rename,[status(thm)],[c_0_999]) ).
fof(c_0_1547,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Omonoid__mult(X14)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X14),X13),c_HOL_Oone__class_Oone(X14)) = X13 ),
inference(variable_rename,[status(thm)],[c_0_1000]) ).
fof(c_0_1548,plain,
! [X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X14)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X14),X13),c_HOL_Oone__class_Oone(X14)) = X13 ),
inference(variable_rename,[status(thm)],[c_0_1001]) ).
fof(c_0_1549,plain,
! [X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X14)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X14),X13),c_HOL_Ozero__class_Ozero(X14)) = X13 ),
inference(variable_rename,[status(thm)],[c_0_1002]) ).
fof(c_0_1550,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X14)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X14),X13),c_HOL_Ozero__class_Ozero(X14)) = X13 ),
inference(variable_rename,[status(thm)],[c_0_1003]) ).
fof(c_0_1551,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Omonoid__add(X14)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X14),X13),c_HOL_Ozero__class_Ozero(X14)) = X13 ),
inference(variable_rename,[status(thm)],[c_0_1004]) ).
fof(c_0_1552,plain,
! [X8,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X9)
| hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),c_HOL_Oone__class_Oone(tc_nat)) = X8 ),
inference(variable_rename,[status(thm)],[c_0_1005]) ).
fof(c_0_1553,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Omonoid__mult(X14)
| hAPP(hAPP(c_Power_Opower__class_Opower(X14),X13),c_HOL_Oone__class_Oone(tc_nat)) = X13 ),
inference(variable_rename,[status(thm)],[c_0_1006]) ).
fof(c_0_1554,plain,
! [X7,X8] :
( ~ class_HOL_Ozero(X8)
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X7,X8) = c_Suc(c_Polynomial_Odegree(X7,X8))
| X7 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ),
inference(variable_rename,[status(thm)],[c_0_1007]) ).
fof(c_0_1555,plain,
! [X8,X9] :
( ~ class_Orderings_Opreorder(X9)
| c_lessequals(X8,X8,X9) ),
inference(variable_rename,[status(thm)],[c_0_1008]) ).
fof(c_0_1556,plain,
! [X8,X9] :
( ~ class_Orderings_Oorder(X9)
| c_lessequals(X8,X8,X9) ),
inference(variable_rename,[status(thm)],[c_0_1009]) ).
fof(c_0_1557,plain,
! [X8,X9] :
( ~ class_RealVector_Oreal__normed__vector(X9)
| c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(X8,X9),X9) = c_RealVector_Onorm__class_Onorm(X8,X9) ),
inference(variable_rename,[status(thm)],[c_0_1010]) ).
fof(c_0_1558,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oidom(X11)
| ~ class_Int_Oring__char__0(X11)
| c_Polynomial_Opoly(X10,X11) != c_Polynomial_Opoly(X9,X11)
| X10 = X9 ),
inference(variable_rename,[status(thm)],[c_0_1011]) ).
fof(c_0_1559,plain,
! [X8,X9] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X9)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X9),X8),X8) = X8 ),
inference(variable_rename,[status(thm)],[c_0_1012]) ).
fof(c_0_1560,plain,
! [X14,X15] :
( ~ class_Ring__and__Field_Oidom(t_a)
| v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2(X15) != c_HOL_Ozero__class_Ozero(t_a)
| hAPP(c_Polynomial_Opoly(X15,t_a),X14) = c_HOL_Ozero__class_Ozero(t_a)
| X14 = c_HOL_Ozero__class_Ozero(t_a) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1013])])]) ).
fof(c_0_1561,plain,
! [X10,X11,X12] :
( ~ class_HOL_Ozero(X12)
| c_Polynomial_Ocoeff(X11,X12) != c_Polynomial_Ocoeff(X10,X12)
| X11 = X10 ),
inference(variable_rename,[status(thm)],[c_0_1014]) ).
fof(c_0_1562,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Oboolean__algebra(X12)
| c_HOL_Ouminus__class_Ouminus(X11,X12) != c_HOL_Ouminus__class_Ouminus(X10,X12)
| X11 = X10 ),
inference(variable_rename,[status(thm)],[c_0_1015]) ).
fof(c_0_1563,plain,
! [X13,X14,X15] :
( ~ class_OrderedGroup_Ogroup__add(X15)
| c_HOL_Ouminus__class_Ouminus(X14,X15) != c_HOL_Ouminus__class_Ouminus(X13,X15)
| X14 = X13 ),
inference(variable_rename,[status(thm)],[c_0_1016]) ).
fof(c_0_1564,plain,
! [X23,X24,X25] :
( ~ class_Nat_Osemiring__char__0(X25)
| c_Nat_Osemiring__1__class_Oof__nat(X24,X25) != c_Nat_Osemiring__1__class_Oof__nat(X23,X25)
| X24 = X23 ),
inference(variable_rename,[status(thm)],[c_0_1017]) ).
fof(c_0_1565,plain,
! [X12,X13] :
( ~ class_OrderedGroup_Ogroup__add(X13)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X12,X13),X13) = X12 ),
inference(variable_rename,[status(thm)],[c_0_1018]) ).
fof(c_0_1566,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Ogroup__add(X14)
| X13 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X13,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_1019]) ).
fof(c_0_1567,plain,
! [X12,X13] :
( ~ class_OrderedGroup_Ogroup__add(X13)
| X12 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X12,X13),X13) ),
inference(variable_rename,[status(thm)],[c_0_1020]) ).
fof(c_0_1568,plain,
! [X8,X9] :
( ~ class_Lattices_Oboolean__algebra(X9)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X8,X9),X9) = X8 ),
inference(variable_rename,[status(thm)],[c_0_1021]) ).
fof(c_0_1569,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Ogroup__add(X14)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X13,X14),X14) = X13 ),
inference(variable_rename,[status(thm)],[c_0_1022]) ).
fof(c_0_1570,plain,
! [X7,X8] :
( ~ class_HOL_Ozero(X8)
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X7,X8) != c_HOL_Ozero__class_Ozero(tc_nat)
| X7 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ),
inference(variable_rename,[status(thm)],[c_0_1023]) ).
fof(c_0_1571,plain,
! [X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1024]) ).
fof(c_0_1572,plain,
! [X4] :
( ~ class_HOL_Ozero(X4)
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1025]) ).
fof(c_0_1573,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Ogroup__add(X14)
| c_HOL_Ouminus__class_Ouminus(X13,X14) != c_HOL_Ozero__class_Ozero(X14)
| X13 = c_HOL_Ozero__class_Ozero(X14) ),
inference(variable_rename,[status(thm)],[c_0_1026]) ).
fof(c_0_1574,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Ogroup__add(X14)
| c_HOL_Ozero__class_Ozero(X14) != c_HOL_Ouminus__class_Ouminus(X13,X14)
| c_HOL_Ozero__class_Ozero(X14) = X13 ),
inference(variable_rename,[status(thm)],[c_0_1027]) ).
fof(c_0_1575,plain,
! [X6,X7] :
( class_Lattices_Oboolean__algebra(tc_fun(X6,X7))
| ~ class_Lattices_Oboolean__algebra(X7) ),
inference(variable_rename,[status(thm)],[c_0_1028]) ).
fof(c_0_1576,plain,
! [X6,X7] :
( class_Orderings_Opreorder(tc_fun(X6,X7))
| ~ class_Orderings_Opreorder(X7) ),
inference(variable_rename,[status(thm)],[c_0_1029]) ).
fof(c_0_1577,plain,
! [X6,X7] :
( class_Orderings_Oorder(tc_fun(X6,X7))
| ~ class_Orderings_Oorder(X7) ),
inference(variable_rename,[status(thm)],[c_0_1030]) ).
fof(c_0_1578,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X14)
| c_HOL_Ouminus__class_Ouminus(X13,X14) != X13
| X13 = c_HOL_Ozero__class_Ozero(X14) ),
inference(variable_rename,[status(thm)],[c_0_1031]) ).
fof(c_0_1579,plain,
! [X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Ozero__class_Ozero(X4) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(variable_rename,[status(thm)],[c_0_1032]) ).
fof(c_0_1580,plain,
! [X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(variable_rename,[status(thm)],[c_0_1033]) ).
fof(c_0_1581,plain,
! [X4] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X4)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(variable_rename,[status(thm)],[c_0_1034]) ).
fof(c_0_1582,plain,
! [X4] :
( ~ class_Ring__and__Field_Osemiring__1(X4)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X4) = c_HOL_Oone__class_Oone(X4) ),
inference(variable_rename,[status(thm)],[c_0_1035]) ).
fof(c_0_1583,plain,
! [X4] :
( ~ class_Ring__and__Field_Osemiring__1(X4)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(variable_rename,[status(thm)],[c_0_1036]) ).
fof(c_0_1584,plain,
! [X4] :
( ~ class_Ring__and__Field_Ozero__neq__one(X4)
| c_HOL_Ozero__class_Ozero(X4) != c_HOL_Oone__class_Oone(X4) ),
inference(variable_rename,[status(thm)],[c_0_1037]) ).
fof(c_0_1585,plain,
! [X4] :
( ~ class_Ring__and__Field_Ozero__neq__one(X4)
| c_HOL_Oone__class_Oone(X4) != c_HOL_Ozero__class_Ozero(X4) ),
inference(variable_rename,[status(thm)],[c_0_1038]) ).
fof(c_0_1586,plain,
! [X5] :
( class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X5))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X5) ),
inference(variable_rename,[status(thm)],[c_0_1039]) ).
fof(c_0_1587,plain,
! [X5] :
( class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Ocomm__ring__1(X5) ),
inference(variable_rename,[status(thm)],[c_0_1040]) ).
fof(c_0_1588,plain,
! [X5] :
( class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Ocomm__ring(X5) ),
inference(variable_rename,[status(thm)],[c_0_1041]) ).
fof(c_0_1589,plain,
! [X5] :
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Oordered__idom(X5) ),
inference(variable_rename,[status(thm)],[c_0_1042]) ).
fof(c_0_1590,plain,
! [X5] :
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Oordered__idom(X5) ),
inference(variable_rename,[status(thm)],[c_0_1043]) ).
fof(c_0_1591,plain,
! [X5] :
( class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Oordered__idom(X5) ),
inference(variable_rename,[status(thm)],[c_0_1044]) ).
fof(c_0_1592,plain,
! [X5] :
( class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Oordered__idom(X5) ),
inference(variable_rename,[status(thm)],[c_0_1045]) ).
fof(c_0_1593,plain,
! [X5] :
( class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(variable_rename,[status(thm)],[c_0_1046]) ).
fof(c_0_1594,plain,
! [X5] :
( class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Oordered__idom(X5) ),
inference(variable_rename,[status(thm)],[c_0_1047]) ).
fof(c_0_1595,plain,
! [X5] :
( class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Oordered__idom(X5) ),
inference(variable_rename,[status(thm)],[c_0_1048]) ).
fof(c_0_1596,plain,
! [X5] :
( class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Oordered__idom(X5) ),
inference(variable_rename,[status(thm)],[c_0_1049]) ).
fof(c_0_1597,plain,
! [X5] :
( class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(variable_rename,[status(thm)],[c_0_1050]) ).
fof(c_0_1598,plain,
! [X5] :
( class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X5))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X5) ),
inference(variable_rename,[status(thm)],[c_0_1051]) ).
fof(c_0_1599,plain,
! [X5] :
( class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Oordered__idom(X5) ),
inference(variable_rename,[status(thm)],[c_0_1052]) ).
fof(c_0_1600,plain,
! [X5] :
( class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Oordered__idom(X5) ),
inference(variable_rename,[status(thm)],[c_0_1053]) ).
fof(c_0_1601,plain,
! [X5] :
( class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Oordered__idom(X5) ),
inference(variable_rename,[status(thm)],[c_0_1054]) ).
fof(c_0_1602,plain,
! [X5] :
( class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X5))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X5) ),
inference(variable_rename,[status(thm)],[c_0_1055]) ).
fof(c_0_1603,plain,
! [X5] :
( class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Oordered__idom(X5) ),
inference(variable_rename,[status(thm)],[c_0_1056]) ).
fof(c_0_1604,plain,
! [X5] :
( class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Oordered__idom(X5) ),
inference(variable_rename,[status(thm)],[c_0_1057]) ).
fof(c_0_1605,plain,
! [X5] :
( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(variable_rename,[status(thm)],[c_0_1058]) ).
fof(c_0_1606,plain,
! [X5] :
( class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Oordered__idom(X5) ),
inference(variable_rename,[status(thm)],[c_0_1059]) ).
fof(c_0_1607,plain,
! [X5] :
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X5) ),
inference(variable_rename,[status(thm)],[c_0_1060]) ).
fof(c_0_1608,plain,
! [X5] :
( class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X5) ),
inference(variable_rename,[status(thm)],[c_0_1061]) ).
fof(c_0_1609,plain,
! [X5] :
( class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X5) ),
inference(variable_rename,[status(thm)],[c_0_1062]) ).
fof(c_0_1610,plain,
! [X5] :
( class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X5) ),
inference(variable_rename,[status(thm)],[c_0_1063]) ).
fof(c_0_1611,plain,
! [X5] :
( class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X5))
| ~ class_OrderedGroup_Ocomm__monoid__add(X5) ),
inference(variable_rename,[status(thm)],[c_0_1064]) ).
fof(c_0_1612,plain,
! [X5] :
( class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Oordered__idom(X5) ),
inference(variable_rename,[status(thm)],[c_0_1065]) ).
fof(c_0_1613,plain,
! [X5] :
( class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X5) ),
inference(variable_rename,[status(thm)],[c_0_1066]) ).
fof(c_0_1614,plain,
! [X5] :
( class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X5))
| ~ class_OrderedGroup_Ocomm__monoid__add(X5) ),
inference(variable_rename,[status(thm)],[c_0_1067]) ).
fof(c_0_1615,plain,
! [X5] :
( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X5) ),
inference(variable_rename,[status(thm)],[c_0_1068]) ).
fof(c_0_1616,plain,
! [X5] :
( class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Oordered__idom(X5) ),
inference(variable_rename,[status(thm)],[c_0_1069]) ).
fof(c_0_1617,plain,
! [X5] :
( class_OrderedGroup_Osemigroup__add(tc_Polynomial_Opoly(X5))
| ~ class_OrderedGroup_Ocomm__monoid__add(X5) ),
inference(variable_rename,[status(thm)],[c_0_1070]) ).
fof(c_0_1618,plain,
! [X5] :
( class_Ring__and__Field_Osemiring__1(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X5) ),
inference(variable_rename,[status(thm)],[c_0_1071]) ).
fof(c_0_1619,plain,
! [X5] :
( class_Ring__and__Field_Osemiring__0(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X5) ),
inference(variable_rename,[status(thm)],[c_0_1072]) ).
fof(c_0_1620,plain,
! [X5] :
( class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Oordered__idom(X5) ),
inference(variable_rename,[status(thm)],[c_0_1073]) ).
fof(c_0_1621,plain,
! [X5] :
( class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X5))
| ~ class_OrderedGroup_Oab__group__add(X5) ),
inference(variable_rename,[status(thm)],[c_0_1074]) ).
fof(c_0_1622,plain,
! [X5] :
( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X5) ),
inference(variable_rename,[status(thm)],[c_0_1075]) ).
fof(c_0_1623,plain,
! [X5] :
( class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Oordered__idom(X5) ),
inference(variable_rename,[status(thm)],[c_0_1076]) ).
fof(c_0_1624,plain,
! [X5] :
( class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X5) ),
inference(variable_rename,[status(thm)],[c_0_1077]) ).
fof(c_0_1625,plain,
! [X5] :
( class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X5) ),
inference(variable_rename,[status(thm)],[c_0_1078]) ).
fof(c_0_1626,plain,
! [X5] :
( class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X5))
| ~ class_OrderedGroup_Ocomm__monoid__add(X5) ),
inference(variable_rename,[status(thm)],[c_0_1079]) ).
fof(c_0_1627,plain,
! [X5] :
( class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X5))
| ~ class_OrderedGroup_Oab__group__add(X5) ),
inference(variable_rename,[status(thm)],[c_0_1080]) ).
fof(c_0_1628,plain,
! [X5] :
( class_Ring__and__Field_Oring__1(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Ocomm__ring__1(X5) ),
inference(variable_rename,[status(thm)],[c_0_1081]) ).
fof(c_0_1629,plain,
! [X5] :
( class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Ocomm__ring(X5) ),
inference(variable_rename,[status(thm)],[c_0_1082]) ).
fof(c_0_1630,plain,
! [X5] :
( class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(variable_rename,[status(thm)],[c_0_1083]) ).
fof(c_0_1631,plain,
! [X5] :
( class_Nat_Osemiring__char__0(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Oordered__idom(X5) ),
inference(variable_rename,[status(thm)],[c_0_1084]) ).
fof(c_0_1632,plain,
! [X5] :
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Oordered__idom(X5) ),
inference(variable_rename,[status(thm)],[c_0_1085]) ).
fof(c_0_1633,plain,
! [X5] :
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Oordered__idom(X5) ),
inference(variable_rename,[status(thm)],[c_0_1086]) ).
fof(c_0_1634,plain,
! [X5] :
( class_Orderings_Oorder(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Oordered__idom(X5) ),
inference(variable_rename,[status(thm)],[c_0_1087]) ).
fof(c_0_1635,plain,
! [X5] :
( class_Int_Oring__char__0(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Oordered__idom(X5) ),
inference(variable_rename,[status(thm)],[c_0_1088]) ).
fof(c_0_1636,plain,
! [X5] :
( class_Int_Onumber__ring(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Ocomm__ring__1(X5) ),
inference(variable_rename,[status(thm)],[c_0_1089]) ).
fof(c_0_1637,plain,
! [X5] :
( class_Power_Opower(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X5) ),
inference(variable_rename,[status(thm)],[c_0_1090]) ).
fof(c_0_1638,plain,
! [X5] :
( class_HOL_Ozero(tc_Polynomial_Opoly(X5))
| ~ class_HOL_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1091]) ).
fof(c_0_1639,plain,
! [X30,X31] :
( c_Suc(X31) != c_Suc(X30)
| X31 = X30 ),
inference(variable_rename,[status(thm)],[c_0_1092]) ).
fof(c_0_1640,plain,
! [X10,X11] :
( c_Suc(X11) != c_Suc(X10)
| X11 = X10 ),
inference(variable_rename,[status(thm)],[c_0_1093]) ).
cnf(c_0_1641,plain,
( c_Polynomial_Opoly__rec(X1,X2,c_Polynomial_OpCons(X3,X4,X5),X6,X5) = hAPP(hAPP(hAPP(X2,X3),X4),c_HOL_OIf(c_fequal(X4,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)),X1,c_Polynomial_Opoly__rec(X1,X2,X4,X6,X5),X6))
| ~ class_HOL_Ozero(X5) ),
inference(split_conjunct,[status(thm)],[c_0_1094]) ).
cnf(c_0_1642,plain,
( c_Polynomial_Opoly__rec(X1,X2,c_Polynomial_OpCons(X3,X4,X5),X6,X5) = hAPP(hAPP(hAPP(X2,X3),X4),c_Polynomial_Opoly__rec(X1,X2,X4,X6,X5))
| hAPP(hAPP(hAPP(X2,c_HOL_Ozero__class_Ozero(X5)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))),X1) != X1
| ~ class_HOL_Ozero(X5) ),
inference(split_conjunct,[status(thm)],[c_0_1095]) ).
cnf(c_0_1643,plain,
( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X3,X4,X1,X1))
| ~ class_OrderedGroup_Osemigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1096]) ).
cnf(c_0_1644,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X3,X1,X1)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1)
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1097]) ).
cnf(c_0_1645,plain,
( hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),X4)),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X3),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1098]) ).
cnf(c_0_1646,plain,
( hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),X3)),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1099]) ).
cnf(c_0_1647,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X1,t_a),t_a,t_a)
| hAPP(c_Polynomial_Opoly(X1,t_a),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(t_a),hAPP(c_Polynomial_Opoly(X1,t_a),c_HOL_Ozero__class_Ozero(t_a))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X2),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1(X1))),hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__2(X1),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__3(X1),t_a),t_a),X2)))
| ~ class_Ring__and__Field_Oidom(t_a) ),
inference(split_conjunct,[status(thm)],[c_0_1100]) ).
cnf(c_0_1648,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),X3)),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),X3))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1101]) ).
cnf(c_0_1649,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)),X5)
| ~ class_Ring__and__Field_Osemiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1102]) ).
cnf(c_0_1650,plain,
( hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),c_Suc(X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),X3)),X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1103]) ).
cnf(c_0_1651,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1104]) ).
cnf(c_0_1652,plain,
( c_Polynomial_Opoly__rec(X1,X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X4,X3) = X1
| hAPP(hAPP(hAPP(X2,c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))),X1) != X1
| ~ class_HOL_Ozero(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1105]) ).
cnf(c_0_1653,plain,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3)),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1106]) ).
cnf(c_0_1654,plain,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3)),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1107]) ).
cnf(c_0_1655,plain,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3)),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1108]) ).
cnf(c_0_1656,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(X1,X2,X3),X4,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X4,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X4,X3),X3)),c_Polynomial_OpCons(X1,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X4,X3),X3))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1109]) ).
cnf(c_0_1657,plain,
( X1 = X2
| X3 = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X3))
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(split_conjunct,[status(thm)],[c_0_1110]) ).
cnf(c_0_1658,plain,
( X1 = X2
| X3 = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X3))
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(split_conjunct,[status(thm)],[c_0_1111]) ).
cnf(c_0_1659,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1112]) ).
cnf(c_0_1660,plain,
( hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),c_Suc(X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),X3))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1113]) ).
cnf(c_0_1661,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1114]) ).
cnf(c_0_1662,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X1)),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1115]) ).
cnf(c_0_1663,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X3)),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1116]) ).
cnf(c_0_1664,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3)),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1117]) ).
cnf(c_0_1665,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X1),X1)),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Ring__and__Field_Oring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1118]) ).
cnf(c_0_1666,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1119]) ).
cnf(c_0_1667,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1120]) ).
cnf(c_0_1668,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1121]) ).
cnf(c_0_1669,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1122]) ).
cnf(c_0_1670,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1123]) ).
cnf(c_0_1671,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X2,X3,X1)),c_Polynomial_OpCons(X4,X5,X1)) = c_Polynomial_OpCons(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),X3),X5),X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1124]) ).
cnf(c_0_1672,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1125]) ).
cnf(c_0_1673,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X2)),c_Polynomial_Osmult(X3,X1,X2)),c_Polynomial_OpCons(X4,X1,X2)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1126]) ).
cnf(c_0_1674,plain,
( hAPP(c_Polynomial_Ocoeff(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),X2),X3),X1),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_Polynomial_Ocoeff(X2,X1),X4)),hAPP(c_Polynomial_Ocoeff(X3,X1),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1127]) ).
cnf(c_0_1675,plain,
( hAPP(c_Polynomial_Opoly(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),X2),X3),X1),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_Polynomial_Opoly(X2,X1),X4)),hAPP(c_Polynomial_Opoly(X3,X1),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1128]) ).
cnf(c_0_1676,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1129]) ).
cnf(c_0_1677,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1130]) ).
cnf(c_0_1678,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1131]) ).
cnf(c_0_1679,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1132]) ).
cnf(c_0_1680,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1133]) ).
cnf(c_0_1681,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1134]) ).
cnf(c_0_1682,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X1,t_a),t_a,t_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__3(X1),t_a)),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1(X1))),c_HOL_Oone__class_Oone(tc_nat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,t_a)
| ~ class_Ring__and__Field_Oidom(t_a) ),
inference(split_conjunct,[status(thm)],[c_0_1135]) ).
cnf(c_0_1683,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1136]) ).
cnf(c_0_1684,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1137]) ).
cnf(c_0_1685,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1138]) ).
cnf(c_0_1686,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1139]) ).
cnf(c_0_1687,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1140]) ).
cnf(c_0_1688,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1141]) ).
cnf(c_0_1689,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1142]) ).
cnf(c_0_1690,plain,
( c_Polynomial_Osmult(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X2)),X3),X4),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X2)),c_Polynomial_Osmult(X1,X3,X2)),c_Polynomial_Osmult(X1,X4,X2))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1143]) ).
cnf(c_0_1691,plain,
( c_lessequals(X2,X4,X1)
| ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),c_Suc(X3)),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1144]) ).
cnf(c_0_1692,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X3)) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1145]) ).
cnf(c_0_1693,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X1)) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1146]) ).
cnf(c_0_1694,plain,
( hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X1,X2,X3),X3),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),hAPP(c_Polynomial_Opoly(X2,X3),X4)))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1147]) ).
cnf(c_0_1695,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1148]) ).
cnf(c_0_1696,plain,
( c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1149]) ).
cnf(c_0_1697,plain,
( c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1150]) ).
cnf(c_0_1698,plain,
( c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1151]) ).
cnf(c_0_1699,plain,
( c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1152]) ).
cnf(c_0_1700,plain,
( c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1153]) ).
cnf(c_0_1701,plain,
( c_lessequals(X2,X4,X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1154]) ).
cnf(c_0_1702,plain,
( c_lessequals(X3,X4,X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1155]) ).
cnf(c_0_1703,plain,
( c_lessequals(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1156]) ).
cnf(c_0_1704,plain,
( c_lessequals(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1157]) ).
cnf(c_0_1705,plain,
( c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1158]) ).
cnf(c_0_1706,plain,
( c_HOL_Oord__class_Oless(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1159]) ).
cnf(c_0_1707,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),c_Polynomial_Omonom(X2,X3,X1)),c_Polynomial_Omonom(X4,X3,X1)) = c_Polynomial_Omonom(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X3,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1160]) ).
cnf(c_0_1708,plain,
( c_Polynomial_Osmult(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),c_Polynomial_Osmult(X2,X4,X1)),c_Polynomial_Osmult(X3,X4,X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1161]) ).
cnf(c_0_1709,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Oone__class_Oone(X1))),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1162]) ).
cnf(c_0_1710,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1163]) ).
cnf(c_0_1711,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1164]) ).
cnf(c_0_1712,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1165]) ).
cnf(c_0_1713,plain,
( c_HOL_Oord__class_Oless(X3,X4,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1166]) ).
cnf(c_0_1714,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_HOL_Oord__class_Oless(X4,X2,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1167]) ).
cnf(c_0_1715,plain,
( c_HOL_Oord__class_Oless(X2,X4,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1168]) ).
cnf(c_0_1716,plain,
( c_HOL_Oord__class_Oless(X3,X4,X1)
| c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1169]) ).
cnf(c_0_1717,plain,
( c_HOL_Oord__class_Oless(X2,X4,X1)
| c_HOL_Oord__class_Oless(X4,X2,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1170]) ).
cnf(c_0_1718,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1171]) ).
cnf(c_0_1719,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1172]) ).
cnf(c_0_1720,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1173]) ).
cnf(c_0_1721,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1174]) ).
cnf(c_0_1722,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1175]) ).
cnf(c_0_1723,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1176]) ).
cnf(c_0_1724,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1177]) ).
cnf(c_0_1725,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4))
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1178]) ).
cnf(c_0_1726,plain,
( c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X5),X2)
| ~ c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X4),X2)
| ~ c_lessequals(X4,X5,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1179]) ).
cnf(c_0_1727,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1180]) ).
cnf(c_0_1728,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1181]) ).
cnf(c_0_1729,plain,
( c_lessequals(X2,X4,X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1182]) ).
cnf(c_0_1730,plain,
( c_lessequals(X3,X4,X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1183]) ).
cnf(c_0_1731,plain,
( c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1184]) ).
cnf(c_0_1732,plain,
( c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1185]) ).
cnf(c_0_1733,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1186]) ).
cnf(c_0_1734,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1187]) ).
cnf(c_0_1735,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1188]) ).
cnf(c_0_1736,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X1),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1189]) ).
cnf(c_0_1737,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X4),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Omult__mono(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1190]) ).
cnf(c_0_1738,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X2),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Omult__mono(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1191]) ).
cnf(c_0_1739,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X2),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Omult__mono1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1192]) ).
cnf(c_0_1740,plain,
( c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X4),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1193]) ).
cnf(c_0_1741,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1194]) ).
cnf(c_0_1742,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1195]) ).
cnf(c_0_1743,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X2),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1196]) ).
cnf(c_0_1744,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X4),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X1),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1197]) ).
cnf(c_0_1745,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1198]) ).
cnf(c_0_1746,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X4),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1199]) ).
cnf(c_0_1747,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1200]) ).
cnf(c_0_1748,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1201]) ).
cnf(c_0_1749,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1202]) ).
cnf(c_0_1750,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X2),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1203]) ).
cnf(c_0_1751,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X1),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1204]) ).
cnf(c_0_1752,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1205]) ).
cnf(c_0_1753,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1206]) ).
cnf(c_0_1754,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_p,t_a) = c_HOL_OIf(c_fequal(v_p,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),tc_Polynomial_Opoly(t_a)),c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_Polynomial_Odegree(v_p,t_a)),tc_nat)
| ~ class_HOL_Ozero(t_a) ),
inference(split_conjunct,[status(thm)],[c_0_1207]) ).
cnf(c_0_1755,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),c_HOL_Oone__class_Oone(X1))),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1208]) ).
cnf(c_0_1756,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1209]) ).
cnf(c_0_1757,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1210]) ).
cnf(c_0_1758,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1211]) ).
cnf(c_0_1759,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1212]) ).
cnf(c_0_1760,plain,
( c_Polynomial_Osmult(X1,c_Polynomial_OpCons(X2,X3,X4),X4) = c_Polynomial_OpCons(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),X1),X2),c_Polynomial_Osmult(X1,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1213]) ).
cnf(c_0_1761,plain,
( X1 = hAPP(c_Polynomial_Opoly(X2,X3),X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X3)),X2),c_Polynomial_Osmult(X4,X5,X3)) != c_Polynomial_OpCons(X1,X5,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1214]) ).
cnf(c_0_1762,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1215]) ).
cnf(c_0_1763,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1216]) ).
cnf(c_0_1764,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1217]) ).
cnf(c_0_1765,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1218]) ).
cnf(c_0_1766,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1219]) ).
cnf(c_0_1767,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1220]) ).
cnf(c_0_1768,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1221]) ).
cnf(c_0_1769,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1222]) ).
cnf(c_0_1770,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1223]) ).
cnf(c_0_1771,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1224]) ).
cnf(c_0_1772,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1225]) ).
cnf(c_0_1773,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1226]) ).
cnf(c_0_1774,plain,
( hAPP(c_Polynomial_Opoly(c_Polynomial_Omonom(X1,X2,X3),X3),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1227]) ).
cnf(c_0_1775,plain,
( hAPP(c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X2,X3),X3),X4) = hAPP(c_Polynomial_Opoly(X1,X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1228]) ).
cnf(c_0_1776,plain,
( hAPP(c_Polynomial_Ocoeff(c_Polynomial_Osmult(X1,X2,X3),X3),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),hAPP(c_Polynomial_Ocoeff(X2,X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1229]) ).
cnf(c_0_1777,plain,
( hAPP(c_Polynomial_Opoly(c_Polynomial_Osmult(X1,X2,X3),X3),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),hAPP(c_Polynomial_Opoly(X2,X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1230]) ).
cnf(c_0_1778,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1))),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1231]) ).
cnf(c_0_1779,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1232]) ).
cnf(c_0_1780,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1233]) ).
cnf(c_0_1781,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1234]) ).
cnf(c_0_1782,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1235]) ).
cnf(c_0_1783,plain,
( c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1236]) ).
cnf(c_0_1784,plain,
( c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1237]) ).
cnf(c_0_1785,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1238]) ).
cnf(c_0_1786,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1239]) ).
cnf(c_0_1787,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X4)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1240]) ).
cnf(c_0_1788,plain,
( X2 = X3
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X4)) != hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Suc(X4))
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1241]) ).
cnf(c_0_1789,plain,
( hAPP(c_Polynomial_Opoly(c_Polynomial_Opcompose(X1,X2,X3),X3),X4) = hAPP(c_Polynomial_Opoly(X1,X3),hAPP(c_Polynomial_Opoly(X2,X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1242]) ).
cnf(c_0_1790,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X3)),c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1243]) ).
cnf(c_0_1791,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_HOL_Ozero__class_Ozero(X1)),X2),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1244]) ).
cnf(c_0_1792,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1245]) ).
cnf(c_0_1793,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1246]) ).
cnf(c_0_1794,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1247]) ).
cnf(c_0_1795,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1248]) ).
cnf(c_0_1796,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1249]) ).
cnf(c_0_1797,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1250]) ).
cnf(c_0_1798,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1251]) ).
cnf(c_0_1799,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1252]) ).
cnf(c_0_1800,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1253]) ).
cnf(c_0_1801,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1254]) ).
cnf(c_0_1802,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1255]) ).
cnf(c_0_1803,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1256]) ).
cnf(c_0_1804,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1257]) ).
cnf(c_0_1805,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1258]) ).
cnf(c_0_1806,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1259]) ).
cnf(c_0_1807,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1260]) ).
cnf(c_0_1808,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1261]) ).
cnf(c_0_1809,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1262]) ).
cnf(c_0_1810,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1263]) ).
cnf(c_0_1811,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1264]) ).
cnf(c_0_1812,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1265]) ).
cnf(c_0_1813,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1266]) ).
cnf(c_0_1814,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1267]) ).
cnf(c_0_1815,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1268]) ).
cnf(c_0_1816,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1269]) ).
cnf(c_0_1817,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1270]) ).
cnf(c_0_1818,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1271]) ).
cnf(c_0_1819,plain,
( c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1272]) ).
cnf(c_0_1820,plain,
( c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1273]) ).
cnf(c_0_1821,plain,
( c_lessequals(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1274]) ).
cnf(c_0_1822,plain,
( c_lessequals(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1275]) ).
cnf(c_0_1823,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1276]) ).
cnf(c_0_1824,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1277]) ).
cnf(c_0_1825,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1278]) ).
cnf(c_0_1826,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1279]) ).
cnf(c_0_1827,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1280]) ).
cnf(c_0_1828,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1281]) ).
cnf(c_0_1829,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1282]) ).
cnf(c_0_1830,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1283]) ).
cnf(c_0_1831,plain,
( c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1284]) ).
cnf(c_0_1832,plain,
( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1285]) ).
cnf(c_0_1833,plain,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1286]) ).
cnf(c_0_1834,plain,
( hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1287]) ).
cnf(c_0_1835,plain,
( c_Polynomial_Osmult(X1,c_Polynomial_Omonom(X2,X3,X4),X4) = c_Polynomial_Omonom(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),X1),X2),X3,X4)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1288]) ).
cnf(c_0_1836,plain,
( c_Polynomial_Osmult(X1,c_Polynomial_Osmult(X2,X3,X4),X4) = c_Polynomial_Osmult(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),X1),X2),X3,X4)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1289]) ).
cnf(c_0_1837,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1290]) ).
cnf(c_0_1838,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1291]) ).
cnf(c_0_1839,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1292]) ).
cnf(c_0_1840,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1293]) ).
cnf(c_0_1841,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1294]) ).
cnf(c_0_1842,plain,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1295]) ).
cnf(c_0_1843,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X3))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1296]) ).
cnf(c_0_1844,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1297]) ).
cnf(c_0_1845,plain,
( hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1298]) ).
cnf(c_0_1846,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1299]) ).
cnf(c_0_1847,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1300]) ).
cnf(c_0_1848,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1301]) ).
cnf(c_0_1849,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1302]) ).
cnf(c_0_1850,plain,
( hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),c_HOL_Oone__class_Oone(tc_nat)) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1303]) ).
cnf(c_0_1851,plain,
( hAPP(c_Polynomial_Ocoeff(c_Polynomial_OpCons(X1,X2,X3),X3),c_Suc(X4)) = hAPP(c_Polynomial_Ocoeff(X2,X3),X4)
| ~ class_HOL_Ozero(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1304]) ).
cnf(c_0_1852,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X2),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Olordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1305]) ).
cnf(c_0_1853,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1306]) ).
cnf(c_0_1854,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1307]) ).
cnf(c_0_1855,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1308]) ).
cnf(c_0_1856,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X3)),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1309]) ).
cnf(c_0_1857,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X3,X2) = c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1310]) ).
cnf(c_0_1858,plain,
( ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1311]) ).
cnf(c_0_1859,plain,
( X1 = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1312]) ).
cnf(c_0_1860,plain,
( X1 = X2
| hAPP(c_Polynomial_Ocoeff(c_Polynomial_Omonom(X3,X1,X4),X4),X2) = c_HOL_Ozero__class_Ozero(X4)
| ~ class_HOL_Ozero(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1313]) ).
cnf(c_0_1861,plain,
( X1 = c_HOL_Ouminus__class_Ouminus(X2,X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)) != X4
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1314]) ).
cnf(c_0_1862,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X3)) = X3
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1315]) ).
cnf(c_0_1863,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1316]) ).
cnf(c_0_1864,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1317]) ).
cnf(c_0_1865,plain,
( c_lessequals(c_HOL_Oone__class_Oone(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1318]) ).
cnf(c_0_1866,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1319]) ).
cnf(c_0_1867,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1320]) ).
cnf(c_0_1868,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1321]) ).
cnf(c_0_1869,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1322]) ).
cnf(c_0_1870,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1323]) ).
cnf(c_0_1871,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1324]) ).
cnf(c_0_1872,plain,
( hAPP(c_Polynomial_Ocoeff(c_Polynomial_OpCons(X1,X2,X3),X3),c_HOL_Ozero__class_Ozero(tc_nat)) = X1
| ~ class_HOL_Ozero(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1325]) ).
cnf(c_0_1873,plain,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1326]) ).
cnf(c_0_1874,plain,
( hAPP(c_Polynomial_Ocoeff(c_Polynomial_Omonom(X1,X2,X3),X3),X2) = X1
| ~ class_HOL_Ozero(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1327]) ).
cnf(c_0_1875,plain,
( c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ouminus__class_Ouminus(X3,X1)),c_HOL_Ouminus__class_Ouminus(X2,X1))
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1328]) ).
cnf(c_0_1876,plain,
( c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),c_HOL_Ouminus__class_Ouminus(X3,X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1329]) ).
cnf(c_0_1877,plain,
( c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Nat_Osemiring__1__class_Oof__nat(X1,X3)),c_Nat_Osemiring__1__class_Oof__nat(X2,X3))
| ~ class_Ring__and__Field_Osemiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1330]) ).
cnf(c_0_1878,plain,
( c_Polynomial_Omonom(X1,c_Suc(X2),X3) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X3),c_Polynomial_Omonom(X1,X2,X3),X3)
| ~ class_HOL_Ozero(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1331]) ).
cnf(c_0_1879,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1332]) ).
cnf(c_0_1880,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1333]) ).
cnf(c_0_1881,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1334]) ).
cnf(c_0_1882,plain,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1335]) ).
cnf(c_0_1883,plain,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1336]) ).
cnf(c_0_1884,plain,
( c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1337]) ).
cnf(c_0_1885,plain,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1338]) ).
cnf(c_0_1886,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1339]) ).
cnf(c_0_1887,plain,
( c_HOL_Oord__class_Oless(X3,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1340]) ).
cnf(c_0_1888,plain,
( c_lessequals(X3,X1,X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1341]) ).
cnf(c_0_1889,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X3) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1342]) ).
cnf(c_0_1890,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X3) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1343]) ).
cnf(c_0_1891,plain,
( c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X3)
| ~ class_Ring__and__Field_Oring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1344]) ).
cnf(c_0_1892,plain,
( c_lessequals(X1,X3,tc_RealDef_Oreal)
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X2,X3,tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[c_0_1345]) ).
cnf(c_0_1893,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X3))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1346]) ).
cnf(c_0_1894,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1347]) ).
cnf(c_0_1895,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Power_Opower(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1348]) ).
cnf(c_0_1896,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1349]) ).
cnf(c_0_1897,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1350]) ).
cnf(c_0_1898,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1351]) ).
cnf(c_0_1899,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1352]) ).
cnf(c_0_1900,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1353]) ).
cnf(c_0_1901,plain,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1354]) ).
cnf(c_0_1902,plain,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1355]) ).
cnf(c_0_1903,plain,
( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1356]) ).
cnf(c_0_1904,plain,
( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1357]) ).
cnf(c_0_1905,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)) = X3
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1358]) ).
cnf(c_0_1906,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)) = X3
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1359]) ).
cnf(c_0_1907,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1360]) ).
cnf(c_0_1908,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1)),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1361]) ).
cnf(c_0_1909,plain,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1362]) ).
cnf(c_0_1910,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1363]) ).
cnf(c_0_1911,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1364]) ).
cnf(c_0_1912,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1365]) ).
cnf(c_0_1913,plain,
( c_lessequals(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1366]) ).
cnf(c_0_1914,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ouminus__class_Ouminus(X3,X1)) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1367]) ).
cnf(c_0_1915,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ouminus__class_Ouminus(X3,X1)) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1368]) ).
cnf(c_0_1916,plain,
( c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ouminus__class_Ouminus(X3,X1))
| ~ class_Ring__and__Field_Oring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1369]) ).
cnf(c_0_1917,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1370]) ).
cnf(c_0_1918,plain,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1371]) ).
cnf(c_0_1919,plain,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1372]) ).
cnf(c_0_1920,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X1,X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1373]) ).
cnf(c_0_1921,plain,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_OrderedGroup_Oordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1374]) ).
cnf(c_0_1922,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X1,X2)
| ~ class_OrderedGroup_Oordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1375]) ).
cnf(c_0_1923,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1376]) ).
cnf(c_0_1924,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Osmult(X3,X1,X2) != c_Polynomial_OpCons(X4,X1,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1377]) ).
cnf(c_0_1925,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1378]) ).
cnf(c_0_1926,plain,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1379]) ).
cnf(c_0_1927,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1380]) ).
cnf(c_0_1928,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1381]) ).
cnf(c_0_1929,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),c_HOL_Ouminus__class_Ouminus(X2,X1)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1382]) ).
cnf(c_0_1930,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),c_HOL_Ouminus__class_Ouminus(X3,X1)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)
| ~ class_Ring__and__Field_Oring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1383]) ).
cnf(c_0_1931,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ouminus__class_Ouminus(X3,X1))
| ~ class_Ring__and__Field_Oring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1384]) ).
cnf(c_0_1932,plain,
( X1 = X2
| X1 = c_HOL_Ouminus__class_Ouminus(X2,X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X1) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X2)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1385]) ).
cnf(c_0_1933,plain,
( c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1386]) ).
cnf(c_0_1934,plain,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1387]) ).
cnf(c_0_1935,plain,
( c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Oordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1388]) ).
cnf(c_0_1936,plain,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1389]) ).
cnf(c_0_1937,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1390]) ).
cnf(c_0_1938,plain,
( X2 = X1
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1391]) ).
cnf(c_0_1939,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1392]) ).
cnf(c_0_1940,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1393]) ).
cnf(c_0_1941,plain,
( X1 = X2
| c_Polynomial_OpCons(X1,X3,X4) != c_Polynomial_OpCons(X2,X5,X4)
| ~ class_HOL_Ozero(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1394]) ).
cnf(c_0_1942,plain,
( X1 = X2
| c_Polynomial_OpCons(X3,X1,X4) != c_Polynomial_OpCons(X5,X2,X4)
| ~ class_HOL_Ozero(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1395]) ).
cnf(c_0_1943,plain,
( X1 = X2
| c_Polynomial_Omonom(X1,X3,X4) != c_Polynomial_Omonom(X2,X3,X4)
| ~ class_HOL_Ozero(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1396]) ).
cnf(c_0_1944,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1397]) ).
cnf(c_0_1945,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1398]) ).
cnf(c_0_1946,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1399]) ).
cnf(c_0_1947,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1400]) ).
cnf(c_0_1948,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1401]) ).
cnf(c_0_1949,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1402]) ).
cnf(c_0_1950,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ c_lessequals(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1403]) ).
cnf(c_0_1951,plain,
( ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1404]) ).
cnf(c_0_1952,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1405]) ).
cnf(c_0_1953,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| hAPP(c_Polynomial_Opoly(X1,X2),X3) != c_HOL_Ozero__class_Ozero(X2)
| c_Polynomial_Oorder(X3,X1,X2) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1406]) ).
cnf(c_0_1954,plain,
( X1 = X2
| ~ hBOOL(c_fequal(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1407]) ).
cnf(c_0_1955,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1408]) ).
cnf(c_0_1956,plain,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Oone__class_Oone(X2)),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1409]) ).
cnf(c_0_1957,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1410]) ).
cnf(c_0_1958,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1411]) ).
cnf(c_0_1959,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1412]) ).
cnf(c_0_1960,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1413]) ).
cnf(c_0_1961,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X2,X1,tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[c_0_1414]) ).
cnf(c_0_1962,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Odegree(c_Polynomial_OpCons(X3,X1,X2),X2) = c_Suc(c_Polynomial_Odegree(X1,X2))
| ~ class_HOL_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1415]) ).
cnf(c_0_1963,plain,
( c_Polynomial_Odegree(c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X2) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_HOL_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1416]) ).
cnf(c_0_1964,plain,
( X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1417]) ).
cnf(c_0_1965,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1418]) ).
cnf(c_0_1966,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1419]) ).
cnf(c_0_1967,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1420]) ).
cnf(c_0_1968,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1421]) ).
cnf(c_0_1969,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1422]) ).
cnf(c_0_1970,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1423]) ).
cnf(c_0_1971,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1424]) ).
cnf(c_0_1972,plain,
( hAPP(c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_HOL_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1425]) ).
cnf(c_0_1973,plain,
( c_HOL_Ouminus__class_Ouminus(X1,X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X2),X2)),X1)
| ~ class_Int_Onumber__ring(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1426]) ).
cnf(c_0_1974,plain,
( c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1427]) ).
cnf(c_0_1975,plain,
( c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1428]) ).
cnf(c_0_1976,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Polynomial_Odegree(c_Polynomial_Osmult(X1,X3,X2),X2) = c_Polynomial_Odegree(X3,X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1429]) ).
cnf(c_0_1977,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1430]) ).
cnf(c_0_1978,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1431]) ).
cnf(c_0_1979,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1432]) ).
cnf(c_0_1980,plain,
( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1433]) ).
cnf(c_0_1981,plain,
( c_Polynomial_Odegree(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X1),X2,X1),X1) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1434]) ).
cnf(c_0_1982,plain,
( c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X2,X3),X3) = c_Polynomial_Odegree(X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1435]) ).
cnf(c_0_1983,plain,
( c_Polynomial_Omonom(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) = c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2)
| ~ class_HOL_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1436]) ).
cnf(c_0_1984,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Polynomial_Odegree(c_Polynomial_Omonom(X1,X3,X2),X2) = X3
| ~ class_HOL_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1437]) ).
cnf(c_0_1985,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| hAPP(c_Polynomial_Ocoeff(X1,X2),c_Polynomial_Odegree(X1,X2)) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_HOL_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1438]) ).
cnf(c_0_1986,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Osmult(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1439]) ).
cnf(c_0_1987,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1440]) ).
cnf(c_0_1988,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Power_Opower(X1)
| ~ class_Ring__and__Field_Omult__zero(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1441]) ).
cnf(c_0_1989,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1442]) ).
cnf(c_0_1990,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1443]) ).
cnf(c_0_1991,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_OpCons(X3,X1,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_HOL_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1444]) ).
cnf(c_0_1992,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1445]) ).
cnf(c_0_1993,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1446]) ).
cnf(c_0_1994,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X2 = X1
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1447]) ).
cnf(c_0_1995,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1448]) ).
cnf(c_0_1996,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1449]) ).
cnf(c_0_1997,plain,
( c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X1),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Oone__class_Oone(X2)),c_Nat_Osemiring__1__class_Oof__nat(X1,X2))
| ~ class_Ring__and__Field_Osemiring__1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1450]) ).
cnf(c_0_1998,plain,
( c_lessequals(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1451]) ).
cnf(c_0_1999,plain,
( c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1452]) ).
cnf(c_0_2000,plain,
( c_lessequals(X1,X1,X2)
| c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1453]) ).
cnf(c_0_2001,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1454]) ).
cnf(c_0_2002,plain,
( c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1455]) ).
cnf(c_0_2003,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1456]) ).
cnf(c_0_2004,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1457]) ).
cnf(c_0_2005,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1458]) ).
cnf(c_0_2006,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Polynomial_Omonom(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_HOL_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1459]) ).
cnf(c_0_2007,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Polynomial_OpCons(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_HOL_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1460]) ).
cnf(c_0_2008,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1461]) ).
cnf(c_0_2009,plain,
( ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1462]) ).
cnf(c_0_2010,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1463]) ).
cnf(c_0_2011,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1464]) ).
cnf(c_0_2012,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1465]) ).
cnf(c_0_2013,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1466]) ).
cnf(c_0_2014,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1467]) ).
cnf(c_0_2015,plain,
( c_HOL_Ouminus__class_Ouminus(X1,X2) = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1468]) ).
cnf(c_0_2016,plain,
( X1 = c_HOL_Ouminus__class_Ouminus(X2,X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X2) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1469]) ).
cnf(c_0_2017,plain,
( hAPP(X1,X2) = hAPP(X1,X3)
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X1,t_a,t_b) ),
inference(split_conjunct,[status(thm)],[c_0_1470]) ).
cnf(c_0_2018,plain,
( c_Polynomial_Oorder(X1,X2,X3) = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(c_Polynomial_Opoly(X2,X3),X1) = c_HOL_Ozero__class_Ozero(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1471]) ).
cnf(c_0_2019,plain,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| c_lessequals(X2,X1,tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[c_0_1472]) ).
cnf(c_0_2020,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1473]) ).
cnf(c_0_2021,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1474]) ).
cnf(c_0_2022,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X1) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1475]) ).
cnf(c_0_2023,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1476]) ).
cnf(c_0_2024,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),X2),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1477]) ).
cnf(c_0_2025,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1478]) ).
cnf(c_0_2026,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1479]) ).
cnf(c_0_2027,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_HOL_Ozero__class_Ozero(X2)),X1) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1480]) ).
cnf(c_0_2028,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_1481]) ).
cnf(c_0_2029,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1482]) ).
cnf(c_0_2030,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Opoly(X1,X2) != c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2)
| ~ class_Int_Oring__char__0(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1483]) ).
cnf(c_0_2031,plain,
( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_HOL_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1484]) ).
cnf(c_0_2032,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_1485]) ).
cnf(c_0_2033,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1486]) ).
cnf(c_0_2034,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_1487]) ).
cnf(c_0_2035,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_1488]) ).
cnf(c_0_2036,plain,
( hAPP(c_Polynomial_Opoly(v_pa____,tc_Complex_Ocomplex),v_sko__unknown__thm__rrS__1(v_pa____)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(v_pa____,tc_Complex_Ocomplex),v_c____) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(split_conjunct,[status(thm)],[c_0_1489]) ).
cnf(c_0_2037,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1490]) ).
cnf(c_0_2038,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1491]) ).
cnf(c_0_2039,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1492]) ).
cnf(c_0_2040,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1493]) ).
cnf(c_0_2041,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1494]) ).
cnf(c_0_2042,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_1495]) ).
cnf(c_0_2043,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_1496]) ).
cnf(c_0_2044,plain,
( c_Polynomial_Osmult(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1497]) ).
cnf(c_0_2045,plain,
( c_Polynomial_Osmult(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1498]) ).
cnf(c_0_2046,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1499]) ).
cnf(c_0_2047,plain,
( c_Polynomial_Opcompose(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1500]) ).
cnf(c_0_2048,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X1,t_a),t_a,t_a)
| v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1(X1) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oidom(t_a) ),
inference(split_conjunct,[status(thm)],[c_0_1501]) ).
cnf(c_0_2049,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X1,t_a),t_a,t_a)
| v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__2(X1) != c_HOL_Ozero__class_Ozero(t_a)
| ~ class_Ring__and__Field_Oidom(t_a) ),
inference(split_conjunct,[status(thm)],[c_0_1502]) ).
cnf(c_0_2050,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ouminus__class_Ouminus(X2,X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1503]) ).
cnf(c_0_2051,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_HOL_Ozero__class_Ozero(X1)),c_Suc(X2)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Power_Opower(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1504]) ).
cnf(c_0_2052,plain,
( hAPP(c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_HOL_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1505]) ).
cnf(c_0_2053,plain,
( hAPP(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1506]) ).
cnf(c_0_2054,plain,
( hAPP(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1507]) ).
cnf(c_0_2055,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_HOL_Ozero__class_Ozero(X2)),X1) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Osemiring__0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1508]) ).
cnf(c_0_2056,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(X1)
| ~ class_Power_Opower(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1509]) ).
cnf(c_0_2057,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1510]) ).
cnf(c_0_2058,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1511]) ).
cnf(c_0_2059,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1512]) ).
cnf(c_0_2060,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_1513]) ).
cnf(c_0_2061,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1514]) ).
cnf(c_0_2062,plain,
( c_Power_Opower__class_Opower(X1) = c_Power_Opower_Opower(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X1),X1)
| ~ class_Power_Opower(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1515]) ).
cnf(c_0_2063,plain,
( c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_HOL_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1516]) ).
cnf(c_0_2064,plain,
( c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1517]) ).
cnf(c_0_2065,plain,
( c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1518]) ).
cnf(c_0_2066,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_HOL_Oone__class_Oone(X1)),X2) = c_HOL_Oone__class_Oone(X1)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1519]) ).
cnf(c_0_2067,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1520]) ).
cnf(c_0_2068,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1521]) ).
cnf(c_0_2069,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1522]) ).
cnf(c_0_2070,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1523]) ).
cnf(c_0_2071,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Omult__zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1524]) ).
cnf(c_0_2072,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1525]) ).
cnf(c_0_2073,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1526]) ).
cnf(c_0_2074,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1527]) ).
cnf(c_0_2075,plain,
( c_OrderedGroup_Ocomm__monoid__add__axioms(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1528]) ).
cnf(c_0_2076,plain,
( c_OrderedGroup_Omonoid__add__axioms(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1)
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1529]) ).
cnf(c_0_2077,plain,
( X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Ozero__class_Ozero(X2))
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1530]) ).
cnf(c_0_2078,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Oone__class_Oone(X1)),X2) = X2
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1531]) ).
cnf(c_0_2079,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Oone__class_Oone(X1)),X2) = X2
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1532]) ).
cnf(c_0_2080,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Oone__class_Oone(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1533]) ).
cnf(c_0_2081,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Oone__class_Oone(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1534]) ).
cnf(c_0_2082,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1535]) ).
cnf(c_0_2083,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1536]) ).
cnf(c_0_2084,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1537]) ).
cnf(c_0_2085,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1538]) ).
cnf(c_0_2086,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1539]) ).
cnf(c_0_2087,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1540]) ).
cnf(c_0_2088,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1541]) ).
cnf(c_0_2089,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Omult__zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1542]) ).
cnf(c_0_2090,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1543]) ).
cnf(c_0_2091,plain,
( c_Polynomial_Osmult(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1544]) ).
cnf(c_0_2092,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1545]) ).
cnf(c_0_2093,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(X1)
| ~ class_Power_Opower(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1546]) ).
cnf(c_0_2094,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Oone__class_Oone(X1)) = X2
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1547]) ).
cnf(c_0_2095,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Oone__class_Oone(X1)) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1548]) ).
cnf(c_0_2096,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1549]) ).
cnf(c_0_2097,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1550]) ).
cnf(c_0_2098,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1551]) ).
cnf(c_0_2099,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_HOL_Oone__class_Oone(tc_nat)) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1552]) ).
cnf(c_0_2100,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_HOL_Oone__class_Oone(tc_nat)) = X2
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1553]) ).
cnf(c_0_2101,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X2) = c_Suc(c_Polynomial_Odegree(X1,X2))
| ~ class_HOL_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1554]) ).
cnf(c_0_2102,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1555]) ).
cnf(c_0_2103,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1556]) ).
cnf(c_0_2104,plain,
( c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = c_RealVector_Onorm__class_Onorm(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1557]) ).
cnf(c_0_2105,plain,
( X1 = X2
| c_Polynomial_Opoly(X1,X3) != c_Polynomial_Opoly(X2,X3)
| ~ class_Int_Oring__char__0(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1558]) ).
cnf(c_0_2106,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2) = X2
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1559]) ).
cnf(c_0_2107,plain,
( X1 = c_HOL_Ozero__class_Ozero(t_a)
| hAPP(c_Polynomial_Opoly(X2,t_a),X1) = c_HOL_Ozero__class_Ozero(t_a)
| v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2(X2) != c_HOL_Ozero__class_Ozero(t_a)
| ~ class_Ring__and__Field_Oidom(t_a) ),
inference(split_conjunct,[status(thm)],[c_0_1560]) ).
cnf(c_0_2108,plain,
( X1 = X2
| c_Polynomial_Ocoeff(X1,X3) != c_Polynomial_Ocoeff(X2,X3)
| ~ class_HOL_Ozero(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1561]) ).
cnf(c_0_2109,plain,
( X1 = X2
| c_HOL_Ouminus__class_Ouminus(X1,X3) != c_HOL_Ouminus__class_Ouminus(X2,X3)
| ~ class_Lattices_Oboolean__algebra(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1562]) ).
cnf(c_0_2110,plain,
( X1 = X2
| c_HOL_Ouminus__class_Ouminus(X1,X3) != c_HOL_Ouminus__class_Ouminus(X2,X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1563]) ).
cnf(c_0_2111,plain,
( X1 = X2
| c_Nat_Osemiring__1__class_Oof__nat(X1,X3) != c_Nat_Osemiring__1__class_Oof__nat(X2,X3)
| ~ class_Nat_Osemiring__char__0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1564]) ).
cnf(c_0_2112,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1565]) ).
cnf(c_0_2113,plain,
( X1 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1566]) ).
cnf(c_0_2114,plain,
( X1 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1567]) ).
cnf(c_0_2115,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_Lattices_Oboolean__algebra(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1568]) ).
cnf(c_0_2116,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1569]) ).
cnf(c_0_2117,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X2) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_HOL_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1570]) ).
cnf(c_0_2118,plain,
( c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_HOL_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1571]) ).
cnf(c_0_2119,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_HOL_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1572]) ).
cnf(c_0_2120,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Ouminus__class_Ouminus(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1573]) ).
cnf(c_0_2121,plain,
( c_HOL_Ozero__class_Ozero(X1) = X2
| c_HOL_Ozero__class_Ozero(X1) != c_HOL_Ouminus__class_Ouminus(X2,X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1574]) ).
cnf(c_0_2122,plain,
( class_Lattices_Oboolean__algebra(tc_fun(X2,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1575]) ).
cnf(c_0_2123,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1576]) ).
cnf(c_0_2124,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1577]) ).
cnf(c_0_2125,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Ouminus__class_Ouminus(X1,X2) != X1
| ~ class_OrderedGroup_Oordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1578]) ).
cnf(c_0_2126,plain,
( c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1579]) ).
cnf(c_0_2127,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1580]) ).
cnf(c_0_2128,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1581]) ).
cnf(c_0_2129,plain,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1582]) ).
cnf(c_0_2130,plain,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1583]) ).
cnf(c_0_2131,plain,
( c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1584]) ).
cnf(c_0_2132,plain,
( c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1585]) ).
cnf(c_0_2133,plain,
( class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1586]) ).
cnf(c_0_2134,plain,
( class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1587]) ).
cnf(c_0_2135,plain,
( class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1588]) ).
cnf(c_0_2136,plain,
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1589]) ).
cnf(c_0_2137,plain,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1590]) ).
cnf(c_0_2138,plain,
( class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1591]) ).
cnf(c_0_2139,plain,
( class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1592]) ).
cnf(c_0_2140,plain,
( class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1593]) ).
cnf(c_0_2141,plain,
( class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1594]) ).
cnf(c_0_2142,plain,
( class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1595]) ).
cnf(c_0_2143,plain,
( class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1596]) ).
cnf(c_0_2144,plain,
( class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1597]) ).
cnf(c_0_2145,plain,
( class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1598]) ).
cnf(c_0_2146,plain,
( class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1599]) ).
cnf(c_0_2147,plain,
( class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1600]) ).
cnf(c_0_2148,plain,
( class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1601]) ).
cnf(c_0_2149,plain,
( class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1602]) ).
cnf(c_0_2150,plain,
( class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1603]) ).
cnf(c_0_2151,plain,
( class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1604]) ).
cnf(c_0_2152,plain,
( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1605]) ).
cnf(c_0_2153,plain,
( class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1606]) ).
cnf(c_0_2154,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1607]) ).
cnf(c_0_2155,plain,
( class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1608]) ).
cnf(c_0_2156,plain,
( class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1609]) ).
cnf(c_0_2157,plain,
( class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1610]) ).
cnf(c_0_2158,plain,
( class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1611]) ).
cnf(c_0_2159,plain,
( class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1612]) ).
cnf(c_0_2160,plain,
( class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1613]) ).
cnf(c_0_2161,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1614]) ).
cnf(c_0_2162,plain,
( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1615]) ).
cnf(c_0_2163,plain,
( class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1616]) ).
cnf(c_0_2164,plain,
( class_OrderedGroup_Osemigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1617]) ).
cnf(c_0_2165,plain,
( class_Ring__and__Field_Osemiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1618]) ).
cnf(c_0_2166,plain,
( class_Ring__and__Field_Osemiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1619]) ).
cnf(c_0_2167,plain,
( class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1620]) ).
cnf(c_0_2168,plain,
( class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1621]) ).
cnf(c_0_2169,plain,
( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1622]) ).
cnf(c_0_2170,plain,
( class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1623]) ).
cnf(c_0_2171,plain,
( class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1624]) ).
cnf(c_0_2172,plain,
( class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1625]) ).
cnf(c_0_2173,plain,
( class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1626]) ).
cnf(c_0_2174,plain,
( class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1627]) ).
cnf(c_0_2175,plain,
( class_Ring__and__Field_Oring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1628]) ).
cnf(c_0_2176,plain,
( class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1629]) ).
cnf(c_0_2177,plain,
( class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1630]) ).
cnf(c_0_2178,plain,
( class_Nat_Osemiring__char__0(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1631]) ).
cnf(c_0_2179,plain,
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1632]) ).
cnf(c_0_2180,plain,
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1633]) ).
cnf(c_0_2181,plain,
( class_Orderings_Oorder(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1634]) ).
cnf(c_0_2182,plain,
( class_Int_Oring__char__0(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1635]) ).
cnf(c_0_2183,plain,
( class_Int_Onumber__ring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1636]) ).
cnf(c_0_2184,plain,
( class_Power_Opower(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1637]) ).
cnf(c_0_2185,plain,
( class_HOL_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_HOL_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1638]) ).
cnf(c_0_2186,plain,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1639]) ).
cnf(c_0_2187,plain,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1640]) ).
cnf(c_0_2188,plain,
( hAPP(hAPP(hAPP(X2,X3),X4),c_HOL_OIf(c_fequal(X4,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)),X1,c_Polynomial_Opoly__rec(X1,X2,X4,X6,X5),X6)) = c_Polynomial_Opoly__rec(X1,X2,c_Polynomial_OpCons(X3,X4,X5),X6,X5)
| ~ class_HOL_Ozero(X5) ),
c_0_1641,
[final] ).
cnf(c_0_2189,plain,
( c_Polynomial_Opoly__rec(X1,X2,c_Polynomial_OpCons(X3,X4,X5),X6,X5) = hAPP(hAPP(hAPP(X2,X3),X4),c_Polynomial_Opoly__rec(X1,X2,X4,X6,X5))
| hAPP(hAPP(hAPP(X2,c_HOL_Ozero__class_Ozero(X5)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))),X1) != X1
| ~ class_HOL_Ozero(X5) ),
c_0_1642,
[final] ).
cnf(c_0_2190,plain,
( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X3,X4,X1,X1))
| ~ class_OrderedGroup_Osemigroup__add(X1) ),
c_0_1643,
[final] ).
cnf(c_0_2191,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X3,X1,X1)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1)
| ~ class_OrderedGroup_Omonoid__add(X1) ),
c_0_1644,
[final] ).
cnf(c_0_2192,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),X4)),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X3),X4)) = hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_1645,
[final] ).
cnf(c_0_2193,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),X3)),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),X4)) = hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_1646,
[final] ).
cnf(c_0_2194,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X1,t_a),t_a,t_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(t_a),hAPP(c_Polynomial_Opoly(X1,t_a),c_HOL_Ozero__class_Ozero(t_a))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X2),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1(X1))),hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__2(X1),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__3(X1),t_a),t_a),X2))) = hAPP(c_Polynomial_Opoly(X1,t_a),X2)
| ~ class_Ring__and__Field_Oidom(t_a) ),
c_0_1647,
[final] ).
cnf(c_0_2195,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),X3)),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),X3))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_1648,
[final] ).
cnf(c_0_2196,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)),X5)
| ~ class_Ring__and__Field_Osemiring(X1) ),
c_0_1649,
[final] ).
cnf(c_0_2197,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),X3)),X2) = hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),c_Suc(X3))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_1650,
[final] ).
cnf(c_0_2198,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1651,
[final] ).
cnf(c_0_2199,plain,
( c_Polynomial_Opoly__rec(X1,X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X4,X3) = X1
| hAPP(hAPP(hAPP(X2,c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))),X1) != X1
| ~ class_HOL_Ozero(X3) ),
c_0_1652,
[final] ).
cnf(c_0_2200,plain,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3)),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1653,
[final] ).
cnf(c_0_2201,plain,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3)),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1654,
[final] ).
cnf(c_0_2202,plain,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3)),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1655,
[final] ).
cnf(c_0_2203,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X4,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X4,X3),X3)),c_Polynomial_OpCons(X1,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X4,X3),X3)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
c_0_1656,
[final] ).
cnf(c_0_2204,plain,
( X1 = X2
| X3 = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X3))
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
c_0_1657,
[final] ).
cnf(c_0_2205,plain,
( X1 = X2
| X3 = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X3))
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
c_0_1658,
[final] ).
cnf(c_0_2206,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1659,
[final] ).
cnf(c_0_2207,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),X3)) = hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),c_Suc(X3))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_1660,
[final] ).
cnf(c_0_2208,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1661,
[final] ).
cnf(c_0_2209,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X1)),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_1662,
[final] ).
cnf(c_0_2210,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X3)),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_1663,
[final] ).
cnf(c_0_2211,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3)),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1664,
[final] ).
cnf(c_0_2212,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X1),X1)),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X3)
| ~ class_Ring__and__Field_Oring__1(X1) ),
c_0_1665,
[final] ).
cnf(c_0_2213,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
c_0_1666,
[final] ).
cnf(c_0_2214,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
c_0_1667,
[final] ).
cnf(c_0_2215,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1668,
[final] ).
cnf(c_0_2216,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1669,
[final] ).
cnf(c_0_2217,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1670,
[final] ).
cnf(c_0_2218,plain,
( c_Polynomial_OpCons(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),X3),X5),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X2,X3,X1)),c_Polynomial_OpCons(X4,X5,X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_1671,
[final] ).
cnf(c_0_2219,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_1672,
[final] ).
cnf(c_0_2220,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X2)),c_Polynomial_Osmult(X3,X1,X2)),c_Polynomial_OpCons(X4,X1,X2)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
c_0_1673,
[final] ).
cnf(c_0_2221,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_Polynomial_Ocoeff(X2,X1),X4)),hAPP(c_Polynomial_Ocoeff(X3,X1),X4)) = hAPP(c_Polynomial_Ocoeff(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),X2),X3),X1),X4)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_1674,
[final] ).
cnf(c_0_2222,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_Polynomial_Opoly(X2,X1),X4)),hAPP(c_Polynomial_Opoly(X3,X1),X4)) = hAPP(c_Polynomial_Opoly(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),X2),X3),X1),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
c_0_1675,
[final] ).
cnf(c_0_2223,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
c_0_1676,
[final] ).
cnf(c_0_2224,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
c_0_1677,
[final] ).
cnf(c_0_2225,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
c_0_1678,
[final] ).
cnf(c_0_2226,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
c_0_1679,
[final] ).
cnf(c_0_2227,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
c_0_1680,
[final] ).
cnf(c_0_2228,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
c_0_1681,
[final] ).
cnf(c_0_2229,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X1,t_a),t_a,t_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__3(X1),t_a)),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1(X1))),c_HOL_Oone__class_Oone(tc_nat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,t_a)
| ~ class_Ring__and__Field_Oidom(t_a) ),
c_0_1682,
[final] ).
cnf(c_0_2230,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
c_0_1683,
[final] ).
cnf(c_0_2231,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1684,
[final] ).
cnf(c_0_2232,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1685,
[final] ).
cnf(c_0_2233,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_1686,
[final] ).
cnf(c_0_2234,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_1687,
[final] ).
cnf(c_0_2235,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
c_0_1688,
[final] ).
cnf(c_0_2236,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1689,
[final] ).
cnf(c_0_2237,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X2)),c_Polynomial_Osmult(X1,X3,X2)),c_Polynomial_Osmult(X1,X4,X2)) = c_Polynomial_Osmult(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X2)),X3),X4),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
c_0_1690,
[final] ).
cnf(c_0_2238,plain,
( c_lessequals(X2,X4,X1)
| ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),c_Suc(X3)),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_1691,
[final] ).
cnf(c_0_2239,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X3)) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_1692,
[final] ).
cnf(c_0_2240,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X1)) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_1693,
[final] ).
cnf(c_0_2241,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),hAPP(c_Polynomial_Opoly(X2,X3),X4))) = hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X1,X2,X3),X3),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
c_0_1694,
[final] ).
cnf(c_0_2242,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_1695,
[final] ).
cnf(c_0_2243,plain,
( c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_1696,
[final] ).
cnf(c_0_2244,plain,
( c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
c_0_1697,
[final] ).
cnf(c_0_2245,plain,
( c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
c_0_1698,
[final] ).
cnf(c_0_2246,plain,
( c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring(X1) ),
c_0_1699,
[final] ).
cnf(c_0_2247,plain,
( c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring(X1) ),
c_0_1700,
[final] ).
cnf(c_0_2248,plain,
( c_lessequals(X2,X4,X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
c_0_1701,
[final] ).
cnf(c_0_2249,plain,
( c_lessequals(X3,X4,X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
c_0_1702,
[final] ).
cnf(c_0_2250,plain,
( c_lessequals(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1703,
[final] ).
cnf(c_0_2251,plain,
( c_lessequals(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_1704,
[final] ).
cnf(c_0_2252,plain,
( c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1705,
[final] ).
cnf(c_0_2253,plain,
( c_HOL_Oord__class_Oless(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_1706,
[final] ).
cnf(c_0_2254,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),c_Polynomial_Omonom(X2,X3,X1)),c_Polynomial_Omonom(X4,X3,X1)) = c_Polynomial_Omonom(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X3,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_1707,
[final] ).
cnf(c_0_2255,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),c_Polynomial_Osmult(X2,X4,X1)),c_Polynomial_Osmult(X3,X4,X1)) = c_Polynomial_Osmult(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
c_0_1708,
[final] ).
cnf(c_0_2256,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Oone__class_Oone(X1))),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1709,
[final] ).
cnf(c_0_2257,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1710,
[final] ).
cnf(c_0_2258,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1711,
[final] ).
cnf(c_0_2259,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1712,
[final] ).
cnf(c_0_2260,plain,
( c_HOL_Oord__class_Oless(X3,X4,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1713,
[final] ).
cnf(c_0_2261,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_HOL_Oord__class_Oless(X4,X2,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1714,
[final] ).
cnf(c_0_2262,plain,
( c_HOL_Oord__class_Oless(X2,X4,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1715,
[final] ).
cnf(c_0_2263,plain,
( c_HOL_Oord__class_Oless(X3,X4,X1)
| c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1716,
[final] ).
cnf(c_0_2264,plain,
( c_HOL_Oord__class_Oless(X2,X4,X1)
| c_HOL_Oord__class_Oless(X4,X2,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1717,
[final] ).
cnf(c_0_2265,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1718,
[final] ).
cnf(c_0_2266,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_1719,
[final] ).
cnf(c_0_2267,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_1720,
[final] ).
cnf(c_0_2268,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1721,
[final] ).
cnf(c_0_2269,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1722,
[final] ).
cnf(c_0_2270,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1723,
[final] ).
cnf(c_0_2271,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4))
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
c_0_1724,
[final] ).
cnf(c_0_2272,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4))
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_1725,
[final] ).
cnf(c_0_2273,plain,
( c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X5),X2)
| ~ c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X4),X2)
| ~ c_lessequals(X4,X5,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
c_0_1726,
[final] ).
cnf(c_0_2274,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1727,
[final] ).
cnf(c_0_2275,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_1728,
[final] ).
cnf(c_0_2276,plain,
( c_lessequals(X2,X4,X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
c_0_1729,
[final] ).
cnf(c_0_2277,plain,
( c_lessequals(X3,X4,X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
c_0_1730,
[final] ).
cnf(c_0_2278,plain,
( c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
c_0_1731,
[final] ).
cnf(c_0_2279,plain,
( c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
c_0_1732,
[final] ).
cnf(c_0_2280,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_1733,
[final] ).
cnf(c_0_2281,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_1734,
[final] ).
cnf(c_0_2282,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
c_0_1735,
[final] ).
cnf(c_0_2283,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X1),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
c_0_1736,
[final] ).
cnf(c_0_2284,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X4),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Omult__mono(X3) ),
c_0_1737,
[final] ).
cnf(c_0_2285,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X2),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Omult__mono(X3) ),
c_0_1738,
[final] ).
cnf(c_0_2286,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X2),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Omult__mono1(X3) ),
c_0_1739,
[final] ).
cnf(c_0_2287,plain,
( c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X4),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
c_0_1740,
[final] ).
cnf(c_0_2288,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1741,
[final] ).
cnf(c_0_2289,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_1742,
[final] ).
cnf(c_0_2290,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X2),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3) ),
c_0_1743,
[final] ).
cnf(c_0_2291,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X4),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X1),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_1744,
[final] ).
cnf(c_0_2292,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1745,
[final] ).
cnf(c_0_2293,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X4),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
c_0_1746,
[final] ).
cnf(c_0_2294,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
c_0_1747,
[final] ).
cnf(c_0_2295,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_1748,
[final] ).
cnf(c_0_2296,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1749,
[final] ).
cnf(c_0_2297,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X2),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
c_0_1750,
[final] ).
cnf(c_0_2298,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X1),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
c_0_1751,
[final] ).
cnf(c_0_2299,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1752,
[final] ).
cnf(c_0_2300,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_1753,
[final] ).
cnf(c_0_2301,plain,
( c_HOL_OIf(c_fequal(v_p,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),tc_Polynomial_Opoly(t_a)),c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_Polynomial_Odegree(v_p,t_a)),tc_nat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_p,t_a)
| ~ class_HOL_Ozero(t_a) ),
c_0_1754,
[final] ).
cnf(c_0_2302,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),c_HOL_Oone__class_Oone(X1))),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1755,
[final] ).
cnf(c_0_2303,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
c_0_1756,
[final] ).
cnf(c_0_2304,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
c_0_1757,
[final] ).
cnf(c_0_2305,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
c_0_1758,
[final] ).
cnf(c_0_2306,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
c_0_1759,
[final] ).
cnf(c_0_2307,plain,
( c_Polynomial_OpCons(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),X1),X2),c_Polynomial_Osmult(X1,X3,X4),X4) = c_Polynomial_Osmult(X1,c_Polynomial_OpCons(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
c_0_1760,
[final] ).
cnf(c_0_2308,plain,
( X1 = hAPP(c_Polynomial_Opoly(X2,X3),X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X3)),X2),c_Polynomial_Osmult(X4,X5,X3)) != c_Polynomial_OpCons(X1,X5,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
c_0_1761,
[final] ).
cnf(c_0_2309,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
c_0_1762,
[final] ).
cnf(c_0_2310,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
c_0_1763,
[final] ).
cnf(c_0_2311,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
c_0_1764,
[final] ).
cnf(c_0_2312,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1765,
[final] ).
cnf(c_0_2313,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1766,
[final] ).
cnf(c_0_2314,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1767,
[final] ).
cnf(c_0_2315,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
c_0_1768,
[final] ).
cnf(c_0_2316,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1769,
[final] ).
cnf(c_0_2317,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1770,
[final] ).
cnf(c_0_2318,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
c_0_1771,
[final] ).
cnf(c_0_2319,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1772,
[final] ).
cnf(c_0_2320,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_1773,
[final] ).
cnf(c_0_2321,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)) = hAPP(c_Polynomial_Opoly(c_Polynomial_Omonom(X1,X2,X3),X3),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1774,
[final] ).
cnf(c_0_2322,plain,
( hAPP(c_Polynomial_Opoly(X1,X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4)) = hAPP(c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X2,X3),X3),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
c_0_1775,
[final] ).
cnf(c_0_2323,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),hAPP(c_Polynomial_Ocoeff(X2,X3),X4)) = hAPP(c_Polynomial_Ocoeff(c_Polynomial_Osmult(X1,X2,X3),X3),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
c_0_1776,
[final] ).
cnf(c_0_2324,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),hAPP(c_Polynomial_Opoly(X2,X3),X4)) = hAPP(c_Polynomial_Opoly(c_Polynomial_Osmult(X1,X2,X3),X3),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
c_0_1777,
[final] ).
cnf(c_0_2325,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1))),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1778,
[final] ).
cnf(c_0_2326,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1779,
[final] ).
cnf(c_0_2327,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1780,
[final] ).
cnf(c_0_2328,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1781,
[final] ).
cnf(c_0_2329,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1782,
[final] ).
cnf(c_0_2330,plain,
( c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1783,
[final] ).
cnf(c_0_2331,plain,
( c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1784,
[final] ).
cnf(c_0_2332,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1785,
[final] ).
cnf(c_0_2333,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1786,
[final] ).
cnf(c_0_2334,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X4)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
c_0_1787,
[final] ).
cnf(c_0_2335,plain,
( X2 = X3
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X4)) != hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Suc(X4))
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_1788,
[final] ).
cnf(c_0_2336,plain,
( hAPP(c_Polynomial_Opoly(X1,X3),hAPP(c_Polynomial_Opoly(X2,X3),X4)) = hAPP(c_Polynomial_Opoly(c_Polynomial_Opcompose(X1,X2,X3),X3),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
c_0_1789,
[final] ).
cnf(c_0_2337,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X3)),c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_1790,
[final] ).
cnf(c_0_2338,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_HOL_Ozero__class_Ozero(X1)),X2),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_1791,
[final] ).
cnf(c_0_2339,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2) ),
c_0_1792,
[final] ).
cnf(c_0_2340,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2) ),
c_0_1793,
[final] ).
cnf(c_0_2341,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
c_0_1794,
[final] ).
cnf(c_0_2342,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1795,
[final] ).
cnf(c_0_2343,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_1796,
[final] ).
cnf(c_0_2344,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
c_0_1797,
[final] ).
cnf(c_0_2345,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1798,
[final] ).
cnf(c_0_2346,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_1799,
[final] ).
cnf(c_0_2347,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
c_0_1800,
[final] ).
cnf(c_0_2348,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X2) ),
c_0_1801,
[final] ).
cnf(c_0_2349,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
c_0_1802,
[final] ).
cnf(c_0_2350,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X2) ),
c_0_1803,
[final] ).
cnf(c_0_2351,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
c_0_1804,
[final] ).
cnf(c_0_2352,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
c_0_1805,
[final] ).
cnf(c_0_2353,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
c_0_1806,
[final] ).
cnf(c_0_2354,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
c_0_1807,
[final] ).
cnf(c_0_2355,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
c_0_1808,
[final] ).
cnf(c_0_2356,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2) ),
c_0_1809,
[final] ).
cnf(c_0_2357,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
c_0_1810,
[final] ).
cnf(c_0_2358,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
c_0_1811,
[final] ).
cnf(c_0_2359,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
c_0_1812,
[final] ).
cnf(c_0_2360,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_1813,
[final] ).
cnf(c_0_2361,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_1814,
[final] ).
cnf(c_0_2362,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
c_0_1815,
[final] ).
cnf(c_0_2363,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
c_0_1816,
[final] ).
cnf(c_0_2364,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
c_0_1817,
[final] ).
cnf(c_0_2365,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
c_0_1818,
[final] ).
cnf(c_0_2366,plain,
( c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
c_0_1819,
[final] ).
cnf(c_0_2367,plain,
( c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
c_0_1820,
[final] ).
cnf(c_0_2368,plain,
( c_lessequals(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
c_0_1821,
[final] ).
cnf(c_0_2369,plain,
( c_lessequals(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
c_0_1822,
[final] ).
cnf(c_0_2370,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
c_0_1823,
[final] ).
cnf(c_0_2371,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
c_0_1824,
[final] ).
cnf(c_0_2372,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
c_0_1825,
[final] ).
cnf(c_0_2373,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
c_0_1826,
[final] ).
cnf(c_0_2374,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
c_0_1827,
[final] ).
cnf(c_0_2375,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
c_0_1828,
[final] ).
cnf(c_0_2376,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
c_0_1829,
[final] ).
cnf(c_0_2377,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
c_0_1830,
[final] ).
cnf(c_0_2378,plain,
( c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_1831,
[final] ).
cnf(c_0_2379,plain,
( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_1832,
[final] ).
cnf(c_0_2380,plain,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_1833,
[final] ).
cnf(c_0_2381,plain,
( hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_1834,
[final] ).
cnf(c_0_2382,plain,
( c_Polynomial_Omonom(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),X1),X2),X3,X4) = c_Polynomial_Osmult(X1,c_Polynomial_Omonom(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
c_0_1835,
[final] ).
cnf(c_0_2383,plain,
( c_Polynomial_Osmult(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),X1),X2),X3,X4) = c_Polynomial_Osmult(X1,c_Polynomial_Osmult(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
c_0_1836,
[final] ).
cnf(c_0_2384,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_1837,
[final] ).
cnf(c_0_2385,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_1838,
[final] ).
cnf(c_0_2386,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_1839,
[final] ).
cnf(c_0_2387,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_1840,
[final] ).
cnf(c_0_2388,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_1841,
[final] ).
cnf(c_0_2389,plain,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_1842,
[final] ).
cnf(c_0_2390,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X3))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1843,
[final] ).
cnf(c_0_2391,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X3))
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
c_0_1844,
[final] ).
cnf(c_0_2392,plain,
( hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_1845,
[final] ).
cnf(c_0_2393,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1846,
[final] ).
cnf(c_0_2394,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1847,
[final] ).
cnf(c_0_2395,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
c_0_1848,
[final] ).
cnf(c_0_2396,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_1849,
[final] ).
cnf(c_0_2397,plain,
( hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),c_HOL_Oone__class_Oone(tc_nat)) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_1850,
[final] ).
cnf(c_0_2398,plain,
( hAPP(c_Polynomial_Ocoeff(c_Polynomial_OpCons(X1,X2,X3),X3),c_Suc(X4)) = hAPP(c_Polynomial_Ocoeff(X2,X3),X4)
| ~ class_HOL_Ozero(X3) ),
c_0_1851,
[final] ).
cnf(c_0_2399,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X2),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Olordered__ab__group__add(X3) ),
c_0_1852,
[final] ).
cnf(c_0_2400,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
c_0_1853,
[final] ).
cnf(c_0_2401,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
c_0_1854,
[final] ).
cnf(c_0_2402,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
c_0_1855,
[final] ).
cnf(c_0_2403,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X3)),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_1856,
[final] ).
cnf(c_0_2404,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X3,X2) = c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
c_0_1857,
[final] ).
cnf(c_0_2405,plain,
( ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_1858,
[final] ).
cnf(c_0_2406,plain,
( X1 = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
c_0_1859,
[final] ).
cnf(c_0_2407,plain,
( X1 = X2
| hAPP(c_Polynomial_Ocoeff(c_Polynomial_Omonom(X3,X1,X4),X4),X2) = c_HOL_Ozero__class_Ozero(X4)
| ~ class_HOL_Ozero(X4) ),
c_0_1860,
[final] ).
cnf(c_0_2408,plain,
( X1 = c_HOL_Ouminus__class_Ouminus(X2,X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)) != X4
| ~ class_OrderedGroup_Oab__group__add(X3) ),
c_0_1861,
[final] ).
cnf(c_0_2409,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X3)) = X3
| ~ class_OrderedGroup_Ogroup__add(X1) ),
c_0_1862,
[final] ).
cnf(c_0_2410,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_1863,
[final] ).
cnf(c_0_2411,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_1864,
[final] ).
cnf(c_0_2412,plain,
( c_lessequals(c_HOL_Oone__class_Oone(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_1865,
[final] ).
cnf(c_0_2413,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_1866,
[final] ).
cnf(c_0_2414,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
c_0_1867,
[final] ).
cnf(c_0_2415,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
c_0_1868,
[final] ).
cnf(c_0_2416,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_1869,
[final] ).
cnf(c_0_2417,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_1870,
[final] ).
cnf(c_0_2418,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
c_0_1871,
[final] ).
cnf(c_0_2419,plain,
( hAPP(c_Polynomial_Ocoeff(c_Polynomial_OpCons(X1,X2,X3),X3),c_HOL_Ozero__class_Ozero(tc_nat)) = X1
| ~ class_HOL_Ozero(X3) ),
c_0_1872,
[final] ).
cnf(c_0_2420,plain,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1873,
[final] ).
cnf(c_0_2421,plain,
( hAPP(c_Polynomial_Ocoeff(c_Polynomial_Omonom(X1,X2,X3),X3),X2) = X1
| ~ class_HOL_Ozero(X3) ),
c_0_1874,
[final] ).
cnf(c_0_2422,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ouminus__class_Ouminus(X3,X1)),c_HOL_Ouminus__class_Ouminus(X2,X1)) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
c_0_1875,
[final] ).
cnf(c_0_2423,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),c_HOL_Ouminus__class_Ouminus(X3,X1)) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
c_0_1876,
[final] ).
cnf(c_0_2424,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Nat_Osemiring__1__class_Oof__nat(X1,X3)),c_Nat_Osemiring__1__class_Oof__nat(X2,X3)) = c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3)
| ~ class_Ring__and__Field_Osemiring__1(X3) ),
c_0_1877,
[final] ).
cnf(c_0_2425,plain,
( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X3),c_Polynomial_Omonom(X1,X2,X3),X3) = c_Polynomial_Omonom(X1,c_Suc(X2),X3)
| ~ class_HOL_Ozero(X3) ),
c_0_1878,
[final] ).
cnf(c_0_2426,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_1879,
[final] ).
cnf(c_0_2427,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_1880,
[final] ).
cnf(c_0_2428,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_1881,
[final] ).
cnf(c_0_2429,plain,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1882,
[final] ).
cnf(c_0_2430,plain,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1883,
[final] ).
cnf(c_0_2431,plain,
( c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1884,
[final] ).
cnf(c_0_2432,plain,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1885,
[final] ).
cnf(c_0_2433,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_1886,
[final] ).
cnf(c_0_2434,plain,
( c_HOL_Oord__class_Oless(X3,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
c_0_1887,
[final] ).
cnf(c_0_2435,plain,
( c_lessequals(X3,X1,X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
c_0_1888,
[final] ).
cnf(c_0_2436,plain,
( c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X3)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_1889,
[final] ).
cnf(c_0_2437,plain,
( c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X3)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_1890,
[final] ).
cnf(c_0_2438,plain,
( c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X3)
| ~ class_Ring__and__Field_Oring(X1) ),
c_0_1891,
[final] ).
cnf(c_0_2439,plain,
( c_lessequals(X1,X3,tc_RealDef_Oreal)
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X2,X3,tc_RealDef_Oreal) ),
c_0_1892,
[final] ).
cnf(c_0_2440,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X3))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1893,
[final] ).
cnf(c_0_2441,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X3))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1894,
[final] ).
cnf(c_0_2442,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X3))
| ~ class_Power_Opower(X1) ),
c_0_1895,
[final] ).
cnf(c_0_2443,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X3))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1896,
[final] ).
cnf(c_0_2444,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
c_0_1897,
[final] ).
cnf(c_0_2445,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
c_0_1898,
[final] ).
cnf(c_0_2446,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_1899,
[final] ).
cnf(c_0_2447,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_1900,
[final] ).
cnf(c_0_2448,plain,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
c_0_1901,
[final] ).
cnf(c_0_2449,plain,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
c_0_1902,
[final] ).
cnf(c_0_2450,plain,
( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_1903,
[final] ).
cnf(c_0_2451,plain,
( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_1904,
[final] ).
cnf(c_0_2452,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)) = X3
| ~ class_OrderedGroup_Oab__group__add(X1) ),
c_0_1905,
[final] ).
cnf(c_0_2453,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)) = X3
| ~ class_OrderedGroup_Ogroup__add(X1) ),
c_0_1906,
[final] ).
cnf(c_0_2454,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
c_0_1907,
[final] ).
cnf(c_0_2455,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1)),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_1908,
[final] ).
cnf(c_0_2456,plain,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
c_0_1909,
[final] ).
cnf(c_0_2457,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
c_0_1910,
[final] ).
cnf(c_0_2458,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
c_0_1911,
[final] ).
cnf(c_0_2459,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
c_0_1912,
[final] ).
cnf(c_0_2460,plain,
( c_lessequals(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_1913,
[final] ).
cnf(c_0_2461,plain,
( c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ouminus__class_Ouminus(X3,X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_1914,
[final] ).
cnf(c_0_2462,plain,
( c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ouminus__class_Ouminus(X3,X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_1915,
[final] ).
cnf(c_0_2463,plain,
( c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ouminus__class_Ouminus(X3,X1))
| ~ class_Ring__and__Field_Oring(X1) ),
c_0_1916,
[final] ).
cnf(c_0_2464,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_1917,
[final] ).
cnf(c_0_2465,plain,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_1918,
[final] ).
cnf(c_0_2466,plain,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
c_0_1919,
[final] ).
cnf(c_0_2467,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X1,X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
c_0_1920,
[final] ).
cnf(c_0_2468,plain,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_OrderedGroup_Oordered__ab__group__add(X2) ),
c_0_1921,
[final] ).
cnf(c_0_2469,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X1,X2)
| ~ class_OrderedGroup_Oordered__ab__group__add(X2) ),
c_0_1922,
[final] ).
cnf(c_0_2470,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
c_0_1923,
[final] ).
cnf(c_0_2471,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Osmult(X3,X1,X2) != c_Polynomial_OpCons(X4,X1,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
c_0_1924,
[final] ).
cnf(c_0_2472,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
c_0_1925,
[final] ).
cnf(c_0_2473,plain,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
c_0_1926,
[final] ).
cnf(c_0_2474,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
c_0_1927,
[final] ).
cnf(c_0_2475,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
c_0_1928,
[final] ).
cnf(c_0_2476,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),c_HOL_Ouminus__class_Ouminus(X2,X1)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)
| ~ class_Ring__and__Field_Oidom(X1) ),
c_0_1929,
[final] ).
cnf(c_0_2477,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),c_HOL_Ouminus__class_Ouminus(X3,X1)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)
| ~ class_Ring__and__Field_Oring(X1) ),
c_0_1930,
[final] ).
cnf(c_0_2478,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ouminus__class_Ouminus(X3,X1))
| ~ class_Ring__and__Field_Oring(X1) ),
c_0_1931,
[final] ).
cnf(c_0_2479,plain,
( X1 = X2
| X1 = c_HOL_Ouminus__class_Ouminus(X2,X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X1) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X2)
| ~ class_Ring__and__Field_Oidom(X3) ),
c_0_1932,
[final] ).
cnf(c_0_2480,plain,
( c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
c_0_1933,
[final] ).
cnf(c_0_2481,plain,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_1934,
[final] ).
cnf(c_0_2482,plain,
( c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Oordered__ab__group__add(X2) ),
c_0_1935,
[final] ).
cnf(c_0_2483,plain,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1) ),
c_0_1936,
[final] ).
cnf(c_0_2484,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
c_0_1937,
[final] ).
cnf(c_0_2485,plain,
( X2 = X1
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1938,
[final] ).
cnf(c_0_2486,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1939,
[final] ).
cnf(c_0_2487,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1940,
[final] ).
cnf(c_0_2488,plain,
( X1 = X2
| c_Polynomial_OpCons(X1,X3,X4) != c_Polynomial_OpCons(X2,X5,X4)
| ~ class_HOL_Ozero(X4) ),
c_0_1941,
[final] ).
cnf(c_0_2489,plain,
( X1 = X2
| c_Polynomial_OpCons(X3,X1,X4) != c_Polynomial_OpCons(X5,X2,X4)
| ~ class_HOL_Ozero(X4) ),
c_0_1942,
[final] ).
cnf(c_0_2490,plain,
( X1 = X2
| c_Polynomial_Omonom(X1,X3,X4) != c_Polynomial_Omonom(X2,X3,X4)
| ~ class_HOL_Ozero(X4) ),
c_0_1943,
[final] ).
cnf(c_0_2491,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
c_0_1944,
[final] ).
cnf(c_0_2492,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_1945,
[final] ).
cnf(c_0_2493,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_1946,
[final] ).
cnf(c_0_2494,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1947,
[final] ).
cnf(c_0_2495,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1948,
[final] ).
cnf(c_0_2496,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_1949,
[final] ).
cnf(c_0_2497,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ c_lessequals(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_1950,
[final] ).
cnf(c_0_2498,plain,
( ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1951,
[final] ).
cnf(c_0_2499,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1952,
[final] ).
cnf(c_0_2500,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| hAPP(c_Polynomial_Opoly(X1,X2),X3) != c_HOL_Ozero__class_Ozero(X2)
| c_Polynomial_Oorder(X3,X1,X2) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_1953,
[final] ).
cnf(c_0_2501,plain,
( X1 = X2
| ~ hBOOL(c_fequal(X1,X2,X3)) ),
c_0_1954,
[final] ).
cnf(c_0_2502,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_1955,
[final] ).
cnf(c_0_2503,plain,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Oone__class_Oone(X2)),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
c_0_1956,
[final] ).
cnf(c_0_2504,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3) ),
c_0_1957,
[final] ).
cnf(c_0_2505,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X3) ),
c_0_1958,
[final] ).
cnf(c_0_2506,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X3) ),
c_0_1959,
[final] ).
cnf(c_0_2507,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1960,
[final] ).
cnf(c_0_2508,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X2,X1,tc_RealDef_Oreal) ),
c_0_1961,
[final] ).
cnf(c_0_2509,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Odegree(c_Polynomial_OpCons(X3,X1,X2),X2) = c_Suc(c_Polynomial_Odegree(X1,X2))
| ~ class_HOL_Ozero(X2) ),
c_0_1962,
[final] ).
cnf(c_0_2510,plain,
( c_Polynomial_Odegree(c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X2) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_HOL_Ozero(X2) ),
c_0_1963,
[final] ).
cnf(c_0_2511,plain,
( X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1964,
[final] ).
cnf(c_0_2512,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1965,
[final] ).
cnf(c_0_2513,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1966,
[final] ).
cnf(c_0_2514,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1967,
[final] ).
cnf(c_0_2515,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1968,
[final] ).
cnf(c_0_2516,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1969,
[final] ).
cnf(c_0_2517,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1970,
[final] ).
cnf(c_0_2518,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1971,
[final] ).
cnf(c_0_2519,plain,
( hAPP(c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_HOL_Ozero(X1) ),
c_0_1972,
[final] ).
cnf(c_0_2520,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X2),X2)),X1) = c_HOL_Ouminus__class_Ouminus(X1,X2)
| ~ class_Int_Onumber__ring(X2) ),
c_0_1973,
[final] ).
cnf(c_0_2521,plain,
( c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1974,
[final] ).
cnf(c_0_2522,plain,
( c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_1975,
[final] ).
cnf(c_0_2523,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Polynomial_Odegree(c_Polynomial_Osmult(X1,X3,X2),X2) = c_Polynomial_Odegree(X3,X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_1976,
[final] ).
cnf(c_0_2524,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3) ),
c_0_1977,
[final] ).
cnf(c_0_2525,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
c_0_1978,
[final] ).
cnf(c_0_2526,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
c_0_1979,
[final] ).
cnf(c_0_2527,plain,
( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
c_0_1980,
[final] ).
cnf(c_0_2528,plain,
( c_Polynomial_Odegree(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X1),X2,X1),X1) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oidom(X1) ),
c_0_1981,
[final] ).
cnf(c_0_2529,plain,
( c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X2,X3),X3) = c_Polynomial_Odegree(X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
c_0_1982,
[final] ).
cnf(c_0_2530,plain,
( c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2) = c_Polynomial_Omonom(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2)
| ~ class_HOL_Ozero(X2) ),
c_0_1983,
[final] ).
cnf(c_0_2531,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Polynomial_Odegree(c_Polynomial_Omonom(X1,X3,X2),X2) = X3
| ~ class_HOL_Ozero(X2) ),
c_0_1984,
[final] ).
cnf(c_0_2532,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| hAPP(c_Polynomial_Ocoeff(X1,X2),c_Polynomial_Odegree(X1,X2)) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_HOL_Ozero(X2) ),
c_0_1985,
[final] ).
cnf(c_0_2533,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Osmult(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_1986,
[final] ).
cnf(c_0_2534,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
c_0_1987,
[final] ).
cnf(c_0_2535,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Power_Opower(X1)
| ~ class_Ring__and__Field_Omult__zero(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
c_0_1988,
[final] ).
cnf(c_0_2536,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_1989,
[final] ).
cnf(c_0_2537,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
c_0_1990,
[final] ).
cnf(c_0_2538,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_OpCons(X3,X1,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_HOL_Ozero(X2) ),
c_0_1991,
[final] ).
cnf(c_0_2539,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
c_0_1992,
[final] ).
cnf(c_0_2540,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
c_0_1993,
[final] ).
cnf(c_0_2541,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X2 = X1
| ~ class_Orderings_Olinorder(X3) ),
c_0_1994,
[final] ).
cnf(c_0_2542,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1995,
[final] ).
cnf(c_0_2543,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1996,
[final] ).
cnf(c_0_2544,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Oone__class_Oone(X2)),c_Nat_Osemiring__1__class_Oof__nat(X1,X2)) = c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X1),X2)
| ~ class_Ring__and__Field_Osemiring__1(X2) ),
c_0_1997,
[final] ).
cnf(c_0_2545,plain,
( c_lessequals(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1998,
[final] ).
cnf(c_0_2546,plain,
( c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1999,
[final] ).
cnf(c_0_2547,plain,
( c_lessequals(X1,X1,X2)
| c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_2000,
[final] ).
cnf(c_0_2548,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_2001,
[final] ).
cnf(c_0_2549,plain,
( c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_2002,
[final] ).
cnf(c_0_2550,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
c_0_2003,
[final] ).
cnf(c_0_2551,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
c_0_2004,
[final] ).
cnf(c_0_2552,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
c_0_2005,
[final] ).
cnf(c_0_2553,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Polynomial_Omonom(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_HOL_Ozero(X2) ),
c_0_2006,
[final] ).
cnf(c_0_2554,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Polynomial_OpCons(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_HOL_Ozero(X2) ),
c_0_2007,
[final] ).
cnf(c_0_2555,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_2008,
[final] ).
cnf(c_0_2556,plain,
( ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_2009,
[final] ).
cnf(c_0_2557,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_2010,
[final] ).
cnf(c_0_2558,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_2011,
[final] ).
cnf(c_0_2559,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_2012,
[final] ).
cnf(c_0_2560,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_2013,
[final] ).
cnf(c_0_2561,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_2014,
[final] ).
cnf(c_0_2562,plain,
( c_HOL_Ouminus__class_Ouminus(X1,X2) = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_2015,
[final] ).
cnf(c_0_2563,plain,
( X1 = c_HOL_Ouminus__class_Ouminus(X2,X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X2) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
c_0_2016,
[final] ).
cnf(c_0_2564,plain,
( hAPP(X1,X2) = hAPP(X1,X3)
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X1,t_a,t_b) ),
c_0_2017,
[final] ).
cnf(c_0_2565,plain,
( c_Polynomial_Oorder(X1,X2,X3) = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(c_Polynomial_Opoly(X2,X3),X1) = c_HOL_Ozero__class_Ozero(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
c_0_2018,
[final] ).
cnf(c_0_2566,plain,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| c_lessequals(X2,X1,tc_RealDef_Oreal) ),
c_0_2019,
[final] ).
cnf(c_0_2567,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
c_0_2020,
[final] ).
cnf(c_0_2568,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
c_0_2021,
[final] ).
cnf(c_0_2569,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X1) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
c_0_2022,
[final] ).
cnf(c_0_2570,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != X3
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_2023,
[final] ).
cnf(c_0_2571,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),X2),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_2024,
[final] ).
cnf(c_0_2572,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X2) ),
c_0_2025,
[final] ).
cnf(c_0_2573,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
c_0_2026,
[final] ).
cnf(c_0_2574,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_HOL_Ozero__class_Ozero(X2)),X1) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
c_0_2027,
[final] ).
cnf(c_0_2575,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_2028,
[final] ).
cnf(c_0_2576,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_2029,
[final] ).
cnf(c_0_2577,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Opoly(X1,X2) != c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2)
| ~ class_Int_Oring__char__0(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_2030,
[final] ).
cnf(c_0_2578,plain,
( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_HOL_Ozero(X1) ),
c_0_2031,
[final] ).
cnf(c_0_2579,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_2032,
[final] ).
cnf(c_0_2580,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_2033,
[final] ).
cnf(c_0_2581,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_2034,
[final] ).
cnf(c_0_2582,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_2035,
[final] ).
cnf(c_0_2583,plain,
( hAPP(c_Polynomial_Opoly(v_pa____,tc_Complex_Ocomplex),v_sko__unknown__thm__rrS__1(v_pa____)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(v_pa____,tc_Complex_Ocomplex),v_c____) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
c_0_2036,
[final] ).
cnf(c_0_2584,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_2037,
[final] ).
cnf(c_0_2585,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_2038,
[final] ).
cnf(c_0_2586,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_2039,
[final] ).
cnf(c_0_2587,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
c_0_2040,
[final] ).
cnf(c_0_2588,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
c_0_2041,
[final] ).
cnf(c_0_2589,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_2042,
[final] ).
cnf(c_0_2590,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_2043,
[final] ).
cnf(c_0_2591,plain,
( c_Polynomial_Osmult(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_2044,
[final] ).
cnf(c_0_2592,plain,
( c_Polynomial_Osmult(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
c_0_2045,
[final] ).
cnf(c_0_2593,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
c_0_2046,
[final] ).
cnf(c_0_2594,plain,
( c_Polynomial_Opcompose(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
c_0_2047,
[final] ).
cnf(c_0_2595,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X1,t_a),t_a,t_a)
| v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1(X1) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oidom(t_a) ),
c_0_2048,
[final] ).
cnf(c_0_2596,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X1,t_a),t_a,t_a)
| v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__2(X1) != c_HOL_Ozero__class_Ozero(t_a)
| ~ class_Ring__and__Field_Oidom(t_a) ),
c_0_2049,
[final] ).
cnf(c_0_2597,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ouminus__class_Ouminus(X2,X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
c_0_2050,
[final] ).
cnf(c_0_2598,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_HOL_Ozero__class_Ozero(X1)),c_Suc(X2)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Power_Opower(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
c_0_2051,
[final] ).
cnf(c_0_2599,plain,
( hAPP(c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_HOL_Ozero(X1) ),
c_0_2052,
[final] ).
cnf(c_0_2600,plain,
( hAPP(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
c_0_2053,
[final] ).
cnf(c_0_2601,plain,
( hAPP(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
c_0_2054,
[final] ).
cnf(c_0_2602,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_HOL_Ozero__class_Ozero(X2)),X1) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Osemiring__0(X2) ),
c_0_2055,
[final] ).
cnf(c_0_2603,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(X1)
| ~ class_Power_Opower(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
c_0_2056,
[final] ).
cnf(c_0_2604,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_2057,
[final] ).
cnf(c_0_2605,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_2058,
[final] ).
cnf(c_0_2606,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_2059,
[final] ).
cnf(c_0_2607,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != X2 ),
c_0_2060,
[final] ).
cnf(c_0_2608,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != X2 ),
c_0_2061,
[final] ).
cnf(c_0_2609,plain,
( c_Power_Opower_Opower(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X1),X1) = c_Power_Opower__class_Opower(X1)
| ~ class_Power_Opower(X1) ),
c_0_2062,
[final] ).
cnf(c_0_2610,plain,
( c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_HOL_Ozero(X1) ),
c_0_2063,
[final] ).
cnf(c_0_2611,plain,
( c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
c_0_2064,
[final] ).
cnf(c_0_2612,plain,
( c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
c_0_2065,
[final] ).
cnf(c_0_2613,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_HOL_Oone__class_Oone(X1)),X2) = c_HOL_Oone__class_Oone(X1)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
c_0_2066,
[final] ).
cnf(c_0_2614,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_2067,
[final] ).
cnf(c_0_2615,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_2068,
[final] ).
cnf(c_0_2616,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_2069,
[final] ).
cnf(c_0_2617,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_2070,
[final] ).
cnf(c_0_2618,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Omult__zero(X1) ),
c_0_2071,
[final] ).
cnf(c_0_2619,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
c_0_2072,
[final] ).
cnf(c_0_2620,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_2073,
[final] ).
cnf(c_0_2621,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_2074,
[final] ).
cnf(c_0_2622,plain,
( c_OrderedGroup_Ocomm__monoid__add__axioms(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_2075,
[final] ).
cnf(c_0_2623,plain,
( c_OrderedGroup_Omonoid__add__axioms(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1)
| ~ class_OrderedGroup_Omonoid__add(X1) ),
c_0_2076,
[final] ).
cnf(c_0_2624,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Ozero__class_Ozero(X2)) = X1
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_2077,
[final] ).
cnf(c_0_2625,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Oone__class_Oone(X1)),X2) = X2
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
c_0_2078,
[final] ).
cnf(c_0_2626,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Oone__class_Oone(X1)),X2) = X2
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
c_0_2079,
[final] ).
cnf(c_0_2627,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Oone__class_Oone(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_2080,
[final] ).
cnf(c_0_2628,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Oone__class_Oone(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_2081,
[final] ).
cnf(c_0_2629,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_2082,
[final] ).
cnf(c_0_2630,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_2083,
[final] ).
cnf(c_0_2631,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_2084,
[final] ).
cnf(c_0_2632,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
c_0_2085,
[final] ).
cnf(c_0_2633,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_2086,
[final] ).
cnf(c_0_2634,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_2087,
[final] ).
cnf(c_0_2635,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
c_0_2088,
[final] ).
cnf(c_0_2636,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Omult__zero(X1) ),
c_0_2089,
[final] ).
cnf(c_0_2637,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
c_0_2090,
[final] ).
cnf(c_0_2638,plain,
( c_Polynomial_Osmult(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_2091,
[final] ).
cnf(c_0_2639,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_2092,
[final] ).
cnf(c_0_2640,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(X1)
| ~ class_Power_Opower(X1) ),
c_0_2093,
[final] ).
cnf(c_0_2641,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Oone__class_Oone(X1)) = X2
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
c_0_2094,
[final] ).
cnf(c_0_2642,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Oone__class_Oone(X1)) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_2095,
[final] ).
cnf(c_0_2643,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_2096,
[final] ).
cnf(c_0_2644,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_2097,
[final] ).
cnf(c_0_2645,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
c_0_2098,
[final] ).
cnf(c_0_2646,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_HOL_Oone__class_Oone(tc_nat)) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_2099,
[final] ).
cnf(c_0_2647,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_HOL_Oone__class_Oone(tc_nat)) = X2
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
c_0_2100,
[final] ).
cnf(c_0_2648,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Suc(c_Polynomial_Odegree(X1,X2)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X2)
| ~ class_HOL_Ozero(X2) ),
c_0_2101,
[final] ).
cnf(c_0_2649,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
c_0_2102,
[final] ).
cnf(c_0_2650,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
c_0_2103,
[final] ).
cnf(c_0_2651,plain,
( c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = c_RealVector_Onorm__class_Onorm(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X2) ),
c_0_2104,
[final] ).
cnf(c_0_2652,plain,
( X1 = X2
| c_Polynomial_Opoly(X1,X3) != c_Polynomial_Opoly(X2,X3)
| ~ class_Int_Oring__char__0(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
c_0_2105,
[final] ).
cnf(c_0_2653,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2) = X2
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
c_0_2106,
[final] ).
cnf(c_0_2654,plain,
( X1 = c_HOL_Ozero__class_Ozero(t_a)
| hAPP(c_Polynomial_Opoly(X2,t_a),X1) = c_HOL_Ozero__class_Ozero(t_a)
| v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2(X2) != c_HOL_Ozero__class_Ozero(t_a)
| ~ class_Ring__and__Field_Oidom(t_a) ),
c_0_2107,
[final] ).
cnf(c_0_2655,plain,
( X1 = X2
| c_Polynomial_Ocoeff(X1,X3) != c_Polynomial_Ocoeff(X2,X3)
| ~ class_HOL_Ozero(X3) ),
c_0_2108,
[final] ).
cnf(c_0_2656,plain,
( X1 = X2
| c_HOL_Ouminus__class_Ouminus(X1,X3) != c_HOL_Ouminus__class_Ouminus(X2,X3)
| ~ class_Lattices_Oboolean__algebra(X3) ),
c_0_2109,
[final] ).
cnf(c_0_2657,plain,
( X1 = X2
| c_HOL_Ouminus__class_Ouminus(X1,X3) != c_HOL_Ouminus__class_Ouminus(X2,X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
c_0_2110,
[final] ).
cnf(c_0_2658,plain,
( X1 = X2
| c_Nat_Osemiring__1__class_Oof__nat(X1,X3) != c_Nat_Osemiring__1__class_Oof__nat(X2,X3)
| ~ class_Nat_Osemiring__char__0(X3) ),
c_0_2111,
[final] ).
cnf(c_0_2659,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_2112,
[final] ).
cnf(c_0_2660,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_2113,
[final] ).
cnf(c_0_2661,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_2114,
[final] ).
cnf(c_0_2662,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_Lattices_Oboolean__algebra(X2) ),
c_0_2115,
[final] ).
cnf(c_0_2663,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_2116,
[final] ).
cnf(c_0_2664,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X2) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_HOL_Ozero(X2) ),
c_0_2117,
[final] ).
cnf(c_0_2665,plain,
( c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_HOL_Ozero(X1) ),
c_0_2118,
[final] ).
cnf(c_0_2666,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_HOL_Ozero(X1) ),
c_0_2119,
[final] ).
cnf(c_0_2667,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Ouminus__class_Ouminus(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_2120,
[final] ).
cnf(c_0_2668,plain,
( c_HOL_Ozero__class_Ozero(X1) = X2
| c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
c_0_2121,
[final] ).
cnf(c_0_2669,plain,
( class_Lattices_Oboolean__algebra(tc_fun(X2,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ),
c_0_2122,
[final] ).
cnf(c_0_2670,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
c_0_2123,
[final] ).
cnf(c_0_2671,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
c_0_2124,
[final] ).
cnf(c_0_2672,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Ouminus__class_Ouminus(X1,X2) != X1
| ~ class_OrderedGroup_Oordered__ab__group__add(X2) ),
c_0_2125,
[final] ).
cnf(c_0_2673,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
c_0_2126,
[final] ).
cnf(c_0_2674,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
c_0_2127,
[final] ).
cnf(c_0_2675,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1) ),
c_0_2128,
[final] ).
cnf(c_0_2676,plain,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
c_0_2129,
[final] ).
cnf(c_0_2677,plain,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
c_0_2130,
[final] ).
cnf(c_0_2678,plain,
( c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
c_0_2131,
[final] ).
cnf(c_0_2679,plain,
( c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
c_0_2132,
[final] ).
cnf(c_0_2680,plain,
( class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
c_0_2133,
[final] ).
cnf(c_0_2681,plain,
( class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
c_0_2134,
[final] ).
cnf(c_0_2682,plain,
( class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
c_0_2135,
[final] ).
cnf(c_0_2683,plain,
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_2136,
[final] ).
cnf(c_0_2684,plain,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_2137,
[final] ).
cnf(c_0_2685,plain,
( class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_2138,
[final] ).
cnf(c_0_2686,plain,
( class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_2139,
[final] ).
cnf(c_0_2687,plain,
( class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
c_0_2140,
[final] ).
cnf(c_0_2688,plain,
( class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_2141,
[final] ).
cnf(c_0_2689,plain,
( class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_2142,
[final] ).
cnf(c_0_2690,plain,
( class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_2143,
[final] ).
cnf(c_0_2691,plain,
( class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
c_0_2144,
[final] ).
cnf(c_0_2692,plain,
( class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
c_0_2145,
[final] ).
cnf(c_0_2693,plain,
( class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_2146,
[final] ).
cnf(c_0_2694,plain,
( class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_2147,
[final] ).
cnf(c_0_2695,plain,
( class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_2148,
[final] ).
cnf(c_0_2696,plain,
( class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
c_0_2149,
[final] ).
cnf(c_0_2697,plain,
( class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_2150,
[final] ).
cnf(c_0_2698,plain,
( class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_2151,
[final] ).
cnf(c_0_2699,plain,
( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
c_0_2152,
[final] ).
cnf(c_0_2700,plain,
( class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_2153,
[final] ).
cnf(c_0_2701,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_2154,
[final] ).
cnf(c_0_2702,plain,
( class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
c_0_2155,
[final] ).
cnf(c_0_2703,plain,
( class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
c_0_2156,
[final] ).
cnf(c_0_2704,plain,
( class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_2157,
[final] ).
cnf(c_0_2705,plain,
( class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_2158,
[final] ).
cnf(c_0_2706,plain,
( class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_2159,
[final] ).
cnf(c_0_2707,plain,
( class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
c_0_2160,
[final] ).
cnf(c_0_2708,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_2161,
[final] ).
cnf(c_0_2709,plain,
( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_2162,
[final] ).
cnf(c_0_2710,plain,
( class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_2163,
[final] ).
cnf(c_0_2711,plain,
( class_OrderedGroup_Osemigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_2164,
[final] ).
cnf(c_0_2712,plain,
( class_Ring__and__Field_Osemiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_2165,
[final] ).
cnf(c_0_2713,plain,
( class_Ring__and__Field_Osemiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
c_0_2166,
[final] ).
cnf(c_0_2714,plain,
( class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_2167,
[final] ).
cnf(c_0_2715,plain,
( class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
c_0_2168,
[final] ).
cnf(c_0_2716,plain,
( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
c_0_2169,
[final] ).
cnf(c_0_2717,plain,
( class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_2170,
[final] ).
cnf(c_0_2718,plain,
( class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_2171,
[final] ).
cnf(c_0_2719,plain,
( class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
c_0_2172,
[final] ).
cnf(c_0_2720,plain,
( class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_2173,
[final] ).
cnf(c_0_2721,plain,
( class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
c_0_2174,
[final] ).
cnf(c_0_2722,plain,
( class_Ring__and__Field_Oring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
c_0_2175,
[final] ).
cnf(c_0_2723,plain,
( class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
c_0_2176,
[final] ).
cnf(c_0_2724,plain,
( class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
c_0_2177,
[final] ).
cnf(c_0_2725,plain,
( class_Nat_Osemiring__char__0(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_2178,
[final] ).
cnf(c_0_2726,plain,
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_2179,
[final] ).
cnf(c_0_2727,plain,
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_2180,
[final] ).
cnf(c_0_2728,plain,
( class_Orderings_Oorder(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_2181,
[final] ).
cnf(c_0_2729,plain,
( class_Int_Oring__char__0(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_2182,
[final] ).
cnf(c_0_2730,plain,
( class_Int_Onumber__ring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
c_0_2183,
[final] ).
cnf(c_0_2731,plain,
( class_Power_Opower(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_2184,
[final] ).
cnf(c_0_2732,plain,
( class_HOL_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_HOL_Ozero(X1) ),
c_0_2185,
[final] ).
cnf(c_0_2733,plain,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
c_0_2186,
[final] ).
cnf(c_0_2734,plain,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
c_0_2187,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_2188_0,axiom,
( hAPP(hAPP(hAPP(X2,X3),X4),c_HOL_OIf(c_fequal(X4,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)),X1,c_Polynomial_Opoly__rec(X1,X2,X4,X6,X5),X6)) = c_Polynomial_Opoly__rec(X1,X2,c_Polynomial_OpCons(X3,X4,X5),X6,X5)
| ~ class_HOL_Ozero(X5) ),
inference(literals_permutation,[status(thm)],[c_0_2188]) ).
cnf(c_0_2188_1,axiom,
( ~ class_HOL_Ozero(X5)
| hAPP(hAPP(hAPP(X2,X3),X4),c_HOL_OIf(c_fequal(X4,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)),X1,c_Polynomial_Opoly__rec(X1,X2,X4,X6,X5),X6)) = c_Polynomial_Opoly__rec(X1,X2,c_Polynomial_OpCons(X3,X4,X5),X6,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2188]) ).
cnf(c_0_2189_0,axiom,
( c_Polynomial_Opoly__rec(X1,X2,c_Polynomial_OpCons(X3,X4,X5),X6,X5) = hAPP(hAPP(hAPP(X2,X3),X4),c_Polynomial_Opoly__rec(X1,X2,X4,X6,X5))
| hAPP(hAPP(hAPP(X2,c_HOL_Ozero__class_Ozero(X5)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))),X1) != X1
| ~ class_HOL_Ozero(X5) ),
inference(literals_permutation,[status(thm)],[c_0_2189]) ).
cnf(c_0_2189_1,axiom,
( hAPP(hAPP(hAPP(X2,c_HOL_Ozero__class_Ozero(X5)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))),X1) != X1
| c_Polynomial_Opoly__rec(X1,X2,c_Polynomial_OpCons(X3,X4,X5),X6,X5) = hAPP(hAPP(hAPP(X2,X3),X4),c_Polynomial_Opoly__rec(X1,X2,X4,X6,X5))
| ~ class_HOL_Ozero(X5) ),
inference(literals_permutation,[status(thm)],[c_0_2189]) ).
cnf(c_0_2189_2,axiom,
( ~ class_HOL_Ozero(X5)
| hAPP(hAPP(hAPP(X2,c_HOL_Ozero__class_Ozero(X5)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))),X1) != X1
| c_Polynomial_Opoly__rec(X1,X2,c_Polynomial_OpCons(X3,X4,X5),X6,X5) = hAPP(hAPP(hAPP(X2,X3),X4),c_Polynomial_Opoly__rec(X1,X2,X4,X6,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2189]) ).
cnf(c_0_2190_0,axiom,
( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X3,X4,X1,X1))
| ~ class_OrderedGroup_Osemigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2190]) ).
cnf(c_0_2190_1,axiom,
( ~ class_OrderedGroup_Osemigroup__add(X1)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X3,X4,X1,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2190]) ).
cnf(c_0_2191_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X3,X1,X1)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1)
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2191]) ).
cnf(c_0_2191_1,axiom,
( ~ class_OrderedGroup_Omonoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X3,X1,X1)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2191]) ).
cnf(c_0_2192_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),X4)),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X3),X4)) = hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2192]) ).
cnf(c_0_2192_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),X4)),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X3),X4)) = hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2192]) ).
cnf(c_0_2193_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),X3)),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),X4)) = hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2193]) ).
cnf(c_0_2193_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),X3)),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),X4)) = hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2193]) ).
cnf(c_0_2194_0,axiom,
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X1,t_a),t_a,t_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(t_a),hAPP(c_Polynomial_Opoly(X1,t_a),c_HOL_Ozero__class_Ozero(t_a))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X2),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1(X1))),hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__2(X1),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__3(X1),t_a),t_a),X2))) = hAPP(c_Polynomial_Opoly(X1,t_a),X2)
| ~ class_Ring__and__Field_Oidom(t_a) ),
inference(literals_permutation,[status(thm)],[c_0_2194]) ).
cnf(c_0_2194_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(t_a),hAPP(c_Polynomial_Opoly(X1,t_a),c_HOL_Ozero__class_Ozero(t_a))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X2),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1(X1))),hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__2(X1),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__3(X1),t_a),t_a),X2))) = hAPP(c_Polynomial_Opoly(X1,t_a),X2)
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X1,t_a),t_a,t_a)
| ~ class_Ring__and__Field_Oidom(t_a) ),
inference(literals_permutation,[status(thm)],[c_0_2194]) ).
cnf(c_0_2194_2,axiom,
( ~ class_Ring__and__Field_Oidom(t_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(t_a),hAPP(c_Polynomial_Opoly(X1,t_a),c_HOL_Ozero__class_Ozero(t_a))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X2),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1(X1))),hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__2(X1),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__3(X1),t_a),t_a),X2))) = hAPP(c_Polynomial_Opoly(X1,t_a),X2)
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X1,t_a),t_a,t_a) ),
inference(literals_permutation,[status(thm)],[c_0_2194]) ).
cnf(c_0_2195_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),X3)),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),X3))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2195]) ).
cnf(c_0_2195_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),X3)),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2195]) ).
cnf(c_0_2196_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)),X5)
| ~ class_Ring__and__Field_Osemiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2196]) ).
cnf(c_0_2196_1,axiom,
( ~ class_Ring__and__Field_Osemiring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)),X5) ),
inference(literals_permutation,[status(thm)],[c_0_2196]) ).
cnf(c_0_2197_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),X3)),X2) = hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),c_Suc(X3))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2197]) ).
cnf(c_0_2197_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),X3)),X2) = hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),c_Suc(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2197]) ).
cnf(c_0_2198_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2198]) ).
cnf(c_0_2198_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2198]) ).
cnf(c_0_2199_0,axiom,
( c_Polynomial_Opoly__rec(X1,X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X4,X3) = X1
| hAPP(hAPP(hAPP(X2,c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))),X1) != X1
| ~ class_HOL_Ozero(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2199]) ).
cnf(c_0_2199_1,axiom,
( hAPP(hAPP(hAPP(X2,c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))),X1) != X1
| c_Polynomial_Opoly__rec(X1,X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X4,X3) = X1
| ~ class_HOL_Ozero(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2199]) ).
cnf(c_0_2199_2,axiom,
( ~ class_HOL_Ozero(X3)
| hAPP(hAPP(hAPP(X2,c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))),X1) != X1
| c_Polynomial_Opoly__rec(X1,X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X4,X3) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2199]) ).
cnf(c_0_2200_0,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3)),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2200]) ).
cnf(c_0_2200_1,axiom,
( ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3)),c_HOL_Ozero__class_Ozero(X1),X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2200]) ).
cnf(c_0_2200_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3)),c_HOL_Ozero__class_Ozero(X1),X1)
| X3 = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2200]) ).
cnf(c_0_2201_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3)),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2201]) ).
cnf(c_0_2201_1,axiom,
( ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3)),c_HOL_Ozero__class_Ozero(X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2201]) ).
cnf(c_0_2201_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3)),c_HOL_Ozero__class_Ozero(X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2201]) ).
cnf(c_0_2202_0,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3)),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2202]) ).
cnf(c_0_2202_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3)),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2202]) ).
cnf(c_0_2203_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X4,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X4,X3),X3)),c_Polynomial_OpCons(X1,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X4,X3),X3)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2203]) ).
cnf(c_0_2203_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X4,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X4,X3),X3)),c_Polynomial_OpCons(X1,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X4,X3),X3)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2203]) ).
cnf(c_0_2204_0,axiom,
( X1 = X2
| X3 = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X3))
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_2204]) ).
cnf(c_0_2204_1,axiom,
( X3 = X4
| X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X3))
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_2204]) ).
cnf(c_0_2204_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X3))
| X3 = X4
| X1 = X2
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_2204]) ).
cnf(c_0_2204_3,axiom,
( ~ class_Int_Onumber__ring(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X3))
| X3 = X4
| X1 = X2
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_2204]) ).
cnf(c_0_2204_4,axiom,
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X3))
| X3 = X4
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2204]) ).
cnf(c_0_2205_0,axiom,
( X1 = X2
| X3 = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X3))
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_2205]) ).
cnf(c_0_2205_1,axiom,
( X3 = X4
| X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X3))
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_2205]) ).
cnf(c_0_2205_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X3))
| X3 = X4
| X1 = X2
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_2205]) ).
cnf(c_0_2205_3,axiom,
( ~ class_Int_Onumber__ring(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X3))
| X3 = X4
| X1 = X2
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_2205]) ).
cnf(c_0_2205_4,axiom,
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X3))
| X3 = X4
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2205]) ).
cnf(c_0_2206_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2206]) ).
cnf(c_0_2206_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2206]) ).
cnf(c_0_2207_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),X3)) = hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),c_Suc(X3))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2207]) ).
cnf(c_0_2207_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),X3)) = hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),c_Suc(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2207]) ).
cnf(c_0_2208_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2208]) ).
cnf(c_0_2208_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2208]) ).
cnf(c_0_2209_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X1)),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2209]) ).
cnf(c_0_2209_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X1)),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2209]) ).
cnf(c_0_2209_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X1)),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2209]) ).
cnf(c_0_2210_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X3)),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2210]) ).
cnf(c_0_2210_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X3)),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2210]) ).
cnf(c_0_2210_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X3)),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2210]) ).
cnf(c_0_2211_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3)),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2211]) ).
cnf(c_0_2211_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2211]) ).
cnf(c_0_2212_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X1),X1)),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X3)
| ~ class_Ring__and__Field_Oring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2212]) ).
cnf(c_0_2212_1,axiom,
( ~ class_Ring__and__Field_Oring__1(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X1),X1)),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2212]) ).
cnf(c_0_2213_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2213]) ).
cnf(c_0_2213_1,axiom,
( ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2213]) ).
cnf(c_0_2213_2,axiom,
( ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2213]) ).
cnf(c_0_2214_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2214]) ).
cnf(c_0_2214_1,axiom,
( ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2214]) ).
cnf(c_0_2214_2,axiom,
( ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2214]) ).
cnf(c_0_2215_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2215]) ).
cnf(c_0_2215_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_2215]) ).
cnf(c_0_2216_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2216]) ).
cnf(c_0_2216_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2216]) ).
cnf(c_0_2217_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2217]) ).
cnf(c_0_2217_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2217]) ).
cnf(c_0_2218_0,axiom,
( c_Polynomial_OpCons(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),X3),X5),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X2,X3,X1)),c_Polynomial_OpCons(X4,X5,X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2218]) ).
cnf(c_0_2218_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_Polynomial_OpCons(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),X3),X5),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X2,X3,X1)),c_Polynomial_OpCons(X4,X5,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2218]) ).
cnf(c_0_2219_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2219]) ).
cnf(c_0_2219_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2219]) ).
cnf(c_0_2219_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2219]) ).
cnf(c_0_2219_3,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2219]) ).
cnf(c_0_2220_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X2)),c_Polynomial_Osmult(X3,X1,X2)),c_Polynomial_OpCons(X4,X1,X2)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2220]) ).
cnf(c_0_2220_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X2)),c_Polynomial_Osmult(X3,X1,X2)),c_Polynomial_OpCons(X4,X1,X2)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2220]) ).
cnf(c_0_2220_2,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X2)),c_Polynomial_Osmult(X3,X1,X2)),c_Polynomial_OpCons(X4,X1,X2)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2220]) ).
cnf(c_0_2221_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_Polynomial_Ocoeff(X2,X1),X4)),hAPP(c_Polynomial_Ocoeff(X3,X1),X4)) = hAPP(c_Polynomial_Ocoeff(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),X2),X3),X1),X4)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2221]) ).
cnf(c_0_2221_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_Polynomial_Ocoeff(X2,X1),X4)),hAPP(c_Polynomial_Ocoeff(X3,X1),X4)) = hAPP(c_Polynomial_Ocoeff(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),X2),X3),X1),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2221]) ).
cnf(c_0_2222_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_Polynomial_Opoly(X2,X1),X4)),hAPP(c_Polynomial_Opoly(X3,X1),X4)) = hAPP(c_Polynomial_Opoly(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),X2),X3),X1),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2222]) ).
cnf(c_0_2222_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_Polynomial_Opoly(X2,X1),X4)),hAPP(c_Polynomial_Opoly(X3,X1),X4)) = hAPP(c_Polynomial_Opoly(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),X2),X3),X1),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2222]) ).
cnf(c_0_2223_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2223]) ).
cnf(c_0_2223_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2223]) ).
cnf(c_0_2223_2,axiom,
( ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2223]) ).
cnf(c_0_2223_3,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2223]) ).
cnf(c_0_2223_4,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2223]) ).
cnf(c_0_2223_5,axiom,
( ~ class_Ring__and__Field_Opordered__semiring(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2223]) ).
cnf(c_0_2224_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2224]) ).
cnf(c_0_2224_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2224]) ).
cnf(c_0_2224_2,axiom,
( ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2224]) ).
cnf(c_0_2224_3,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2224]) ).
cnf(c_0_2224_4,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2224]) ).
cnf(c_0_2224_5,axiom,
( ~ class_Ring__and__Field_Opordered__semiring(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2224]) ).
cnf(c_0_2225_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2225]) ).
cnf(c_0_2225_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2225]) ).
cnf(c_0_2225_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2225]) ).
cnf(c_0_2225_3,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2225]) ).
cnf(c_0_2225_4,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2225]) ).
cnf(c_0_2225_5,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2225]) ).
cnf(c_0_2226_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2226]) ).
cnf(c_0_2226_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2226]) ).
cnf(c_0_2226_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2226]) ).
cnf(c_0_2226_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2226]) ).
cnf(c_0_2226_4,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2226]) ).
cnf(c_0_2226_5,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2226]) ).
cnf(c_0_2227_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2227]) ).
cnf(c_0_2227_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2227]) ).
cnf(c_0_2227_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2227]) ).
cnf(c_0_2227_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2227]) ).
cnf(c_0_2227_4,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2227]) ).
cnf(c_0_2227_5,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2227]) ).
cnf(c_0_2228_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2228]) ).
cnf(c_0_2228_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2228]) ).
cnf(c_0_2228_2,axiom,
( ~ c_lessequals(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2228]) ).
cnf(c_0_2228_3,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2228]) ).
cnf(c_0_2228_4,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2228]) ).
cnf(c_0_2228_5,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2228]) ).
cnf(c_0_2229_0,axiom,
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X1,t_a),t_a,t_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__3(X1),t_a)),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1(X1))),c_HOL_Oone__class_Oone(tc_nat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,t_a)
| ~ class_Ring__and__Field_Oidom(t_a) ),
inference(literals_permutation,[status(thm)],[c_0_2229]) ).
cnf(c_0_2229_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__3(X1),t_a)),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1(X1))),c_HOL_Oone__class_Oone(tc_nat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,t_a)
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X1,t_a),t_a,t_a)
| ~ class_Ring__and__Field_Oidom(t_a) ),
inference(literals_permutation,[status(thm)],[c_0_2229]) ).
cnf(c_0_2229_2,axiom,
( ~ class_Ring__and__Field_Oidom(t_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__3(X1),t_a)),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1(X1))),c_HOL_Oone__class_Oone(tc_nat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,t_a)
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X1,t_a),t_a,t_a) ),
inference(literals_permutation,[status(thm)],[c_0_2229]) ).
cnf(c_0_2230_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2230]) ).
cnf(c_0_2230_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2230]) ).
cnf(c_0_2231_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2231]) ).
cnf(c_0_2231_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2231]) ).
cnf(c_0_2232_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2232]) ).
cnf(c_0_2232_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2232]) ).
cnf(c_0_2233_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2233]) ).
cnf(c_0_2233_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2233]) ).
cnf(c_0_2234_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2234]) ).
cnf(c_0_2234_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2234]) ).
cnf(c_0_2235_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2235]) ).
cnf(c_0_2235_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2235]) ).
cnf(c_0_2236_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2236]) ).
cnf(c_0_2236_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2236]) ).
cnf(c_0_2237_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X2)),c_Polynomial_Osmult(X1,X3,X2)),c_Polynomial_Osmult(X1,X4,X2)) = c_Polynomial_Osmult(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X2)),X3),X4),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2237]) ).
cnf(c_0_2237_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X2)),c_Polynomial_Osmult(X1,X3,X2)),c_Polynomial_Osmult(X1,X4,X2)) = c_Polynomial_Osmult(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X2)),X3),X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2237]) ).
cnf(c_0_2238_0,axiom,
( c_lessequals(X2,X4,X1)
| ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),c_Suc(X3)),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2238]) ).
cnf(c_0_2238_1,axiom,
( ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),c_Suc(X3)),X1)
| c_lessequals(X2,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2238]) ).
cnf(c_0_2238_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),c_Suc(X3)),X1)
| c_lessequals(X2,X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2238]) ).
cnf(c_0_2238_3,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),c_Suc(X3)),X1)
| c_lessequals(X2,X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2238]) ).
cnf(c_0_2239_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X3)) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2239]) ).
cnf(c_0_2239_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X3)) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2239]) ).
cnf(c_0_2239_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X3)) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2239]) ).
cnf(c_0_2240_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X1)) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2240]) ).
cnf(c_0_2240_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X1)) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2240]) ).
cnf(c_0_2240_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X1)) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2240]) ).
cnf(c_0_2241_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),hAPP(c_Polynomial_Opoly(X2,X3),X4))) = hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X1,X2,X3),X3),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2241]) ).
cnf(c_0_2241_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),hAPP(c_Polynomial_Opoly(X2,X3),X4))) = hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X1,X2,X3),X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2241]) ).
cnf(c_0_2242_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2242]) ).
cnf(c_0_2242_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2242]) ).
cnf(c_0_2242_2,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2242]) ).
cnf(c_0_2243_0,axiom,
( c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2243]) ).
cnf(c_0_2243_1,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3),X1)
| c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2243]) ).
cnf(c_0_2243_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3),X1)
| c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2243]) ).
cnf(c_0_2243_3,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3),X1)
| c_HOL_Oord__class_Oless(X2,X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2243]) ).
cnf(c_0_2244_0,axiom,
( c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2244]) ).
cnf(c_0_2244_1,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2244]) ).
cnf(c_0_2244_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2244]) ).
cnf(c_0_2244_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| c_HOL_Oord__class_Oless(X2,X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2244]) ).
cnf(c_0_2245_0,axiom,
( c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2245]) ).
cnf(c_0_2245_1,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2245]) ).
cnf(c_0_2245_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2245]) ).
cnf(c_0_2245_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| c_HOL_Oord__class_Oless(X3,X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2245]) ).
cnf(c_0_2246_0,axiom,
( c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2246]) ).
cnf(c_0_2246_1,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2246]) ).
cnf(c_0_2246_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ class_Ring__and__Field_Oordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2246]) ).
cnf(c_0_2246_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| c_HOL_Oord__class_Oless(X2,X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2246]) ).
cnf(c_0_2247_0,axiom,
( c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2247]) ).
cnf(c_0_2247_1,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2247]) ).
cnf(c_0_2247_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2247]) ).
cnf(c_0_2247_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| c_HOL_Oord__class_Oless(X3,X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2247]) ).
cnf(c_0_2248_0,axiom,
( c_lessequals(X2,X4,X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2248]) ).
cnf(c_0_2248_1,axiom,
( ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| c_lessequals(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2248]) ).
cnf(c_0_2248_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| c_lessequals(X2,X4,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2248]) ).
cnf(c_0_2248_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| c_lessequals(X2,X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2248]) ).
cnf(c_0_2249_0,axiom,
( c_lessequals(X3,X4,X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2249]) ).
cnf(c_0_2249_1,axiom,
( ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| c_lessequals(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2249]) ).
cnf(c_0_2249_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| c_lessequals(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2249]) ).
cnf(c_0_2249_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| c_lessequals(X3,X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2249]) ).
cnf(c_0_2250_0,axiom,
( c_lessequals(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2250]) ).
cnf(c_0_2250_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,X4,X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2250]) ).
cnf(c_0_2250_2,axiom,
( ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2250]) ).
cnf(c_0_2250_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2250]) ).
cnf(c_0_2251_0,axiom,
( c_lessequals(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2251]) ).
cnf(c_0_2251_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(X4,X3,X2)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2251]) ).
cnf(c_0_2251_2,axiom,
( ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(X4,X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2251]) ).
cnf(c_0_2251_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(X4,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2251]) ).
cnf(c_0_2252_0,axiom,
( c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2252]) ).
cnf(c_0_2252_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2252]) ).
cnf(c_0_2252_2,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2252]) ).
cnf(c_0_2252_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2252]) ).
cnf(c_0_2253_0,axiom,
( c_HOL_Oord__class_Oless(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2253]) ).
cnf(c_0_2253_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2253]) ).
cnf(c_0_2253_2,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(X4,X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2253]) ).
cnf(c_0_2253_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(X4,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2253]) ).
cnf(c_0_2254_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),c_Polynomial_Omonom(X2,X3,X1)),c_Polynomial_Omonom(X4,X3,X1)) = c_Polynomial_Omonom(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X3,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2254]) ).
cnf(c_0_2254_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),c_Polynomial_Omonom(X2,X3,X1)),c_Polynomial_Omonom(X4,X3,X1)) = c_Polynomial_Omonom(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2254]) ).
cnf(c_0_2255_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),c_Polynomial_Osmult(X2,X4,X1)),c_Polynomial_Osmult(X3,X4,X1)) = c_Polynomial_Osmult(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2255]) ).
cnf(c_0_2255_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),c_Polynomial_Osmult(X2,X4,X1)),c_Polynomial_Osmult(X3,X4,X1)) = c_Polynomial_Osmult(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2255]) ).
cnf(c_0_2256_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Oone__class_Oone(X1))),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2256]) ).
cnf(c_0_2256_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Oone__class_Oone(X1))),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2256]) ).
cnf(c_0_2257_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2257]) ).
cnf(c_0_2257_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2257]) ).
cnf(c_0_2257_2,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2257]) ).
cnf(c_0_2257_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2257]) ).
cnf(c_0_2258_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2258]) ).
cnf(c_0_2258_1,axiom,
( c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2258]) ).
cnf(c_0_2258_2,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2258]) ).
cnf(c_0_2258_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2258]) ).
cnf(c_0_2259_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2259]) ).
cnf(c_0_2259_1,axiom,
( c_HOL_Oord__class_Oless(X4,X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2259]) ).
cnf(c_0_2259_2,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| c_HOL_Oord__class_Oless(X4,X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2259]) ).
cnf(c_0_2259_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| c_HOL_Oord__class_Oless(X4,X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2259]) ).
cnf(c_0_2260_0,axiom,
( c_HOL_Oord__class_Oless(X3,X4,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2260]) ).
cnf(c_0_2260_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2260]) ).
cnf(c_0_2260_2,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2260]) ).
cnf(c_0_2260_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2260]) ).
cnf(c_0_2261_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_HOL_Oord__class_Oless(X4,X2,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2261]) ).
cnf(c_0_2261_1,axiom,
( c_HOL_Oord__class_Oless(X4,X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2261]) ).
cnf(c_0_2261_2,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| c_HOL_Oord__class_Oless(X4,X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2261]) ).
cnf(c_0_2261_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| c_HOL_Oord__class_Oless(X4,X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2261]) ).
cnf(c_0_2262_0,axiom,
( c_HOL_Oord__class_Oless(X2,X4,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2262]) ).
cnf(c_0_2262_1,axiom,
( c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2262]) ).
cnf(c_0_2262_2,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2262]) ).
cnf(c_0_2262_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X2,X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2262]) ).
cnf(c_0_2263_0,axiom,
( c_HOL_Oord__class_Oless(X3,X4,X1)
| c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2263]) ).
cnf(c_0_2263_1,axiom,
( c_HOL_Oord__class_Oless(X4,X3,X1)
| c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2263]) ).
cnf(c_0_2263_2,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| c_HOL_Oord__class_Oless(X4,X3,X1)
| c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2263]) ).
cnf(c_0_2263_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| c_HOL_Oord__class_Oless(X4,X3,X1)
| c_HOL_Oord__class_Oless(X3,X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2263]) ).
cnf(c_0_2264_0,axiom,
( c_HOL_Oord__class_Oless(X2,X4,X1)
| c_HOL_Oord__class_Oless(X4,X2,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2264]) ).
cnf(c_0_2264_1,axiom,
( c_HOL_Oord__class_Oless(X4,X2,X1)
| c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2264]) ).
cnf(c_0_2264_2,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| c_HOL_Oord__class_Oless(X4,X2,X1)
| c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2264]) ).
cnf(c_0_2264_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| c_HOL_Oord__class_Oless(X4,X2,X1)
| c_HOL_Oord__class_Oless(X2,X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2264]) ).
cnf(c_0_2265_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2265]) ).
cnf(c_0_2265_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2265]) ).
cnf(c_0_2266_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2266]) ).
cnf(c_0_2266_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2266]) ).
cnf(c_0_2267_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2267]) ).
cnf(c_0_2267_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2267]) ).
cnf(c_0_2268_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2268]) ).
cnf(c_0_2268_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2268]) ).
cnf(c_0_2269_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2269]) ).
cnf(c_0_2269_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2269]) ).
cnf(c_0_2270_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2270]) ).
cnf(c_0_2270_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2270]) ).
cnf(c_0_2271_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4))
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2271]) ).
cnf(c_0_2271_1,axiom,
( ~ class_OrderedGroup_Omonoid__mult(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2271]) ).
cnf(c_0_2272_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4))
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2272]) ).
cnf(c_0_2272_1,axiom,
( X3 = X4
| X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4))
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2272]) ).
cnf(c_0_2272_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4))
| X3 = X4
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2272]) ).
cnf(c_0_2272_3,axiom,
( ~ class_Int_Onumber__ring(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4))
| X3 = X4
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2272]) ).
cnf(c_0_2272_4,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4))
| X3 = X4
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2272]) ).
cnf(c_0_2273_0,axiom,
( c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X5),X2)
| ~ c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X4),X2)
| ~ c_lessequals(X4,X5,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2273]) ).
cnf(c_0_2273_1,axiom,
( ~ c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X4),X2)
| c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X5),X2)
| ~ c_lessequals(X4,X5,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2273]) ).
cnf(c_0_2273_2,axiom,
( ~ c_lessequals(X4,X5,X2)
| ~ c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X4),X2)
| c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X5),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2273]) ).
cnf(c_0_2273_3,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_lessequals(X4,X5,X2)
| ~ c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X4),X2)
| c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2273]) ).
cnf(c_0_2274_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2274]) ).
cnf(c_0_2274_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2274]) ).
cnf(c_0_2275_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2275]) ).
cnf(c_0_2275_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2275]) ).
cnf(c_0_2275_2,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2275]) ).
cnf(c_0_2276_0,axiom,
( c_lessequals(X2,X4,X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2276]) ).
cnf(c_0_2276_1,axiom,
( ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
| c_lessequals(X2,X4,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2276]) ).
cnf(c_0_2276_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
| c_lessequals(X2,X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2276]) ).
cnf(c_0_2277_0,axiom,
( c_lessequals(X3,X4,X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2277]) ).
cnf(c_0_2277_1,axiom,
( ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| c_lessequals(X3,X4,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2277]) ).
cnf(c_0_2277_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| c_lessequals(X3,X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2277]) ).
cnf(c_0_2278_0,axiom,
( c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2278]) ).
cnf(c_0_2278_1,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2278]) ).
cnf(c_0_2278_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| c_HOL_Oord__class_Oless(X3,X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2278]) ).
cnf(c_0_2279_0,axiom,
( c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2279]) ).
cnf(c_0_2279_1,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
| c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2279]) ).
cnf(c_0_2279_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
| c_HOL_Oord__class_Oless(X2,X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2279]) ).
cnf(c_0_2280_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2280]) ).
cnf(c_0_2280_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2280]) ).
cnf(c_0_2280_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2),X2,X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2280]) ).
cnf(c_0_2280_3,axiom,
( ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2280]) ).
cnf(c_0_2280_4,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2280]) ).
cnf(c_0_2281_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2281]) ).
cnf(c_0_2281_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2281]) ).
cnf(c_0_2281_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X2,X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2281]) ).
cnf(c_0_2281_3,axiom,
( ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2281]) ).
cnf(c_0_2281_4,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2281]) ).
cnf(c_0_2282_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2282]) ).
cnf(c_0_2282_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2282]) ).
cnf(c_0_2282_2,axiom,
( ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2282]) ).
cnf(c_0_2282_3,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2282]) ).
cnf(c_0_2283_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X1),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2283]) ).
cnf(c_0_2283_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X1),X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2283]) ).
cnf(c_0_2283_2,axiom,
( ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X1),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2283]) ).
cnf(c_0_2283_3,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2283]) ).
cnf(c_0_2284_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X4),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Omult__mono(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2284]) ).
cnf(c_0_2284_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X4),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Omult__mono(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2284]) ).
cnf(c_0_2284_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X4),X3)
| ~ class_Ring__and__Field_Omult__mono(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2284]) ).
cnf(c_0_2284_3,axiom,
( ~ class_Ring__and__Field_Omult__mono(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2284]) ).
cnf(c_0_2285_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X2),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Omult__mono(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2285]) ).
cnf(c_0_2285_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X2),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Omult__mono(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2285]) ).
cnf(c_0_2285_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X2),X3)
| ~ class_Ring__and__Field_Omult__mono(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2285]) ).
cnf(c_0_2285_3,axiom,
( ~ class_Ring__and__Field_Omult__mono(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2285]) ).
cnf(c_0_2286_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X2),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Omult__mono1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2286]) ).
cnf(c_0_2286_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X2),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Omult__mono1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2286]) ).
cnf(c_0_2286_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X2),X3)
| ~ class_Ring__and__Field_Omult__mono1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2286]) ).
cnf(c_0_2286_3,axiom,
( ~ class_Ring__and__Field_Omult__mono1(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2286]) ).
cnf(c_0_2287_0,axiom,
( c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X4),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2287]) ).
cnf(c_0_2287_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X4),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2287]) ).
cnf(c_0_2287_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X4),X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2287]) ).
cnf(c_0_2287_3,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2287]) ).
cnf(c_0_2288_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2288]) ).
cnf(c_0_2288_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2288]) ).
cnf(c_0_2288_2,axiom,
( ~ c_lessequals(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2288]) ).
cnf(c_0_2288_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2288]) ).
cnf(c_0_2289_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2289]) ).
cnf(c_0_2289_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2)
| ~ c_lessequals(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2289]) ).
cnf(c_0_2289_2,axiom,
( ~ c_lessequals(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2289]) ).
cnf(c_0_2289_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_lessequals(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2289]) ).
cnf(c_0_2290_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X2),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2290]) ).
cnf(c_0_2290_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X2),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2290]) ).
cnf(c_0_2290_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X2),X3)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2290]) ).
cnf(c_0_2290_3,axiom,
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2290]) ).
cnf(c_0_2291_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X4),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X1),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2291]) ).
cnf(c_0_2291_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X4),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X1),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2291]) ).
cnf(c_0_2291_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X4),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X1),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2291]) ).
cnf(c_0_2291_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X4),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2291]) ).
cnf(c_0_2292_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2292]) ).
cnf(c_0_2292_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2),X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2292]) ).
cnf(c_0_2292_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2292]) ).
cnf(c_0_2292_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2292]) ).
cnf(c_0_2293_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X4),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2293]) ).
cnf(c_0_2293_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X4),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2293]) ).
cnf(c_0_2293_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X4),X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2293]) ).
cnf(c_0_2293_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2293]) ).
cnf(c_0_2294_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2294]) ).
cnf(c_0_2294_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2294]) ).
cnf(c_0_2294_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2294]) ).
cnf(c_0_2294_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2294]) ).
cnf(c_0_2295_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2295]) ).
cnf(c_0_2295_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2295]) ).
cnf(c_0_2295_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2295]) ).
cnf(c_0_2295_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2295]) ).
cnf(c_0_2296_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2296]) ).
cnf(c_0_2296_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2296]) ).
cnf(c_0_2296_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2296]) ).
cnf(c_0_2296_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2296]) ).
cnf(c_0_2297_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X2),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2297]) ).
cnf(c_0_2297_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X2),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2297]) ).
cnf(c_0_2297_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X2),X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2297]) ).
cnf(c_0_2297_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2297]) ).
cnf(c_0_2298_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X1),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2298]) ).
cnf(c_0_2298_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X1),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2298]) ).
cnf(c_0_2298_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X1),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2298]) ).
cnf(c_0_2298_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2298]) ).
cnf(c_0_2299_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2299]) ).
cnf(c_0_2299_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2299]) ).
cnf(c_0_2299_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2299]) ).
cnf(c_0_2299_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2299]) ).
cnf(c_0_2300_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2300]) ).
cnf(c_0_2300_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2300]) ).
cnf(c_0_2300_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2300]) ).
cnf(c_0_2300_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2300]) ).
cnf(c_0_2301_0,axiom,
( c_HOL_OIf(c_fequal(v_p,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),tc_Polynomial_Opoly(t_a)),c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_Polynomial_Odegree(v_p,t_a)),tc_nat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_p,t_a)
| ~ class_HOL_Ozero(t_a) ),
inference(literals_permutation,[status(thm)],[c_0_2301]) ).
cnf(c_0_2301_1,axiom,
( ~ class_HOL_Ozero(t_a)
| c_HOL_OIf(c_fequal(v_p,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),tc_Polynomial_Opoly(t_a)),c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_Polynomial_Odegree(v_p,t_a)),tc_nat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_p,t_a) ),
inference(literals_permutation,[status(thm)],[c_0_2301]) ).
cnf(c_0_2302_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),c_HOL_Oone__class_Oone(X1))),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2302]) ).
cnf(c_0_2302_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),c_HOL_Oone__class_Oone(X1))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2302]) ).
cnf(c_0_2303_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2303]) ).
cnf(c_0_2303_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
| ~ c_lessequals(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2303]) ).
cnf(c_0_2303_2,axiom,
( ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2303]) ).
cnf(c_0_2303_3,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2303]) ).
cnf(c_0_2304_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2304]) ).
cnf(c_0_2304_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2304]) ).
cnf(c_0_2304_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2304]) ).
cnf(c_0_2304_3,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2304]) ).
cnf(c_0_2305_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2305]) ).
cnf(c_0_2305_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
| ~ c_lessequals(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2305]) ).
cnf(c_0_2305_2,axiom,
( ~ c_lessequals(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2305]) ).
cnf(c_0_2305_3,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2305]) ).
cnf(c_0_2306_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2306]) ).
cnf(c_0_2306_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2306]) ).
cnf(c_0_2306_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2306]) ).
cnf(c_0_2306_3,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2306]) ).
cnf(c_0_2307_0,axiom,
( c_Polynomial_OpCons(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),X1),X2),c_Polynomial_Osmult(X1,X3,X4),X4) = c_Polynomial_Osmult(X1,c_Polynomial_OpCons(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2307]) ).
cnf(c_0_2307_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_OpCons(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),X1),X2),c_Polynomial_Osmult(X1,X3,X4),X4) = c_Polynomial_Osmult(X1,c_Polynomial_OpCons(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2307]) ).
cnf(c_0_2308_0,axiom,
( X1 = hAPP(c_Polynomial_Opoly(X2,X3),X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X3)),X2),c_Polynomial_Osmult(X4,X5,X3)) != c_Polynomial_OpCons(X1,X5,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2308]) ).
cnf(c_0_2308_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X3)),X2),c_Polynomial_Osmult(X4,X5,X3)) != c_Polynomial_OpCons(X1,X5,X3)
| X1 = hAPP(c_Polynomial_Opoly(X2,X3),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2308]) ).
cnf(c_0_2308_2,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X3)),X2),c_Polynomial_Osmult(X4,X5,X3)) != c_Polynomial_OpCons(X1,X5,X3)
| X1 = hAPP(c_Polynomial_Opoly(X2,X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2308]) ).
cnf(c_0_2309_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2309]) ).
cnf(c_0_2309_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2309]) ).
cnf(c_0_2309_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2309]) ).
cnf(c_0_2309_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2309]) ).
cnf(c_0_2310_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2310]) ).
cnf(c_0_2310_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2310]) ).
cnf(c_0_2310_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2310]) ).
cnf(c_0_2310_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2310]) ).
cnf(c_0_2311_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2311]) ).
cnf(c_0_2311_1,axiom,
( ~ class_OrderedGroup_Oab__semigroup__mult(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2311]) ).
cnf(c_0_2312_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2312]) ).
cnf(c_0_2312_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2312]) ).
cnf(c_0_2313_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2313]) ).
cnf(c_0_2313_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2313]) ).
cnf(c_0_2314_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2314]) ).
cnf(c_0_2314_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2314]) ).
cnf(c_0_2315_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2315]) ).
cnf(c_0_2315_1,axiom,
( ~ class_OrderedGroup_Omonoid__mult(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2315]) ).
cnf(c_0_2316_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2316]) ).
cnf(c_0_2316_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2316]) ).
cnf(c_0_2317_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2317]) ).
cnf(c_0_2317_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2317]) ).
cnf(c_0_2318_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2318]) ).
cnf(c_0_2318_1,axiom,
( ~ class_OrderedGroup_Oab__semigroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2318]) ).
cnf(c_0_2319_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2319]) ).
cnf(c_0_2319_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2319]) ).
cnf(c_0_2320_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2320]) ).
cnf(c_0_2320_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2320]) ).
cnf(c_0_2321_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)) = hAPP(c_Polynomial_Opoly(c_Polynomial_Omonom(X1,X2,X3),X3),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2321]) ).
cnf(c_0_2321_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)) = hAPP(c_Polynomial_Opoly(c_Polynomial_Omonom(X1,X2,X3),X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2321]) ).
cnf(c_0_2322_0,axiom,
( hAPP(c_Polynomial_Opoly(X1,X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4)) = hAPP(c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X2,X3),X3),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2322]) ).
cnf(c_0_2322_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| hAPP(c_Polynomial_Opoly(X1,X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4)) = hAPP(c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X2,X3),X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2322]) ).
cnf(c_0_2323_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),hAPP(c_Polynomial_Ocoeff(X2,X3),X4)) = hAPP(c_Polynomial_Ocoeff(c_Polynomial_Osmult(X1,X2,X3),X3),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2323]) ).
cnf(c_0_2323_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),hAPP(c_Polynomial_Ocoeff(X2,X3),X4)) = hAPP(c_Polynomial_Ocoeff(c_Polynomial_Osmult(X1,X2,X3),X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2323]) ).
cnf(c_0_2324_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),hAPP(c_Polynomial_Opoly(X2,X3),X4)) = hAPP(c_Polynomial_Opoly(c_Polynomial_Osmult(X1,X2,X3),X3),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2324]) ).
cnf(c_0_2324_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),hAPP(c_Polynomial_Opoly(X2,X3),X4)) = hAPP(c_Polynomial_Opoly(c_Polynomial_Osmult(X1,X2,X3),X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2324]) ).
cnf(c_0_2325_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1))),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2325]) ).
cnf(c_0_2325_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2325]) ).
cnf(c_0_2326_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2326]) ).
cnf(c_0_2326_1,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2326]) ).
cnf(c_0_2326_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2326]) ).
cnf(c_0_2326_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2326]) ).
cnf(c_0_2327_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2327]) ).
cnf(c_0_2327_1,axiom,
( c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2327]) ).
cnf(c_0_2327_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2327]) ).
cnf(c_0_2327_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2327]) ).
cnf(c_0_2328_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2328]) ).
cnf(c_0_2328_1,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2328]) ).
cnf(c_0_2328_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2328]) ).
cnf(c_0_2328_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2328]) ).
cnf(c_0_2329_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2329]) ).
cnf(c_0_2329_1,axiom,
( c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2329]) ).
cnf(c_0_2329_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2329]) ).
cnf(c_0_2329_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2329]) ).
cnf(c_0_2330_0,axiom,
( c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2330]) ).
cnf(c_0_2330_1,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2330]) ).
cnf(c_0_2330_2,axiom,
( ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2330]) ).
cnf(c_0_2330_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2330]) ).
cnf(c_0_2331_0,axiom,
( c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2331]) ).
cnf(c_0_2331_1,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2331]) ).
cnf(c_0_2331_2,axiom,
( ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2331]) ).
cnf(c_0_2331_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2331]) ).
cnf(c_0_2332_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2332]) ).
cnf(c_0_2332_1,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2332]) ).
cnf(c_0_2332_2,axiom,
( ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2332]) ).
cnf(c_0_2332_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2332]) ).
cnf(c_0_2333_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2333]) ).
cnf(c_0_2333_1,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2333]) ).
cnf(c_0_2333_2,axiom,
( ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2333]) ).
cnf(c_0_2333_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2333]) ).
cnf(c_0_2334_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X4)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2334]) ).
cnf(c_0_2334_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = X4
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2334]) ).
cnf(c_0_2334_2,axiom,
( ~ class_OrderedGroup_Oab__group__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_2334]) ).
cnf(c_0_2335_0,axiom,
( X2 = X3
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X4)) != hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Suc(X4))
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2335]) ).
cnf(c_0_2335_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| X2 = X3
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X4)) != hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Suc(X4))
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2335]) ).
cnf(c_0_2335_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| X2 = X3
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X4)) != hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Suc(X4))
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2335]) ).
cnf(c_0_2335_3,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X4)) != hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Suc(X4))
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| X2 = X3
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2335]) ).
cnf(c_0_2335_4,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X4)) != hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Suc(X4))
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2335]) ).
cnf(c_0_2336_0,axiom,
( hAPP(c_Polynomial_Opoly(X1,X3),hAPP(c_Polynomial_Opoly(X2,X3),X4)) = hAPP(c_Polynomial_Opoly(c_Polynomial_Opcompose(X1,X2,X3),X3),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2336]) ).
cnf(c_0_2336_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| hAPP(c_Polynomial_Opoly(X1,X3),hAPP(c_Polynomial_Opoly(X2,X3),X4)) = hAPP(c_Polynomial_Opoly(c_Polynomial_Opcompose(X1,X2,X3),X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2336]) ).
cnf(c_0_2337_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X3)),c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2337]) ).
cnf(c_0_2337_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X3)),c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2337]) ).
cnf(c_0_2337_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X3)),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2337]) ).
cnf(c_0_2337_3,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X3)),c_HOL_Oone__class_Oone(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2337]) ).
cnf(c_0_2338_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_HOL_Ozero__class_Ozero(X1)),X2),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2338]) ).
cnf(c_0_2338_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_HOL_Ozero__class_Ozero(X1)),X2),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2338]) ).
cnf(c_0_2338_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_HOL_Ozero__class_Ozero(X1)),X2),X1)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2338]) ).
cnf(c_0_2338_3,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_HOL_Ozero__class_Ozero(X1)),X2),X1)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2338]) ).
cnf(c_0_2339_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2339]) ).
cnf(c_0_2339_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2339]) ).
cnf(c_0_2339_2,axiom,
( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2339]) ).
cnf(c_0_2339_3,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2339]) ).
cnf(c_0_2340_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2340]) ).
cnf(c_0_2340_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2340]) ).
cnf(c_0_2340_2,axiom,
( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2340]) ).
cnf(c_0_2340_3,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2340]) ).
cnf(c_0_2341_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2341]) ).
cnf(c_0_2341_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2341]) ).
cnf(c_0_2341_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2341]) ).
cnf(c_0_2341_3,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2341]) ).
cnf(c_0_2342_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2342]) ).
cnf(c_0_2342_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2342]) ).
cnf(c_0_2342_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2342]) ).
cnf(c_0_2342_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2342]) ).
cnf(c_0_2343_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2343]) ).
cnf(c_0_2343_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2343]) ).
cnf(c_0_2343_2,axiom,
( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2343]) ).
cnf(c_0_2343_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2343]) ).
cnf(c_0_2344_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2344]) ).
cnf(c_0_2344_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2344]) ).
cnf(c_0_2344_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2344]) ).
cnf(c_0_2344_3,axiom,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2344]) ).
cnf(c_0_2345_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2345]) ).
cnf(c_0_2345_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2345]) ).
cnf(c_0_2345_2,axiom,
( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2345]) ).
cnf(c_0_2345_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2345]) ).
cnf(c_0_2346_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2346]) ).
cnf(c_0_2346_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2346]) ).
cnf(c_0_2346_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2346]) ).
cnf(c_0_2346_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2346]) ).
cnf(c_0_2347_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2347]) ).
cnf(c_0_2347_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2347]) ).
cnf(c_0_2347_2,axiom,
( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2347]) ).
cnf(c_0_2347_3,axiom,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2347]) ).
cnf(c_0_2348_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2348]) ).
cnf(c_0_2348_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2348]) ).
cnf(c_0_2348_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2348]) ).
cnf(c_0_2348_3,axiom,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2348]) ).
cnf(c_0_2349_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2349]) ).
cnf(c_0_2349_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2349]) ).
cnf(c_0_2349_2,axiom,
( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2349]) ).
cnf(c_0_2349_3,axiom,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2349]) ).
cnf(c_0_2350_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2350]) ).
cnf(c_0_2350_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2350]) ).
cnf(c_0_2350_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2350]) ).
cnf(c_0_2350_3,axiom,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2350]) ).
cnf(c_0_2351_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2351]) ).
cnf(c_0_2351_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2351]) ).
cnf(c_0_2351_2,axiom,
( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2351]) ).
cnf(c_0_2351_3,axiom,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2351]) ).
cnf(c_0_2352_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2352]) ).
cnf(c_0_2352_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2352]) ).
cnf(c_0_2352_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2352]) ).
cnf(c_0_2352_3,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2352]) ).
cnf(c_0_2353_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2353]) ).
cnf(c_0_2353_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2353]) ).
cnf(c_0_2353_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2353]) ).
cnf(c_0_2353_3,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2353]) ).
cnf(c_0_2354_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2354]) ).
cnf(c_0_2354_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2354]) ).
cnf(c_0_2354_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2354]) ).
cnf(c_0_2354_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2354]) ).
cnf(c_0_2355_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2355]) ).
cnf(c_0_2355_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2355]) ).
cnf(c_0_2355_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2355]) ).
cnf(c_0_2355_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2355]) ).
cnf(c_0_2356_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2356]) ).
cnf(c_0_2356_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2356]) ).
cnf(c_0_2356_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2356]) ).
cnf(c_0_2356_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2356]) ).
cnf(c_0_2357_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2357]) ).
cnf(c_0_2357_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2357]) ).
cnf(c_0_2357_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2357]) ).
cnf(c_0_2357_3,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2357]) ).
cnf(c_0_2358_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2358]) ).
cnf(c_0_2358_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2358]) ).
cnf(c_0_2358_2,axiom,
( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2358]) ).
cnf(c_0_2358_3,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2358]) ).
cnf(c_0_2359_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2359]) ).
cnf(c_0_2359_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2359]) ).
cnf(c_0_2359_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2359]) ).
cnf(c_0_2359_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2359]) ).
cnf(c_0_2360_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2360]) ).
cnf(c_0_2360_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2360]) ).
cnf(c_0_2360_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2360]) ).
cnf(c_0_2360_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2360]) ).
cnf(c_0_2361_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2361]) ).
cnf(c_0_2361_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2361]) ).
cnf(c_0_2361_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2361]) ).
cnf(c_0_2361_3,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2361]) ).
cnf(c_0_2362_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2362]) ).
cnf(c_0_2362_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2362]) ).
cnf(c_0_2362_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2362]) ).
cnf(c_0_2362_3,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2362]) ).
cnf(c_0_2363_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2363]) ).
cnf(c_0_2363_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2363]) ).
cnf(c_0_2363_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2363]) ).
cnf(c_0_2363_3,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2363]) ).
cnf(c_0_2364_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2364]) ).
cnf(c_0_2364_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2364]) ).
cnf(c_0_2364_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2364]) ).
cnf(c_0_2364_3,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2364]) ).
cnf(c_0_2365_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2365]) ).
cnf(c_0_2365_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2365]) ).
cnf(c_0_2365_2,axiom,
( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2365]) ).
cnf(c_0_2365_3,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2365]) ).
cnf(c_0_2366_0,axiom,
( c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2366]) ).
cnf(c_0_2366_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2366]) ).
cnf(c_0_2366_2,axiom,
( ~ c_lessequals(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2366]) ).
cnf(c_0_2366_3,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2366]) ).
cnf(c_0_2366_4,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2366]) ).
cnf(c_0_2367_0,axiom,
( c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2367]) ).
cnf(c_0_2367_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2367]) ).
cnf(c_0_2367_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2367]) ).
cnf(c_0_2367_3,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2367]) ).
cnf(c_0_2367_4,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2367]) ).
cnf(c_0_2368_0,axiom,
( c_lessequals(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2368]) ).
cnf(c_0_2368_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2368]) ).
cnf(c_0_2368_2,axiom,
( ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2368]) ).
cnf(c_0_2368_3,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2368]) ).
cnf(c_0_2368_4,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2368]) ).
cnf(c_0_2369_0,axiom,
( c_lessequals(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2369]) ).
cnf(c_0_2369_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2),X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2369]) ).
cnf(c_0_2369_2,axiom,
( ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2),X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2369]) ).
cnf(c_0_2369_3,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2369]) ).
cnf(c_0_2369_4,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2369]) ).
cnf(c_0_2370_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2370]) ).
cnf(c_0_2370_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2370]) ).
cnf(c_0_2370_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2370]) ).
cnf(c_0_2371_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2371]) ).
cnf(c_0_2371_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2371]) ).
cnf(c_0_2371_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2371]) ).
cnf(c_0_2372_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2372]) ).
cnf(c_0_2372_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2372]) ).
cnf(c_0_2372_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2372]) ).
cnf(c_0_2373_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2373]) ).
cnf(c_0_2373_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2373]) ).
cnf(c_0_2373_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2373]) ).
cnf(c_0_2374_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2374]) ).
cnf(c_0_2374_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2374]) ).
cnf(c_0_2374_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2374]) ).
cnf(c_0_2375_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2375]) ).
cnf(c_0_2375_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2375]) ).
cnf(c_0_2375_2,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2375]) ).
cnf(c_0_2376_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2376]) ).
cnf(c_0_2376_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2376]) ).
cnf(c_0_2376_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2376]) ).
cnf(c_0_2377_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2377]) ).
cnf(c_0_2377_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2377]) ).
cnf(c_0_2377_2,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2377]) ).
cnf(c_0_2378_0,axiom,
( c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2378]) ).
cnf(c_0_2378_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2378]) ).
cnf(c_0_2378_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2378]) ).
cnf(c_0_2378_3,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2378]) ).
cnf(c_0_2379_0,axiom,
( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2379]) ).
cnf(c_0_2379_1,axiom,
( ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2379]) ).
cnf(c_0_2379_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2379]) ).
cnf(c_0_2380_0,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2380]) ).
cnf(c_0_2380_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2380]) ).
cnf(c_0_2380_2,axiom,
( ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2380]) ).
cnf(c_0_2380_3,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2380]) ).
cnf(c_0_2381_0,axiom,
( hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2381]) ).
cnf(c_0_2381_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2381]) ).
cnf(c_0_2382_0,axiom,
( c_Polynomial_Omonom(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),X1),X2),X3,X4) = c_Polynomial_Osmult(X1,c_Polynomial_Omonom(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2382]) ).
cnf(c_0_2382_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Omonom(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),X1),X2),X3,X4) = c_Polynomial_Osmult(X1,c_Polynomial_Omonom(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2382]) ).
cnf(c_0_2383_0,axiom,
( c_Polynomial_Osmult(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),X1),X2),X3,X4) = c_Polynomial_Osmult(X1,c_Polynomial_Osmult(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2383]) ).
cnf(c_0_2383_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Osmult(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),X1),X2),X3,X4) = c_Polynomial_Osmult(X1,c_Polynomial_Osmult(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2383]) ).
cnf(c_0_2384_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2384]) ).
cnf(c_0_2384_1,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2384]) ).
cnf(c_0_2384_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2384]) ).
cnf(c_0_2385_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2385]) ).
cnf(c_0_2385_1,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2385]) ).
cnf(c_0_2385_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2385]) ).
cnf(c_0_2386_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2386]) ).
cnf(c_0_2386_1,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2386]) ).
cnf(c_0_2386_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2386]) ).
cnf(c_0_2387_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2387]) ).
cnf(c_0_2387_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2387]) ).
cnf(c_0_2387_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2387]) ).
cnf(c_0_2388_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2388]) ).
cnf(c_0_2388_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2388]) ).
cnf(c_0_2388_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2388]) ).
cnf(c_0_2389_0,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2389]) ).
cnf(c_0_2389_1,axiom,
( ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2389]) ).
cnf(c_0_2389_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2389]) ).
cnf(c_0_2390_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X3))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2390]) ).
cnf(c_0_2390_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2390]) ).
cnf(c_0_2391_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X3))
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2391]) ).
cnf(c_0_2391_1,axiom,
( ~ class_OrderedGroup_Omonoid__mult(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2391]) ).
cnf(c_0_2392_0,axiom,
( hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2392]) ).
cnf(c_0_2392_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2392]) ).
cnf(c_0_2393_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2393]) ).
cnf(c_0_2393_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2393]) ).
cnf(c_0_2394_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2394]) ).
cnf(c_0_2394_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2394]) ).
cnf(c_0_2395_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2395]) ).
cnf(c_0_2395_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2395]) ).
cnf(c_0_2396_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2396]) ).
cnf(c_0_2396_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2396]) ).
cnf(c_0_2397_0,axiom,
( hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),c_HOL_Oone__class_Oone(tc_nat)) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2397]) ).
cnf(c_0_2397_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1),X2),c_HOL_Oone__class_Oone(tc_nat)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2397]) ).
cnf(c_0_2398_0,axiom,
( hAPP(c_Polynomial_Ocoeff(c_Polynomial_OpCons(X1,X2,X3),X3),c_Suc(X4)) = hAPP(c_Polynomial_Ocoeff(X2,X3),X4)
| ~ class_HOL_Ozero(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2398]) ).
cnf(c_0_2398_1,axiom,
( ~ class_HOL_Ozero(X3)
| hAPP(c_Polynomial_Ocoeff(c_Polynomial_OpCons(X1,X2,X3),X3),c_Suc(X4)) = hAPP(c_Polynomial_Ocoeff(X2,X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2398]) ).
cnf(c_0_2399_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X2),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Olordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2399]) ).
cnf(c_0_2399_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X2),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_OrderedGroup_Olordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2399]) ).
cnf(c_0_2399_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X2),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2399]) ).
cnf(c_0_2400_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2400]) ).
cnf(c_0_2400_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2400]) ).
cnf(c_0_2400_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2400]) ).
cnf(c_0_2400_3,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2400]) ).
cnf(c_0_2400_4,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2400]) ).
cnf(c_0_2401_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2401]) ).
cnf(c_0_2401_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2401]) ).
cnf(c_0_2401_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2401]) ).
cnf(c_0_2401_3,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2401]) ).
cnf(c_0_2401_4,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2401]) ).
cnf(c_0_2402_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2402]) ).
cnf(c_0_2402_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2402]) ).
cnf(c_0_2402_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2402]) ).
cnf(c_0_2402_3,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2402]) ).
cnf(c_0_2403_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X3)),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2403]) ).
cnf(c_0_2403_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X3)),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2403]) ).
cnf(c_0_2403_2,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X3)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2403]) ).
cnf(c_0_2404_0,axiom,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X3,X2) = c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2404]) ).
cnf(c_0_2404_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X2)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X3,X2) = c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2404]) ).
cnf(c_0_2405_0,axiom,
( ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2405]) ).
cnf(c_0_2405_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2405]) ).
cnf(c_0_2406_0,axiom,
( X1 = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2406]) ).
cnf(c_0_2406_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| X1 = X2
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2406]) ).
cnf(c_0_2406_2,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| X1 = X2
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2406]) ).
cnf(c_0_2406_3,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2406]) ).
cnf(c_0_2407_0,axiom,
( X1 = X2
| hAPP(c_Polynomial_Ocoeff(c_Polynomial_Omonom(X3,X1,X4),X4),X2) = c_HOL_Ozero__class_Ozero(X4)
| ~ class_HOL_Ozero(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2407]) ).
cnf(c_0_2407_1,axiom,
( hAPP(c_Polynomial_Ocoeff(c_Polynomial_Omonom(X3,X1,X4),X4),X2) = c_HOL_Ozero__class_Ozero(X4)
| X1 = X2
| ~ class_HOL_Ozero(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2407]) ).
cnf(c_0_2407_2,axiom,
( ~ class_HOL_Ozero(X4)
| hAPP(c_Polynomial_Ocoeff(c_Polynomial_Omonom(X3,X1,X4),X4),X2) = c_HOL_Ozero__class_Ozero(X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2407]) ).
cnf(c_0_2408_0,axiom,
( X1 = c_HOL_Ouminus__class_Ouminus(X2,X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)) != X4
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2408]) ).
cnf(c_0_2408_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)) != X4
| X1 = c_HOL_Ouminus__class_Ouminus(X2,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2408]) ).
cnf(c_0_2408_2,axiom,
( ~ class_OrderedGroup_Oab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)) != X4
| X1 = c_HOL_Ouminus__class_Ouminus(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2408]) ).
cnf(c_0_2409_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X3)) = X3
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2409]) ).
cnf(c_0_2409_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X3)) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2409]) ).
cnf(c_0_2410_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2410]) ).
cnf(c_0_2410_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2410]) ).
cnf(c_0_2410_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2410]) ).
cnf(c_0_2411_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2411]) ).
cnf(c_0_2411_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2411]) ).
cnf(c_0_2411_2,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2411]) ).
cnf(c_0_2412_0,axiom,
( c_lessequals(c_HOL_Oone__class_Oone(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2412]) ).
cnf(c_0_2412_1,axiom,
( ~ c_lessequals(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_lessequals(c_HOL_Oone__class_Oone(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2412]) ).
cnf(c_0_2412_2,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_lessequals(c_HOL_Oone__class_Oone(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2412]) ).
cnf(c_0_2413_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2413]) ).
cnf(c_0_2413_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2413]) ).
cnf(c_0_2413_2,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2413]) ).
cnf(c_0_2414_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2414]) ).
cnf(c_0_2414_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2414]) ).
cnf(c_0_2414_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2414]) ).
cnf(c_0_2415_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2415]) ).
cnf(c_0_2415_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2415]) ).
cnf(c_0_2415_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2415]) ).
cnf(c_0_2416_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2416]) ).
cnf(c_0_2416_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2416]) ).
cnf(c_0_2416_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2416]) ).
cnf(c_0_2417_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2417]) ).
cnf(c_0_2417_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2417]) ).
cnf(c_0_2417_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2417]) ).
cnf(c_0_2418_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2418]) ).
cnf(c_0_2418_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2418]) ).
cnf(c_0_2418_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2418]) ).
cnf(c_0_2419_0,axiom,
( hAPP(c_Polynomial_Ocoeff(c_Polynomial_OpCons(X1,X2,X3),X3),c_HOL_Ozero__class_Ozero(tc_nat)) = X1
| ~ class_HOL_Ozero(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2419]) ).
cnf(c_0_2419_1,axiom,
( ~ class_HOL_Ozero(X3)
| hAPP(c_Polynomial_Ocoeff(c_Polynomial_OpCons(X1,X2,X3),X3),c_HOL_Ozero__class_Ozero(tc_nat)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2419]) ).
cnf(c_0_2420_0,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2420]) ).
cnf(c_0_2420_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2420]) ).
cnf(c_0_2421_0,axiom,
( hAPP(c_Polynomial_Ocoeff(c_Polynomial_Omonom(X1,X2,X3),X3),X2) = X1
| ~ class_HOL_Ozero(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2421]) ).
cnf(c_0_2421_1,axiom,
( ~ class_HOL_Ozero(X3)
| hAPP(c_Polynomial_Ocoeff(c_Polynomial_Omonom(X1,X2,X3),X3),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2421]) ).
cnf(c_0_2422_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ouminus__class_Ouminus(X3,X1)),c_HOL_Ouminus__class_Ouminus(X2,X1)) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2422]) ).
cnf(c_0_2422_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ouminus__class_Ouminus(X3,X1)),c_HOL_Ouminus__class_Ouminus(X2,X1)) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2422]) ).
cnf(c_0_2423_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),c_HOL_Ouminus__class_Ouminus(X3,X1)) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2423]) ).
cnf(c_0_2423_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),c_HOL_Ouminus__class_Ouminus(X3,X1)) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2423]) ).
cnf(c_0_2424_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Nat_Osemiring__1__class_Oof__nat(X1,X3)),c_Nat_Osemiring__1__class_Oof__nat(X2,X3)) = c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3)
| ~ class_Ring__and__Field_Osemiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2424]) ).
cnf(c_0_2424_1,axiom,
( ~ class_Ring__and__Field_Osemiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Nat_Osemiring__1__class_Oof__nat(X1,X3)),c_Nat_Osemiring__1__class_Oof__nat(X2,X3)) = c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2424]) ).
cnf(c_0_2425_0,axiom,
( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X3),c_Polynomial_Omonom(X1,X2,X3),X3) = c_Polynomial_Omonom(X1,c_Suc(X2),X3)
| ~ class_HOL_Ozero(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2425]) ).
cnf(c_0_2425_1,axiom,
( ~ class_HOL_Ozero(X3)
| c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X3),c_Polynomial_Omonom(X1,X2,X3),X3) = c_Polynomial_Omonom(X1,c_Suc(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2425]) ).
cnf(c_0_2426_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2426]) ).
cnf(c_0_2426_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2426]) ).
cnf(c_0_2426_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2426]) ).
cnf(c_0_2426_3,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2426]) ).
cnf(c_0_2427_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2427]) ).
cnf(c_0_2427_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2427]) ).
cnf(c_0_2427_2,axiom,
( ~ c_lessequals(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2427]) ).
cnf(c_0_2427_3,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2427]) ).
cnf(c_0_2428_0,axiom,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2428]) ).
cnf(c_0_2428_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,X4,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2428]) ).
cnf(c_0_2428_2,axiom,
( ~ c_lessequals(X2,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2428]) ).
cnf(c_0_2428_3,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X2,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2428]) ).
cnf(c_0_2429_0,axiom,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2429]) ).
cnf(c_0_2429_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2429]) ).
cnf(c_0_2429_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2429]) ).
cnf(c_0_2429_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2429]) ).
cnf(c_0_2430_0,axiom,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2430]) ).
cnf(c_0_2430_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2430]) ).
cnf(c_0_2430_2,axiom,
( ~ c_lessequals(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2430]) ).
cnf(c_0_2430_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2430]) ).
cnf(c_0_2431_0,axiom,
( c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2431]) ).
cnf(c_0_2431_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2431]) ).
cnf(c_0_2431_2,axiom,
( ~ c_lessequals(X4,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2431]) ).
cnf(c_0_2431_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X4,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2431]) ).
cnf(c_0_2432_0,axiom,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2432]) ).
cnf(c_0_2432_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2432]) ).
cnf(c_0_2432_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2432]) ).
cnf(c_0_2432_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2432]) ).
cnf(c_0_2433_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2433]) ).
cnf(c_0_2433_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2433]) ).
cnf(c_0_2433_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2433]) ).
cnf(c_0_2433_3,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2433]) ).
cnf(c_0_2434_0,axiom,
( c_HOL_Oord__class_Oless(X3,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2434]) ).
cnf(c_0_2434_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2)
| c_HOL_Oord__class_Oless(X3,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2434]) ).
cnf(c_0_2434_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2)
| c_HOL_Oord__class_Oless(X3,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2434]) ).
cnf(c_0_2435_0,axiom,
( c_lessequals(X3,X1,X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2435]) ).
cnf(c_0_2435_1,axiom,
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2)
| c_lessequals(X3,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2435]) ).
cnf(c_0_2435_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2)
| c_lessequals(X3,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2435]) ).
cnf(c_0_2436_0,axiom,
( c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X3)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2436]) ).
cnf(c_0_2436_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2436]) ).
cnf(c_0_2437_0,axiom,
( c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X3)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2437]) ).
cnf(c_0_2437_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2437]) ).
cnf(c_0_2438_0,axiom,
( c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X3)
| ~ class_Ring__and__Field_Oring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2438]) ).
cnf(c_0_2438_1,axiom,
( ~ class_Ring__and__Field_Oring(X1)
| c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2438]) ).
cnf(c_0_2439_0,axiom,
( c_lessequals(X1,X3,tc_RealDef_Oreal)
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X2,X3,tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_2439]) ).
cnf(c_0_2439_1,axiom,
( ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| c_lessequals(X1,X3,tc_RealDef_Oreal)
| ~ c_lessequals(X2,X3,tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_2439]) ).
cnf(c_0_2439_2,axiom,
( ~ c_lessequals(X2,X3,tc_RealDef_Oreal)
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| c_lessequals(X1,X3,tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_2439]) ).
cnf(c_0_2440_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X3))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2440]) ).
cnf(c_0_2440_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2440]) ).
cnf(c_0_2441_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X3))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2441]) ).
cnf(c_0_2441_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2441]) ).
cnf(c_0_2442_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X3))
| ~ class_Power_Opower(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2442]) ).
cnf(c_0_2442_1,axiom,
( ~ class_Power_Opower(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2442]) ).
cnf(c_0_2443_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X3))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2443]) ).
cnf(c_0_2443_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Suc(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2443]) ).
cnf(c_0_2444_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2444]) ).
cnf(c_0_2444_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2444]) ).
cnf(c_0_2444_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2444]) ).
cnf(c_0_2445_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2445]) ).
cnf(c_0_2445_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2445]) ).
cnf(c_0_2445_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2445]) ).
cnf(c_0_2446_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2446]) ).
cnf(c_0_2446_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2446]) ).
cnf(c_0_2446_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2446]) ).
cnf(c_0_2447_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2447]) ).
cnf(c_0_2447_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2447]) ).
cnf(c_0_2447_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2447]) ).
cnf(c_0_2448_0,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2448]) ).
cnf(c_0_2448_1,axiom,
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2448]) ).
cnf(c_0_2448_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2448]) ).
cnf(c_0_2449_0,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2449]) ).
cnf(c_0_2449_1,axiom,
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2449]) ).
cnf(c_0_2449_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2449]) ).
cnf(c_0_2450_0,axiom,
( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2450]) ).
cnf(c_0_2450_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2450]) ).
cnf(c_0_2450_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2450]) ).
cnf(c_0_2451_0,axiom,
( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2451]) ).
cnf(c_0_2451_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2451]) ).
cnf(c_0_2451_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2451]) ).
cnf(c_0_2452_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)) = X3
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2452]) ).
cnf(c_0_2452_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2452]) ).
cnf(c_0_2453_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)) = X3
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2453]) ).
cnf(c_0_2453_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2453]) ).
cnf(c_0_2454_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2454]) ).
cnf(c_0_2454_1,axiom,
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2454]) ).
cnf(c_0_2455_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1)),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2455]) ).
cnf(c_0_2455_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2455]) ).
cnf(c_0_2456_0,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2456]) ).
cnf(c_0_2456_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2456]) ).
cnf(c_0_2456_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2456]) ).
cnf(c_0_2457_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2457]) ).
cnf(c_0_2457_1,axiom,
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2457]) ).
cnf(c_0_2457_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2457]) ).
cnf(c_0_2458_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2458]) ).
cnf(c_0_2458_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2458]) ).
cnf(c_0_2458_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2458]) ).
cnf(c_0_2459_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2459]) ).
cnf(c_0_2459_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2459]) ).
cnf(c_0_2459_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2459]) ).
cnf(c_0_2460_0,axiom,
( c_lessequals(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2460]) ).
cnf(c_0_2460_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2460]) ).
cnf(c_0_2460_2,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2460]) ).
cnf(c_0_2460_3,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2460]) ).
cnf(c_0_2461_0,axiom,
( c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ouminus__class_Ouminus(X3,X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2461]) ).
cnf(c_0_2461_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ouminus__class_Ouminus(X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2461]) ).
cnf(c_0_2462_0,axiom,
( c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ouminus__class_Ouminus(X3,X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2462]) ).
cnf(c_0_2462_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ouminus__class_Ouminus(X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2462]) ).
cnf(c_0_2463_0,axiom,
( c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ouminus__class_Ouminus(X3,X1))
| ~ class_Ring__and__Field_Oring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2463]) ).
cnf(c_0_2463_1,axiom,
( ~ class_Ring__and__Field_Oring(X1)
| c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ouminus__class_Ouminus(X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2463]) ).
cnf(c_0_2464_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2464]) ).
cnf(c_0_2464_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2464]) ).
cnf(c_0_2464_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ouminus__class_Ouminus(X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2464]) ).
cnf(c_0_2465_0,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2465]) ).
cnf(c_0_2465_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2465]) ).
cnf(c_0_2465_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ouminus__class_Ouminus(X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2465]) ).
cnf(c_0_2466_0,axiom,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2466]) ).
cnf(c_0_2466_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2466]) ).
cnf(c_0_2466_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2466]) ).
cnf(c_0_2467_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X1,X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2467]) ).
cnf(c_0_2467_1,axiom,
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X1,X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2467]) ).
cnf(c_0_2467_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X1,X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2467]) ).
cnf(c_0_2468_0,axiom,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_OrderedGroup_Oordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2468]) ).
cnf(c_0_2468_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Oordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2468]) ).
cnf(c_0_2468_2,axiom,
( ~ class_OrderedGroup_Oordered__ab__group__add(X2)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2468]) ).
cnf(c_0_2469_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X1,X2)
| ~ class_OrderedGroup_Oordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2469]) ).
cnf(c_0_2469_1,axiom,
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X1,X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ class_OrderedGroup_Oordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2469]) ).
cnf(c_0_2469_2,axiom,
( ~ class_OrderedGroup_Oordered__ab__group__add(X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X1,X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2469]) ).
cnf(c_0_2470_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2470]) ).
cnf(c_0_2470_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2470]) ).
cnf(c_0_2470_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2470]) ).
cnf(c_0_2471_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Osmult(X3,X1,X2) != c_Polynomial_OpCons(X4,X1,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2471]) ).
cnf(c_0_2471_1,axiom,
( c_Polynomial_Osmult(X3,X1,X2) != c_Polynomial_OpCons(X4,X1,X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2471]) ).
cnf(c_0_2471_2,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X2)
| c_Polynomial_Osmult(X3,X1,X2) != c_Polynomial_OpCons(X4,X1,X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2471]) ).
cnf(c_0_2472_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2472]) ).
cnf(c_0_2472_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2472]) ).
cnf(c_0_2472_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ouminus__class_Ouminus(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2472]) ).
cnf(c_0_2473_0,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2473]) ).
cnf(c_0_2473_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2473]) ).
cnf(c_0_2473_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2473]) ).
cnf(c_0_2474_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2474]) ).
cnf(c_0_2474_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2474]) ).
cnf(c_0_2474_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ouminus__class_Ouminus(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2474]) ).
cnf(c_0_2475_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2475]) ).
cnf(c_0_2475_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2475]) ).
cnf(c_0_2475_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2475]) ).
cnf(c_0_2476_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),c_HOL_Ouminus__class_Ouminus(X2,X1)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2476]) ).
cnf(c_0_2476_1,axiom,
( ~ class_Ring__and__Field_Oidom(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),c_HOL_Ouminus__class_Ouminus(X2,X1)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2476]) ).
cnf(c_0_2477_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),c_HOL_Ouminus__class_Ouminus(X3,X1)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)
| ~ class_Ring__and__Field_Oring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2477]) ).
cnf(c_0_2477_1,axiom,
( ~ class_Ring__and__Field_Oring(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),c_HOL_Ouminus__class_Ouminus(X3,X1)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2477]) ).
cnf(c_0_2478_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ouminus__class_Ouminus(X3,X1))
| ~ class_Ring__and__Field_Oring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2478]) ).
cnf(c_0_2478_1,axiom,
( ~ class_Ring__and__Field_Oring(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ouminus__class_Ouminus(X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2478]) ).
cnf(c_0_2479_0,axiom,
( X1 = X2
| X1 = c_HOL_Ouminus__class_Ouminus(X2,X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X1) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X2)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2479]) ).
cnf(c_0_2479_1,axiom,
( X1 = c_HOL_Ouminus__class_Ouminus(X2,X3)
| X1 = X2
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X1) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X2)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2479]) ).
cnf(c_0_2479_2,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X1) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X2)
| X1 = c_HOL_Ouminus__class_Ouminus(X2,X3)
| X1 = X2
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2479]) ).
cnf(c_0_2479_3,axiom,
( ~ class_Ring__and__Field_Oidom(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X1) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X2),X2)
| X1 = c_HOL_Ouminus__class_Ouminus(X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2479]) ).
cnf(c_0_2480_0,axiom,
( c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2480]) ).
cnf(c_0_2480_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2480]) ).
cnf(c_0_2480_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2480]) ).
cnf(c_0_2481_0,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2481]) ).
cnf(c_0_2481_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2481]) ).
cnf(c_0_2481_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2481]) ).
cnf(c_0_2482_0,axiom,
( c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Oordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2482]) ).
cnf(c_0_2482_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_OrderedGroup_Oordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2482]) ).
cnf(c_0_2482_2,axiom,
( ~ class_OrderedGroup_Oordered__ab__group__add(X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2482]) ).
cnf(c_0_2483_0,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2483]) ).
cnf(c_0_2483_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2483]) ).
cnf(c_0_2483_2,axiom,
( ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2483]) ).
cnf(c_0_2484_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2484]) ).
cnf(c_0_2484_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2484]) ).
cnf(c_0_2484_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2484]) ).
cnf(c_0_2485_0,axiom,
( X2 = X1
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2485]) ).
cnf(c_0_2485_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| X2 = X1
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2485]) ).
cnf(c_0_2485_2,axiom,
( ~ c_lessequals(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| X2 = X1
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2485]) ).
cnf(c_0_2485_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2485]) ).
cnf(c_0_2486_0,axiom,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2486]) ).
cnf(c_0_2486_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2486]) ).
cnf(c_0_2486_2,axiom,
( ~ c_lessequals(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| X1 = X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2486]) ).
cnf(c_0_2486_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2486]) ).
cnf(c_0_2487_0,axiom,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2487]) ).
cnf(c_0_2487_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2487]) ).
cnf(c_0_2487_2,axiom,
( ~ c_lessequals(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| X1 = X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2487]) ).
cnf(c_0_2487_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2487]) ).
cnf(c_0_2488_0,axiom,
( X1 = X2
| c_Polynomial_OpCons(X1,X3,X4) != c_Polynomial_OpCons(X2,X5,X4)
| ~ class_HOL_Ozero(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2488]) ).
cnf(c_0_2488_1,axiom,
( c_Polynomial_OpCons(X1,X3,X4) != c_Polynomial_OpCons(X2,X5,X4)
| X1 = X2
| ~ class_HOL_Ozero(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2488]) ).
cnf(c_0_2488_2,axiom,
( ~ class_HOL_Ozero(X4)
| c_Polynomial_OpCons(X1,X3,X4) != c_Polynomial_OpCons(X2,X5,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2488]) ).
cnf(c_0_2489_0,axiom,
( X1 = X2
| c_Polynomial_OpCons(X3,X1,X4) != c_Polynomial_OpCons(X5,X2,X4)
| ~ class_HOL_Ozero(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2489]) ).
cnf(c_0_2489_1,axiom,
( c_Polynomial_OpCons(X3,X1,X4) != c_Polynomial_OpCons(X5,X2,X4)
| X1 = X2
| ~ class_HOL_Ozero(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2489]) ).
cnf(c_0_2489_2,axiom,
( ~ class_HOL_Ozero(X4)
| c_Polynomial_OpCons(X3,X1,X4) != c_Polynomial_OpCons(X5,X2,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2489]) ).
cnf(c_0_2490_0,axiom,
( X1 = X2
| c_Polynomial_Omonom(X1,X3,X4) != c_Polynomial_Omonom(X2,X3,X4)
| ~ class_HOL_Ozero(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2490]) ).
cnf(c_0_2490_1,axiom,
( c_Polynomial_Omonom(X1,X3,X4) != c_Polynomial_Omonom(X2,X3,X4)
| X1 = X2
| ~ class_HOL_Ozero(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2490]) ).
cnf(c_0_2490_2,axiom,
( ~ class_HOL_Ozero(X4)
| c_Polynomial_Omonom(X1,X3,X4) != c_Polynomial_Omonom(X2,X3,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2490]) ).
cnf(c_0_2491_0,axiom,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2491]) ).
cnf(c_0_2491_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| X1 = X2
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2491]) ).
cnf(c_0_2491_2,axiom,
( ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| X1 = X2
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2491]) ).
cnf(c_0_2491_3,axiom,
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2491]) ).
cnf(c_0_2492_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2492]) ).
cnf(c_0_2492_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2492]) ).
cnf(c_0_2492_2,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2492]) ).
cnf(c_0_2493_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2493]) ).
cnf(c_0_2493_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2493]) ).
cnf(c_0_2493_2,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2493]) ).
cnf(c_0_2494_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2494]) ).
cnf(c_0_2494_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2494]) ).
cnf(c_0_2494_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2494]) ).
cnf(c_0_2495_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2495]) ).
cnf(c_0_2495_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2495]) ).
cnf(c_0_2495_2,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2495]) ).
cnf(c_0_2496_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2496]) ).
cnf(c_0_2496_1,axiom,
( ~ c_lessequals(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2496]) ).
cnf(c_0_2496_2,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2496]) ).
cnf(c_0_2497_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ c_lessequals(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2497]) ).
cnf(c_0_2497_1,axiom,
( ~ c_lessequals(X1,X1,X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2497]) ).
cnf(c_0_2497_2,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X1,X1,X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2497]) ).
cnf(c_0_2498_0,axiom,
( ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2498]) ).
cnf(c_0_2498_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2498]) ).
cnf(c_0_2498_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2498]) ).
cnf(c_0_2499_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2499]) ).
cnf(c_0_2499_1,axiom,
( ~ c_lessequals(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2499]) ).
cnf(c_0_2499_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2499]) ).
cnf(c_0_2500_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| hAPP(c_Polynomial_Opoly(X1,X2),X3) != c_HOL_Ozero__class_Ozero(X2)
| c_Polynomial_Oorder(X3,X1,X2) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2500]) ).
cnf(c_0_2500_1,axiom,
( hAPP(c_Polynomial_Opoly(X1,X2),X3) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Oorder(X3,X1,X2) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2500]) ).
cnf(c_0_2500_2,axiom,
( c_Polynomial_Oorder(X3,X1,X2) != c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(c_Polynomial_Opoly(X1,X2),X3) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2500]) ).
cnf(c_0_2500_3,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| c_Polynomial_Oorder(X3,X1,X2) != c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(c_Polynomial_Opoly(X1,X2),X3) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2500]) ).
cnf(c_0_2501_0,axiom,
( X1 = X2
| ~ hBOOL(c_fequal(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2501]) ).
cnf(c_0_2501_1,axiom,
( ~ hBOOL(c_fequal(X1,X2,X3))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2501]) ).
cnf(c_0_2502_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2502]) ).
cnf(c_0_2502_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2502]) ).
cnf(c_0_2503_0,axiom,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Oone__class_Oone(X2)),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2503]) ).
cnf(c_0_2503_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Oone__class_Oone(X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2503]) ).
cnf(c_0_2504_0,axiom,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2504]) ).
cnf(c_0_2504_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| X1 = X2
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2504]) ).
cnf(c_0_2504_2,axiom,
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2504]) ).
cnf(c_0_2505_0,axiom,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2505]) ).
cnf(c_0_2505_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| X1 = X2
| ~ class_OrderedGroup_Ocancel__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2505]) ).
cnf(c_0_2505_2,axiom,
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2505]) ).
cnf(c_0_2506_0,axiom,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2506]) ).
cnf(c_0_2506_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4)
| X1 = X2
| ~ class_OrderedGroup_Ocancel__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2506]) ).
cnf(c_0_2506_2,axiom,
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2506]) ).
cnf(c_0_2507_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2507]) ).
cnf(c_0_2507_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2507]) ).
cnf(c_0_2508_0,axiom,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X2,X1,tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_2508]) ).
cnf(c_0_2508_1,axiom,
( ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| X1 = X2
| ~ c_lessequals(X2,X1,tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_2508]) ).
cnf(c_0_2508_2,axiom,
( ~ c_lessequals(X2,X1,tc_RealDef_Oreal)
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2508]) ).
cnf(c_0_2509_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Odegree(c_Polynomial_OpCons(X3,X1,X2),X2) = c_Suc(c_Polynomial_Odegree(X1,X2))
| ~ class_HOL_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2509]) ).
cnf(c_0_2509_1,axiom,
( c_Polynomial_Odegree(c_Polynomial_OpCons(X3,X1,X2),X2) = c_Suc(c_Polynomial_Odegree(X1,X2))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_HOL_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2509]) ).
cnf(c_0_2509_2,axiom,
( ~ class_HOL_Ozero(X2)
| c_Polynomial_Odegree(c_Polynomial_OpCons(X3,X1,X2),X2) = c_Suc(c_Polynomial_Odegree(X1,X2))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2509]) ).
cnf(c_0_2510_0,axiom,
( c_Polynomial_Odegree(c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X2) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_HOL_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2510]) ).
cnf(c_0_2510_1,axiom,
( ~ class_HOL_Ozero(X2)
| c_Polynomial_Odegree(c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X2) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2510]) ).
cnf(c_0_2511_0,axiom,
( X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2511]) ).
cnf(c_0_2511_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X2 = X1
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2511]) ).
cnf(c_0_2511_2,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X2 = X1
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2511]) ).
cnf(c_0_2511_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2511]) ).
cnf(c_0_2512_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2512]) ).
cnf(c_0_2512_1,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2512]) ).
cnf(c_0_2512_2,axiom,
( ~ c_lessequals(X2,X1,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2512]) ).
cnf(c_0_2512_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X2,X1,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2512]) ).
cnf(c_0_2513_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2513]) ).
cnf(c_0_2513_1,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2513]) ).
cnf(c_0_2513_2,axiom,
( ~ c_lessequals(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2513]) ).
cnf(c_0_2513_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2513]) ).
cnf(c_0_2514_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2514]) ).
cnf(c_0_2514_1,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2514]) ).
cnf(c_0_2514_2,axiom,
( ~ c_lessequals(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2514]) ).
cnf(c_0_2514_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2514]) ).
cnf(c_0_2515_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2515]) ).
cnf(c_0_2515_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2515]) ).
cnf(c_0_2515_2,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2515]) ).
cnf(c_0_2515_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2515]) ).
cnf(c_0_2516_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2516]) ).
cnf(c_0_2516_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2516]) ).
cnf(c_0_2516_2,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2516]) ).
cnf(c_0_2516_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2516]) ).
cnf(c_0_2517_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2517]) ).
cnf(c_0_2517_1,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2517]) ).
cnf(c_0_2517_2,axiom,
( ~ c_lessequals(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2517]) ).
cnf(c_0_2517_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2517]) ).
cnf(c_0_2518_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2518]) ).
cnf(c_0_2518_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2518]) ).
cnf(c_0_2518_2,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2518]) ).
cnf(c_0_2518_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2518]) ).
cnf(c_0_2519_0,axiom,
( hAPP(c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_HOL_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2519]) ).
cnf(c_0_2519_1,axiom,
( ~ class_HOL_Ozero(X1)
| hAPP(c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1)) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2519]) ).
cnf(c_0_2520_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X2),X2)),X1) = c_HOL_Ouminus__class_Ouminus(X1,X2)
| ~ class_Int_Onumber__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2520]) ).
cnf(c_0_2520_1,axiom,
( ~ class_Int_Onumber__ring(X2)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X2),X2)),X1) = c_HOL_Ouminus__class_Ouminus(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2520]) ).
cnf(c_0_2521_0,axiom,
( c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2521]) ).
cnf(c_0_2521_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2521]) ).
cnf(c_0_2521_2,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2521]) ).
cnf(c_0_2522_0,axiom,
( c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2522]) ).
cnf(c_0_2522_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2522]) ).
cnf(c_0_2522_2,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2522]) ).
cnf(c_0_2523_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Polynomial_Odegree(c_Polynomial_Osmult(X1,X3,X2),X2) = c_Polynomial_Odegree(X3,X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2523]) ).
cnf(c_0_2523_1,axiom,
( c_Polynomial_Odegree(c_Polynomial_Osmult(X1,X3,X2),X2) = c_Polynomial_Odegree(X3,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2523]) ).
cnf(c_0_2523_2,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| c_Polynomial_Odegree(c_Polynomial_Osmult(X1,X3,X2),X2) = c_Polynomial_Odegree(X3,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2523]) ).
cnf(c_0_2524_0,axiom,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2524]) ).
cnf(c_0_2524_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2524]) ).
cnf(c_0_2525_0,axiom,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2525]) ).
cnf(c_0_2525_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2525]) ).
cnf(c_0_2526_0,axiom,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2526]) ).
cnf(c_0_2526_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2526]) ).
cnf(c_0_2527_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2527]) ).
cnf(c_0_2527_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2527]) ).
cnf(c_0_2528_0,axiom,
( c_Polynomial_Odegree(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X1),X2,X1),X1) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2528]) ).
cnf(c_0_2528_1,axiom,
( ~ class_Ring__and__Field_Oidom(X1)
| c_Polynomial_Odegree(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X1),X2,X1),X1) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2528]) ).
cnf(c_0_2529_0,axiom,
( c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X2,X3),X3) = c_Polynomial_Odegree(X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2529]) ).
cnf(c_0_2529_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X2,X3),X3) = c_Polynomial_Odegree(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2529]) ).
cnf(c_0_2530_0,axiom,
( c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2) = c_Polynomial_Omonom(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2)
| ~ class_HOL_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2530]) ).
cnf(c_0_2530_1,axiom,
( ~ class_HOL_Ozero(X2)
| c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2) = c_Polynomial_Omonom(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2530]) ).
cnf(c_0_2531_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Polynomial_Odegree(c_Polynomial_Omonom(X1,X3,X2),X2) = X3
| ~ class_HOL_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2531]) ).
cnf(c_0_2531_1,axiom,
( c_Polynomial_Odegree(c_Polynomial_Omonom(X1,X3,X2),X2) = X3
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_HOL_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2531]) ).
cnf(c_0_2531_2,axiom,
( ~ class_HOL_Ozero(X2)
| c_Polynomial_Odegree(c_Polynomial_Omonom(X1,X3,X2),X2) = X3
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2531]) ).
cnf(c_0_2532_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| hAPP(c_Polynomial_Ocoeff(X1,X2),c_Polynomial_Odegree(X1,X2)) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_HOL_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2532]) ).
cnf(c_0_2532_1,axiom,
( hAPP(c_Polynomial_Ocoeff(X1,X2),c_Polynomial_Odegree(X1,X2)) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_HOL_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2532]) ).
cnf(c_0_2532_2,axiom,
( ~ class_HOL_Ozero(X2)
| hAPP(c_Polynomial_Ocoeff(X1,X2),c_Polynomial_Odegree(X1,X2)) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2532]) ).
cnf(c_0_2533_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Osmult(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2533]) ).
cnf(c_0_2533_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Polynomial_Osmult(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2533]) ).
cnf(c_0_2533_2,axiom,
( c_Polynomial_Osmult(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2533]) ).
cnf(c_0_2533_3,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| c_Polynomial_Osmult(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2533]) ).
cnf(c_0_2534_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2534]) ).
cnf(c_0_2534_1,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2534]) ).
cnf(c_0_2534_2,axiom,
( ~ class_Power_Opower(X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2534]) ).
cnf(c_0_2534_3,axiom,
( ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2534]) ).
cnf(c_0_2534_4,axiom,
( ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2534]) ).
cnf(c_0_2534_5,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2534]) ).
cnf(c_0_2535_0,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Power_Opower(X1)
| ~ class_Ring__and__Field_Omult__zero(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2535]) ).
cnf(c_0_2535_1,axiom,
( ~ class_Power_Opower(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Omult__zero(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2535]) ).
cnf(c_0_2535_2,axiom,
( ~ class_Ring__and__Field_Omult__zero(X1)
| ~ class_Power_Opower(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2535]) ).
cnf(c_0_2535_3,axiom,
( ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| ~ class_Ring__and__Field_Omult__zero(X1)
| ~ class_Power_Opower(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2535]) ).
cnf(c_0_2535_4,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| ~ class_Ring__and__Field_Omult__zero(X1)
| ~ class_Power_Opower(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2535]) ).
cnf(c_0_2536_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2536]) ).
cnf(c_0_2536_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2536]) ).
cnf(c_0_2537_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2537]) ).
cnf(c_0_2537_1,axiom,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2537]) ).
cnf(c_0_2537_2,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X2)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2537]) ).
cnf(c_0_2538_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_OpCons(X3,X1,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_HOL_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2538]) ).
cnf(c_0_2538_1,axiom,
( c_Polynomial_OpCons(X3,X1,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_HOL_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2538]) ).
cnf(c_0_2538_2,axiom,
( ~ class_HOL_Ozero(X2)
| c_Polynomial_OpCons(X3,X1,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2538]) ).
cnf(c_0_2539_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2539]) ).
cnf(c_0_2539_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2539]) ).
cnf(c_0_2539_2,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2539]) ).
cnf(c_0_2539_3,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2539]) ).
cnf(c_0_2540_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2540]) ).
cnf(c_0_2540_1,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2540]) ).
cnf(c_0_2540_2,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2540]) ).
cnf(c_0_2540_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2540]) ).
cnf(c_0_2541_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X2 = X1
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2541]) ).
cnf(c_0_2541_1,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X2 = X1
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2541]) ).
cnf(c_0_2541_2,axiom,
( X2 = X1
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2541]) ).
cnf(c_0_2541_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| X2 = X1
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2541]) ).
cnf(c_0_2542_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2542]) ).
cnf(c_0_2542_1,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2542]) ).
cnf(c_0_2542_2,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2542]) ).
cnf(c_0_2542_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2542]) ).
cnf(c_0_2543_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2543]) ).
cnf(c_0_2543_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2543]) ).
cnf(c_0_2543_2,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2543]) ).
cnf(c_0_2543_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2543]) ).
cnf(c_0_2544_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Oone__class_Oone(X2)),c_Nat_Osemiring__1__class_Oof__nat(X1,X2)) = c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X1),X2)
| ~ class_Ring__and__Field_Osemiring__1(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2544]) ).
cnf(c_0_2544_1,axiom,
( ~ class_Ring__and__Field_Osemiring__1(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Oone__class_Oone(X2)),c_Nat_Osemiring__1__class_Oof__nat(X1,X2)) = c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2544]) ).
cnf(c_0_2545_0,axiom,
( c_lessequals(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2545]) ).
cnf(c_0_2545_1,axiom,
( c_lessequals(X2,X1,X3)
| c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2545]) ).
cnf(c_0_2545_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X2,X1,X3)
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2545]) ).
cnf(c_0_2546_0,axiom,
( c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2546]) ).
cnf(c_0_2546_1,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2546]) ).
cnf(c_0_2546_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2546]) ).
cnf(c_0_2547_0,axiom,
( c_lessequals(X1,X1,X2)
| c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2547]) ).
cnf(c_0_2547_1,axiom,
( c_HOL_Oord__class_Oless(X1,X1,X2)
| c_lessequals(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2547]) ).
cnf(c_0_2547_2,axiom,
( ~ class_Orderings_Olinorder(X2)
| c_HOL_Oord__class_Oless(X1,X1,X2)
| c_lessequals(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2547]) ).
cnf(c_0_2548_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2548]) ).
cnf(c_0_2548_1,axiom,
( c_lessequals(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2548]) ).
cnf(c_0_2548_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2548]) ).
cnf(c_0_2549_0,axiom,
( c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2549]) ).
cnf(c_0_2549_1,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2549]) ).
cnf(c_0_2549_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2549]) ).
cnf(c_0_2550_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2550]) ).
cnf(c_0_2550_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X2) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2550]) ).
cnf(c_0_2551_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2551]) ).
cnf(c_0_2551_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X2) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2551]) ).
cnf(c_0_2552_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2552]) ).
cnf(c_0_2552_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X2) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2552]) ).
cnf(c_0_2553_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Polynomial_Omonom(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_HOL_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2553]) ).
cnf(c_0_2553_1,axiom,
( c_Polynomial_Omonom(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_HOL_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2553]) ).
cnf(c_0_2553_2,axiom,
( ~ class_HOL_Ozero(X2)
| c_Polynomial_Omonom(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2553]) ).
cnf(c_0_2554_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Polynomial_OpCons(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_HOL_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2554]) ).
cnf(c_0_2554_1,axiom,
( c_Polynomial_OpCons(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_HOL_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2554]) ).
cnf(c_0_2554_2,axiom,
( ~ class_HOL_Ozero(X2)
| c_Polynomial_OpCons(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2554]) ).
cnf(c_0_2555_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2555]) ).
cnf(c_0_2555_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2555]) ).
cnf(c_0_2556_0,axiom,
( ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2556]) ).
cnf(c_0_2556_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2556]) ).
cnf(c_0_2557_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2557]) ).
cnf(c_0_2557_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2557]) ).
cnf(c_0_2558_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2558]) ).
cnf(c_0_2558_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2558]) ).
cnf(c_0_2559_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2559]) ).
cnf(c_0_2559_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2559]) ).
cnf(c_0_2560_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2560]) ).
cnf(c_0_2560_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2560]) ).
cnf(c_0_2561_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2561]) ).
cnf(c_0_2561_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2561]) ).
cnf(c_0_2562_0,axiom,
( c_HOL_Ouminus__class_Ouminus(X1,X2) = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2562]) ).
cnf(c_0_2562_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Ouminus__class_Ouminus(X1,X2) = X3
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2562]) ).
cnf(c_0_2562_2,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Ouminus__class_Ouminus(X1,X2) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2562]) ).
cnf(c_0_2563_0,axiom,
( X1 = c_HOL_Ouminus__class_Ouminus(X2,X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X2) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2563]) ).
cnf(c_0_2563_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X2) != c_HOL_Ozero__class_Ozero(X3)
| X1 = c_HOL_Ouminus__class_Ouminus(X2,X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2563]) ).
cnf(c_0_2563_2,axiom,
( ~ class_OrderedGroup_Ogroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X2) != c_HOL_Ozero__class_Ozero(X3)
| X1 = c_HOL_Ouminus__class_Ouminus(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2563]) ).
cnf(c_0_2564_0,axiom,
( hAPP(X1,X2) = hAPP(X1,X3)
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X1,t_a,t_b) ),
inference(literals_permutation,[status(thm)],[c_0_2564]) ).
cnf(c_0_2564_1,axiom,
( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X1,t_a,t_b)
| hAPP(X1,X2) = hAPP(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2564]) ).
cnf(c_0_2565_0,axiom,
( c_Polynomial_Oorder(X1,X2,X3) = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(c_Polynomial_Opoly(X2,X3),X1) = c_HOL_Ozero__class_Ozero(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2565]) ).
cnf(c_0_2565_1,axiom,
( hAPP(c_Polynomial_Opoly(X2,X3),X1) = c_HOL_Ozero__class_Ozero(X3)
| c_Polynomial_Oorder(X1,X2,X3) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2565]) ).
cnf(c_0_2565_2,axiom,
( ~ class_Ring__and__Field_Oidom(X3)
| hAPP(c_Polynomial_Opoly(X2,X3),X1) = c_HOL_Ozero__class_Ozero(X3)
| c_Polynomial_Oorder(X1,X2,X3) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2565]) ).
cnf(c_0_2566_0,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| c_lessequals(X2,X1,tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_2566]) ).
cnf(c_0_2566_1,axiom,
( c_lessequals(X2,X1,tc_RealDef_Oreal)
| c_lessequals(X1,X2,tc_RealDef_Oreal) ),
inference(literals_permutation,[status(thm)],[c_0_2566]) ).
cnf(c_0_2567_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2567]) ).
cnf(c_0_2567_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2567]) ).
cnf(c_0_2567_2,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2567]) ).
cnf(c_0_2567_3,axiom,
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X2)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2567]) ).
cnf(c_0_2568_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2568]) ).
cnf(c_0_2568_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2568]) ).
cnf(c_0_2568_2,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2568]) ).
cnf(c_0_2568_3,axiom,
( ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2568]) ).
cnf(c_0_2569_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X1) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2569]) ).
cnf(c_0_2569_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X1) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2569]) ).
cnf(c_0_2569_2,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X1) != c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2569]) ).
cnf(c_0_2569_3,axiom,
( ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X1) != c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2569]) ).
cnf(c_0_2570_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != X3
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2570]) ).
cnf(c_0_2570_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != X3
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2570]) ).
cnf(c_0_2570_2,axiom,
( ~ class_Int_Onumber__ring(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != X3
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2570]) ).
cnf(c_0_2570_3,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != X3
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2570]) ).
cnf(c_0_2571_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),X2),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2571]) ).
cnf(c_0_2571_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),X2),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2571]) ).
cnf(c_0_2572_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2572]) ).
cnf(c_0_2572_1,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2572]) ).
cnf(c_0_2572_2,axiom,
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2572]) ).
cnf(c_0_2573_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2573]) ).
cnf(c_0_2573_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2573]) ).
cnf(c_0_2573_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2573]) ).
cnf(c_0_2574_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_HOL_Ozero__class_Ozero(X2)),X1) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2574]) ).
cnf(c_0_2574_1,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_HOL_Ozero__class_Ozero(X2)),X1) = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2574]) ).
cnf(c_0_2574_2,axiom,
( ~ class_Power_Opower(X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_HOL_Ozero__class_Ozero(X2)),X1) = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2574]) ).
cnf(c_0_2574_3,axiom,
( ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_HOL_Ozero__class_Ozero(X2)),X1) = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2574]) ).
cnf(c_0_2574_4,axiom,
( ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_HOL_Ozero__class_Ozero(X2)),X1) = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2574]) ).
cnf(c_0_2574_5,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_HOL_Ozero__class_Ozero(X2)),X1) = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2574]) ).
cnf(c_0_2575_0,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_2575]) ).
cnf(c_0_2575_1,axiom,
( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_2575]) ).
cnf(c_0_2575_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_2575]) ).
cnf(c_0_2576_0,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_2576]) ).
cnf(c_0_2576_1,axiom,
( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_2576]) ).
cnf(c_0_2576_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_2576]) ).
cnf(c_0_2577_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Opoly(X1,X2) != c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2)
| ~ class_Int_Oring__char__0(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2577]) ).
cnf(c_0_2577_1,axiom,
( c_Polynomial_Opoly(X1,X2) != c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Int_Oring__char__0(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2577]) ).
cnf(c_0_2577_2,axiom,
( ~ class_Int_Oring__char__0(X2)
| c_Polynomial_Opoly(X1,X2) != c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2577]) ).
cnf(c_0_2577_3,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Oring__char__0(X2)
| c_Polynomial_Opoly(X1,X2) != c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2577]) ).
cnf(c_0_2578_0,axiom,
( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_HOL_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2578]) ).
cnf(c_0_2578_1,axiom,
( ~ class_HOL_Ozero(X1)
| c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2578]) ).
cnf(c_0_2579_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_2579]) ).
cnf(c_0_2579_1,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_2579]) ).
cnf(c_0_2579_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2579]) ).
cnf(c_0_2580_0,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_2580]) ).
cnf(c_0_2580_1,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_2580]) ).
cnf(c_0_2580_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_2580]) ).
cnf(c_0_2581_0,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_2581]) ).
cnf(c_0_2581_1,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_2581]) ).
cnf(c_0_2581_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_2581]) ).
cnf(c_0_2582_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_2582]) ).
cnf(c_0_2582_1,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_2582]) ).
cnf(c_0_2582_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2582]) ).
cnf(c_0_2583_0,axiom,
( hAPP(c_Polynomial_Opoly(v_pa____,tc_Complex_Ocomplex),v_sko__unknown__thm__rrS__1(v_pa____)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(v_pa____,tc_Complex_Ocomplex),v_c____) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_2583]) ).
cnf(c_0_2583_1,axiom,
( hAPP(c_Polynomial_Opoly(v_pa____,tc_Complex_Ocomplex),v_c____) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(v_pa____,tc_Complex_Ocomplex),v_sko__unknown__thm__rrS__1(v_pa____)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_2583]) ).
cnf(c_0_2584_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2584]) ).
cnf(c_0_2584_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2584]) ).
cnf(c_0_2585_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2585]) ).
cnf(c_0_2585_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2585]) ).
cnf(c_0_2586_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2586]) ).
cnf(c_0_2586_1,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2586]) ).
cnf(c_0_2587_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2587]) ).
cnf(c_0_2587_1,axiom,
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2587]) ).
cnf(c_0_2588_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2588]) ).
cnf(c_0_2588_1,axiom,
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2588]) ).
cnf(c_0_2589_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_2589]) ).
cnf(c_0_2589_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_2589]) ).
cnf(c_0_2589_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2589]) ).
cnf(c_0_2590_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_2590]) ).
cnf(c_0_2590_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_2590]) ).
cnf(c_0_2590_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2590]) ).
cnf(c_0_2591_0,axiom,
( c_Polynomial_Osmult(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2591]) ).
cnf(c_0_2591_1,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| c_Polynomial_Osmult(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2591]) ).
cnf(c_0_2592_0,axiom,
( c_Polynomial_Osmult(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2592]) ).
cnf(c_0_2592_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X2)
| c_Polynomial_Osmult(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2592]) ).
cnf(c_0_2593_0,axiom,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2593]) ).
cnf(c_0_2593_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2593]) ).
cnf(c_0_2594_0,axiom,
( c_Polynomial_Opcompose(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2594]) ).
cnf(c_0_2594_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| c_Polynomial_Opcompose(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2594]) ).
cnf(c_0_2595_0,axiom,
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X1,t_a),t_a,t_a)
| v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1(X1) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oidom(t_a) ),
inference(literals_permutation,[status(thm)],[c_0_2595]) ).
cnf(c_0_2595_1,axiom,
( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1(X1) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X1,t_a),t_a,t_a)
| ~ class_Ring__and__Field_Oidom(t_a) ),
inference(literals_permutation,[status(thm)],[c_0_2595]) ).
cnf(c_0_2595_2,axiom,
( ~ class_Ring__and__Field_Oidom(t_a)
| v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1(X1) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X1,t_a),t_a,t_a) ),
inference(literals_permutation,[status(thm)],[c_0_2595]) ).
cnf(c_0_2596_0,axiom,
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X1,t_a),t_a,t_a)
| v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__2(X1) != c_HOL_Ozero__class_Ozero(t_a)
| ~ class_Ring__and__Field_Oidom(t_a) ),
inference(literals_permutation,[status(thm)],[c_0_2596]) ).
cnf(c_0_2596_1,axiom,
( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__2(X1) != c_HOL_Ozero__class_Ozero(t_a)
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X1,t_a),t_a,t_a)
| ~ class_Ring__and__Field_Oidom(t_a) ),
inference(literals_permutation,[status(thm)],[c_0_2596]) ).
cnf(c_0_2596_2,axiom,
( ~ class_Ring__and__Field_Oidom(t_a)
| v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__2(X1) != c_HOL_Ozero__class_Ozero(t_a)
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X1,t_a),t_a,t_a) ),
inference(literals_permutation,[status(thm)],[c_0_2596]) ).
cnf(c_0_2597_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ouminus__class_Ouminus(X2,X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2597]) ).
cnf(c_0_2597_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ouminus__class_Ouminus(X2,X1)) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2597]) ).
cnf(c_0_2598_0,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_HOL_Ozero__class_Ozero(X1)),c_Suc(X2)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Power_Opower(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2598]) ).
cnf(c_0_2598_1,axiom,
( ~ class_Power_Opower(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_HOL_Ozero__class_Ozero(X1)),c_Suc(X2)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2598]) ).
cnf(c_0_2598_2,axiom,
( ~ class_Ring__and__Field_Osemiring__0(X1)
| ~ class_Power_Opower(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_HOL_Ozero__class_Ozero(X1)),c_Suc(X2)) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2598]) ).
cnf(c_0_2599_0,axiom,
( hAPP(c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_HOL_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2599]) ).
cnf(c_0_2599_1,axiom,
( ~ class_HOL_Ozero(X1)
| hAPP(c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X2) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2599]) ).
cnf(c_0_2600_0,axiom,
( hAPP(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2600]) ).
cnf(c_0_2600_1,axiom,
( ~ class_Ring__and__Field_Oidom(X1)
| hAPP(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X2) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2600]) ).
cnf(c_0_2601_0,axiom,
( hAPP(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2601]) ).
cnf(c_0_2601_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| hAPP(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X2) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2601]) ).
cnf(c_0_2602_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_HOL_Ozero__class_Ozero(X2)),X1) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Osemiring__0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2602]) ).
cnf(c_0_2602_1,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_HOL_Ozero__class_Ozero(X2)),X1) = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Osemiring__0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2602]) ).
cnf(c_0_2602_2,axiom,
( ~ class_Power_Opower(X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_HOL_Ozero__class_Ozero(X2)),X1) = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Osemiring__0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2602]) ).
cnf(c_0_2602_3,axiom,
( ~ class_Ring__and__Field_Osemiring__0(X2)
| ~ class_Power_Opower(X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_HOL_Ozero__class_Ozero(X2)),X1) = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2602]) ).
cnf(c_0_2603_0,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(X1)
| ~ class_Power_Opower(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2603]) ).
cnf(c_0_2603_1,axiom,
( ~ class_Power_Opower(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2603]) ).
cnf(c_0_2603_2,axiom,
( ~ class_Ring__and__Field_Osemiring__0(X1)
| ~ class_Power_Opower(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2603]) ).
cnf(c_0_2604_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2604]) ).
cnf(c_0_2604_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2604]) ).
cnf(c_0_2605_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2605]) ).
cnf(c_0_2605_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2605]) ).
cnf(c_0_2606_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2606]) ).
cnf(c_0_2606_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2606]) ).
cnf(c_0_2607_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2607]) ).
cnf(c_0_2607_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != X2
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2607]) ).
cnf(c_0_2608_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2608]) ).
cnf(c_0_2608_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != X2
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2608]) ).
cnf(c_0_2609_0,axiom,
( c_Power_Opower_Opower(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X1),X1) = c_Power_Opower__class_Opower(X1)
| ~ class_Power_Opower(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2609]) ).
cnf(c_0_2609_1,axiom,
( ~ class_Power_Opower(X1)
| c_Power_Opower_Opower(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X1),X1) = c_Power_Opower__class_Opower(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2609]) ).
cnf(c_0_2610_0,axiom,
( c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_HOL_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2610]) ).
cnf(c_0_2610_1,axiom,
( ~ class_HOL_Ozero(X1)
| c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2610]) ).
cnf(c_0_2611_0,axiom,
( c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2611]) ).
cnf(c_0_2611_1,axiom,
( ~ class_Ring__and__Field_Oidom(X1)
| c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2611]) ).
cnf(c_0_2612_0,axiom,
( c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2612]) ).
cnf(c_0_2612_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2612]) ).
cnf(c_0_2613_0,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_HOL_Oone__class_Oone(X1)),X2) = c_HOL_Oone__class_Oone(X1)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2613]) ).
cnf(c_0_2613_1,axiom,
( ~ class_OrderedGroup_Omonoid__mult(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_HOL_Oone__class_Oone(X1)),X2) = c_HOL_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2613]) ).
cnf(c_0_2614_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2614]) ).
cnf(c_0_2614_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2614]) ).
cnf(c_0_2615_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2615]) ).
cnf(c_0_2615_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2615]) ).
cnf(c_0_2616_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2616]) ).
cnf(c_0_2616_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2616]) ).
cnf(c_0_2617_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2617]) ).
cnf(c_0_2617_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2617]) ).
cnf(c_0_2618_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Omult__zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2618]) ).
cnf(c_0_2618_1,axiom,
( ~ class_Ring__and__Field_Omult__zero(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2618]) ).
cnf(c_0_2619_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2619]) ).
cnf(c_0_2619_1,axiom,
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2619]) ).
cnf(c_0_2620_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2620]) ).
cnf(c_0_2620_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2620]) ).
cnf(c_0_2621_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2621]) ).
cnf(c_0_2621_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2621]) ).
cnf(c_0_2622_0,axiom,
( c_OrderedGroup_Ocomm__monoid__add__axioms(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2622]) ).
cnf(c_0_2622_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_OrderedGroup_Ocomm__monoid__add__axioms(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2622]) ).
cnf(c_0_2623_0,axiom,
( c_OrderedGroup_Omonoid__add__axioms(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1)
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2623]) ).
cnf(c_0_2623_1,axiom,
( ~ class_OrderedGroup_Omonoid__add(X1)
| c_OrderedGroup_Omonoid__add__axioms(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2623]) ).
cnf(c_0_2624_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Ozero__class_Ozero(X2)) = X1
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2624]) ).
cnf(c_0_2624_1,axiom,
( ~ class_Int_Onumber__ring(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Ozero__class_Ozero(X2)) = X1
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2624]) ).
cnf(c_0_2624_2,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Ozero__class_Ozero(X2)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2624]) ).
cnf(c_0_2625_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Oone__class_Oone(X1)),X2) = X2
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2625]) ).
cnf(c_0_2625_1,axiom,
( ~ class_OrderedGroup_Omonoid__mult(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Oone__class_Oone(X1)),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2625]) ).
cnf(c_0_2626_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Oone__class_Oone(X1)),X2) = X2
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2626]) ).
cnf(c_0_2626_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Oone__class_Oone(X1)),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2626]) ).
cnf(c_0_2627_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Oone__class_Oone(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2627]) ).
cnf(c_0_2627_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Oone__class_Oone(X1)),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2627]) ).
cnf(c_0_2628_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Oone__class_Oone(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2628]) ).
cnf(c_0_2628_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Oone__class_Oone(X1)),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2628]) ).
cnf(c_0_2629_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2629]) ).
cnf(c_0_2629_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2629]) ).
cnf(c_0_2630_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2630]) ).
cnf(c_0_2630_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2630]) ).
cnf(c_0_2631_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2631]) ).
cnf(c_0_2631_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2631]) ).
cnf(c_0_2632_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2632]) ).
cnf(c_0_2632_1,axiom,
( ~ class_OrderedGroup_Omonoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2632]) ).
cnf(c_0_2633_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2633]) ).
cnf(c_0_2633_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2633]) ).
cnf(c_0_2634_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2634]) ).
cnf(c_0_2634_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2634]) ).
cnf(c_0_2635_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2635]) ).
cnf(c_0_2635_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2635]) ).
cnf(c_0_2636_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Omult__zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2636]) ).
cnf(c_0_2636_1,axiom,
( ~ class_Ring__and__Field_Omult__zero(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2636]) ).
cnf(c_0_2637_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2637]) ).
cnf(c_0_2637_1,axiom,
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2637]) ).
cnf(c_0_2638_0,axiom,
( c_Polynomial_Osmult(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2638]) ).
cnf(c_0_2638_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Polynomial_Osmult(c_HOL_Oone__class_Oone(X1),X2,X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2638]) ).
cnf(c_0_2639_0,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2639]) ).
cnf(c_0_2639_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2639]) ).
cnf(c_0_2640_0,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(X1)
| ~ class_Power_Opower(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2640]) ).
cnf(c_0_2640_1,axiom,
( ~ class_Power_Opower(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2640]) ).
cnf(c_0_2641_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Oone__class_Oone(X1)) = X2
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2641]) ).
cnf(c_0_2641_1,axiom,
( ~ class_OrderedGroup_Omonoid__mult(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Oone__class_Oone(X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2641]) ).
cnf(c_0_2642_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Oone__class_Oone(X1)) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2642]) ).
cnf(c_0_2642_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Oone__class_Oone(X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2642]) ).
cnf(c_0_2643_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2643]) ).
cnf(c_0_2643_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2643]) ).
cnf(c_0_2644_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2644]) ).
cnf(c_0_2644_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2644]) ).
cnf(c_0_2645_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2645]) ).
cnf(c_0_2645_1,axiom,
( ~ class_OrderedGroup_Omonoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2645]) ).
cnf(c_0_2646_0,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_HOL_Oone__class_Oone(tc_nat)) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2646]) ).
cnf(c_0_2646_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_HOL_Oone__class_Oone(tc_nat)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2646]) ).
cnf(c_0_2647_0,axiom,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_HOL_Oone__class_Oone(tc_nat)) = X2
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2647]) ).
cnf(c_0_2647_1,axiom,
( ~ class_OrderedGroup_Omonoid__mult(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_HOL_Oone__class_Oone(tc_nat)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2647]) ).
cnf(c_0_2648_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Suc(c_Polynomial_Odegree(X1,X2)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X2)
| ~ class_HOL_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2648]) ).
cnf(c_0_2648_1,axiom,
( c_Suc(c_Polynomial_Odegree(X1,X2)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_HOL_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2648]) ).
cnf(c_0_2648_2,axiom,
( ~ class_HOL_Ozero(X2)
| c_Suc(c_Polynomial_Odegree(X1,X2)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2648]) ).
cnf(c_0_2649_0,axiom,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2649]) ).
cnf(c_0_2649_1,axiom,
( ~ class_Orderings_Opreorder(X2)
| c_lessequals(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2649]) ).
cnf(c_0_2650_0,axiom,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2650]) ).
cnf(c_0_2650_1,axiom,
( ~ class_Orderings_Oorder(X2)
| c_lessequals(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2650]) ).
cnf(c_0_2651_0,axiom,
( c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = c_RealVector_Onorm__class_Onorm(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2651]) ).
cnf(c_0_2651_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(X2)
| c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = c_RealVector_Onorm__class_Onorm(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2651]) ).
cnf(c_0_2652_0,axiom,
( X1 = X2
| c_Polynomial_Opoly(X1,X3) != c_Polynomial_Opoly(X2,X3)
| ~ class_Int_Oring__char__0(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2652]) ).
cnf(c_0_2652_1,axiom,
( c_Polynomial_Opoly(X1,X3) != c_Polynomial_Opoly(X2,X3)
| X1 = X2
| ~ class_Int_Oring__char__0(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2652]) ).
cnf(c_0_2652_2,axiom,
( ~ class_Int_Oring__char__0(X3)
| c_Polynomial_Opoly(X1,X3) != c_Polynomial_Opoly(X2,X3)
| X1 = X2
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2652]) ).
cnf(c_0_2652_3,axiom,
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Oring__char__0(X3)
| c_Polynomial_Opoly(X1,X3) != c_Polynomial_Opoly(X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2652]) ).
cnf(c_0_2653_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2) = X2
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2653]) ).
cnf(c_0_2653_1,axiom,
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2653]) ).
cnf(c_0_2654_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(t_a)
| hAPP(c_Polynomial_Opoly(X2,t_a),X1) = c_HOL_Ozero__class_Ozero(t_a)
| v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2(X2) != c_HOL_Ozero__class_Ozero(t_a)
| ~ class_Ring__and__Field_Oidom(t_a) ),
inference(literals_permutation,[status(thm)],[c_0_2654]) ).
cnf(c_0_2654_1,axiom,
( hAPP(c_Polynomial_Opoly(X2,t_a),X1) = c_HOL_Ozero__class_Ozero(t_a)
| X1 = c_HOL_Ozero__class_Ozero(t_a)
| v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2(X2) != c_HOL_Ozero__class_Ozero(t_a)
| ~ class_Ring__and__Field_Oidom(t_a) ),
inference(literals_permutation,[status(thm)],[c_0_2654]) ).
cnf(c_0_2654_2,axiom,
( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2(X2) != c_HOL_Ozero__class_Ozero(t_a)
| hAPP(c_Polynomial_Opoly(X2,t_a),X1) = c_HOL_Ozero__class_Ozero(t_a)
| X1 = c_HOL_Ozero__class_Ozero(t_a)
| ~ class_Ring__and__Field_Oidom(t_a) ),
inference(literals_permutation,[status(thm)],[c_0_2654]) ).
cnf(c_0_2654_3,axiom,
( ~ class_Ring__and__Field_Oidom(t_a)
| v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2(X2) != c_HOL_Ozero__class_Ozero(t_a)
| hAPP(c_Polynomial_Opoly(X2,t_a),X1) = c_HOL_Ozero__class_Ozero(t_a)
| X1 = c_HOL_Ozero__class_Ozero(t_a) ),
inference(literals_permutation,[status(thm)],[c_0_2654]) ).
cnf(c_0_2655_0,axiom,
( X1 = X2
| c_Polynomial_Ocoeff(X1,X3) != c_Polynomial_Ocoeff(X2,X3)
| ~ class_HOL_Ozero(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2655]) ).
cnf(c_0_2655_1,axiom,
( c_Polynomial_Ocoeff(X1,X3) != c_Polynomial_Ocoeff(X2,X3)
| X1 = X2
| ~ class_HOL_Ozero(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2655]) ).
cnf(c_0_2655_2,axiom,
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Ocoeff(X1,X3) != c_Polynomial_Ocoeff(X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2655]) ).
cnf(c_0_2656_0,axiom,
( X1 = X2
| c_HOL_Ouminus__class_Ouminus(X1,X3) != c_HOL_Ouminus__class_Ouminus(X2,X3)
| ~ class_Lattices_Oboolean__algebra(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2656]) ).
cnf(c_0_2656_1,axiom,
( c_HOL_Ouminus__class_Ouminus(X1,X3) != c_HOL_Ouminus__class_Ouminus(X2,X3)
| X1 = X2
| ~ class_Lattices_Oboolean__algebra(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2656]) ).
cnf(c_0_2656_2,axiom,
( ~ class_Lattices_Oboolean__algebra(X3)
| c_HOL_Ouminus__class_Ouminus(X1,X3) != c_HOL_Ouminus__class_Ouminus(X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2656]) ).
cnf(c_0_2657_0,axiom,
( X1 = X2
| c_HOL_Ouminus__class_Ouminus(X1,X3) != c_HOL_Ouminus__class_Ouminus(X2,X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2657]) ).
cnf(c_0_2657_1,axiom,
( c_HOL_Ouminus__class_Ouminus(X1,X3) != c_HOL_Ouminus__class_Ouminus(X2,X3)
| X1 = X2
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2657]) ).
cnf(c_0_2657_2,axiom,
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(X1,X3) != c_HOL_Ouminus__class_Ouminus(X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2657]) ).
cnf(c_0_2658_0,axiom,
( X1 = X2
| c_Nat_Osemiring__1__class_Oof__nat(X1,X3) != c_Nat_Osemiring__1__class_Oof__nat(X2,X3)
| ~ class_Nat_Osemiring__char__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2658]) ).
cnf(c_0_2658_1,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(X1,X3) != c_Nat_Osemiring__1__class_Oof__nat(X2,X3)
| X1 = X2
| ~ class_Nat_Osemiring__char__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2658]) ).
cnf(c_0_2658_2,axiom,
( ~ class_Nat_Osemiring__char__0(X3)
| c_Nat_Osemiring__1__class_Oof__nat(X1,X3) != c_Nat_Osemiring__1__class_Oof__nat(X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2658]) ).
cnf(c_0_2659_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2659]) ).
cnf(c_0_2659_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2659]) ).
cnf(c_0_2660_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2660]) ).
cnf(c_0_2660_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2660]) ).
cnf(c_0_2661_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2661]) ).
cnf(c_0_2661_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2661]) ).
cnf(c_0_2662_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_Lattices_Oboolean__algebra(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2662]) ).
cnf(c_0_2662_1,axiom,
( ~ class_Lattices_Oboolean__algebra(X2)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2662]) ).
cnf(c_0_2663_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2663]) ).
cnf(c_0_2663_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2663]) ).
cnf(c_0_2664_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X2) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_HOL_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2664]) ).
cnf(c_0_2664_1,axiom,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X2) != c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_HOL_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2664]) ).
cnf(c_0_2664_2,axiom,
( ~ class_HOL_Ozero(X2)
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X2) != c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2664]) ).
cnf(c_0_2665_0,axiom,
( c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_HOL_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2665]) ).
cnf(c_0_2665_1,axiom,
( ~ class_HOL_Ozero(X1)
| c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2665]) ).
cnf(c_0_2666_0,axiom,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_HOL_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2666]) ).
cnf(c_0_2666_1,axiom,
( ~ class_HOL_Ozero(X1)
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2666]) ).
cnf(c_0_2667_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Ouminus__class_Ouminus(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2667]) ).
cnf(c_0_2667_1,axiom,
( c_HOL_Ouminus__class_Ouminus(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2667]) ).
cnf(c_0_2667_2,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ouminus__class_Ouminus(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2667]) ).
cnf(c_0_2668_0,axiom,
( c_HOL_Ozero__class_Ozero(X1) = X2
| c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2668]) ).
cnf(c_0_2668_1,axiom,
( c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ozero__class_Ozero(X1)
| c_HOL_Ozero__class_Ozero(X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2668]) ).
cnf(c_0_2668_2,axiom,
( ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ozero__class_Ozero(X1)
| c_HOL_Ozero__class_Ozero(X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2668]) ).
cnf(c_0_2669_0,axiom,
( class_Lattices_Oboolean__algebra(tc_fun(X2,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2669]) ).
cnf(c_0_2669_1,axiom,
( ~ class_Lattices_Oboolean__algebra(X1)
| class_Lattices_Oboolean__algebra(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2669]) ).
cnf(c_0_2670_0,axiom,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2670]) ).
cnf(c_0_2670_1,axiom,
( ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2670]) ).
cnf(c_0_2671_0,axiom,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2671]) ).
cnf(c_0_2671_1,axiom,
( ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2671]) ).
cnf(c_0_2672_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Ouminus__class_Ouminus(X1,X2) != X1
| ~ class_OrderedGroup_Oordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2672]) ).
cnf(c_0_2672_1,axiom,
( c_HOL_Ouminus__class_Ouminus(X1,X2) != X1
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Oordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2672]) ).
cnf(c_0_2672_2,axiom,
( ~ class_OrderedGroup_Oordered__ab__group__add(X2)
| c_HOL_Ouminus__class_Ouminus(X1,X2) != X1
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2672]) ).
cnf(c_0_2673_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2673]) ).
cnf(c_0_2673_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2673]) ).
cnf(c_0_2674_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2674]) ).
cnf(c_0_2674_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2674]) ).
cnf(c_0_2675_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2675]) ).
cnf(c_0_2675_1,axiom,
( ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2675]) ).
cnf(c_0_2676_0,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2676]) ).
cnf(c_0_2676_1,axiom,
( ~ class_Ring__and__Field_Osemiring__1(X1)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X1) = c_HOL_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2676]) ).
cnf(c_0_2677_0,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2677]) ).
cnf(c_0_2677_1,axiom,
( ~ class_Ring__and__Field_Osemiring__1(X1)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2677]) ).
cnf(c_0_2678_0,axiom,
( c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2678]) ).
cnf(c_0_2678_1,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2678]) ).
cnf(c_0_2679_0,axiom,
( c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2679]) ).
cnf(c_0_2679_1,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2679]) ).
cnf(c_0_2680_0,axiom,
( class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2680]) ).
cnf(c_0_2680_1,axiom,
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1)
| class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2680]) ).
cnf(c_0_2681_0,axiom,
( class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2681]) ).
cnf(c_0_2681_1,axiom,
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2681]) ).
cnf(c_0_2682_0,axiom,
( class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2682]) ).
cnf(c_0_2682_1,axiom,
( ~ class_Ring__and__Field_Ocomm__ring(X1)
| class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2682]) ).
cnf(c_0_2683_0,axiom,
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2683]) ).
cnf(c_0_2683_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2683]) ).
cnf(c_0_2684_0,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2684]) ).
cnf(c_0_2684_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2684]) ).
cnf(c_0_2685_0,axiom,
( class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2685]) ).
cnf(c_0_2685_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2685]) ).
cnf(c_0_2686_0,axiom,
( class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2686]) ).
cnf(c_0_2686_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2686]) ).
cnf(c_0_2687_0,axiom,
( class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2687]) ).
cnf(c_0_2687_1,axiom,
( ~ class_Ring__and__Field_Oidom(X1)
| class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2687]) ).
cnf(c_0_2688_0,axiom,
( class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2688]) ).
cnf(c_0_2688_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2688]) ).
cnf(c_0_2689_0,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2689]) ).
cnf(c_0_2689_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2689]) ).
cnf(c_0_2690_0,axiom,
( class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2690]) ).
cnf(c_0_2690_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2690]) ).
cnf(c_0_2691_0,axiom,
( class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2691]) ).
cnf(c_0_2691_1,axiom,
( ~ class_Ring__and__Field_Oidom(X1)
| class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2691]) ).
cnf(c_0_2692_0,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2692]) ).
cnf(c_0_2692_1,axiom,
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1)
| class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2692]) ).
cnf(c_0_2693_0,axiom,
( class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2693]) ).
cnf(c_0_2693_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2693]) ).
cnf(c_0_2694_0,axiom,
( class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2694]) ).
cnf(c_0_2694_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2694]) ).
cnf(c_0_2695_0,axiom,
( class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2695]) ).
cnf(c_0_2695_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2695]) ).
cnf(c_0_2696_0,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2696]) ).
cnf(c_0_2696_1,axiom,
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1)
| class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2696]) ).
cnf(c_0_2697_0,axiom,
( class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2697]) ).
cnf(c_0_2697_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2697]) ).
cnf(c_0_2698_0,axiom,
( class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2698]) ).
cnf(c_0_2698_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2698]) ).
cnf(c_0_2699_0,axiom,
( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2699]) ).
cnf(c_0_2699_1,axiom,
( ~ class_Ring__and__Field_Oidom(X1)
| class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2699]) ).
cnf(c_0_2700_0,axiom,
( class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2700]) ).
cnf(c_0_2700_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2700]) ).
cnf(c_0_2701_0,axiom,
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2701]) ).
cnf(c_0_2701_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2701]) ).
cnf(c_0_2702_0,axiom,
( class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2702]) ).
cnf(c_0_2702_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2702]) ).
cnf(c_0_2703_0,axiom,
( class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2703]) ).
cnf(c_0_2703_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2703]) ).
cnf(c_0_2704_0,axiom,
( class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2704]) ).
cnf(c_0_2704_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2704]) ).
cnf(c_0_2705_0,axiom,
( class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2705]) ).
cnf(c_0_2705_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2705]) ).
cnf(c_0_2706_0,axiom,
( class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2706]) ).
cnf(c_0_2706_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2706]) ).
cnf(c_0_2707_0,axiom,
( class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2707]) ).
cnf(c_0_2707_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2707]) ).
cnf(c_0_2708_0,axiom,
( class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2708]) ).
cnf(c_0_2708_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2708]) ).
cnf(c_0_2709_0,axiom,
( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2709]) ).
cnf(c_0_2709_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2709]) ).
cnf(c_0_2710_0,axiom,
( class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2710]) ).
cnf(c_0_2710_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2710]) ).
cnf(c_0_2711_0,axiom,
( class_OrderedGroup_Osemigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2711]) ).
cnf(c_0_2711_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| class_OrderedGroup_Osemigroup__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2711]) ).
cnf(c_0_2712_0,axiom,
( class_Ring__and__Field_Osemiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2712]) ).
cnf(c_0_2712_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| class_Ring__and__Field_Osemiring__1(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2712]) ).
cnf(c_0_2713_0,axiom,
( class_Ring__and__Field_Osemiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2713]) ).
cnf(c_0_2713_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| class_Ring__and__Field_Osemiring__0(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2713]) ).
cnf(c_0_2714_0,axiom,
( class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2714]) ).
cnf(c_0_2714_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2714]) ).
cnf(c_0_2715_0,axiom,
( class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2715]) ).
cnf(c_0_2715_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X1)
| class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2715]) ).
cnf(c_0_2716_0,axiom,
( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2716]) ).
cnf(c_0_2716_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2716]) ).
cnf(c_0_2717_0,axiom,
( class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2717]) ).
cnf(c_0_2717_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2717]) ).
cnf(c_0_2718_0,axiom,
( class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2718]) ).
cnf(c_0_2718_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2718]) ).
cnf(c_0_2719_0,axiom,
( class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2719]) ).
cnf(c_0_2719_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2719]) ).
cnf(c_0_2720_0,axiom,
( class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2720]) ).
cnf(c_0_2720_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2720]) ).
cnf(c_0_2721_0,axiom,
( class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2721]) ).
cnf(c_0_2721_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X1)
| class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2721]) ).
cnf(c_0_2722_0,axiom,
( class_Ring__and__Field_Oring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2722]) ).
cnf(c_0_2722_1,axiom,
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| class_Ring__and__Field_Oring__1(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2722]) ).
cnf(c_0_2723_0,axiom,
( class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2723]) ).
cnf(c_0_2723_1,axiom,
( ~ class_Ring__and__Field_Ocomm__ring(X1)
| class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2723]) ).
cnf(c_0_2724_0,axiom,
( class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2724]) ).
cnf(c_0_2724_1,axiom,
( ~ class_Ring__and__Field_Oidom(X1)
| class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2724]) ).
cnf(c_0_2725_0,axiom,
( class_Nat_Osemiring__char__0(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2725]) ).
cnf(c_0_2725_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Nat_Osemiring__char__0(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2725]) ).
cnf(c_0_2726_0,axiom,
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2726]) ).
cnf(c_0_2726_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Orderings_Opreorder(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2726]) ).
cnf(c_0_2727_0,axiom,
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2727]) ).
cnf(c_0_2727_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Orderings_Olinorder(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2727]) ).
cnf(c_0_2728_0,axiom,
( class_Orderings_Oorder(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2728]) ).
cnf(c_0_2728_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Orderings_Oorder(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2728]) ).
cnf(c_0_2729_0,axiom,
( class_Int_Oring__char__0(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2729]) ).
cnf(c_0_2729_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Int_Oring__char__0(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2729]) ).
cnf(c_0_2730_0,axiom,
( class_Int_Onumber__ring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2730]) ).
cnf(c_0_2730_1,axiom,
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| class_Int_Onumber__ring(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2730]) ).
cnf(c_0_2731_0,axiom,
( class_Power_Opower(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2731]) ).
cnf(c_0_2731_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| class_Power_Opower(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2731]) ).
cnf(c_0_2732_0,axiom,
( class_HOL_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_HOL_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2732]) ).
cnf(c_0_2732_1,axiom,
( ~ class_HOL_Ozero(X1)
| class_HOL_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2732]) ).
cnf(c_0_2733_0,axiom,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2733]) ).
cnf(c_0_2733_1,axiom,
( c_Suc(X1) != c_Suc(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2733]) ).
cnf(c_0_2734_0,axiom,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2734]) ).
cnf(c_0_2734_1,axiom,
( c_Suc(X1) != c_Suc(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2734]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_826,negated_conjecture,
c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(v_q____,tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex),
file('<stdin>',cls_conjecture_0) ).
fof(c_0_1_827,negated_conjecture,
c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(v_q____,tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex),
c_0_0 ).
fof(c_0_2_828,negated_conjecture,
c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(v_q____,tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex),
c_0_1 ).
cnf(c_0_3_829,negated_conjecture,
c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(v_q____,tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4_830,negated_conjecture,
c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(v_q____,tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex),
c_0_3,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_1564,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(v_q____,tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex),
file('/export/starexec/sandbox/tmp/iprover_modulo_3ae58a.p',c_0_813_0) ).
cnf(c_1718,negated_conjecture,
c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(v_q____,tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex),
file('/export/starexec/sandbox/tmp/iprover_modulo_3ae58a.p',c_0_4) ).
cnf(contradiction,plain,
$false,
inference(minisat,[status(thm)],[c_1564,c_1718]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG397-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : iprover_modulo %s %d
% 0.13/0.33 % Computer : n018.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 9 05:27:23 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 % Running in mono-core mode
% 0.20/0.48 % Orienting using strategy Equiv(ClausalAll)
% 0.20/0.48 % Orientation found
% 0.20/0.48 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_94d456.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_3ae58a.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_7eef93 | grep -v "SZS"
% 0.20/0.50
% 0.20/0.50 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.20/0.50
% 0.20/0.50 %
% 0.20/0.50 % ------ iProver source info
% 0.20/0.50
% 0.20/0.50 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.20/0.50 % git: non_committed_changes: true
% 0.20/0.50 % git: last_make_outside_of_git: true
% 0.20/0.50
% 0.20/0.50 %
% 0.20/0.50 % ------ Input Options
% 0.20/0.50
% 0.20/0.50 % --out_options all
% 0.20/0.50 % --tptp_safe_out true
% 0.20/0.50 % --problem_path ""
% 0.20/0.50 % --include_path ""
% 0.20/0.50 % --clausifier .//eprover
% 0.20/0.50 % --clausifier_options --tstp-format
% 0.20/0.50 % --stdin false
% 0.20/0.50 % --dbg_backtrace false
% 0.20/0.50 % --dbg_dump_prop_clauses false
% 0.20/0.50 % --dbg_dump_prop_clauses_file -
% 0.20/0.50 % --dbg_out_stat false
% 0.20/0.50
% 0.20/0.50 % ------ General Options
% 0.20/0.50
% 0.20/0.50 % --fof false
% 0.20/0.50 % --time_out_real 150.
% 0.20/0.50 % --time_out_prep_mult 0.2
% 0.20/0.50 % --time_out_virtual -1.
% 0.20/0.50 % --schedule none
% 0.20/0.50 % --ground_splitting input
% 0.20/0.50 % --splitting_nvd 16
% 0.20/0.50 % --non_eq_to_eq false
% 0.20/0.50 % --prep_gs_sim true
% 0.20/0.50 % --prep_unflatten false
% 0.20/0.50 % --prep_res_sim true
% 0.20/0.50 % --prep_upred true
% 0.20/0.50 % --res_sim_input true
% 0.20/0.50 % --clause_weak_htbl true
% 0.20/0.50 % --gc_record_bc_elim false
% 0.20/0.50 % --symbol_type_check false
% 0.20/0.50 % --clausify_out false
% 0.20/0.50 % --large_theory_mode false
% 0.20/0.50 % --prep_sem_filter none
% 0.20/0.50 % --prep_sem_filter_out false
% 0.20/0.50 % --preprocessed_out false
% 0.20/0.50 % --sub_typing false
% 0.20/0.50 % --brand_transform false
% 0.20/0.50 % --pure_diseq_elim true
% 0.20/0.50 % --min_unsat_core false
% 0.20/0.50 % --pred_elim true
% 0.20/0.50 % --add_important_lit false
% 0.20/0.50 % --soft_assumptions false
% 0.20/0.50 % --reset_solvers false
% 0.20/0.50 % --bc_imp_inh []
% 0.20/0.50 % --conj_cone_tolerance 1.5
% 0.20/0.50 % --prolific_symb_bound 500
% 0.20/0.50 % --lt_threshold 2000
% 0.20/0.50
% 0.20/0.50 % ------ SAT Options
% 0.20/0.50
% 0.20/0.50 % --sat_mode false
% 0.20/0.50 % --sat_fm_restart_options ""
% 0.20/0.50 % --sat_gr_def false
% 0.20/0.50 % --sat_epr_types true
% 0.20/0.50 % --sat_non_cyclic_types false
% 0.20/0.50 % --sat_finite_models false
% 0.20/0.50 % --sat_fm_lemmas false
% 0.20/0.50 % --sat_fm_prep false
% 0.20/0.50 % --sat_fm_uc_incr true
% 0.20/0.50 % --sat_out_model small
% 0.20/0.50 % --sat_out_clauses false
% 0.20/0.50
% 0.20/0.50 % ------ QBF Options
% 0.20/0.50
% 0.20/0.50 % --qbf_mode false
% 0.20/0.50 % --qbf_elim_univ true
% 0.20/0.50 % --qbf_sk_in true
% 0.20/0.50 % --qbf_pred_elim true
% 0.20/0.50 % --qbf_split 32
% 0.20/0.50
% 0.20/0.50 % ------ BMC1 Options
% 0.20/0.50
% 0.20/0.50 % --bmc1_incremental false
% 0.20/0.50 % --bmc1_axioms reachable_all
% 0.20/0.50 % --bmc1_min_bound 0
% 0.20/0.50 % --bmc1_max_bound -1
% 0.20/0.50 % --bmc1_max_bound_default -1
% 0.20/0.50 % --bmc1_symbol_reachability true
% 0.20/0.50 % --bmc1_property_lemmas false
% 0.20/0.50 % --bmc1_k_induction false
% 0.20/0.50 % --bmc1_non_equiv_states false
% 0.20/0.50 % --bmc1_deadlock false
% 0.20/0.50 % --bmc1_ucm false
% 0.20/0.50 % --bmc1_add_unsat_core none
% 0.20/0.50 % --bmc1_unsat_core_children false
% 0.20/0.50 % --bmc1_unsat_core_extrapolate_axioms false
% 0.20/0.50 % --bmc1_out_stat full
% 0.20/0.50 % --bmc1_ground_init false
% 0.20/0.50 % --bmc1_pre_inst_next_state false
% 0.20/0.50 % --bmc1_pre_inst_state false
% 0.20/0.50 % --bmc1_pre_inst_reach_state false
% 0.20/0.50 % --bmc1_out_unsat_core false
% 0.20/0.50 % --bmc1_aig_witness_out false
% 0.20/0.50 % --bmc1_verbose false
% 0.20/0.50 % --bmc1_dump_clauses_tptp false
% 0.20/0.56 % --bmc1_dump_unsat_core_tptp false
% 0.20/0.56 % --bmc1_dump_file -
% 0.20/0.56 % --bmc1_ucm_expand_uc_limit 128
% 0.20/0.56 % --bmc1_ucm_n_expand_iterations 6
% 0.20/0.56 % --bmc1_ucm_extend_mode 1
% 0.20/0.56 % --bmc1_ucm_init_mode 2
% 0.20/0.56 % --bmc1_ucm_cone_mode none
% 0.20/0.56 % --bmc1_ucm_reduced_relation_type 0
% 0.20/0.56 % --bmc1_ucm_relax_model 4
% 0.20/0.56 % --bmc1_ucm_full_tr_after_sat true
% 0.20/0.56 % --bmc1_ucm_expand_neg_assumptions false
% 0.20/0.56 % --bmc1_ucm_layered_model none
% 0.20/0.56 % --bmc1_ucm_max_lemma_size 10
% 0.20/0.56
% 0.20/0.56 % ------ AIG Options
% 0.20/0.56
% 0.20/0.56 % --aig_mode false
% 0.20/0.56
% 0.20/0.56 % ------ Instantiation Options
% 0.20/0.56
% 0.20/0.56 % --instantiation_flag true
% 0.20/0.56 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.20/0.56 % --inst_solver_per_active 750
% 0.20/0.56 % --inst_solver_calls_frac 0.5
% 0.20/0.56 % --inst_passive_queue_type priority_queues
% 0.20/0.56 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.20/0.56 % --inst_passive_queues_freq [25;2]
% 0.20/0.56 % --inst_dismatching true
% 0.20/0.56 % --inst_eager_unprocessed_to_passive true
% 0.20/0.56 % --inst_prop_sim_given true
% 0.20/0.56 % --inst_prop_sim_new false
% 0.20/0.56 % --inst_orphan_elimination true
% 0.20/0.56 % --inst_learning_loop_flag true
% 0.20/0.56 % --inst_learning_start 3000
% 0.20/0.56 % --inst_learning_factor 2
% 0.20/0.56 % --inst_start_prop_sim_after_learn 3
% 0.20/0.56 % --inst_sel_renew solver
% 0.20/0.56 % --inst_lit_activity_flag true
% 0.20/0.56 % --inst_out_proof true
% 0.20/0.56
% 0.20/0.56 % ------ Resolution Options
% 0.20/0.56
% 0.20/0.56 % --resolution_flag true
% 0.20/0.56 % --res_lit_sel kbo_max
% 0.20/0.56 % --res_to_prop_solver none
% 0.20/0.56 % --res_prop_simpl_new false
% 0.20/0.56 % --res_prop_simpl_given false
% 0.20/0.56 % --res_passive_queue_type priority_queues
% 0.20/0.56 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.20/0.56 % --res_passive_queues_freq [15;5]
% 0.20/0.56 % --res_forward_subs full
% 0.20/0.56 % --res_backward_subs full
% 0.20/0.56 % --res_forward_subs_resolution true
% 0.20/0.56 % --res_backward_subs_resolution true
% 0.20/0.56 % --res_orphan_elimination false
% 0.20/0.56 % --res_time_limit 1000.
% 0.20/0.56 % --res_out_proof true
% 0.20/0.56 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_94d456.s
% 0.20/0.56 % --modulo true
% 0.20/0.56
% 0.20/0.56 % ------ Combination Options
% 0.20/0.56
% 0.20/0.56 % --comb_res_mult 1000
% 0.20/0.56 % --comb_inst_mult 300
% 0.20/0.56 % ------
% 0.20/0.56
% 0.20/0.56 % ------ Parsing...% successful
% 0.20/0.56
% 0.20/0.56 %
% 0.20/0.56
% 0.20/0.56
% 0.20/0.56 % ------ Statistics
% 0.20/0.56
% 0.20/0.56 % ------ General
% 0.20/0.56
% 0.20/0.56 % num_of_input_clauses: 1719
% 0.20/0.56 % num_of_input_neg_conjectures: 1
% 0.20/0.56 % num_of_splits: 0
% 0.20/0.56 % num_of_split_atoms: 0
% 0.20/0.56 % num_of_sem_filtered_clauses: 0
% 0.20/0.56 % num_of_subtypes: 0
% 0.20/0.56 % monotx_restored_types: 0
% 0.20/0.56 % sat_num_of_epr_types: 0
% 0.20/0.56 % sat_num_of_non_cyclic_types: 0
% 0.20/0.56 % sat_guarded_non_collapsed_types: 0
% 0.20/0.56 % is_epr: 0
% 0.20/0.56 % is_horn: 0
% 0.20/0.56 % has_eq: 0
% 0.20/0.56 % num_pure_diseq_elim: 0
% 0.20/0.56 % simp_replaced_by: 0
% 0.20/0.56 % res_preprocessed: 0
% 0.20/0.56 % prep_upred: 0
% 0.20/0.56 % prep_unflattend: 0
% 0.20/0.56 % pred_elim_cands: 0
% 0.20/0.56 % pred_elim: 0
% 0.20/0.56 % pred_elim_cl: 0
% 0.20/0.56 % pred_elim_cycles: 0
% 0.20/0.56 % forced_gc_time: 0
% 0.20/0.56 % gc_basic_clause_elim: 0
% 0.20/0.56 % parsing_time: 0.055
% 0.20/0.56 % sem_filter_time: 0.
% 0.20/0.56 % pred_elim_time: 0.
% 0.20/0.56 % out_proof_time: 0.
% 0.20/0.56 % monotx_time: 0.
% 0.20/0.56 % subtype_inf_time: 0.
% 0.20/0.56 % unif_index_cands_time: 0.
% 0.20/0.56 % unif_index_add_time: 0.
% 0.20/0.56 % total_time: 0.069
% 0.20/0.56 % num_of_symbols: 132
% 0.20/0.56 % num_of_terms: 3062
% 0.20/0.56
% 0.20/0.56 % ------ Propositional Solver
% 0.20/0.56
% 0.20/0.56 % prop_solver_calls: 0
% 0.20/0.56 % prop_fast_solver_calls: 0
% 0.20/0.56 % prop_num_of_clauses: 175
% 0.20/0.56 % prop_preprocess_simplified: 5
% 0.20/0.56 % prop_fo_subsumed: 0
% 0.20/0.56 % prop_solver_time: 0.
% 0.20/0.56 % prop_fast_solver_time: 0.
% 0.20/0.56 % prop_unsat_core_time: 0.
% 0.20/0.56
% 0.20/0.56 % ------ QBF
% 0.20/0.56
% 0.20/0.56 % qbf_q_res: 0
% 0.20/0.56 % qbf_num_tautologies: 0
% 0.20/0.56 % qbf_prep_cycles: 0
% 0.20/0.56
% 0.20/0.56 % ------ BMC1
% 0.20/0.56
% 0.20/0.56 % bmc1_current_bound: -1
% 0.20/0.56 % bmc1_last_solved_bound: -1
% 0.20/0.56 % bmc1_unsat_core_size: -1
% 0.20/0.56 % bmc1_unsat_core_parents_size: -1
% 0.20/0.56 % bmc1_merge_next_fun: 0
% 0.20/0.56 % bmc1_unsat_core_clauses_time: 0.
% 0.20/0.56
% 0.20/0.56 % ------ Instantiation
% 0.20/0.56
% 0.20/0.56 % inst_num_of_clauses: undef
% 0.20/0.56 % inst_num_in_passive: undef
% 0.20/0.56 % inst_num_in_active: 0
% 0.20/0.56 % inst_num_in_unprocessed: 0
% 0.20/0.56 % inst_num_of_loops: 0
% 0.20/0.56 % inst_num_of_learning_restarts: 0
% 0.20/0.56 % inst_num_moves_active_passive: 0
% 0.20/0.56 % inst_lit_activity: 0
% 0.20/0.56 % inst_lit_activity_moves: 0
% 0.20/0.56 % inst_num_tautologies: 0
% 0.20/0.56 % inst_num_prop_implied: 0
% 0.20/0.56 % inst_num_existing_simplified: 0
% 0.20/0.56 % inst_num_eq_res_simplified: 0
% 0.20/0.56 % inst_num_child_elim: 0
% 0.20/0.56 % inst_num_of_dismatching_blockings: 0
% 0.20/0.56 % inst_num_of_non_proper_insts: 0
% 0.20/0.56 % inst_num_of_duplicates: 0
% 0.20/0.56 % inst_inst_num_from_inst_to_res: 0
% 0.20/0.56 % inst_dismatching_checking_time: 0.
% 0.20/0.56
% 0.20/0.56 % ------ Resolution
% 0.20/0.56
% 0.20/0.56 % res_num_of_clauses: undef
% 0.20/0.56 % res_num_in_passive: undef
% 0.20/0.56 % res_num_in_active: 0
% 0.20/0.56 % res_num_of_loops: 0
% 0.20/0.56 % res_forward_subset_subsumed: 0
% 0.20/0.56 % res_backward_subset_subsumed: 0
% 0.20/0.56 % res_forward_subsumed: 0
% 0.20/0.56 % res_backward_subsumed: 0
% 0.20/0.56 % res_forward_subsumption_resolution: 0
% 0.20/0.56 % res_backward_subsumption_resolution: 0
% 0.20/0.56 % res_clause_to_clause_subsumption: 0
% 0.20/0.56 % res_orphan_elimination: 0
% 0.20/0.56 % res_tautology_del: 0
% 0.20/0.56 % res_num_eq_res_simplified: 0
% 0.20/0.56 % res_num_sel_changes: 0
% 0.20/0.56 % res_moves_from_active_to_pass: 0
% 0.20/0.56
% 0.20/0.56 % Status Unsatisfiable
% 0.20/0.56 % SZS status Unsatisfiable
% 0.20/0.56 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------