%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : LCL836-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 12:22:20 PM UTC 2026
% Result : Unsatisfiable 30.01s 30.36s
% Output : CNFRefutation 30.11s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named inputERROR: Could not build tree for root to_be_clausified_0ERROR: MakeTreeStats fails)
% 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(hAPP(hAPP(c_fequal(T_a),V_x),V_x)),
input ).
fof(cls_ATP__Linkup_Oequal__imp__fequal_0_0,plain,
! [T_a,V_x] :
( hBOOL(hAPP(hAPP(c_fequal(T_a),V_x),V_x))
| $false ),
inference(orientation,[status(thm)],[cls_ATP__Linkup_Oequal__imp__fequal_0]) ).
cnf(clsarity_bool__Orderings_Obot,axiom,
class_Orderings_Obot(tc_bool),
input ).
fof(clsarity_bool__Orderings_Obot_0,plain,
( class_Orderings_Obot(tc_bool)
| $false ),
inference(orientation,[status(thm)],[clsarity_bool__Orderings_Obot]) ).
cnf(clsarity_bool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_bool),
input ).
fof(clsarity_bool__Orderings_Oorder_0,plain,
( class_Orderings_Oorder(tc_bool)
| $false ),
inference(orientation,[status(thm)],[clsarity_bool__Orderings_Oorder]) ).
cnf(clsarity_bool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_bool),
input ).
fof(clsarity_bool__Orderings_Opreorder_0,plain,
( class_Orderings_Opreorder(tc_bool)
| $false ),
inference(orientation,[status(thm)],[clsarity_bool__Orderings_Opreorder]) ).
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_Obot,axiom,
class_Orderings_Obot(tc_nat),
input ).
fof(clsarity_nat__Orderings_Obot_0,plain,
( class_Orderings_Obot(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Orderings_Obot]) ).
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_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_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__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__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__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__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(cls_CHAINED_0_02,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
input ).
fof(cls_CHAINED_0_02_0,plain,
( c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____)
| $false ),
inference(orientation,[status(thm)],[cls_CHAINED_0_02]) ).
cnf(cls_CHAINED_0_01,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
input ).
fof(cls_CHAINED_0_01_0,plain,
( hBOOL(hAPP(c_InductTermi_OIT,v_u____))
| $false ),
inference(orientation,[status(thm)],[cls_CHAINED_0_01]) ).
cnf(cls_CHAINED_0,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
input ).
fof(cls_CHAINED_0_0,plain,
( c_Type_Otyping(v_e____,v_u____,v_T____)
| $false ),
inference(orientation,[status(thm)],[cls_CHAINED_0]) ).
cnf(cls_uIT_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
input ).
fof(cls_uIT_0_0,plain,
( hBOOL(hAPP(c_InductTermi_OIT,v_u____))
| $false ),
inference(orientation,[status(thm)],[cls_uIT_0]) ).
cnf(cls_Beta_I1_J_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))),
input ).
fof(cls_Beta_I1_J_0_0,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)))
| $false ),
inference(orientation,[status(thm)],[cls_Beta_I1_J_0]) ).
cnf(cls_subst__App_0,axiom,
hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u)),V_s),V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_k)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_u),V_s),V_k)),
input ).
fof(cls_subst__App_0_0,plain,
! [V_k,V_s,V_t,V_u] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u)),V_s),V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_k)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_u),V_s),V_k))
| $false ),
inference(orientation,[status(thm)],[cls_subst__App_0]) ).
cnf(cls_Beta_I3_J_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_a____)),
input ).
fof(cls_Beta_I3_J_0_0,plain,
( hBOOL(hAPP(c_InductTermi_OIT,v_a____))
| $false ),
inference(orientation,[status(thm)],[cls_Beta_I3_J_0]) ).
cnf(cls_App__eq__foldl__conv_4,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
input ).
fof(cls_App__eq__foldl__conv_4_0,plain,
! [V_r,V_s] :
( hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
| $false ),
inference(orientation,[status(thm)],[cls_App__eq__foldl__conv_4]) ).
cnf(cls_substn__subst__0_0,axiom,
c_Lambda_Osubstn(V_t,V_s,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),c_HOL_Ozero__class_Ozero(tc_nat)),
input ).
fof(cls_substn__subst__0_0_0,plain,
! [V_s,V_t] :
( c_Lambda_Osubstn(V_t,V_s,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),c_HOL_Ozero__class_Ozero(tc_nat))
| $false ),
inference(orientation,[status(thm)],[cls_substn__subst__0_0]) ).
cnf(cls_T_0,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
input ).
fof(cls_T_0_0,plain,
( c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____)
| $false ),
inference(orientation,[status(thm)],[cls_T_0]) ).
cnf(cls_beta_0,axiom,
hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_s),V_t),c_HOL_Ozero__class_Ozero(tc_nat)))),
input ).
fof(cls_beta_0_0,plain,
! [V_s,V_t] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_s),V_t),c_HOL_Ozero__class_Ozero(tc_nat))))
| $false ),
inference(orientation,[status(thm)],[cls_beta_0]) ).
cnf(cls_Beta_I6_J_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_ua______)),
input ).
fof(cls_Beta_I6_J_0_0,plain,
( hBOOL(hAPP(c_InductTermi_OIT,v_ua______))
| $false ),
inference(orientation,[status(thm)],[cls_Beta_I6_J_0]) ).
cnf(cls_Var__IT_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(V_n))),
input ).
fof(cls_Var__IT_0_0,plain,
! [V_n] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(V_n)))
| $false ),
inference(orientation,[status(thm)],[cls_Var__IT_0]) ).
cnf(cls_subst__lift_0,axiom,
hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,V_t),V_k)),V_s),V_k) = V_t,
input ).
fof(cls_subst__lift_0_0,plain,
! [V_k,V_s,V_t] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,V_t),V_k)),V_s),V_k) = V_t
| $false ),
inference(orientation,[status(thm)],[cls_subst__lift_0]) ).
cnf(cls_subst__eq_0,axiom,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_k)),V_u),V_k) = V_u,
input ).
fof(cls_subst__eq_0_0,plain,
! [V_k,V_u] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_k)),V_u),V_k) = V_u
| $false ),
inference(orientation,[status(thm)],[cls_subst__eq_0]) ).
cnf(cls_subst__map_0,axiom,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_u),V_i) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,V_u,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
input ).
fof(cls_subst__map_0_0,plain,
! [V_i,V_t,V_ts,V_u] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_u),V_i) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,V_u,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
| $false ),
inference(orientation,[status(thm)],[cls_subst__map_0]) ).
cnf(cls_foldl__append_0,axiom,
c_List_Ofoldl(V_f,V_a,c_List_Oappend(V_xs,V_ys,T_b),T_a,T_b) = c_List_Ofoldl(V_f,c_List_Ofoldl(V_f,V_a,V_xs,T_a,T_b),V_ys,T_a,T_b),
input ).
fof(cls_foldl__append_0_0,plain,
! [T_a,T_b,V_a,V_f,V_xs,V_ys] :
( c_List_Ofoldl(V_f,V_a,c_List_Oappend(V_xs,V_ys,T_b),T_a,T_b) = c_List_Ofoldl(V_f,c_List_Ofoldl(V_f,V_a,V_xs,T_a,T_b),V_ys,T_a,T_b)
| $false ),
inference(orientation,[status(thm)],[cls_foldl__append_0]) ).
cnf(cls_foldl__Cons_0,axiom,
c_List_Ofoldl(V_f,V_a,c_List_Olist_OCons(V_x,V_xs,T_b),T_a,T_b) = c_List_Ofoldl(V_f,hAPP(hAPP(V_f,V_a),V_x),V_xs,T_a,T_b),
input ).
fof(cls_foldl__Cons_0_0,plain,
! [T_a,T_b,V_a,V_f,V_x,V_xs] :
( c_List_Ofoldl(V_f,V_a,c_List_Olist_OCons(V_x,V_xs,T_b),T_a,T_b) = c_List_Ofoldl(V_f,hAPP(hAPP(V_f,V_a),V_x),V_xs,T_a,T_b)
| $false ),
inference(orientation,[status(thm)],[cls_foldl__Cons_0]) ).
cnf(cls_foldl__Nil_0,axiom,
c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b) = V_a,
input ).
fof(cls_foldl__Nil_0_0,plain,
! [T_a,T_b,V_a,V_f] :
( c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b) = V_a
| $false ),
inference(orientation,[status(thm)],[cls_foldl__Nil_0]) ).
cnf(cls_Abs__App__neq__Var__apps_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ss,tc_Lambda_OdB,tc_Lambda_OdB),
input ).
fof(cls_Abs__App__neq__Var__apps_0_0,plain,
! [V_n,V_s,V_ss,V_t] :
( hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ss,tc_Lambda_OdB,tc_Lambda_OdB)
| $false ),
inference(orientation,[status(thm)],[cls_Abs__App__neq__Var__apps_0]) ).
cnf(cls_apps__eq__Abs__conv_2,axiom,
c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OAbs(V_r),
input ).
fof(cls_apps__eq__Abs__conv_2_0,plain,
! [V_r] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OAbs(V_r)
| $false ),
inference(orientation,[status(thm)],[cls_apps__eq__Abs__conv_2]) ).
cnf(cls_ex__head__tail_0,axiom,
V_t = c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2(V_t),c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1(V_t),tc_Lambda_OdB,tc_Lambda_OdB),
input ).
fof(cls_ex__head__tail_0_0,plain,
! [V_t] :
( V_t = c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2(V_t),c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1(V_t),tc_Lambda_OdB,tc_Lambda_OdB)
| $false ),
inference(orientation,[status(thm)],[cls_ex__head__tail_0]) ).
cnf(cls_Abs__eq__apps__conv_2,axiom,
c_Lambda_OdB_OAbs(V_r) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
input ).
fof(cls_Abs__eq__apps__conv_2_0,plain,
! [V_r] :
( c_Lambda_OdB_OAbs(V_r) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
| $false ),
inference(orientation,[status(thm)],[cls_Abs__eq__apps__conv_2]) ).
cnf(cls_Var__eq__apps__conv_2,axiom,
c_Lambda_OdB_OVar(V_m) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_m),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
input ).
fof(cls_Var__eq__apps__conv_2_0,plain,
! [V_m] :
( c_Lambda_OdB_OVar(V_m) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_m),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
| $false ),
inference(orientation,[status(thm)],[cls_Var__eq__apps__conv_2]) ).
cnf(cls_Var__apps__neq__Abs__apps_0,axiom,
c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ts,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),V_ss,tc_Lambda_OdB,tc_Lambda_OdB),
input ).
fof(cls_Var__apps__neq__Abs__apps_0_0,plain,
! [V_n,V_r,V_ss,V_ts] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ts,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),V_ss,tc_Lambda_OdB,tc_Lambda_OdB)
| $false ),
inference(orientation,[status(thm)],[cls_Var__apps__neq__Abs__apps_0]) ).
cnf(cls_substn__subst__n_0,axiom,
c_Lambda_Osubstn(V_t,V_s,V_n) = hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),c_Lambda_Oliftn(V_n,V_s,c_HOL_Ozero__class_Ozero(tc_nat))),V_n),
input ).
fof(cls_substn__subst__n_0_0,plain,
! [V_n,V_s,V_t] :
( c_Lambda_Osubstn(V_t,V_s,V_n) = hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),c_Lambda_Oliftn(V_n,V_s,c_HOL_Ozero__class_Ozero(tc_nat))),V_n)
| $false ),
inference(orientation,[status(thm)],[cls_substn__subst__n_0]) ).
cnf(cls_dB_Osimps_I5_J_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) != c_Lambda_OdB_OVar(V_nat),
input ).
fof(cls_dB_Osimps_I5_J_0_0,plain,
! [V_dB1_H,V_dB2_H,V_nat] :
( hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) != c_Lambda_OdB_OVar(V_nat)
| $false ),
inference(orientation,[status(thm)],[cls_dB_Osimps_I5_J_0]) ).
cnf(cls_substn_Osimps_I2_J_0,axiom,
c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_s,V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(V_t,V_s,V_k)),c_Lambda_Osubstn(V_u,V_s,V_k)),
input ).
fof(cls_substn_Osimps_I2_J_0_0,plain,
! [V_k,V_s,V_t,V_u] :
( c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_s,V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(V_t,V_s,V_k)),c_Lambda_Osubstn(V_u,V_s,V_k))
| $false ),
inference(orientation,[status(thm)],[cls_substn_Osimps_I2_J_0]) ).
cnf(cls_liftn_Osimps_I2_J_0,axiom,
c_Lambda_Oliftn(V_n,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(V_n,V_s,V_k)),c_Lambda_Oliftn(V_n,V_t,V_k)),
input ).
fof(cls_liftn_Osimps_I2_J_0_0,plain,
! [V_k,V_n,V_s,V_t] :
( c_Lambda_Oliftn(V_n,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(V_n,V_s,V_k)),c_Lambda_Oliftn(V_n,V_t,V_k))
| $false ),
inference(orientation,[status(thm)],[cls_liftn_Osimps_I2_J_0]) ).
cnf(cls_dB_Orecs_I2_J_0,axiom,
c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),T_a) = hAPP(hAPP(hAPP(hAPP(V_f2,V_dB1),V_dB2),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB1,T_a)),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB2,T_a)),
input ).
fof(cls_dB_Orecs_I2_J_0_0,plain,
! [T_a,V_dB1,V_dB2,V_f1,V_f2,V_f3] :
( c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),T_a) = hAPP(hAPP(hAPP(hAPP(V_f2,V_dB1),V_dB2),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB1,T_a)),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB2,T_a))
| $false ),
inference(orientation,[status(thm)],[cls_dB_Orecs_I2_J_0]) ).
cnf(cls_dB_Osimps_I11_J_0,axiom,
c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),T_a) = hAPP(hAPP(V_f2,V_dB1),V_dB2),
input ).
fof(cls_dB_Osimps_I11_J_0_0,plain,
! [T_a,V_dB1,V_dB2,V_f1,V_f2,V_f3] :
( c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),T_a) = hAPP(hAPP(V_f2,V_dB1),V_dB2)
| $false ),
inference(orientation,[status(thm)],[cls_dB_Osimps_I11_J_0]) ).
cnf(cls_lift_Osimps_I2_J_0,axiom,
hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,V_s),V_k)),hAPP(hAPP(c_Lambda_Olift,V_t),V_k)),
input ).
fof(cls_lift_Osimps_I2_J_0_0,plain,
! [V_k,V_s,V_t] :
( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,V_s),V_k)),hAPP(hAPP(c_Lambda_Olift,V_t),V_k))
| $false ),
inference(orientation,[status(thm)],[cls_lift_Osimps_I2_J_0]) ).
cnf(cls_dB_Osimps_I4_J_0,axiom,
c_Lambda_OdB_OVar(V_nat) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H),
input ).
fof(cls_dB_Osimps_I4_J_0_0,plain,
! [V_dB1_H,V_dB2_H,V_nat] :
( c_Lambda_OdB_OVar(V_nat) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H)
| $false ),
inference(orientation,[status(thm)],[cls_dB_Osimps_I4_J_0]) ).
cnf(cls_dB_Osimps_I9_J_0,axiom,
c_Lambda_OdB_OAbs(V_dB_H) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),
input ).
fof(cls_dB_Osimps_I9_J_0_0,plain,
! [V_dB1,V_dB2,V_dB_H] :
( c_Lambda_OdB_OAbs(V_dB_H) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2)
| $false ),
inference(orientation,[status(thm)],[cls_dB_Osimps_I9_J_0]) ).
cnf(cls_dB_Osimps_I8_J_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != c_Lambda_OdB_OAbs(V_dB_H),
input ).
fof(cls_dB_Osimps_I8_J_0_0,plain,
! [V_dB1,V_dB2,V_dB_H] :
( hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != c_Lambda_OdB_OAbs(V_dB_H)
| $false ),
inference(orientation,[status(thm)],[cls_dB_Osimps_I8_J_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_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_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_max__0L_0,axiom,
c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = V_n,
input ).
fof(cls_max__0L_0_0,plain,
! [V_n] :
( c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = V_n
| $false ),
inference(orientation,[status(thm)],[cls_max__0L_0]) ).
cnf(cls_max__0R_0,axiom,
c_Orderings_Oord__class_Omax(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_n,
input ).
fof(cls_max__0R_0_0,plain,
! [V_n] :
( c_Orderings_Oord__class_Omax(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_n
| $false ),
inference(orientation,[status(thm)],[cls_max__0R_0]) ).
cnf(cls_replicate__eq__replicate_2,axiom,
c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_y,T_a),
input ).
fof(cls_replicate__eq__replicate_2_0,plain,
! [T_a,V_x,V_y] :
( c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_y,T_a)
| c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_y,T_a) ),
inference(orientation,[status(thm)],[cls_replicate__eq__replicate_2]) ).
cnf(cls_size__char_0,axiom,
c_Nat_Osize__class_Osize(V_c,tc_String_Ochar) = c_HOL_Ozero__class_Ozero(tc_nat),
input ).
fof(cls_size__char_0_0,plain,
! [V_c] :
( c_Nat_Osize__class_Osize(V_c,tc_String_Ochar) = c_HOL_Ozero__class_Ozero(tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_size__char_0]) ).
cnf(cls_le0_0,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat),
input ).
fof(cls_le0_0_0,plain,
! [V_n] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_le0_0]) ).
cnf(cls_diff__0__eq__0_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
input ).
fof(cls_diff__0__eq__0_0_0,plain,
! [V_n] :
( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_diff__0__eq__0_0]) ).
cnf(cls_drop__0_0,axiom,
c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),V_xs,T_a) = V_xs,
input ).
fof(cls_drop__0_0_0,plain,
! [T_a,V_xs] :
( c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),V_xs,T_a) = V_xs
| $false ),
inference(orientation,[status(thm)],[cls_drop__0_0]) ).
cnf(cls_bot__nat__def_0,axiom,
c_Orderings_Obot__class_Obot(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
input ).
fof(cls_bot__nat__def_0_0,plain,
( c_Orderings_Obot__class_Obot(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_bot__nat__def_0]) ).
cnf(cls_not__less0_0,axiom,
~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
input ).
fof(cls_not__less0_0_0,plain,
! [V_n] :
( ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_not__less0_0]) ).
cnf(cls_gr__implies__not0_0,axiom,
~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
input ).
fof(cls_gr__implies__not0_0_0,plain,
! [V_m] :
( ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_gr__implies__not0_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_char__size_0,axiom,
c_String_Ochar_Ochar__size(V_c) = c_HOL_Ozero__class_Ozero(tc_nat),
input ).
fof(cls_char__size_0_0,plain,
! [V_c] :
( c_String_Ochar_Ochar__size(V_c) = c_HOL_Ozero__class_Ozero(tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_char__size_0]) ).
cnf(cls_nat_Osize_I1_J_0,axiom,
c_nat_Onat__size(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat),
input ).
fof(cls_nat_Osize_I1_J_0_0,plain,
( c_nat_Onat__size(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_nat_Osize_I1_J_0]) ).
cnf(cls_nat__gcd_Osimps_0,axiom,
c_Nitpick_Onat__gcd(V_x,c_HOL_Ozero__class_Ozero(tc_nat)) = V_x,
input ).
fof(cls_nat__gcd_Osimps_0_0,plain,
! [V_x] :
( c_Nitpick_Onat__gcd(V_x,c_HOL_Ozero__class_Ozero(tc_nat)) = V_x
| $false ),
inference(orientation,[status(thm)],[cls_nat__gcd_Osimps_0]) ).
cnf(cls_append__eq__append__conv2_5,axiom,
c_List_Oappend(V_xs,c_List_Oappend(V_x,V_ts,T_a),T_a) = c_List_Oappend(c_List_Oappend(V_xs,V_x,T_a),V_ts,T_a),
input ).
fof(cls_append__eq__append__conv2_5_0,plain,
! [T_a,V_ts,V_x,V_xs] :
( c_List_Oappend(V_xs,c_List_Oappend(V_x,V_ts,T_a),T_a) = c_List_Oappend(c_List_Oappend(V_xs,V_x,T_a),V_ts,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_append__eq__append__conv2_5]) ).
cnf(cls_append__eq__append__conv2_4,axiom,
c_List_Oappend(c_List_Oappend(V_zs,V_x,T_a),V_ys,T_a) = c_List_Oappend(V_zs,c_List_Oappend(V_x,V_ys,T_a),T_a),
input ).
fof(cls_append__eq__append__conv2_4_0,plain,
! [T_a,V_x,V_ys,V_zs] :
( c_List_Oappend(c_List_Oappend(V_zs,V_x,T_a),V_ys,T_a) = c_List_Oappend(V_zs,c_List_Oappend(V_x,V_ys,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_append__eq__append__conv2_4]) ).
cnf(cls_append__eq__appendI_0,axiom,
c_List_Oappend(V_xs,c_List_Oappend(V_xs1,V_us,T_a),T_a) = c_List_Oappend(c_List_Oappend(V_xs,V_xs1,T_a),V_us,T_a),
input ).
fof(cls_append__eq__appendI_0_0,plain,
! [T_a,V_us,V_xs,V_xs1] :
( c_List_Oappend(V_xs,c_List_Oappend(V_xs1,V_us,T_a),T_a) = c_List_Oappend(c_List_Oappend(V_xs,V_xs1,T_a),V_us,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_append__eq__appendI_0]) ).
cnf(cls_append__assoc_0,axiom,
c_List_Oappend(c_List_Oappend(V_xs,V_ys,T_a),V_zs,T_a) = c_List_Oappend(V_xs,c_List_Oappend(V_ys,V_zs,T_a),T_a),
input ).
fof(cls_append__assoc_0_0,plain,
! [T_a,V_xs,V_ys,V_zs] :
( c_List_Oappend(c_List_Oappend(V_xs,V_ys,T_a),V_zs,T_a) = c_List_Oappend(V_xs,c_List_Oappend(V_ys,V_zs,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_append__assoc_0]) ).
cnf(cls_append__is__Nil__conv_2,axiom,
c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a),
input ).
fof(cls_append__is__Nil__conv_2_0,plain,
! [T_a] :
( c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a)
| $false ),
inference(orientation,[status(thm)],[cls_append__is__Nil__conv_2]) ).
cnf(cls_uT_0,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
input ).
fof(cls_uT_0_0,plain,
( c_Type_Otyping(v_e____,v_u____,v_T____)
| $false ),
inference(orientation,[status(thm)],[cls_uT_0]) ).
cnf(cls_drop__map_0,axiom,
c_List_Odrop(V_n,c_List_Omap(V_f,V_xs,T_b,T_a),T_a) = c_List_Omap(V_f,c_List_Odrop(V_n,V_xs,T_b),T_b,T_a),
input ).
fof(cls_drop__map_0_0,plain,
! [T_a,T_b,V_f,V_n,V_xs] :
( c_List_Odrop(V_n,c_List_Omap(V_f,V_xs,T_b,T_a),T_a) = c_List_Omap(V_f,c_List_Odrop(V_n,V_xs,T_b),T_b,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_drop__map_0]) ).
cnf(cls_replicate__app__Cons__same_0,axiom,
c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),V_xs,T_a),T_a),
input ).
fof(cls_replicate__app__Cons__same_0_0,plain,
! [T_a,V_n,V_x,V_xs] :
( c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),V_xs,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_replicate__app__Cons__same_0]) ).
cnf(cls_dB_Osimps_I7_J_0,axiom,
c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat),
input ).
fof(cls_dB_Osimps_I7_J_0_0,plain,
! [V_dB_H,V_nat] :
( c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat)
| $false ),
inference(orientation,[status(thm)],[cls_dB_Osimps_I7_J_0]) ).
cnf(cls_eq__imp__le_0,axiom,
c_lessequals(V_x,V_x,tc_nat),
input ).
fof(cls_eq__imp__le_0_0,plain,
! [V_x] :
( c_lessequals(V_x,V_x,tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_eq__imp__le_0]) ).
cnf(cls_le__refl_0,axiom,
c_lessequals(V_n,V_n,tc_nat),
input ).
fof(cls_le__refl_0_0,plain,
! [V_n] :
( c_lessequals(V_n,V_n,tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_le__refl_0]) ).
cnf(cls_append__eq__Cons__conv_4,axiom,
c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,V_xs,T_a),
input ).
fof(cls_append__eq__Cons__conv_4_0,plain,
! [T_a,V_x,V_xs] :
( c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,V_xs,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_append__eq__Cons__conv_4]) ).
cnf(cls_not__add__less2_0,axiom,
~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_i),V_i,tc_nat),
input ).
fof(cls_not__add__less2_0_0,plain,
! [V_i,V_j] :
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_i),V_i,tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_not__add__less2_0]) ).
cnf(cls_not__add__less1_0,axiom,
~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_i,tc_nat),
input ).
fof(cls_not__add__less1_0_0,plain,
! [V_i,V_j] :
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_i,tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_not__add__less1_0]) ).
cnf(cls_conversep__conversep_0,axiom,
c_Predicate_Oconversep(c_Predicate_Oconversep(V_r,T_a,T_b),T_b,T_a) = V_r,
input ).
fof(cls_conversep__conversep_0_0,plain,
! [T_a,T_b,V_r] :
( c_Predicate_Oconversep(c_Predicate_Oconversep(V_r,T_a,T_b),T_b,T_a) = V_r
| $false ),
inference(orientation,[status(thm)],[cls_conversep__conversep_0]) ).
cnf(cls_foldr_Osimps_I2_J_0,axiom,
c_List_Ofoldr(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),V_a,T_b,T_a) = hAPP(hAPP(V_f,V_x),c_List_Ofoldr(V_f,V_xs,V_a,T_b,T_a)),
input ).
fof(cls_foldr_Osimps_I2_J_0_0,plain,
! [T_a,T_b,V_a,V_f,V_x,V_xs] :
( c_List_Ofoldr(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),V_a,T_b,T_a) = hAPP(hAPP(V_f,V_x),c_List_Ofoldr(V_f,V_xs,V_a,T_b,T_a))
| $false ),
inference(orientation,[status(thm)],[cls_foldr_Osimps_I2_J_0]) ).
cnf(cls_dB_Orecs_I3_J_0,axiom,
c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_dB),T_a) = hAPP(hAPP(V_f3,V_dB),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB,T_a)),
input ).
fof(cls_dB_Orecs_I3_J_0_0,plain,
! [T_a,V_dB,V_f1,V_f2,V_f3] :
( c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_dB),T_a) = hAPP(hAPP(V_f3,V_dB),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB,T_a))
| $false ),
inference(orientation,[status(thm)],[cls_dB_Orecs_I3_J_0]) ).
cnf(cls_diff__self__eq__0_0,axiom,
c_HOL_Ominus__class_Ominus(V_m,V_m,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
input ).
fof(cls_diff__self__eq__0_0_0,plain,
! [V_m] :
( c_HOL_Ominus__class_Ominus(V_m,V_m,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_diff__self__eq__0_0]) ).
cnf(cls_minus__nat_Odiff__0_0,axiom,
c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m,
input ).
fof(cls_minus__nat_Odiff__0_0_0,plain,
! [V_m] :
( c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m
| $false ),
inference(orientation,[status(thm)],[cls_minus__nat_Odiff__0_0]) ).
cnf(cls_nat__case__0_0,axiom,
c_Nat_Onat_Onat__case(V_f1,V_f2,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = V_f1,
input ).
fof(cls_nat__case__0_0_0,plain,
! [T_a,V_f1,V_f2] :
( c_Nat_Onat_Onat__case(V_f1,V_f2,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = V_f1
| $false ),
inference(orientation,[status(thm)],[cls_nat__case__0_0]) ).
cnf(cls_Nitpick_Onat__case__def_0,axiom,
c_Nat_Onat_Onat__case(V_x,V_f,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = V_x,
input ).
fof(cls_Nitpick_Onat__case__def_0_0,plain,
! [T_a,V_f,V_x] :
( c_Nat_Onat_Onat__case(V_x,V_f,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = V_x
| $false ),
inference(orientation,[status(thm)],[cls_Nitpick_Onat__case__def_0]) ).
cnf(cls_liftn__0_0,axiom,
c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),V_t,V_k) = V_t,
input ).
fof(cls_liftn__0_0_0,plain,
! [V_k,V_t] :
( c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),V_t,V_k) = V_t
| $false ),
inference(orientation,[status(thm)],[cls_liftn__0_0]) ).
cnf(cls_neq0__conv_1,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
input ).
fof(cls_neq0__conv_1_0,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_neq0__conv_1]) ).
cnf(cls_le__0__eq_1,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
input ).
fof(cls_le__0__eq_1_0,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_le__0__eq_1]) ).
cnf(cls_diff__add__inverse_0,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),V_n,tc_nat) = V_m,
input ).
fof(cls_diff__add__inverse_0_0,plain,
! [V_m,V_n] :
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),V_n,tc_nat) = V_m
| $false ),
inference(orientation,[status(thm)],[cls_diff__add__inverse_0]) ).
cnf(cls_diff__add__inverse2_0,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),V_n,tc_nat) = V_m,
input ).
fof(cls_diff__add__inverse2_0_0,plain,
! [V_m,V_n] :
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),V_n,tc_nat) = V_m
| $false ),
inference(orientation,[status(thm)],[cls_diff__add__inverse2_0]) ).
cnf(cls_replicate__append__same_0,axiom,
c_List_Oappend(c_List_Oreplicate(V_i,V_x,T_a),c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Oreplicate(V_i,V_x,T_a),T_a),
input ).
fof(cls_replicate__append__same_0_0,plain,
! [T_a,V_i,V_x] :
( c_List_Oappend(c_List_Oreplicate(V_i,V_x,T_a),c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Oreplicate(V_i,V_x,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_replicate__append__same_0]) ).
cnf(cls_rtranclp__idemp_0,axiom,
c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(V_r,T_a),T_a) = c_Transitive__Closure_Ortranclp(V_r,T_a),
input ).
fof(cls_rtranclp__idemp_0_0,plain,
! [T_a,V_r] :
( c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(V_r,T_a),T_a) = c_Transitive__Closure_Ortranclp(V_r,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_rtranclp__idemp_0]) ).
cnf(cls_Nil__is__append__conv_2,axiom,
c_List_Olist_ONil(T_a) = c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a),
input ).
fof(cls_Nil__is__append__conv_2_0,plain,
! [T_a] :
( c_List_Olist_ONil(T_a) = c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_Nil__is__append__conv_2]) ).
cnf(cls_Nil__is__map__conv_1,axiom,
c_List_Olist_ONil(T_a) = c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a),
input ).
fof(cls_Nil__is__map__conv_1_0,plain,
! [T_a,T_b,V_f] :
( c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a) = c_List_Olist_ONil(T_a)
| $false ),
inference(orientation,[status(thm)],[cls_Nil__is__map__conv_1]) ).
cnf(cls_Cons__eq__append__conv_4,axiom,
c_List_Olist_OCons(V_x,V_xs,T_a) = c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a),
input ).
fof(cls_Cons__eq__append__conv_4_0,plain,
! [T_a,V_x,V_xs] :
( c_List_Olist_OCons(V_x,V_xs,T_a) = c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_Cons__eq__append__conv_4]) ).
cnf(cls_not__Cons__self_0,axiom,
V_xs != c_List_Olist_OCons(V_x,V_xs,T_a),
input ).
fof(cls_not__Cons__self_0_0,plain,
! [T_a,V_x,V_xs] :
( V_xs != c_List_Olist_OCons(V_x,V_xs,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_not__Cons__self_0]) ).
cnf(cls_not__Cons__self2_0,axiom,
c_List_Olist_OCons(V_x,V_t,T_a) != V_t,
input ).
fof(cls_not__Cons__self2_0_0,plain,
! [T_a,V_t,V_x] :
( c_List_Olist_OCons(V_x,V_t,T_a) != V_t
| $false ),
inference(orientation,[status(thm)],[cls_not__Cons__self2_0]) ).
cnf(cls_replicate__empty_1,axiom,
c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a) = c_List_Olist_ONil(T_a),
input ).
fof(cls_replicate__empty_1_0,plain,
! [T_a,V_x] :
( c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a) = c_List_Olist_ONil(T_a)
| $false ),
inference(orientation,[status(thm)],[cls_replicate__empty_1]) ).
cnf(cls_drop__replicate_0,axiom,
c_List_Odrop(V_i,c_List_Oreplicate(V_k,V_x,T_a),T_a) = c_List_Oreplicate(c_HOL_Ominus__class_Ominus(V_k,V_i,tc_nat),V_x,T_a),
input ).
fof(cls_drop__replicate_0_0,plain,
! [T_a,V_i,V_k,V_x] :
( c_List_Odrop(V_i,c_List_Oreplicate(V_k,V_x,T_a),T_a) = c_List_Oreplicate(c_HOL_Ominus__class_Ominus(V_k,V_i,tc_nat),V_x,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_drop__replicate_0]) ).
cnf(cls_lift__map_0,axiom,
hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_i) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,V_t),V_i),c_List_Omap(c_COMBC(c_Lambda_Olift,V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
input ).
fof(cls_lift__map_0_0,plain,
! [V_i,V_t,V_ts] :
( hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_i) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,V_t),V_i),c_List_Omap(c_COMBC(c_Lambda_Olift,V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
| $false ),
inference(orientation,[status(thm)],[cls_lift__map_0]) ).
cnf(cls_replicate__add_0,axiom,
c_List_Oreplicate(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),V_x,T_a) = c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),c_List_Oreplicate(V_m,V_x,T_a),T_a),
input ).
fof(cls_replicate__add_0_0,plain,
! [T_a,V_m,V_n,V_x] :
( c_List_Oreplicate(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),V_x,T_a) = c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),c_List_Oreplicate(V_m,V_x,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_replicate__add_0]) ).
cnf(cls_drop__drop_0,axiom,
c_List_Odrop(V_n,c_List_Odrop(V_m,V_xs,T_a),T_a) = c_List_Odrop(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),V_xs,T_a),
input ).
fof(cls_drop__drop_0_0,plain,
! [T_a,V_m,V_n,V_xs] :
( c_List_Odrop(V_n,c_List_Odrop(V_m,V_xs,T_a),T_a) = c_List_Odrop(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),V_xs,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_drop__drop_0]) ).
cnf(cls_beta__cases_I1_J_0,axiom,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(V_i)),V_t)),
input ).
fof(cls_beta__cases_I1_J_0_0,plain,
! [V_i,V_t] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(V_i)),V_t))
| $false ),
inference(orientation,[status(thm)],[cls_beta__cases_I1_J_0]) ).
cnf(cls_list_Osimps_I2_J_0,axiom,
c_List_Olist_ONil(T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a),
input ).
fof(cls_list_Osimps_I2_J_0_0,plain,
! [T_a,V_a_H,V_list_H] :
( c_List_Olist_ONil(T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_list_Osimps_I2_J_0]) ).
cnf(cls_append__replicate__commute_0,axiom,
c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),c_List_Oreplicate(V_k,V_x,T_a),T_a) = c_List_Oappend(c_List_Oreplicate(V_k,V_x,T_a),c_List_Oreplicate(V_n,V_x,T_a),T_a),
input ).
fof(cls_append__replicate__commute_0_0,plain,
! [T_a,V_k,V_n,V_x] :
( c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),c_List_Oreplicate(V_k,V_x,T_a),T_a) = c_List_Oappend(c_List_Oreplicate(V_k,V_x,T_a),c_List_Oreplicate(V_n,V_x,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_append__replicate__commute_0]) ).
cnf(cls_map__append_0,axiom,
c_List_Omap(V_f,c_List_Oappend(V_xs,V_ys,T_b),T_b,T_a) = c_List_Oappend(c_List_Omap(V_f,V_xs,T_b,T_a),c_List_Omap(V_f,V_ys,T_b,T_a),T_a),
input ).
fof(cls_map__append_0_0,plain,
! [T_a,T_b,V_f,V_xs,V_ys] :
( c_List_Omap(V_f,c_List_Oappend(V_xs,V_ys,T_b),T_b,T_a) = c_List_Oappend(c_List_Omap(V_f,V_xs,T_b,T_a),c_List_Omap(V_f,V_ys,T_b,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_map__append_0]) ).
cnf(cls_nat__minus__add__max_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat)),V_m) = c_Orderings_Oord__class_Omax(V_n,V_m,tc_nat),
input ).
fof(cls_nat__minus__add__max_0_0,plain,
! [V_m,V_n] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat)),V_m) = c_Orderings_Oord__class_Omax(V_n,V_m,tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_nat__minus__add__max_0]) ).
cnf(cls_le__iff__add_1,axiom,
c_lessequals(V_m,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_x),tc_nat),
input ).
fof(cls_le__iff__add_1_0,plain,
! [V_m,V_x] :
( c_lessequals(V_m,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_x),tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_le__iff__add_1]) ).
cnf(cls_le__add2_0,axiom,
c_lessequals(V_n,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),tc_nat),
input ).
fof(cls_le__add2_0_0,plain,
! [V_m,V_n] :
( c_lessequals(V_n,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_le__add2_0]) ).
cnf(cls_le__add1_0,axiom,
c_lessequals(V_n,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),tc_nat),
input ).
fof(cls_le__add1_0_0,plain,
! [V_m,V_n] :
( c_lessequals(V_n,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_le__add1_0]) ).
cnf(cls_less__not__refl_0,axiom,
~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat),
input ).
fof(cls_less__not__refl_0_0,plain,
! [V_n] :
( ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_less__not__refl_0]) ).
cnf(cls_nat__less__le_1,axiom,
~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat),
input ).
fof(cls_nat__less__le_1_0,plain,
! [V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_nat__less__le_1]) ).
cnf(cls_empty__replicate_1,axiom,
c_List_Olist_ONil(T_a) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a),
input ).
fof(cls_empty__replicate_1_0,plain,
! [T_a,V_x] :
( c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a) = c_List_Olist_ONil(T_a)
| $false ),
inference(orientation,[status(thm)],[cls_empty__replicate_1]) ).
cnf(cls_dB_Orecs_I1_J_0,axiom,
c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_nat),T_a) = hAPP(V_f1,V_nat),
input ).
fof(cls_dB_Orecs_I1_J_0_0,plain,
! [T_a,V_f1,V_f2,V_f3,V_nat] :
( c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_nat),T_a) = hAPP(V_f1,V_nat)
| $false ),
inference(orientation,[status(thm)],[cls_dB_Orecs_I1_J_0]) ).
cnf(cls_conversep__eq_0,axiom,
c_Predicate_Oconversep(c_fequal(T_a),T_a,T_a) = c_fequal(T_a),
input ).
fof(cls_conversep__eq_0_0,plain,
! [T_a] :
( c_Predicate_Oconversep(c_fequal(T_a),T_a,T_a) = c_fequal(T_a)
| $false ),
inference(orientation,[status(thm)],[cls_conversep__eq_0]) ).
cnf(cls_shift__eq_0,axiom,
hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T,
input ).
fof(cls_shift__eq_0_0,plain,
! [T_a,V_T,V_e,V_x] :
( hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T
| $false ),
inference(orientation,[status(thm)],[cls_shift__eq_0]) ).
cnf(cls_list_Osimps_I3_J_0,axiom,
c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a),
input ).
fof(cls_list_Osimps_I3_J_0_0,plain,
! [T_a,V_a_H,V_list_H] :
( c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a)
| $false ),
inference(orientation,[status(thm)],[cls_list_Osimps_I3_J_0]) ).
cnf(cls_neq__Nil__conv_1,axiom,
c_List_Olist_OCons(V_x,V_xa,T_a) != c_List_Olist_ONil(T_a),
input ).
fof(cls_neq__Nil__conv_1_0,plain,
! [T_a,V_x,V_xa] :
( c_List_Olist_OCons(V_x,V_xa,T_a) != c_List_Olist_ONil(T_a)
| $false ),
inference(orientation,[status(thm)],[cls_neq__Nil__conv_1]) ).
cnf(cls_Cons__eq__appendI_0,axiom,
c_List_Olist_OCons(V_x,c_List_Oappend(V_xs1,V_zs,T_a),T_a) = c_List_Oappend(c_List_Olist_OCons(V_x,V_xs1,T_a),V_zs,T_a),
input ).
fof(cls_Cons__eq__appendI_0_0,plain,
! [T_a,V_x,V_xs1,V_zs] :
( c_List_Olist_OCons(V_x,c_List_Oappend(V_xs1,V_zs,T_a),T_a) = c_List_Oappend(c_List_Olist_OCons(V_x,V_xs1,T_a),V_zs,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_Cons__eq__appendI_0]) ).
cnf(cls_Cons__eq__append__conv_5,axiom,
c_List_Olist_OCons(V_x,c_List_Oappend(V_xa,V_zs,T_a),T_a) = c_List_Oappend(c_List_Olist_OCons(V_x,V_xa,T_a),V_zs,T_a),
input ).
fof(cls_Cons__eq__append__conv_5_0,plain,
! [T_a,V_x,V_xa,V_zs] :
( c_List_Olist_OCons(V_x,c_List_Oappend(V_xa,V_zs,T_a),T_a) = c_List_Oappend(c_List_Olist_OCons(V_x,V_xa,T_a),V_zs,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_Cons__eq__append__conv_5]) ).
cnf(cls_map_Osimps_I2_J_0,axiom,
c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),T_b,T_a) = c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xs,T_b,T_a),T_a),
input ).
fof(cls_map_Osimps_I2_J_0_0,plain,
! [T_a,T_b,V_f,V_x,V_xs] :
( c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),T_b,T_a) = c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xs,T_b,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_map_Osimps_I2_J_0]) ).
cnf(cls_Cons__eq__map__conv_3,axiom,
c_List_Olist_OCons(hAPP(V_f,V_xa),c_List_Omap(V_f,V_xb,T_b,T_a),T_a) = c_List_Omap(V_f,c_List_Olist_OCons(V_xa,V_xb,T_b),T_b,T_a),
input ).
fof(cls_Cons__eq__map__conv_3_0,plain,
! [T_a,T_b,V_f,V_xa,V_xb] :
( c_List_Olist_OCons(hAPP(V_f,V_xa),c_List_Omap(V_f,V_xb,T_b,T_a),T_a) = c_List_Omap(V_f,c_List_Olist_OCons(V_xa,V_xb,T_b),T_b,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_Cons__eq__map__conv_3]) ).
cnf(cls_map__eq__Cons__conv_3,axiom,
c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xa,T_b),T_b,T_a) = c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xa,T_b,T_a),T_a),
input ).
fof(cls_map__eq__Cons__conv_3_0,plain,
! [T_a,T_b,V_f,V_x,V_xa] :
( c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xa,T_b),T_b,T_a) = c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xa,T_b,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_map__eq__Cons__conv_3]) ).
cnf(cls_diff__commute_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_k,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_k,tc_nat),V_j,tc_nat),
input ).
fof(cls_diff__commute_0_0,plain,
! [V_i,V_j,V_k] :
( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_k,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_k,tc_nat),V_j,tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_diff__commute_0]) ).
cnf(cls_append__Cons_0,axiom,
c_List_Oappend(c_List_Olist_OCons(V_x,V_xs,T_a),V_ys,T_a) = c_List_Olist_OCons(V_x,c_List_Oappend(V_xs,V_ys,T_a),T_a),
input ).
fof(cls_append__Cons_0_0,plain,
! [T_a,V_x,V_xs,V_ys] :
( c_List_Oappend(c_List_Olist_OCons(V_x,V_xs,T_a),V_ys,T_a) = c_List_Olist_OCons(V_x,c_List_Oappend(V_xs,V_ys,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_append__Cons_0]) ).
cnf(cls_append__eq__Cons__conv_5,axiom,
c_List_Oappend(c_List_Olist_OCons(V_x,V_xa,T_a),V_zs,T_a) = c_List_Olist_OCons(V_x,c_List_Oappend(V_xa,V_zs,T_a),T_a),
input ).
fof(cls_append__eq__Cons__conv_5_0,plain,
! [T_a,V_x,V_xa,V_zs] :
( c_List_Oappend(c_List_Olist_OCons(V_x,V_xa,T_a),V_zs,T_a) = c_List_Olist_OCons(V_x,c_List_Oappend(V_xa,V_zs,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_append__eq__Cons__conv_5]) ).
cnf(cls_typing_OVar_0,axiom,
c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x)),
input ).
fof(cls_typing_OVar_0_0,plain,
! [V_env,V_x] :
( c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x))
| $false ),
inference(orientation,[status(thm)],[cls_typing_OVar_0]) ).
cnf(cls_diff__le__self_0,axiom,
c_lessequals(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_m,tc_nat),
input ).
fof(cls_diff__le__self_0_0,plain,
! [V_m,V_n] :
( c_lessequals(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_m,tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_diff__le__self_0]) ).
cnf(cls_diff__cancel_0,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),
input ).
fof(cls_diff__cancel_0_0,plain,
! [V_k,V_m,V_n] :
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_diff__cancel_0]) ).
cnf(cls_diff__cancel2_0,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_k),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),
input ).
fof(cls_diff__cancel2_0_0,plain,
! [V_k,V_m,V_n] :
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_k),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_diff__cancel2_0]) ).
cnf(cls_diff__diff__left_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_k,tc_nat) = c_HOL_Ominus__class_Ominus(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_k),tc_nat),
input ).
fof(cls_diff__diff__left_0_0,plain,
! [V_i,V_j,V_k] :
( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_k,tc_nat) = c_HOL_Ominus__class_Ominus(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_k),tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_diff__diff__left_0]) ).
cnf(cls_diff__add__0_0,axiom,
c_HOL_Ominus__class_Ominus(V_n,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
input ).
fof(cls_diff__add__0_0_0,plain,
! [V_m,V_n] :
( c_HOL_Ominus__class_Ominus(V_n,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_diff__add__0_0]) ).
cnf(cls_map__is__Nil__conv_1,axiom,
c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a) = c_List_Olist_ONil(T_a),
input ).
fof(cls_map__is__Nil__conv_1_0,plain,
! [T_a,T_b,V_f] :
( c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a) = c_List_Olist_ONil(T_a)
| $false ),
inference(orientation,[status(thm)],[cls_map__is__Nil__conv_1]) ).
cnf(cls_foldr_Osimps_I1_J_0,axiom,
c_List_Ofoldr(V_f,c_List_Olist_ONil(T_b),V_a,T_b,T_a) = V_a,
input ).
fof(cls_foldr_Osimps_I1_J_0_0,plain,
! [T_a,T_b,V_a,V_f] :
( c_List_Ofoldr(V_f,c_List_Olist_ONil(T_b),V_a,T_b,T_a) = V_a
| $false ),
inference(orientation,[status(thm)],[cls_foldr_Osimps_I1_J_0]) ).
cnf(cls_COMBC__def_0,axiom,
hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R) = hAPP(hAPP(V_P,V_R),V_Q),
input ).
fof(cls_COMBC__def_0_0,plain,
! [T_a,T_b,T_c,V_P,V_Q,V_R] :
( hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R) = hAPP(hAPP(V_P,V_R),V_Q)
| $false ),
inference(orientation,[status(thm)],[cls_COMBC__def_0]) ).
cnf(cls_dB_Osimps_I10_J_0,axiom,
c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_nat),T_a) = hAPP(V_f1,V_nat),
input ).
fof(cls_dB_Osimps_I10_J_0_0,plain,
! [T_a,V_f1,V_f2,V_f3,V_nat] :
( c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_nat),T_a) = hAPP(V_f1,V_nat)
| $false ),
inference(orientation,[status(thm)],[cls_dB_Osimps_I10_J_0]) ).
cnf(cls_drop__Cons_H_0,axiom,
c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,V_xs,T_a),
input ).
fof(cls_drop__Cons_H_0_0,plain,
! [T_a,V_x,V_xs] :
( c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,V_xs,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_drop__Cons_H_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_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_not__step1__Nil_0,axiom,
~ c_ListOrder_Ostep1(V_r,V_xs,c_List_Olist_ONil(T_a),T_a),
input ).
fof(cls_not__step1__Nil_0_0,plain,
! [T_a,V_r,V_xs] :
( ~ c_ListOrder_Ostep1(V_r,V_xs,c_List_Olist_ONil(T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_not__step1__Nil_0]) ).
cnf(cls_not__Nil__step1_0,axiom,
~ c_ListOrder_Ostep1(V_r,c_List_Olist_ONil(T_a),V_xs,T_a),
input ).
fof(cls_not__Nil__step1_0_0,plain,
! [T_a,V_r,V_xs] :
( ~ c_ListOrder_Ostep1(V_r,c_List_Olist_ONil(T_a),V_xs,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_not__Nil__step1_0]) ).
cnf(cls_dB_Osimps_I6_J_0,axiom,
c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H),
input ).
fof(cls_dB_Osimps_I6_J_0_0,plain,
! [V_dB_H,V_nat] :
( c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H)
| $false ),
inference(orientation,[status(thm)],[cls_dB_Osimps_I6_J_0]) ).
cnf(cls_drop__Nil_0,axiom,
c_List_Odrop(V_n,c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a),
input ).
fof(cls_drop__Nil_0_0,plain,
! [T_a,V_n] :
( c_List_Odrop(V_n,c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a)
| $false ),
inference(orientation,[status(thm)],[cls_drop__Nil_0]) ).
cnf(cls_foldr__append_0,axiom,
c_List_Ofoldr(V_f,c_List_Oappend(V_xs,V_ys,T_b),V_a,T_b,T_a) = c_List_Ofoldr(V_f,V_xs,c_List_Ofoldr(V_f,V_ys,V_a,T_b,T_a),T_b,T_a),
input ).
fof(cls_foldr__append_0_0,plain,
! [T_a,T_b,V_a,V_f,V_xs,V_ys] :
( c_List_Ofoldr(V_f,c_List_Oappend(V_xs,V_ys,T_b),V_a,T_b,T_a) = c_List_Ofoldr(V_f,V_xs,c_List_Ofoldr(V_f,V_ys,V_a,T_b,T_a),T_b,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_foldr__append_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_map__replicate_0,axiom,
c_List_Omap(V_f,c_List_Oreplicate(V_n,V_x,T_b),T_b,T_a) = c_List_Oreplicate(V_n,hAPP(V_f,V_x),T_a),
input ).
fof(cls_map__replicate_0_0,plain,
! [T_a,T_b,V_f,V_n,V_x] :
( c_List_Omap(V_f,c_List_Oreplicate(V_n,V_x,T_b),T_b,T_a) = c_List_Oreplicate(V_n,hAPP(V_f,V_x),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_map__replicate_0]) ).
cnf(cls_self__append__conv2_1,axiom,
V_ys = c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a),
input ).
fof(cls_self__append__conv2_1_0,plain,
! [T_a,V_ys] :
( c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a) = V_ys
| $false ),
inference(orientation,[status(thm)],[cls_self__append__conv2_1]) ).
cnf(cls_append__Nil_0,axiom,
c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a) = V_ys,
input ).
fof(cls_append__Nil_0_0,plain,
! [T_a,V_ys] :
( c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a) = V_ys
| $false ),
inference(orientation,[status(thm)],[cls_append__Nil_0]) ).
cnf(cls_self__append__conv_1,axiom,
V_xs = c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a),
input ).
fof(cls_self__append__conv_1_0,plain,
! [T_a,V_xs] :
( c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a) = V_xs
| $false ),
inference(orientation,[status(thm)],[cls_self__append__conv_1]) ).
cnf(cls_eq__Nil__appendI_0,axiom,
V_x = c_List_Oappend(c_List_Olist_ONil(T_a),V_x,T_a),
input ).
fof(cls_eq__Nil__appendI_0_0,plain,
! [T_a,V_x] :
( c_List_Oappend(c_List_Olist_ONil(T_a),V_x,T_a) = V_x
| $false ),
inference(orientation,[status(thm)],[cls_eq__Nil__appendI_0]) ).
cnf(cls_append__Nil2_0,axiom,
c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a) = V_xs,
input ).
fof(cls_append__Nil2_0_0,plain,
! [T_a,V_xs] :
( c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a) = V_xs
| $false ),
inference(orientation,[status(thm)],[cls_append__Nil2_0]) ).
cnf(cls_Nitpick_Ortranclp__def_1,axiom,
hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_x)),
input ).
fof(cls_Nitpick_Ortranclp__def_1_0,plain,
! [T_a,V_r,V_x] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_x))
| $false ),
inference(orientation,[status(thm)],[cls_Nitpick_Ortranclp__def_1]) ).
cnf(cls_rtranclp_Ortrancl__refl_0,axiom,
hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_a)),
input ).
fof(cls_rtranclp_Ortrancl__refl_0_0,plain,
! [T_a,V_a,V_r] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_a))
| $false ),
inference(orientation,[status(thm)],[cls_rtranclp_Ortrancl__refl_0]) ).
cnf(cls_listsp_ONil_0,axiom,
c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a),
input ).
fof(cls_listsp_ONil_0_0,plain,
! [T_a,V_A] :
( c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_listsp_ONil_0]) ).
cnf(cls_dB_Osimps_I12_J_0,axiom,
c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_dB),T_a) = hAPP(V_f3,V_dB),
input ).
fof(cls_dB_Osimps_I12_J_0_0,plain,
! [T_a,V_dB,V_f1,V_f2,V_f3] :
( c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_dB),T_a) = hAPP(V_f3,V_dB)
| $false ),
inference(orientation,[status(thm)],[cls_dB_Osimps_I12_J_0]) ).
fof(def_lhs_atom1,axiom,
! [V_f3,V_f2,V_f1,V_dB,T_a] :
( lhs_atom1(V_f3,V_f2,V_f1,V_dB,T_a)
<=> c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_dB),T_a) = hAPP(V_f3,V_dB) ),
inference(definition,[],[]) ).
fof(to_be_clausified_0,plain,
! [T_a,V_dB,V_f1,V_f2,V_f3] :
( lhs_atom1(V_f3,V_f2,V_f1,V_dB,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_dB_Osimps_I12_J_0_0,def_lhs_atom1]) ).
fof(def_lhs_atom2,axiom,
! [V_A,T_a] :
( lhs_atom2(V_A,T_a)
<=> c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_1,plain,
! [T_a,V_A] :
( lhs_atom2(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_listsp_ONil_0_0,def_lhs_atom2]) ).
fof(def_lhs_atom3,axiom,
! [V_r,V_a,T_a] :
( lhs_atom3(V_r,V_a,T_a)
<=> hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_a)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_2,plain,
! [T_a,V_a,V_r] :
( lhs_atom3(V_r,V_a,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_rtranclp_Ortrancl__refl_0_0,def_lhs_atom3]) ).
fof(def_lhs_atom4,axiom,
! [V_x,V_r,T_a] :
( lhs_atom4(V_x,V_r,T_a)
<=> hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_x)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_3,plain,
! [T_a,V_r,V_x] :
( lhs_atom4(V_x,V_r,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Nitpick_Ortranclp__def_1_0,def_lhs_atom4]) ).
fof(def_lhs_atom5,axiom,
! [V_xs,T_a] :
( lhs_atom5(V_xs,T_a)
<=> c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a) = V_xs ),
inference(definition,[],[]) ).
fof(to_be_clausified_4,plain,
! [T_a,V_xs] :
( lhs_atom5(V_xs,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_append__Nil2_0_0,def_lhs_atom5]) ).
fof(def_lhs_atom6,axiom,
! [V_x,T_a] :
( lhs_atom6(V_x,T_a)
<=> c_List_Oappend(c_List_Olist_ONil(T_a),V_x,T_a) = V_x ),
inference(definition,[],[]) ).
fof(to_be_clausified_5,plain,
! [T_a,V_x] :
( lhs_atom6(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_eq__Nil__appendI_0_0,def_lhs_atom6]) ).
fof(to_be_clausified_6,plain,
! [T_a,V_xs] :
( lhs_atom5(V_xs,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_self__append__conv_1_0,def_lhs_atom5]) ).
fof(def_lhs_atom7,axiom,
! [V_ys,T_a] :
( lhs_atom7(V_ys,T_a)
<=> c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a) = V_ys ),
inference(definition,[],[]) ).
fof(to_be_clausified_7,plain,
! [T_a,V_ys] :
( lhs_atom7(V_ys,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_append__Nil_0_0,def_lhs_atom7]) ).
fof(to_be_clausified_8,plain,
! [T_a,V_ys] :
( lhs_atom7(V_ys,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_self__append__conv2_1_0,def_lhs_atom7]) ).
fof(def_lhs_atom8,axiom,
! [V_x,V_n,V_f,T_b,T_a] :
( lhs_atom8(V_x,V_n,V_f,T_b,T_a)
<=> c_List_Omap(V_f,c_List_Oreplicate(V_n,V_x,T_b),T_b,T_a) = c_List_Oreplicate(V_n,hAPP(V_f,V_x),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_9,plain,
! [T_a,T_b,V_f,V_n,V_x] :
( lhs_atom8(V_x,V_n,V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_map__replicate_0_0,def_lhs_atom8]) ).
fof(def_lhs_atom9,axiom,
! [V_n,V_m] :
( lhs_atom9(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_10,plain,
! [V_m,V_n] :
( lhs_atom9(V_n,V_m)
| $false ),
inference(fold_definition,[status(thm)],[cls_nat__add__commute_0_0,def_lhs_atom9]) ).
fof(def_lhs_atom10,axiom,
! [V_ys,V_xs,V_f,V_a,T_b,T_a] :
( lhs_atom10(V_ys,V_xs,V_f,V_a,T_b,T_a)
<=> c_List_Ofoldr(V_f,c_List_Oappend(V_xs,V_ys,T_b),V_a,T_b,T_a) = c_List_Ofoldr(V_f,V_xs,c_List_Ofoldr(V_f,V_ys,V_a,T_b,T_a),T_b,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_11,plain,
! [T_a,T_b,V_a,V_f,V_xs,V_ys] :
( lhs_atom10(V_ys,V_xs,V_f,V_a,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_foldr__append_0_0,def_lhs_atom10]) ).
fof(def_lhs_atom11,axiom,
! [V_n,T_a] :
( lhs_atom11(V_n,T_a)
<=> c_List_Odrop(V_n,c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_12,plain,
! [T_a,V_n] :
( lhs_atom11(V_n,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_drop__Nil_0_0,def_lhs_atom11]) ).
fof(def_lhs_atom12,axiom,
! [V_nat,V_dB_H] :
( lhs_atom12(V_nat,V_dB_H)
<=> c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H) ),
inference(definition,[],[]) ).
fof(to_be_clausified_13,plain,
! [V_dB_H,V_nat] :
( lhs_atom12(V_nat,V_dB_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_dB_Osimps_I6_J_0_0,def_lhs_atom12]) ).
fof(def_lhs_atom13,axiom,
! [V_xs,V_r,T_a] :
( lhs_atom13(V_xs,V_r,T_a)
<=> ~ c_ListOrder_Ostep1(V_r,c_List_Olist_ONil(T_a),V_xs,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_14,plain,
! [T_a,V_r,V_xs] :
( lhs_atom13(V_xs,V_r,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_not__Nil__step1_0_0,def_lhs_atom13]) ).
fof(def_lhs_atom14,axiom,
! [V_xs,V_r,T_a] :
( lhs_atom14(V_xs,V_r,T_a)
<=> ~ c_ListOrder_Ostep1(V_r,V_xs,c_List_Olist_ONil(T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_15,plain,
! [T_a,V_r,V_xs] :
( lhs_atom14(V_xs,V_r,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_not__step1__Nil_0_0,def_lhs_atom14]) ).
fof(def_lhs_atom15,axiom,
! [V_z,V_y,V_x] :
( lhs_atom15(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_16,plain,
! [V_x,V_y,V_z] :
( lhs_atom15(V_z,V_y,V_x)
| $false ),
inference(fold_definition,[status(thm)],[cls_nat__add__left__commute_0_0,def_lhs_atom15]) ).
fof(def_lhs_atom16,axiom,
! [V_n,V_m,V_k] :
( lhs_atom16(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_17,plain,
! [V_k,V_m,V_n] :
( lhs_atom16(V_n,V_m,V_k)
| $false ),
inference(fold_definition,[status(thm)],[cls_nat__add__assoc_0_0,def_lhs_atom16]) ).
fof(def_lhs_atom17,axiom,
! [V_xs,V_x,T_a] :
( lhs_atom17(V_xs,V_x,T_a)
<=> c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,V_xs,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_18,plain,
! [T_a,V_x,V_xs] :
( lhs_atom17(V_xs,V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_drop__Cons_H_0_0,def_lhs_atom17]) ).
fof(def_lhs_atom18,axiom,
! [V_nat,V_f3,V_f2,V_f1,T_a] :
( lhs_atom18(V_nat,V_f3,V_f2,V_f1,T_a)
<=> c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_nat),T_a) = hAPP(V_f1,V_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_19,plain,
! [T_a,V_f1,V_f2,V_f3,V_nat] :
( lhs_atom18(V_nat,V_f3,V_f2,V_f1,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_dB_Osimps_I10_J_0_0,def_lhs_atom18]) ).
fof(def_lhs_atom19,axiom,
! [V_R,V_Q,V_P,T_c,T_b,T_a] :
( lhs_atom19(V_R,V_Q,V_P,T_c,T_b,T_a)
<=> hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R) = hAPP(hAPP(V_P,V_R),V_Q) ),
inference(definition,[],[]) ).
fof(to_be_clausified_20,plain,
! [T_a,T_b,T_c,V_P,V_Q,V_R] :
( lhs_atom19(V_R,V_Q,V_P,T_c,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_COMBC__def_0_0,def_lhs_atom19]) ).
fof(def_lhs_atom20,axiom,
! [V_f,V_a,T_b,T_a] :
( lhs_atom20(V_f,V_a,T_b,T_a)
<=> c_List_Ofoldr(V_f,c_List_Olist_ONil(T_b),V_a,T_b,T_a) = V_a ),
inference(definition,[],[]) ).
fof(to_be_clausified_21,plain,
! [T_a,T_b,V_a,V_f] :
( lhs_atom20(V_f,V_a,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_foldr_Osimps_I1_J_0_0,def_lhs_atom20]) ).
fof(def_lhs_atom21,axiom,
! [V_f,T_b,T_a] :
( lhs_atom21(V_f,T_b,T_a)
<=> c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a) = c_List_Olist_ONil(T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_22,plain,
! [T_a,T_b,V_f] :
( lhs_atom21(V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_map__is__Nil__conv_1_0,def_lhs_atom21]) ).
fof(def_lhs_atom22,axiom,
! [V_n,V_m] :
( lhs_atom22(V_n,V_m)
<=> c_HOL_Ominus__class_Ominus(V_n,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_23,plain,
! [V_m,V_n] :
( lhs_atom22(V_n,V_m)
| $false ),
inference(fold_definition,[status(thm)],[cls_diff__add__0_0_0,def_lhs_atom22]) ).
fof(def_lhs_atom23,axiom,
! [V_k,V_j,V_i] :
( lhs_atom23(V_k,V_j,V_i)
<=> c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_k,tc_nat) = c_HOL_Ominus__class_Ominus(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_k),tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_24,plain,
! [V_i,V_j,V_k] :
( lhs_atom23(V_k,V_j,V_i)
| $false ),
inference(fold_definition,[status(thm)],[cls_diff__diff__left_0_0,def_lhs_atom23]) ).
fof(def_lhs_atom24,axiom,
! [V_n,V_m,V_k] :
( lhs_atom24(V_n,V_m,V_k)
<=> c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_k),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_25,plain,
! [V_k,V_m,V_n] :
( lhs_atom24(V_n,V_m,V_k)
| $false ),
inference(fold_definition,[status(thm)],[cls_diff__cancel2_0_0,def_lhs_atom24]) ).
fof(def_lhs_atom25,axiom,
! [V_n,V_m,V_k] :
( lhs_atom25(V_n,V_m,V_k)
<=> c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_26,plain,
! [V_k,V_m,V_n] :
( lhs_atom25(V_n,V_m,V_k)
| $false ),
inference(fold_definition,[status(thm)],[cls_diff__cancel_0_0,def_lhs_atom25]) ).
fof(def_lhs_atom26,axiom,
! [V_n,V_m] :
( lhs_atom26(V_n,V_m)
<=> c_lessequals(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_m,tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_27,plain,
! [V_m,V_n] :
( lhs_atom26(V_n,V_m)
| $false ),
inference(fold_definition,[status(thm)],[cls_diff__le__self_0_0,def_lhs_atom26]) ).
fof(def_lhs_atom27,axiom,
! [V_x,V_env] :
( lhs_atom27(V_x,V_env)
<=> c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_28,plain,
! [V_env,V_x] :
( lhs_atom27(V_x,V_env)
| $false ),
inference(fold_definition,[status(thm)],[cls_typing_OVar_0_0,def_lhs_atom27]) ).
fof(def_lhs_atom28,axiom,
! [V_zs,V_xa,V_x,T_a] :
( lhs_atom28(V_zs,V_xa,V_x,T_a)
<=> c_List_Oappend(c_List_Olist_OCons(V_x,V_xa,T_a),V_zs,T_a) = c_List_Olist_OCons(V_x,c_List_Oappend(V_xa,V_zs,T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_29,plain,
! [T_a,V_x,V_xa,V_zs] :
( lhs_atom28(V_zs,V_xa,V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_append__eq__Cons__conv_5_0,def_lhs_atom28]) ).
fof(def_lhs_atom29,axiom,
! [V_ys,V_xs,V_x,T_a] :
( lhs_atom29(V_ys,V_xs,V_x,T_a)
<=> c_List_Oappend(c_List_Olist_OCons(V_x,V_xs,T_a),V_ys,T_a) = c_List_Olist_OCons(V_x,c_List_Oappend(V_xs,V_ys,T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_30,plain,
! [T_a,V_x,V_xs,V_ys] :
( lhs_atom29(V_ys,V_xs,V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_append__Cons_0_0,def_lhs_atom29]) ).
fof(def_lhs_atom30,axiom,
! [V_k,V_j,V_i] :
( lhs_atom30(V_k,V_j,V_i)
<=> c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_k,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_k,tc_nat),V_j,tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_31,plain,
! [V_i,V_j,V_k] :
( lhs_atom30(V_k,V_j,V_i)
| $false ),
inference(fold_definition,[status(thm)],[cls_diff__commute_0_0,def_lhs_atom30]) ).
fof(def_lhs_atom31,axiom,
! [V_xa,V_x,V_f,T_b,T_a] :
( lhs_atom31(V_xa,V_x,V_f,T_b,T_a)
<=> c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xa,T_b),T_b,T_a) = c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xa,T_b,T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_32,plain,
! [T_a,T_b,V_f,V_x,V_xa] :
( lhs_atom31(V_xa,V_x,V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_map__eq__Cons__conv_3_0,def_lhs_atom31]) ).
fof(def_lhs_atom32,axiom,
! [V_xb,V_xa,V_f,T_b,T_a] :
( lhs_atom32(V_xb,V_xa,V_f,T_b,T_a)
<=> c_List_Olist_OCons(hAPP(V_f,V_xa),c_List_Omap(V_f,V_xb,T_b,T_a),T_a) = c_List_Omap(V_f,c_List_Olist_OCons(V_xa,V_xb,T_b),T_b,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_33,plain,
! [T_a,T_b,V_f,V_xa,V_xb] :
( lhs_atom32(V_xb,V_xa,V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Cons__eq__map__conv_3_0,def_lhs_atom32]) ).
fof(def_lhs_atom33,axiom,
! [V_xs,V_x,V_f,T_b,T_a] :
( lhs_atom33(V_xs,V_x,V_f,T_b,T_a)
<=> c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),T_b,T_a) = c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xs,T_b,T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_34,plain,
! [T_a,T_b,V_f,V_x,V_xs] :
( lhs_atom33(V_xs,V_x,V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_map_Osimps_I2_J_0_0,def_lhs_atom33]) ).
fof(def_lhs_atom34,axiom,
! [V_zs,V_xa,V_x,T_a] :
( lhs_atom34(V_zs,V_xa,V_x,T_a)
<=> c_List_Olist_OCons(V_x,c_List_Oappend(V_xa,V_zs,T_a),T_a) = c_List_Oappend(c_List_Olist_OCons(V_x,V_xa,T_a),V_zs,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_35,plain,
! [T_a,V_x,V_xa,V_zs] :
( lhs_atom34(V_zs,V_xa,V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Cons__eq__append__conv_5_0,def_lhs_atom34]) ).
fof(def_lhs_atom35,axiom,
! [V_zs,V_xs1,V_x,T_a] :
( lhs_atom35(V_zs,V_xs1,V_x,T_a)
<=> c_List_Olist_OCons(V_x,c_List_Oappend(V_xs1,V_zs,T_a),T_a) = c_List_Oappend(c_List_Olist_OCons(V_x,V_xs1,T_a),V_zs,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_36,plain,
! [T_a,V_x,V_xs1,V_zs] :
( lhs_atom35(V_zs,V_xs1,V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Cons__eq__appendI_0_0,def_lhs_atom35]) ).
fof(def_lhs_atom36,axiom,
! [V_xa,V_x,T_a] :
( lhs_atom36(V_xa,V_x,T_a)
<=> c_List_Olist_OCons(V_x,V_xa,T_a) != c_List_Olist_ONil(T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_37,plain,
! [T_a,V_x,V_xa] :
( lhs_atom36(V_xa,V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_neq__Nil__conv_1_0,def_lhs_atom36]) ).
fof(def_lhs_atom37,axiom,
! [V_list_H,V_a_H,T_a] :
( lhs_atom37(V_list_H,V_a_H,T_a)
<=> c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_38,plain,
! [T_a,V_a_H,V_list_H] :
( lhs_atom37(V_list_H,V_a_H,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_list_Osimps_I3_J_0_0,def_lhs_atom37]) ).
fof(def_lhs_atom38,axiom,
! [V_x,V_e,V_T,T_a] :
( lhs_atom38(V_x,V_e,V_T,T_a)
<=> hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T ),
inference(definition,[],[]) ).
fof(to_be_clausified_39,plain,
! [T_a,V_T,V_e,V_x] :
( lhs_atom38(V_x,V_e,V_T,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_shift__eq_0_0,def_lhs_atom38]) ).
fof(def_lhs_atom39,axiom,
! [T_a] :
( lhs_atom39(T_a)
<=> c_Predicate_Oconversep(c_fequal(T_a),T_a,T_a) = c_fequal(T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_40,plain,
! [T_a] :
( lhs_atom39(T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_conversep__eq_0_0,def_lhs_atom39]) ).
fof(def_lhs_atom40,axiom,
! [V_nat,V_f3,V_f2,V_f1,T_a] :
( lhs_atom40(V_nat,V_f3,V_f2,V_f1,T_a)
<=> c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_nat),T_a) = hAPP(V_f1,V_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_41,plain,
! [T_a,V_f1,V_f2,V_f3,V_nat] :
( lhs_atom40(V_nat,V_f3,V_f2,V_f1,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_dB_Orecs_I1_J_0_0,def_lhs_atom40]) ).
fof(def_lhs_atom41,axiom,
! [V_x,T_a] :
( lhs_atom41(V_x,T_a)
<=> c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a) = c_List_Olist_ONil(T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_42,plain,
! [T_a,V_x] :
( lhs_atom41(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_empty__replicate_1_0,def_lhs_atom41]) ).
fof(def_lhs_atom42,axiom,
! [V_x] :
( lhs_atom42(V_x)
<=> ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_43,plain,
! [V_x] :
( lhs_atom42(V_x)
| $false ),
inference(fold_definition,[status(thm)],[cls_nat__less__le_1_0,def_lhs_atom42]) ).
fof(def_lhs_atom43,axiom,
! [V_n] :
( lhs_atom43(V_n)
<=> ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_44,plain,
! [V_n] :
( lhs_atom43(V_n)
| $false ),
inference(fold_definition,[status(thm)],[cls_less__not__refl_0_0,def_lhs_atom43]) ).
fof(def_lhs_atom44,axiom,
! [V_n,V_m] :
( lhs_atom44(V_n,V_m)
<=> c_lessequals(V_n,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_45,plain,
! [V_m,V_n] :
( lhs_atom44(V_n,V_m)
| $false ),
inference(fold_definition,[status(thm)],[cls_le__add1_0_0,def_lhs_atom44]) ).
fof(def_lhs_atom45,axiom,
! [V_n,V_m] :
( lhs_atom45(V_n,V_m)
<=> c_lessequals(V_n,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_46,plain,
! [V_m,V_n] :
( lhs_atom45(V_n,V_m)
| $false ),
inference(fold_definition,[status(thm)],[cls_le__add2_0_0,def_lhs_atom45]) ).
fof(def_lhs_atom46,axiom,
! [V_x,V_m] :
( lhs_atom46(V_x,V_m)
<=> c_lessequals(V_m,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_x),tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_47,plain,
! [V_m,V_x] :
( lhs_atom46(V_x,V_m)
| $false ),
inference(fold_definition,[status(thm)],[cls_le__iff__add_1_0,def_lhs_atom46]) ).
fof(def_lhs_atom47,axiom,
! [V_n,V_m] :
( lhs_atom47(V_n,V_m)
<=> hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat)),V_m) = c_Orderings_Oord__class_Omax(V_n,V_m,tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_48,plain,
! [V_m,V_n] :
( lhs_atom47(V_n,V_m)
| $false ),
inference(fold_definition,[status(thm)],[cls_nat__minus__add__max_0_0,def_lhs_atom47]) ).
fof(def_lhs_atom48,axiom,
! [V_ys,V_xs,V_f,T_b,T_a] :
( lhs_atom48(V_ys,V_xs,V_f,T_b,T_a)
<=> c_List_Omap(V_f,c_List_Oappend(V_xs,V_ys,T_b),T_b,T_a) = c_List_Oappend(c_List_Omap(V_f,V_xs,T_b,T_a),c_List_Omap(V_f,V_ys,T_b,T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_49,plain,
! [T_a,T_b,V_f,V_xs,V_ys] :
( lhs_atom48(V_ys,V_xs,V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_map__append_0_0,def_lhs_atom48]) ).
fof(def_lhs_atom49,axiom,
! [V_x,V_n,V_k,T_a] :
( lhs_atom49(V_x,V_n,V_k,T_a)
<=> c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),c_List_Oreplicate(V_k,V_x,T_a),T_a) = c_List_Oappend(c_List_Oreplicate(V_k,V_x,T_a),c_List_Oreplicate(V_n,V_x,T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_50,plain,
! [T_a,V_k,V_n,V_x] :
( lhs_atom49(V_x,V_n,V_k,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_append__replicate__commute_0_0,def_lhs_atom49]) ).
fof(def_lhs_atom50,axiom,
! [V_list_H,V_a_H,T_a] :
( lhs_atom50(V_list_H,V_a_H,T_a)
<=> c_List_Olist_ONil(T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_51,plain,
! [T_a,V_a_H,V_list_H] :
( lhs_atom50(V_list_H,V_a_H,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_list_Osimps_I2_J_0_0,def_lhs_atom50]) ).
fof(def_lhs_atom51,axiom,
! [V_t,V_i] :
( lhs_atom51(V_t,V_i)
<=> ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(V_i)),V_t)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_52,plain,
! [V_i,V_t] :
( lhs_atom51(V_t,V_i)
| $false ),
inference(fold_definition,[status(thm)],[cls_beta__cases_I1_J_0_0,def_lhs_atom51]) ).
fof(def_lhs_atom52,axiom,
! [V_xs,V_n,V_m,T_a] :
( lhs_atom52(V_xs,V_n,V_m,T_a)
<=> c_List_Odrop(V_n,c_List_Odrop(V_m,V_xs,T_a),T_a) = c_List_Odrop(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),V_xs,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_53,plain,
! [T_a,V_m,V_n,V_xs] :
( lhs_atom52(V_xs,V_n,V_m,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_drop__drop_0_0,def_lhs_atom52]) ).
fof(def_lhs_atom53,axiom,
! [V_x,V_n,V_m,T_a] :
( lhs_atom53(V_x,V_n,V_m,T_a)
<=> c_List_Oreplicate(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),V_x,T_a) = c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),c_List_Oreplicate(V_m,V_x,T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_54,plain,
! [T_a,V_m,V_n,V_x] :
( lhs_atom53(V_x,V_n,V_m,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_replicate__add_0_0,def_lhs_atom53]) ).
fof(def_lhs_atom54,axiom,
! [V_ts,V_t,V_i] :
( lhs_atom54(V_ts,V_t,V_i)
<=> hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_i) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,V_t),V_i),c_List_Omap(c_COMBC(c_Lambda_Olift,V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(definition,[],[]) ).
fof(to_be_clausified_55,plain,
! [V_i,V_t,V_ts] :
( lhs_atom54(V_ts,V_t,V_i)
| $false ),
inference(fold_definition,[status(thm)],[cls_lift__map_0_0,def_lhs_atom54]) ).
fof(def_lhs_atom55,axiom,
! [V_x,V_k,V_i,T_a] :
( lhs_atom55(V_x,V_k,V_i,T_a)
<=> c_List_Odrop(V_i,c_List_Oreplicate(V_k,V_x,T_a),T_a) = c_List_Oreplicate(c_HOL_Ominus__class_Ominus(V_k,V_i,tc_nat),V_x,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_56,plain,
! [T_a,V_i,V_k,V_x] :
( lhs_atom55(V_x,V_k,V_i,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_drop__replicate_0_0,def_lhs_atom55]) ).
fof(to_be_clausified_57,plain,
! [T_a,V_x] :
( lhs_atom41(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_replicate__empty_1_0,def_lhs_atom41]) ).
fof(def_lhs_atom56,axiom,
! [V_x,V_t,T_a] :
( lhs_atom56(V_x,V_t,T_a)
<=> c_List_Olist_OCons(V_x,V_t,T_a) != V_t ),
inference(definition,[],[]) ).
fof(to_be_clausified_58,plain,
! [T_a,V_t,V_x] :
( lhs_atom56(V_x,V_t,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_not__Cons__self2_0_0,def_lhs_atom56]) ).
fof(def_lhs_atom57,axiom,
! [V_xs,V_x,T_a] :
( lhs_atom57(V_xs,V_x,T_a)
<=> V_xs != c_List_Olist_OCons(V_x,V_xs,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_59,plain,
! [T_a,V_x,V_xs] :
( lhs_atom57(V_xs,V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_not__Cons__self_0_0,def_lhs_atom57]) ).
fof(def_lhs_atom58,axiom,
! [V_xs,V_x,T_a] :
( lhs_atom58(V_xs,V_x,T_a)
<=> c_List_Olist_OCons(V_x,V_xs,T_a) = c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_60,plain,
! [T_a,V_x,V_xs] :
( lhs_atom58(V_xs,V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Cons__eq__append__conv_4_0,def_lhs_atom58]) ).
fof(to_be_clausified_61,plain,
! [T_a,T_b,V_f] :
( lhs_atom21(V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Nil__is__map__conv_1_0,def_lhs_atom21]) ).
fof(def_lhs_atom59,axiom,
! [T_a] :
( lhs_atom59(T_a)
<=> c_List_Olist_ONil(T_a) = c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_62,plain,
! [T_a] :
( lhs_atom59(T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Nil__is__append__conv_2_0,def_lhs_atom59]) ).
fof(def_lhs_atom60,axiom,
! [V_r,T_a] :
( lhs_atom60(V_r,T_a)
<=> c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(V_r,T_a),T_a) = c_Transitive__Closure_Ortranclp(V_r,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_63,plain,
! [T_a,V_r] :
( lhs_atom60(V_r,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_rtranclp__idemp_0_0,def_lhs_atom60]) ).
fof(def_lhs_atom61,axiom,
! [V_x,V_i,T_a] :
( lhs_atom61(V_x,V_i,T_a)
<=> c_List_Oappend(c_List_Oreplicate(V_i,V_x,T_a),c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Oreplicate(V_i,V_x,T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_64,plain,
! [T_a,V_i,V_x] :
( lhs_atom61(V_x,V_i,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_replicate__append__same_0_0,def_lhs_atom61]) ).
fof(def_lhs_atom62,axiom,
! [V_n,V_m] :
( lhs_atom62(V_n,V_m)
<=> c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),V_n,tc_nat) = V_m ),
inference(definition,[],[]) ).
fof(to_be_clausified_65,plain,
! [V_m,V_n] :
( lhs_atom62(V_n,V_m)
| $false ),
inference(fold_definition,[status(thm)],[cls_diff__add__inverse2_0_0,def_lhs_atom62]) ).
fof(def_lhs_atom63,axiom,
! [V_n,V_m] :
( lhs_atom63(V_n,V_m)
<=> c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),V_n,tc_nat) = V_m ),
inference(definition,[],[]) ).
fof(to_be_clausified_66,plain,
! [V_m,V_n] :
( lhs_atom63(V_n,V_m)
| $false ),
inference(fold_definition,[status(thm)],[cls_diff__add__inverse_0_0,def_lhs_atom63]) ).
fof(def_lhs_atom64,axiom,
( lhs_atom64
<=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_67,plain,
( lhs_atom64
| $false ),
inference(fold_definition,[status(thm)],[cls_le__0__eq_1_0,def_lhs_atom64]) ).
fof(def_lhs_atom65,axiom,
( lhs_atom65
<=> ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_68,plain,
( lhs_atom65
| $false ),
inference(fold_definition,[status(thm)],[cls_neq0__conv_1_0,def_lhs_atom65]) ).
fof(def_lhs_atom66,axiom,
! [V_t,V_k] :
( lhs_atom66(V_t,V_k)
<=> c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),V_t,V_k) = V_t ),
inference(definition,[],[]) ).
fof(to_be_clausified_69,plain,
! [V_k,V_t] :
( lhs_atom66(V_t,V_k)
| $false ),
inference(fold_definition,[status(thm)],[cls_liftn__0_0_0,def_lhs_atom66]) ).
fof(def_lhs_atom67,axiom,
! [V_x,V_f,T_a] :
( lhs_atom67(V_x,V_f,T_a)
<=> c_Nat_Onat_Onat__case(V_x,V_f,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = V_x ),
inference(definition,[],[]) ).
fof(to_be_clausified_70,plain,
! [T_a,V_f,V_x] :
( lhs_atom67(V_x,V_f,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Nitpick_Onat__case__def_0_0,def_lhs_atom67]) ).
fof(def_lhs_atom68,axiom,
! [V_f2,V_f1,T_a] :
( lhs_atom68(V_f2,V_f1,T_a)
<=> c_Nat_Onat_Onat__case(V_f1,V_f2,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = V_f1 ),
inference(definition,[],[]) ).
fof(to_be_clausified_71,plain,
! [T_a,V_f1,V_f2] :
( lhs_atom68(V_f2,V_f1,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_nat__case__0_0_0,def_lhs_atom68]) ).
fof(def_lhs_atom69,axiom,
! [V_m] :
( lhs_atom69(V_m)
<=> c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m ),
inference(definition,[],[]) ).
fof(to_be_clausified_72,plain,
! [V_m] :
( lhs_atom69(V_m)
| $false ),
inference(fold_definition,[status(thm)],[cls_minus__nat_Odiff__0_0_0,def_lhs_atom69]) ).
fof(def_lhs_atom70,axiom,
! [V_m] :
( lhs_atom70(V_m)
<=> c_HOL_Ominus__class_Ominus(V_m,V_m,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_73,plain,
! [V_m] :
( lhs_atom70(V_m)
| $false ),
inference(fold_definition,[status(thm)],[cls_diff__self__eq__0_0_0,def_lhs_atom70]) ).
fof(def_lhs_atom71,axiom,
! [V_f3,V_f2,V_f1,V_dB,T_a] :
( lhs_atom71(V_f3,V_f2,V_f1,V_dB,T_a)
<=> c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_dB),T_a) = hAPP(hAPP(V_f3,V_dB),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB,T_a)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_74,plain,
! [T_a,V_dB,V_f1,V_f2,V_f3] :
( lhs_atom71(V_f3,V_f2,V_f1,V_dB,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_dB_Orecs_I3_J_0_0,def_lhs_atom71]) ).
fof(def_lhs_atom72,axiom,
! [V_xs,V_x,V_f,V_a,T_b,T_a] :
( lhs_atom72(V_xs,V_x,V_f,V_a,T_b,T_a)
<=> c_List_Ofoldr(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),V_a,T_b,T_a) = hAPP(hAPP(V_f,V_x),c_List_Ofoldr(V_f,V_xs,V_a,T_b,T_a)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_75,plain,
! [T_a,T_b,V_a,V_f,V_x,V_xs] :
( lhs_atom72(V_xs,V_x,V_f,V_a,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_foldr_Osimps_I2_J_0_0,def_lhs_atom72]) ).
fof(def_lhs_atom73,axiom,
! [V_r,T_b,T_a] :
( lhs_atom73(V_r,T_b,T_a)
<=> c_Predicate_Oconversep(c_Predicate_Oconversep(V_r,T_a,T_b),T_b,T_a) = V_r ),
inference(definition,[],[]) ).
fof(to_be_clausified_76,plain,
! [T_a,T_b,V_r] :
( lhs_atom73(V_r,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_conversep__conversep_0_0,def_lhs_atom73]) ).
fof(def_lhs_atom74,axiom,
! [V_j,V_i] :
( lhs_atom74(V_j,V_i)
<=> ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_i,tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_77,plain,
! [V_i,V_j] :
( lhs_atom74(V_j,V_i)
| $false ),
inference(fold_definition,[status(thm)],[cls_not__add__less1_0_0,def_lhs_atom74]) ).
fof(def_lhs_atom75,axiom,
! [V_j,V_i] :
( lhs_atom75(V_j,V_i)
<=> ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_i),V_i,tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_78,plain,
! [V_i,V_j] :
( lhs_atom75(V_j,V_i)
| $false ),
inference(fold_definition,[status(thm)],[cls_not__add__less2_0_0,def_lhs_atom75]) ).
fof(def_lhs_atom76,axiom,
! [V_xs,V_x,T_a] :
( lhs_atom76(V_xs,V_x,T_a)
<=> c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,V_xs,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_79,plain,
! [T_a,V_x,V_xs] :
( lhs_atom76(V_xs,V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_append__eq__Cons__conv_4_0,def_lhs_atom76]) ).
fof(def_lhs_atom77,axiom,
! [V_n] :
( lhs_atom77(V_n)
<=> c_lessequals(V_n,V_n,tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_80,plain,
! [V_n] :
( lhs_atom77(V_n)
| $false ),
inference(fold_definition,[status(thm)],[cls_le__refl_0_0,def_lhs_atom77]) ).
fof(def_lhs_atom78,axiom,
! [V_x] :
( lhs_atom78(V_x)
<=> c_lessequals(V_x,V_x,tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_81,plain,
! [V_x] :
( lhs_atom78(V_x)
| $false ),
inference(fold_definition,[status(thm)],[cls_eq__imp__le_0_0,def_lhs_atom78]) ).
fof(def_lhs_atom79,axiom,
! [V_nat,V_dB_H] :
( lhs_atom79(V_nat,V_dB_H)
<=> c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_82,plain,
! [V_dB_H,V_nat] :
( lhs_atom79(V_nat,V_dB_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_dB_Osimps_I7_J_0_0,def_lhs_atom79]) ).
fof(def_lhs_atom80,axiom,
! [V_xs,V_x,V_n,T_a] :
( lhs_atom80(V_xs,V_x,V_n,T_a)
<=> c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),V_xs,T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_83,plain,
! [T_a,V_n,V_x,V_xs] :
( lhs_atom80(V_xs,V_x,V_n,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_replicate__app__Cons__same_0_0,def_lhs_atom80]) ).
fof(def_lhs_atom81,axiom,
! [V_xs,V_n,V_f,T_b,T_a] :
( lhs_atom81(V_xs,V_n,V_f,T_b,T_a)
<=> c_List_Odrop(V_n,c_List_Omap(V_f,V_xs,T_b,T_a),T_a) = c_List_Omap(V_f,c_List_Odrop(V_n,V_xs,T_b),T_b,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_84,plain,
! [T_a,T_b,V_f,V_n,V_xs] :
( lhs_atom81(V_xs,V_n,V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_drop__map_0_0,def_lhs_atom81]) ).
fof(def_lhs_atom82,axiom,
( lhs_atom82
<=> c_Type_Otyping(v_e____,v_u____,v_T____) ),
inference(definition,[],[]) ).
fof(to_be_clausified_85,plain,
( lhs_atom82
| $false ),
inference(fold_definition,[status(thm)],[cls_uT_0_0,def_lhs_atom82]) ).
fof(def_lhs_atom83,axiom,
! [T_a] :
( lhs_atom83(T_a)
<=> c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_86,plain,
! [T_a] :
( lhs_atom83(T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_append__is__Nil__conv_2_0,def_lhs_atom83]) ).
fof(def_lhs_atom84,axiom,
! [V_zs,V_ys,V_xs,T_a] :
( lhs_atom84(V_zs,V_ys,V_xs,T_a)
<=> c_List_Oappend(c_List_Oappend(V_xs,V_ys,T_a),V_zs,T_a) = c_List_Oappend(V_xs,c_List_Oappend(V_ys,V_zs,T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_87,plain,
! [T_a,V_xs,V_ys,V_zs] :
( lhs_atom84(V_zs,V_ys,V_xs,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_append__assoc_0_0,def_lhs_atom84]) ).
fof(def_lhs_atom85,axiom,
! [V_xs1,V_xs,V_us,T_a] :
( lhs_atom85(V_xs1,V_xs,V_us,T_a)
<=> c_List_Oappend(V_xs,c_List_Oappend(V_xs1,V_us,T_a),T_a) = c_List_Oappend(c_List_Oappend(V_xs,V_xs1,T_a),V_us,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_88,plain,
! [T_a,V_us,V_xs,V_xs1] :
( lhs_atom85(V_xs1,V_xs,V_us,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_append__eq__appendI_0_0,def_lhs_atom85]) ).
fof(def_lhs_atom86,axiom,
! [V_zs,V_ys,V_x,T_a] :
( lhs_atom86(V_zs,V_ys,V_x,T_a)
<=> c_List_Oappend(c_List_Oappend(V_zs,V_x,T_a),V_ys,T_a) = c_List_Oappend(V_zs,c_List_Oappend(V_x,V_ys,T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_89,plain,
! [T_a,V_x,V_ys,V_zs] :
( lhs_atom86(V_zs,V_ys,V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_append__eq__append__conv2_4_0,def_lhs_atom86]) ).
fof(def_lhs_atom87,axiom,
! [V_xs,V_x,V_ts,T_a] :
( lhs_atom87(V_xs,V_x,V_ts,T_a)
<=> c_List_Oappend(V_xs,c_List_Oappend(V_x,V_ts,T_a),T_a) = c_List_Oappend(c_List_Oappend(V_xs,V_x,T_a),V_ts,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_90,plain,
! [T_a,V_ts,V_x,V_xs] :
( lhs_atom87(V_xs,V_x,V_ts,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_append__eq__append__conv2_5_0,def_lhs_atom87]) ).
fof(def_lhs_atom88,axiom,
! [V_x] :
( lhs_atom88(V_x)
<=> c_Nitpick_Onat__gcd(V_x,c_HOL_Ozero__class_Ozero(tc_nat)) = V_x ),
inference(definition,[],[]) ).
fof(to_be_clausified_91,plain,
! [V_x] :
( lhs_atom88(V_x)
| $false ),
inference(fold_definition,[status(thm)],[cls_nat__gcd_Osimps_0_0,def_lhs_atom88]) ).
fof(def_lhs_atom89,axiom,
( lhs_atom89
<=> c_nat_Onat__size(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_92,plain,
( lhs_atom89
| $false ),
inference(fold_definition,[status(thm)],[cls_nat_Osize_I1_J_0_0,def_lhs_atom89]) ).
fof(def_lhs_atom90,axiom,
! [V_c] :
( lhs_atom90(V_c)
<=> c_String_Ochar_Ochar__size(V_c) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_93,plain,
! [V_c] :
( lhs_atom90(V_c)
| $false ),
inference(fold_definition,[status(thm)],[cls_char__size_0_0,def_lhs_atom90]) ).
fof(def_lhs_atom91,axiom,
( lhs_atom91
<=> 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_94,plain,
( lhs_atom91
| $false ),
inference(fold_definition,[status(thm)],[cls_add__is__0_2_0,def_lhs_atom91]) ).
fof(def_lhs_atom92,axiom,
! [V_m] :
( lhs_atom92(V_m)
<=> ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_95,plain,
! [V_m] :
( lhs_atom92(V_m)
| $false ),
inference(fold_definition,[status(thm)],[cls_gr__implies__not0_0_0,def_lhs_atom92]) ).
fof(def_lhs_atom93,axiom,
! [V_n] :
( lhs_atom93(V_n)
<=> ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_96,plain,
! [V_n] :
( lhs_atom93(V_n)
| $false ),
inference(fold_definition,[status(thm)],[cls_not__less0_0_0,def_lhs_atom93]) ).
fof(def_lhs_atom94,axiom,
( lhs_atom94
<=> c_Orderings_Obot__class_Obot(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_97,plain,
( lhs_atom94
| $false ),
inference(fold_definition,[status(thm)],[cls_bot__nat__def_0_0,def_lhs_atom94]) ).
fof(def_lhs_atom95,axiom,
! [V_xs,T_a] :
( lhs_atom95(V_xs,T_a)
<=> c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),V_xs,T_a) = V_xs ),
inference(definition,[],[]) ).
fof(to_be_clausified_98,plain,
! [T_a,V_xs] :
( lhs_atom95(V_xs,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_drop__0_0_0,def_lhs_atom95]) ).
fof(def_lhs_atom96,axiom,
! [V_n] :
( lhs_atom96(V_n)
<=> c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_99,plain,
! [V_n] :
( lhs_atom96(V_n)
| $false ),
inference(fold_definition,[status(thm)],[cls_diff__0__eq__0_0_0,def_lhs_atom96]) ).
fof(def_lhs_atom97,axiom,
! [V_n] :
( lhs_atom97(V_n)
<=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_100,plain,
! [V_n] :
( lhs_atom97(V_n)
| $false ),
inference(fold_definition,[status(thm)],[cls_le0_0_0,def_lhs_atom97]) ).
fof(def_lhs_atom98,axiom,
! [V_c] :
( lhs_atom98(V_c)
<=> c_Nat_Osize__class_Osize(V_c,tc_String_Ochar) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_101,plain,
! [V_c] :
( lhs_atom98(V_c)
| $false ),
inference(fold_definition,[status(thm)],[cls_size__char_0_0,def_lhs_atom98]) ).
fof(def_lhs_atom99,axiom,
! [V_y,V_x,T_a] :
( lhs_atom99(V_y,V_x,T_a)
<=> c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_y,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_102,plain,
! [T_a,V_x,V_y] :
( lhs_atom99(V_y,V_x,T_a)
| c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_y,T_a) ),
inference(fold_definition,[status(thm)],[cls_replicate__eq__replicate_2_0,def_lhs_atom99]) ).
fof(def_lhs_atom100,axiom,
! [V_n] :
( lhs_atom100(V_n)
<=> c_Orderings_Oord__class_Omax(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_n ),
inference(definition,[],[]) ).
fof(to_be_clausified_103,plain,
! [V_n] :
( lhs_atom100(V_n)
| $false ),
inference(fold_definition,[status(thm)],[cls_max__0R_0_0,def_lhs_atom100]) ).
fof(def_lhs_atom101,axiom,
! [V_n] :
( lhs_atom101(V_n)
<=> c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = V_n ),
inference(definition,[],[]) ).
fof(to_be_clausified_104,plain,
! [V_n] :
( lhs_atom101(V_n)
| $false ),
inference(fold_definition,[status(thm)],[cls_max__0L_0_0,def_lhs_atom101]) ).
fof(def_lhs_atom102,axiom,
! [V_x] :
( lhs_atom102(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_105,plain,
! [V_x] :
( lhs_atom102(V_x)
| $false ),
inference(fold_definition,[status(thm)],[cls_natgb_Oadd__r0__iff_1_0,def_lhs_atom102]) ).
fof(def_lhs_atom103,axiom,
! [V_n] :
( lhs_atom103(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_106,plain,
! [V_n] :
( lhs_atom103(V_n)
| $false ),
inference(fold_definition,[status(thm)],[cls_plus__nat_Oadd__0_0_0,def_lhs_atom103]) ).
fof(def_lhs_atom104,axiom,
! [V_m] :
( lhs_atom104(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_107,plain,
! [V_m] :
( lhs_atom104(V_m)
| $false ),
inference(fold_definition,[status(thm)],[cls_Nat_Oadd__0__right_0_0,def_lhs_atom104]) ).
fof(def_lhs_atom105,axiom,
! [V_dB_H,V_dB2,V_dB1] :
( lhs_atom105(V_dB_H,V_dB2,V_dB1)
<=> hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != c_Lambda_OdB_OAbs(V_dB_H) ),
inference(definition,[],[]) ).
fof(to_be_clausified_108,plain,
! [V_dB1,V_dB2,V_dB_H] :
( lhs_atom105(V_dB_H,V_dB2,V_dB1)
| $false ),
inference(fold_definition,[status(thm)],[cls_dB_Osimps_I8_J_0_0,def_lhs_atom105]) ).
fof(def_lhs_atom106,axiom,
! [V_dB_H,V_dB2,V_dB1] :
( lhs_atom106(V_dB_H,V_dB2,V_dB1)
<=> c_Lambda_OdB_OAbs(V_dB_H) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) ),
inference(definition,[],[]) ).
fof(to_be_clausified_109,plain,
! [V_dB1,V_dB2,V_dB_H] :
( lhs_atom106(V_dB_H,V_dB2,V_dB1)
| $false ),
inference(fold_definition,[status(thm)],[cls_dB_Osimps_I9_J_0_0,def_lhs_atom106]) ).
fof(def_lhs_atom107,axiom,
! [V_nat,V_dB2_H,V_dB1_H] :
( lhs_atom107(V_nat,V_dB2_H,V_dB1_H)
<=> c_Lambda_OdB_OVar(V_nat) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) ),
inference(definition,[],[]) ).
fof(to_be_clausified_110,plain,
! [V_dB1_H,V_dB2_H,V_nat] :
( lhs_atom107(V_nat,V_dB2_H,V_dB1_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_dB_Osimps_I4_J_0_0,def_lhs_atom107]) ).
fof(def_lhs_atom108,axiom,
! [V_t,V_s,V_k] :
( lhs_atom108(V_t,V_s,V_k)
<=> hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,V_s),V_k)),hAPP(hAPP(c_Lambda_Olift,V_t),V_k)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_111,plain,
! [V_k,V_s,V_t] :
( lhs_atom108(V_t,V_s,V_k)
| $false ),
inference(fold_definition,[status(thm)],[cls_lift_Osimps_I2_J_0_0,def_lhs_atom108]) ).
fof(def_lhs_atom109,axiom,
! [V_f3,V_f2,V_f1,V_dB2,V_dB1,T_a] :
( lhs_atom109(V_f3,V_f2,V_f1,V_dB2,V_dB1,T_a)
<=> c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),T_a) = hAPP(hAPP(V_f2,V_dB1),V_dB2) ),
inference(definition,[],[]) ).
fof(to_be_clausified_112,plain,
! [T_a,V_dB1,V_dB2,V_f1,V_f2,V_f3] :
( lhs_atom109(V_f3,V_f2,V_f1,V_dB2,V_dB1,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_dB_Osimps_I11_J_0_0,def_lhs_atom109]) ).
fof(def_lhs_atom110,axiom,
! [V_f3,V_f2,V_f1,V_dB2,V_dB1,T_a] :
( lhs_atom110(V_f3,V_f2,V_f1,V_dB2,V_dB1,T_a)
<=> c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),T_a) = hAPP(hAPP(hAPP(hAPP(V_f2,V_dB1),V_dB2),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB1,T_a)),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB2,T_a)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_113,plain,
! [T_a,V_dB1,V_dB2,V_f1,V_f2,V_f3] :
( lhs_atom110(V_f3,V_f2,V_f1,V_dB2,V_dB1,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_dB_Orecs_I2_J_0_0,def_lhs_atom110]) ).
fof(def_lhs_atom111,axiom,
! [V_t,V_s,V_n,V_k] :
( lhs_atom111(V_t,V_s,V_n,V_k)
<=> c_Lambda_Oliftn(V_n,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(V_n,V_s,V_k)),c_Lambda_Oliftn(V_n,V_t,V_k)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_114,plain,
! [V_k,V_n,V_s,V_t] :
( lhs_atom111(V_t,V_s,V_n,V_k)
| $false ),
inference(fold_definition,[status(thm)],[cls_liftn_Osimps_I2_J_0_0,def_lhs_atom111]) ).
fof(def_lhs_atom112,axiom,
! [V_u,V_t,V_s,V_k] :
( lhs_atom112(V_u,V_t,V_s,V_k)
<=> c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_s,V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(V_t,V_s,V_k)),c_Lambda_Osubstn(V_u,V_s,V_k)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_115,plain,
! [V_k,V_s,V_t,V_u] :
( lhs_atom112(V_u,V_t,V_s,V_k)
| $false ),
inference(fold_definition,[status(thm)],[cls_substn_Osimps_I2_J_0_0,def_lhs_atom112]) ).
fof(def_lhs_atom113,axiom,
! [V_nat,V_dB2_H,V_dB1_H] :
( lhs_atom113(V_nat,V_dB2_H,V_dB1_H)
<=> hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) != c_Lambda_OdB_OVar(V_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_116,plain,
! [V_dB1_H,V_dB2_H,V_nat] :
( lhs_atom113(V_nat,V_dB2_H,V_dB1_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_dB_Osimps_I5_J_0_0,def_lhs_atom113]) ).
fof(def_lhs_atom114,axiom,
! [V_t,V_s,V_n] :
( lhs_atom114(V_t,V_s,V_n)
<=> c_Lambda_Osubstn(V_t,V_s,V_n) = hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),c_Lambda_Oliftn(V_n,V_s,c_HOL_Ozero__class_Ozero(tc_nat))),V_n) ),
inference(definition,[],[]) ).
fof(to_be_clausified_117,plain,
! [V_n,V_s,V_t] :
( lhs_atom114(V_t,V_s,V_n)
| $false ),
inference(fold_definition,[status(thm)],[cls_substn__subst__n_0_0,def_lhs_atom114]) ).
fof(def_lhs_atom115,axiom,
! [V_ts,V_ss,V_r,V_n] :
( lhs_atom115(V_ts,V_ss,V_r,V_n)
<=> c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ts,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),V_ss,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(definition,[],[]) ).
fof(to_be_clausified_118,plain,
! [V_n,V_r,V_ss,V_ts] :
( lhs_atom115(V_ts,V_ss,V_r,V_n)
| $false ),
inference(fold_definition,[status(thm)],[cls_Var__apps__neq__Abs__apps_0_0,def_lhs_atom115]) ).
fof(def_lhs_atom116,axiom,
! [V_m] :
( lhs_atom116(V_m)
<=> c_Lambda_OdB_OVar(V_m) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_m),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(definition,[],[]) ).
fof(to_be_clausified_119,plain,
! [V_m] :
( lhs_atom116(V_m)
| $false ),
inference(fold_definition,[status(thm)],[cls_Var__eq__apps__conv_2_0,def_lhs_atom116]) ).
fof(def_lhs_atom117,axiom,
! [V_r] :
( lhs_atom117(V_r)
<=> c_Lambda_OdB_OAbs(V_r) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(definition,[],[]) ).
fof(to_be_clausified_120,plain,
! [V_r] :
( lhs_atom117(V_r)
| $false ),
inference(fold_definition,[status(thm)],[cls_Abs__eq__apps__conv_2_0,def_lhs_atom117]) ).
fof(def_lhs_atom118,axiom,
! [V_t] :
( lhs_atom118(V_t)
<=> V_t = c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2(V_t),c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1(V_t),tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(definition,[],[]) ).
fof(to_be_clausified_121,plain,
! [V_t] :
( lhs_atom118(V_t)
| $false ),
inference(fold_definition,[status(thm)],[cls_ex__head__tail_0_0,def_lhs_atom118]) ).
fof(def_lhs_atom119,axiom,
! [V_r] :
( lhs_atom119(V_r)
<=> c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OAbs(V_r) ),
inference(definition,[],[]) ).
fof(to_be_clausified_122,plain,
! [V_r] :
( lhs_atom119(V_r)
| $false ),
inference(fold_definition,[status(thm)],[cls_apps__eq__Abs__conv_2_0,def_lhs_atom119]) ).
fof(def_lhs_atom120,axiom,
! [V_t,V_ss,V_s,V_n] :
( lhs_atom120(V_t,V_ss,V_s,V_n)
<=> hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ss,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(definition,[],[]) ).
fof(to_be_clausified_123,plain,
! [V_n,V_s,V_ss,V_t] :
( lhs_atom120(V_t,V_ss,V_s,V_n)
| $false ),
inference(fold_definition,[status(thm)],[cls_Abs__App__neq__Var__apps_0_0,def_lhs_atom120]) ).
fof(def_lhs_atom121,axiom,
! [V_f,V_a,T_b,T_a] :
( lhs_atom121(V_f,V_a,T_b,T_a)
<=> c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b) = V_a ),
inference(definition,[],[]) ).
fof(to_be_clausified_124,plain,
! [T_a,T_b,V_a,V_f] :
( lhs_atom121(V_f,V_a,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_foldl__Nil_0_0,def_lhs_atom121]) ).
fof(def_lhs_atom122,axiom,
! [V_xs,V_x,V_f,V_a,T_b,T_a] :
( lhs_atom122(V_xs,V_x,V_f,V_a,T_b,T_a)
<=> c_List_Ofoldl(V_f,V_a,c_List_Olist_OCons(V_x,V_xs,T_b),T_a,T_b) = c_List_Ofoldl(V_f,hAPP(hAPP(V_f,V_a),V_x),V_xs,T_a,T_b) ),
inference(definition,[],[]) ).
fof(to_be_clausified_125,plain,
! [T_a,T_b,V_a,V_f,V_x,V_xs] :
( lhs_atom122(V_xs,V_x,V_f,V_a,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_foldl__Cons_0_0,def_lhs_atom122]) ).
fof(def_lhs_atom123,axiom,
! [V_ys,V_xs,V_f,V_a,T_b,T_a] :
( lhs_atom123(V_ys,V_xs,V_f,V_a,T_b,T_a)
<=> c_List_Ofoldl(V_f,V_a,c_List_Oappend(V_xs,V_ys,T_b),T_a,T_b) = c_List_Ofoldl(V_f,c_List_Ofoldl(V_f,V_a,V_xs,T_a,T_b),V_ys,T_a,T_b) ),
inference(definition,[],[]) ).
fof(to_be_clausified_126,plain,
! [T_a,T_b,V_a,V_f,V_xs,V_ys] :
( lhs_atom123(V_ys,V_xs,V_f,V_a,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_foldl__append_0_0,def_lhs_atom123]) ).
fof(def_lhs_atom124,axiom,
! [V_u,V_ts,V_t,V_i] :
( lhs_atom124(V_u,V_ts,V_t,V_i)
<=> hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_u),V_i) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,V_u,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(definition,[],[]) ).
fof(to_be_clausified_127,plain,
! [V_i,V_t,V_ts,V_u] :
( lhs_atom124(V_u,V_ts,V_t,V_i)
| $false ),
inference(fold_definition,[status(thm)],[cls_subst__map_0_0,def_lhs_atom124]) ).
fof(def_lhs_atom125,axiom,
! [V_u,V_k] :
( lhs_atom125(V_u,V_k)
<=> hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_k)),V_u),V_k) = V_u ),
inference(definition,[],[]) ).
fof(to_be_clausified_128,plain,
! [V_k,V_u] :
( lhs_atom125(V_u,V_k)
| $false ),
inference(fold_definition,[status(thm)],[cls_subst__eq_0_0,def_lhs_atom125]) ).
fof(def_lhs_atom126,axiom,
! [V_t,V_s,V_k] :
( lhs_atom126(V_t,V_s,V_k)
<=> hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,V_t),V_k)),V_s),V_k) = V_t ),
inference(definition,[],[]) ).
fof(to_be_clausified_129,plain,
! [V_k,V_s,V_t] :
( lhs_atom126(V_t,V_s,V_k)
| $false ),
inference(fold_definition,[status(thm)],[cls_subst__lift_0_0,def_lhs_atom126]) ).
fof(def_lhs_atom127,axiom,
! [V_n] :
( lhs_atom127(V_n)
<=> hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(V_n))) ),
inference(definition,[],[]) ).
fof(to_be_clausified_130,plain,
! [V_n] :
( lhs_atom127(V_n)
| $false ),
inference(fold_definition,[status(thm)],[cls_Var__IT_0_0,def_lhs_atom127]) ).
fof(def_lhs_atom128,axiom,
( lhs_atom128
<=> hBOOL(hAPP(c_InductTermi_OIT,v_ua______)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_131,plain,
( lhs_atom128
| $false ),
inference(fold_definition,[status(thm)],[cls_Beta_I6_J_0_0,def_lhs_atom128]) ).
fof(def_lhs_atom129,axiom,
! [V_t,V_s] :
( lhs_atom129(V_t,V_s)
<=> hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_s),V_t),c_HOL_Ozero__class_Ozero(tc_nat)))) ),
inference(definition,[],[]) ).
fof(to_be_clausified_132,plain,
! [V_s,V_t] :
( lhs_atom129(V_t,V_s)
| $false ),
inference(fold_definition,[status(thm)],[cls_beta_0_0,def_lhs_atom129]) ).
fof(def_lhs_atom130,axiom,
( lhs_atom130
<=> c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____) ),
inference(definition,[],[]) ).
fof(to_be_clausified_133,plain,
( lhs_atom130
| $false ),
inference(fold_definition,[status(thm)],[cls_T_0_0,def_lhs_atom130]) ).
fof(def_lhs_atom131,axiom,
! [V_t,V_s] :
( lhs_atom131(V_t,V_s)
<=> c_Lambda_Osubstn(V_t,V_s,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_134,plain,
! [V_s,V_t] :
( lhs_atom131(V_t,V_s)
| $false ),
inference(fold_definition,[status(thm)],[cls_substn__subst__0_0_0,def_lhs_atom131]) ).
fof(def_lhs_atom132,axiom,
! [V_s,V_r] :
( lhs_atom132(V_s,V_r)
<=> hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(definition,[],[]) ).
fof(to_be_clausified_135,plain,
! [V_r,V_s] :
( lhs_atom132(V_s,V_r)
| $false ),
inference(fold_definition,[status(thm)],[cls_App__eq__foldl__conv_4_0,def_lhs_atom132]) ).
fof(def_lhs_atom133,axiom,
( lhs_atom133
<=> hBOOL(hAPP(c_InductTermi_OIT,v_a____)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_136,plain,
( lhs_atom133
| $false ),
inference(fold_definition,[status(thm)],[cls_Beta_I3_J_0_0,def_lhs_atom133]) ).
fof(def_lhs_atom134,axiom,
! [V_u,V_t,V_s,V_k] :
( lhs_atom134(V_u,V_t,V_s,V_k)
<=> hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u)),V_s),V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_k)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_u),V_s),V_k)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_137,plain,
! [V_k,V_s,V_t,V_u] :
( lhs_atom134(V_u,V_t,V_s,V_k)
| $false ),
inference(fold_definition,[status(thm)],[cls_subst__App_0_0,def_lhs_atom134]) ).
fof(def_lhs_atom135,axiom,
( lhs_atom135
<=> hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(definition,[],[]) ).
fof(to_be_clausified_138,plain,
( lhs_atom135
| $false ),
inference(fold_definition,[status(thm)],[cls_Beta_I1_J_0_0,def_lhs_atom135]) ).
fof(def_lhs_atom136,axiom,
( lhs_atom136
<=> hBOOL(hAPP(c_InductTermi_OIT,v_u____)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_139,plain,
( lhs_atom136
| $false ),
inference(fold_definition,[status(thm)],[cls_uIT_0_0,def_lhs_atom136]) ).
fof(to_be_clausified_140,plain,
( lhs_atom82
| $false ),
inference(fold_definition,[status(thm)],[cls_CHAINED_0_0,def_lhs_atom82]) ).
fof(to_be_clausified_141,plain,
( lhs_atom136
| $false ),
inference(fold_definition,[status(thm)],[cls_CHAINED_0_01_0,def_lhs_atom136]) ).
fof(def_lhs_atom137,axiom,
( lhs_atom137
<=> c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____) ),
inference(definition,[],[]) ).
fof(to_be_clausified_142,plain,
( lhs_atom137
| $false ),
inference(fold_definition,[status(thm)],[cls_CHAINED_0_02_0,def_lhs_atom137]) ).
fof(def_lhs_atom138,axiom,
( lhs_atom138
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_143,plain,
( lhs_atom138
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add_0,def_lhs_atom138]) ).
fof(def_lhs_atom139,axiom,
( lhs_atom139
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_144,plain,
( lhs_atom139
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le_0,def_lhs_atom139]) ).
fof(def_lhs_atom140,axiom,
( lhs_atom140
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_145,plain,
( lhs_atom140
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add_0,def_lhs_atom140]) ).
fof(def_lhs_atom141,axiom,
( lhs_atom141
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_146,plain,
( lhs_atom141
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__comm__monoid__add_0,def_lhs_atom141]) ).
fof(def_lhs_atom142,axiom,
( lhs_atom142
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_147,plain,
( lhs_atom142
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add_0,def_lhs_atom142]) ).
fof(def_lhs_atom143,axiom,
( lhs_atom143
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_148,plain,
( lhs_atom143
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Ocancel__semigroup__add_0,def_lhs_atom143]) ).
fof(def_lhs_atom144,axiom,
( lhs_atom144
<=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_149,plain,
( lhs_atom144
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Ono__zero__divisors_0,def_lhs_atom144]) ).
fof(def_lhs_atom145,axiom,
( lhs_atom145
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_150,plain,
( lhs_atom145
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Oordered__semidom_0,def_lhs_atom145]) ).
fof(def_lhs_atom146,axiom,
( lhs_atom146
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_151,plain,
( lhs_atom146
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Ocomm__semiring__1_0,def_lhs_atom146]) ).
fof(def_lhs_atom147,axiom,
( lhs_atom147
<=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_152,plain,
( lhs_atom147
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Oab__semigroup__add_0,def_lhs_atom147]) ).
fof(def_lhs_atom148,axiom,
( lhs_atom148
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_153,plain,
( lhs_atom148
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Ocomm__monoid__add_0,def_lhs_atom148]) ).
fof(def_lhs_atom149,axiom,
( lhs_atom149
<=> class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_154,plain,
( lhs_atom149
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Ozero__neq__one_0,def_lhs_atom149]) ).
fof(def_lhs_atom150,axiom,
( lhs_atom150
<=> class_OrderedGroup_Osemigroup__add(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_155,plain,
( lhs_atom150
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Osemigroup__add_0,def_lhs_atom150]) ).
fof(def_lhs_atom151,axiom,
( lhs_atom151
<=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_156,plain,
( lhs_atom151
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Osemiring__1_0,def_lhs_atom151]) ).
fof(def_lhs_atom152,axiom,
( lhs_atom152
<=> class_Ring__and__Field_Osemiring__0(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_157,plain,
( lhs_atom152
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Osemiring__0_0,def_lhs_atom152]) ).
fof(def_lhs_atom153,axiom,
( lhs_atom153
<=> class_Ring__and__Field_Omult__zero(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_158,plain,
( lhs_atom153
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Omult__zero_0,def_lhs_atom153]) ).
fof(def_lhs_atom154,axiom,
( lhs_atom154
<=> class_OrderedGroup_Omonoid__add(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_159,plain,
( lhs_atom154
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Omonoid__add_0,def_lhs_atom154]) ).
fof(def_lhs_atom155,axiom,
( lhs_atom155
<=> class_Nat_Osemiring__char__0(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_160,plain,
( lhs_atom155
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Nat_Osemiring__char__0_0,def_lhs_atom155]) ).
fof(def_lhs_atom156,axiom,
( lhs_atom156
<=> class_Orderings_Opreorder(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_161,plain,
( lhs_atom156
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Opreorder_0,def_lhs_atom156]) ).
fof(def_lhs_atom157,axiom,
( lhs_atom157
<=> class_Orderings_Olinorder(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_162,plain,
( lhs_atom157
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Olinorder_0,def_lhs_atom157]) ).
fof(def_lhs_atom158,axiom,
( lhs_atom158
<=> class_Orderings_Oorder(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_163,plain,
( lhs_atom158
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Oorder_0,def_lhs_atom158]) ).
fof(def_lhs_atom159,axiom,
( lhs_atom159
<=> class_Orderings_Obot(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_164,plain,
( lhs_atom159
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Obot_0,def_lhs_atom159]) ).
fof(def_lhs_atom160,axiom,
( lhs_atom160
<=> class_Power_Opower(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_165,plain,
( lhs_atom160
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Power_Opower_0,def_lhs_atom160]) ).
fof(def_lhs_atom161,axiom,
( lhs_atom161
<=> class_Orderings_Opreorder(tc_bool) ),
inference(definition,[],[]) ).
fof(to_be_clausified_166,plain,
( lhs_atom161
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Orderings_Opreorder_0,def_lhs_atom161]) ).
fof(def_lhs_atom162,axiom,
( lhs_atom162
<=> class_Orderings_Oorder(tc_bool) ),
inference(definition,[],[]) ).
fof(to_be_clausified_167,plain,
( lhs_atom162
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Orderings_Oorder_0,def_lhs_atom162]) ).
fof(def_lhs_atom163,axiom,
( lhs_atom163
<=> class_Orderings_Obot(tc_bool) ),
inference(definition,[],[]) ).
fof(to_be_clausified_168,plain,
( lhs_atom163
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Orderings_Obot_0,def_lhs_atom163]) ).
fof(def_lhs_atom164,axiom,
! [V_x,T_a] :
( lhs_atom164(V_x,T_a)
<=> hBOOL(hAPP(hAPP(c_fequal(T_a),V_x),V_x)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_169,plain,
! [T_a,V_x] :
( lhs_atom164(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_ATP__Linkup_Oequal__imp__fequal_0_0,def_lhs_atom164]) ).
% Start CNF derivation
fof(c_0_0,axiom,
! [X11,X10,X13,X8,X14,X5] :
( lhs_atom123(X11,X10,X13,X8,X14,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_126) ).
fof(c_0_1,axiom,
! [X10,X9,X13,X8,X14,X5] :
( lhs_atom122(X10,X9,X13,X8,X14,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_125) ).
fof(c_0_2,axiom,
! [X1,X2,X3,X40,X41,X5] :
( lhs_atom110(X1,X2,X3,X40,X41,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_113) ).
fof(c_0_3,axiom,
! [X1,X2,X3,X40,X41,X5] :
( lhs_atom109(X1,X2,X3,X40,X41,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_112) ).
fof(c_0_4,axiom,
! [X10,X9,X13,X8,X14,X5] :
( lhs_atom72(X10,X9,X13,X8,X14,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_75) ).
fof(c_0_5,axiom,
! [X21,X22,X23,X24,X14,X5] :
( lhs_atom19(X21,X22,X23,X24,X14,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_20) ).
fof(c_0_6,axiom,
! [X11,X10,X13,X8,X14,X5] :
( lhs_atom10(X11,X10,X13,X8,X14,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_11) ).
fof(c_0_7,axiom,
! [X10,X12,X13,X14,X5] :
( lhs_atom81(X10,X12,X13,X14,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_84) ).
fof(c_0_8,axiom,
! [X1,X2,X3,X4,X5] :
( lhs_atom71(X1,X2,X3,X4,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_74) ).
fof(c_0_9,axiom,
! [X11,X10,X13,X14,X5] :
( lhs_atom48(X11,X10,X13,X14,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_49) ).
fof(c_0_10,axiom,
! [X16,X1,X2,X3,X5] :
( lhs_atom40(X16,X1,X2,X3,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_41) ).
fof(c_0_11,axiom,
! [X10,X9,X13,X14,X5] :
( lhs_atom33(X10,X9,X13,X14,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_34) ).
fof(c_0_12,axiom,
! [X30,X29,X13,X14,X5] :
( lhs_atom32(X30,X29,X13,X14,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_33) ).
fof(c_0_13,axiom,
! [X29,X9,X13,X14,X5] :
( lhs_atom31(X29,X9,X13,X14,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_32) ).
fof(c_0_14,axiom,
! [X16,X1,X2,X3,X5] :
( lhs_atom18(X16,X1,X2,X3,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_19) ).
fof(c_0_15,axiom,
! [X9,X12,X13,X14,X5] :
( lhs_atom8(X9,X12,X13,X14,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_9) ).
fof(c_0_16,axiom,
! [X1,X2,X3,X4,X5] :
( lhs_atom1(X1,X2,X3,X4,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_0) ).
fof(c_0_17,axiom,
! [X45,X36,X44,X20] :
( lhs_atom134(X45,X36,X44,X20)
| ~ $true ),
file('<stdin>',to_be_clausified_137) ).
fof(c_0_18,axiom,
! [X45,X37,X36,X26] :
( lhs_atom124(X45,X37,X36,X26)
| ~ $true ),
file('<stdin>',to_be_clausified_127) ).
fof(c_0_19,axiom,
! [X13,X8,X14,X5] :
( lhs_atom121(X13,X8,X14,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_124) ).
fof(c_0_20,axiom,
! [X36,X46,X44,X12] :
( lhs_atom120(X36,X46,X44,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_123) ).
fof(c_0_21,axiom,
! [X37,X46,X7,X12] :
( lhs_atom115(X37,X46,X7,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_118) ).
fof(c_0_22,axiom,
! [X45,X36,X44,X20] :
( lhs_atom112(X45,X36,X44,X20)
| ~ $true ),
file('<stdin>',to_be_clausified_115) ).
fof(c_0_23,axiom,
! [X36,X44,X12,X20] :
( lhs_atom111(X36,X44,X12,X20)
| ~ $true ),
file('<stdin>',to_be_clausified_114) ).
fof(c_0_24,axiom,
! [X10,X9,X37,X5] :
( lhs_atom87(X10,X9,X37,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_90) ).
fof(c_0_25,axiom,
! [X28,X11,X9,X5] :
( lhs_atom86(X28,X11,X9,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_89) ).
fof(c_0_26,axiom,
! [X31,X10,X38,X5] :
( lhs_atom85(X31,X10,X38,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_88) ).
fof(c_0_27,axiom,
! [X28,X11,X10,X5] :
( lhs_atom84(X28,X11,X10,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_87) ).
fof(c_0_28,axiom,
! [X10,X9,X12,X5] :
( lhs_atom80(X10,X9,X12,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_83) ).
fof(c_0_29,axiom,
! [X9,X20,X26,X5] :
( lhs_atom55(X9,X20,X26,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_56) ).
fof(c_0_30,axiom,
! [X9,X12,X15,X5] :
( lhs_atom53(X9,X12,X15,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_54) ).
fof(c_0_31,axiom,
! [X10,X12,X15,X5] :
( lhs_atom52(X10,X12,X15,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_53) ).
fof(c_0_32,axiom,
! [X9,X12,X20,X5] :
( lhs_atom49(X9,X12,X20,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_50) ).
fof(c_0_33,axiom,
! [X9,X34,X35,X5] :
( lhs_atom38(X9,X34,X35,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_39) ).
fof(c_0_34,axiom,
! [X28,X31,X9,X5] :
( lhs_atom35(X28,X31,X9,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_36) ).
fof(c_0_35,axiom,
! [X28,X29,X9,X5] :
( lhs_atom34(X28,X29,X9,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_35) ).
fof(c_0_36,axiom,
! [X11,X10,X9,X5] :
( lhs_atom29(X11,X10,X9,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_30) ).
fof(c_0_37,axiom,
! [X28,X29,X9,X5] :
( lhs_atom28(X28,X29,X9,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_29) ).
fof(c_0_38,axiom,
! [X13,X8,X14,X5] :
( lhs_atom20(X13,X8,X14,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_21) ).
fof(c_0_39,axiom,
! [X19,X9,X5] :
( lhs_atom99(X19,X9,X5)
| c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X9,X5) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X19,X5) ),
file('<stdin>',to_be_clausified_102) ).
fof(c_0_40,axiom,
! [X36,X44,X20] :
( lhs_atom126(X36,X44,X20)
| ~ $true ),
file('<stdin>',to_be_clausified_129) ).
fof(c_0_41,axiom,
! [X36,X44,X12] :
( lhs_atom114(X36,X44,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_117) ).
fof(c_0_42,axiom,
! [X16,X42,X43] :
( lhs_atom113(X16,X42,X43)
| ~ $true ),
file('<stdin>',to_be_clausified_116) ).
fof(c_0_43,axiom,
! [X36,X44,X20] :
( lhs_atom108(X36,X44,X20)
| ~ $true ),
file('<stdin>',to_be_clausified_111) ).
fof(c_0_44,axiom,
! [X16,X42,X43] :
( lhs_atom107(X16,X42,X43)
| ~ $true ),
file('<stdin>',to_be_clausified_110) ).
fof(c_0_45,axiom,
! [X17,X40,X41] :
( lhs_atom106(X17,X40,X41)
| ~ $true ),
file('<stdin>',to_be_clausified_109) ).
fof(c_0_46,axiom,
! [X17,X40,X41] :
( lhs_atom105(X17,X40,X41)
| ~ $true ),
file('<stdin>',to_be_clausified_108) ).
fof(c_0_47,axiom,
! [X10,X9,X5] :
( lhs_atom76(X10,X9,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_79) ).
fof(c_0_48,axiom,
! [X7,X14,X5] :
( lhs_atom73(X7,X14,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_76) ).
fof(c_0_49,axiom,
! [X2,X3,X5] :
( lhs_atom68(X2,X3,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_71) ).
fof(c_0_50,axiom,
! [X9,X13,X5] :
( lhs_atom67(X9,X13,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_70) ).
fof(c_0_51,axiom,
! [X9,X26,X5] :
( lhs_atom61(X9,X26,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_64) ).
fof(c_0_52,axiom,
! [X13,X14,X5] :
( lhs_atom21(X13,X14,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_61) ).
fof(c_0_53,axiom,
! [X10,X9,X5] :
( lhs_atom58(X10,X9,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_60) ).
fof(c_0_54,axiom,
! [X10,X9,X5] :
( lhs_atom57(X10,X9,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_59) ).
fof(c_0_55,axiom,
! [X9,X36,X5] :
( lhs_atom56(X9,X36,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_58) ).
fof(c_0_56,axiom,
! [X37,X36,X26] :
( lhs_atom54(X37,X36,X26)
| ~ $true ),
file('<stdin>',to_be_clausified_55) ).
fof(c_0_57,axiom,
! [X32,X33,X5] :
( lhs_atom50(X32,X33,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_51) ).
fof(c_0_58,axiom,
! [X32,X33,X5] :
( lhs_atom37(X32,X33,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_38) ).
fof(c_0_59,axiom,
! [X29,X9,X5] :
( lhs_atom36(X29,X9,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_37) ).
fof(c_0_60,axiom,
! [X20,X25,X26] :
( lhs_atom30(X20,X25,X26)
| ~ $true ),
file('<stdin>',to_be_clausified_31) ).
fof(c_0_61,axiom,
! [X12,X15,X20] :
( lhs_atom25(X12,X15,X20)
| ~ $true ),
file('<stdin>',to_be_clausified_26) ).
fof(c_0_62,axiom,
! [X12,X15,X20] :
( lhs_atom24(X12,X15,X20)
| ~ $true ),
file('<stdin>',to_be_clausified_25) ).
fof(c_0_63,axiom,
! [X20,X25,X26] :
( lhs_atom23(X20,X25,X26)
| ~ $true ),
file('<stdin>',to_be_clausified_24) ).
fof(c_0_64,axiom,
! [X13,X14,X5] :
( lhs_atom21(X13,X14,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_22) ).
fof(c_0_65,axiom,
! [X10,X9,X5] :
( lhs_atom17(X10,X9,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_18) ).
fof(c_0_66,axiom,
! [X12,X15,X20] :
( lhs_atom16(X12,X15,X20)
| ~ $true ),
file('<stdin>',to_be_clausified_17) ).
fof(c_0_67,axiom,
! [X18,X19,X9] :
( lhs_atom15(X18,X19,X9)
| ~ $true ),
file('<stdin>',to_be_clausified_16) ).
fof(c_0_68,axiom,
! [X10,X7,X5] :
( lhs_atom14(X10,X7,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_15) ).
fof(c_0_69,axiom,
! [X10,X7,X5] :
( lhs_atom13(X10,X7,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_14) ).
fof(c_0_70,axiom,
! [X9,X7,X5] :
( lhs_atom4(X9,X7,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_3) ).
fof(c_0_71,axiom,
! [X7,X8,X5] :
( lhs_atom3(X7,X8,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_2) ).
fof(c_0_72,axiom,
! [X9,X5] :
( lhs_atom164(X9,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_169) ).
fof(c_0_73,axiom,
! [X44,X7] :
( lhs_atom132(X44,X7)
| ~ $true ),
file('<stdin>',to_be_clausified_135) ).
fof(c_0_74,axiom,
! [X36,X44] :
( lhs_atom131(X36,X44)
| ~ $true ),
file('<stdin>',to_be_clausified_134) ).
fof(c_0_75,axiom,
! [X36,X44] :
( lhs_atom129(X36,X44)
| ~ $true ),
file('<stdin>',to_be_clausified_132) ).
fof(c_0_76,axiom,
! [X45,X20] :
( lhs_atom125(X45,X20)
| ~ $true ),
file('<stdin>',to_be_clausified_128) ).
fof(c_0_77,axiom,
! [X10,X5] :
( lhs_atom95(X10,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_98) ).
fof(c_0_78,axiom,
! [X16,X17] :
( lhs_atom79(X16,X17)
| ~ $true ),
file('<stdin>',to_be_clausified_82) ).
fof(c_0_79,axiom,
! [X25,X26] :
( lhs_atom75(X25,X26)
| ~ $true ),
file('<stdin>',to_be_clausified_78) ).
fof(c_0_80,axiom,
! [X25,X26] :
( lhs_atom74(X25,X26)
| ~ $true ),
file('<stdin>',to_be_clausified_77) ).
fof(c_0_81,axiom,
! [X36,X20] :
( lhs_atom66(X36,X20)
| ~ $true ),
file('<stdin>',to_be_clausified_69) ).
fof(c_0_82,axiom,
! [X12,X15] :
( lhs_atom63(X12,X15)
| ~ $true ),
file('<stdin>',to_be_clausified_66) ).
fof(c_0_83,axiom,
! [X12,X15] :
( lhs_atom62(X12,X15)
| ~ $true ),
file('<stdin>',to_be_clausified_65) ).
fof(c_0_84,axiom,
! [X7,X5] :
( lhs_atom60(X7,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_63) ).
fof(c_0_85,axiom,
! [X9,X5] :
( lhs_atom41(X9,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_57) ).
fof(c_0_86,axiom,
! [X36,X26] :
( lhs_atom51(X36,X26)
| ~ $true ),
file('<stdin>',to_be_clausified_52) ).
fof(c_0_87,axiom,
! [X12,X15] :
( lhs_atom47(X12,X15)
| ~ $true ),
file('<stdin>',to_be_clausified_48) ).
fof(c_0_88,axiom,
! [X9,X15] :
( lhs_atom46(X9,X15)
| ~ $true ),
file('<stdin>',to_be_clausified_47) ).
fof(c_0_89,axiom,
! [X12,X15] :
( lhs_atom45(X12,X15)
| ~ $true ),
file('<stdin>',to_be_clausified_46) ).
fof(c_0_90,axiom,
! [X12,X15] :
( lhs_atom44(X12,X15)
| ~ $true ),
file('<stdin>',to_be_clausified_45) ).
fof(c_0_91,axiom,
! [X9,X5] :
( lhs_atom41(X9,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_42) ).
fof(c_0_92,axiom,
! [X9,X27] :
( lhs_atom27(X9,X27)
| ~ $true ),
file('<stdin>',to_be_clausified_28) ).
fof(c_0_93,axiom,
! [X12,X15] :
( lhs_atom26(X12,X15)
| ~ $true ),
file('<stdin>',to_be_clausified_27) ).
fof(c_0_94,axiom,
! [X12,X15] :
( lhs_atom22(X12,X15)
| ~ $true ),
file('<stdin>',to_be_clausified_23) ).
fof(c_0_95,axiom,
! [X16,X17] :
( lhs_atom12(X16,X17)
| ~ $true ),
file('<stdin>',to_be_clausified_13) ).
fof(c_0_96,axiom,
! [X12,X5] :
( lhs_atom11(X12,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_12) ).
fof(c_0_97,axiom,
! [X12,X15] :
( lhs_atom9(X12,X15)
| ~ $true ),
file('<stdin>',to_be_clausified_10) ).
fof(c_0_98,axiom,
! [X11,X5] :
( lhs_atom7(X11,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_8) ).
fof(c_0_99,axiom,
! [X11,X5] :
( lhs_atom7(X11,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_7) ).
fof(c_0_100,axiom,
! [X10,X5] :
( lhs_atom5(X10,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_6) ).
fof(c_0_101,axiom,
! [X9,X5] :
( lhs_atom6(X9,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_5) ).
fof(c_0_102,axiom,
! [X10,X5] :
( lhs_atom5(X10,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_4) ).
fof(c_0_103,axiom,
! [X6,X5] :
( lhs_atom2(X6,X5)
| ~ $true ),
file('<stdin>',to_be_clausified_1) ).
fof(c_0_104,axiom,
! [X12] :
( lhs_atom127(X12)
| ~ $true ),
file('<stdin>',to_be_clausified_130) ).
fof(c_0_105,axiom,
! [X7] :
( lhs_atom119(X7)
| ~ $true ),
file('<stdin>',to_be_clausified_122) ).
fof(c_0_106,axiom,
! [X36] :
( lhs_atom118(X36)
| ~ $true ),
file('<stdin>',to_be_clausified_121) ).
fof(c_0_107,axiom,
! [X7] :
( lhs_atom117(X7)
| ~ $true ),
file('<stdin>',to_be_clausified_120) ).
fof(c_0_108,axiom,
! [X15] :
( lhs_atom116(X15)
| ~ $true ),
file('<stdin>',to_be_clausified_119) ).
fof(c_0_109,axiom,
! [X15] :
( lhs_atom104(X15)
| ~ $true ),
file('<stdin>',to_be_clausified_107) ).
fof(c_0_110,axiom,
! [X12] :
( lhs_atom103(X12)
| ~ $true ),
file('<stdin>',to_be_clausified_106) ).
fof(c_0_111,axiom,
! [X9] :
( lhs_atom102(X9)
| ~ $true ),
file('<stdin>',to_be_clausified_105) ).
fof(c_0_112,axiom,
! [X12] :
( lhs_atom101(X12)
| ~ $true ),
file('<stdin>',to_be_clausified_104) ).
fof(c_0_113,axiom,
! [X12] :
( lhs_atom100(X12)
| ~ $true ),
file('<stdin>',to_be_clausified_103) ).
fof(c_0_114,axiom,
! [X39] :
( lhs_atom98(X39)
| ~ $true ),
file('<stdin>',to_be_clausified_101) ).
fof(c_0_115,axiom,
! [X12] :
( lhs_atom97(X12)
| ~ $true ),
file('<stdin>',to_be_clausified_100) ).
fof(c_0_116,axiom,
! [X12] :
( lhs_atom96(X12)
| ~ $true ),
file('<stdin>',to_be_clausified_99) ).
fof(c_0_117,axiom,
! [X12] :
( lhs_atom93(X12)
| ~ $true ),
file('<stdin>',to_be_clausified_96) ).
fof(c_0_118,axiom,
! [X15] :
( lhs_atom92(X15)
| ~ $true ),
file('<stdin>',to_be_clausified_95) ).
fof(c_0_119,axiom,
! [X39] :
( lhs_atom90(X39)
| ~ $true ),
file('<stdin>',to_be_clausified_93) ).
fof(c_0_120,axiom,
! [X9] :
( lhs_atom88(X9)
| ~ $true ),
file('<stdin>',to_be_clausified_91) ).
fof(c_0_121,axiom,
! [X5] :
( lhs_atom83(X5)
| ~ $true ),
file('<stdin>',to_be_clausified_86) ).
fof(c_0_122,axiom,
! [X9] :
( lhs_atom78(X9)
| ~ $true ),
file('<stdin>',to_be_clausified_81) ).
fof(c_0_123,axiom,
! [X12] :
( lhs_atom77(X12)
| ~ $true ),
file('<stdin>',to_be_clausified_80) ).
fof(c_0_124,axiom,
! [X15] :
( lhs_atom70(X15)
| ~ $true ),
file('<stdin>',to_be_clausified_73) ).
fof(c_0_125,axiom,
! [X15] :
( lhs_atom69(X15)
| ~ $true ),
file('<stdin>',to_be_clausified_72) ).
fof(c_0_126,axiom,
! [X5] :
( lhs_atom59(X5)
| ~ $true ),
file('<stdin>',to_be_clausified_62) ).
fof(c_0_127,axiom,
! [X12] :
( lhs_atom43(X12)
| ~ $true ),
file('<stdin>',to_be_clausified_44) ).
fof(c_0_128,axiom,
! [X9] :
( lhs_atom42(X9)
| ~ $true ),
file('<stdin>',to_be_clausified_43) ).
fof(c_0_129,axiom,
! [X5] :
( lhs_atom39(X5)
| ~ $true ),
file('<stdin>',to_be_clausified_40) ).
fof(c_0_130,axiom,
( lhs_atom163
| ~ $true ),
file('<stdin>',to_be_clausified_168) ).
fof(c_0_131,axiom,
( lhs_atom162
| ~ $true ),
file('<stdin>',to_be_clausified_167) ).
fof(c_0_132,axiom,
( lhs_atom161
| ~ $true ),
file('<stdin>',to_be_clausified_166) ).
fof(c_0_133,axiom,
( lhs_atom160
| ~ $true ),
file('<stdin>',to_be_clausified_165) ).
fof(c_0_134,axiom,
( lhs_atom159
| ~ $true ),
file('<stdin>',to_be_clausified_164) ).
fof(c_0_135,axiom,
( lhs_atom158
| ~ $true ),
file('<stdin>',to_be_clausified_163) ).
fof(c_0_136,axiom,
( lhs_atom157
| ~ $true ),
file('<stdin>',to_be_clausified_162) ).
fof(c_0_137,axiom,
( lhs_atom156
| ~ $true ),
file('<stdin>',to_be_clausified_161) ).
fof(c_0_138,axiom,
( lhs_atom155
| ~ $true ),
file('<stdin>',to_be_clausified_160) ).
fof(c_0_139,axiom,
( lhs_atom154
| ~ $true ),
file('<stdin>',to_be_clausified_159) ).
fof(c_0_140,axiom,
( lhs_atom153
| ~ $true ),
file('<stdin>',to_be_clausified_158) ).
fof(c_0_141,axiom,
( lhs_atom152
| ~ $true ),
file('<stdin>',to_be_clausified_157) ).
fof(c_0_142,axiom,
( lhs_atom151
| ~ $true ),
file('<stdin>',to_be_clausified_156) ).
fof(c_0_143,axiom,
( lhs_atom150
| ~ $true ),
file('<stdin>',to_be_clausified_155) ).
fof(c_0_144,axiom,
( lhs_atom149
| ~ $true ),
file('<stdin>',to_be_clausified_154) ).
fof(c_0_145,axiom,
( lhs_atom148
| ~ $true ),
file('<stdin>',to_be_clausified_153) ).
fof(c_0_146,axiom,
( lhs_atom147
| ~ $true ),
file('<stdin>',to_be_clausified_152) ).
fof(c_0_147,axiom,
( lhs_atom146
| ~ $true ),
file('<stdin>',to_be_clausified_151) ).
fof(c_0_148,axiom,
( lhs_atom145
| ~ $true ),
file('<stdin>',to_be_clausified_150) ).
fof(c_0_149,axiom,
( lhs_atom144
| ~ $true ),
file('<stdin>',to_be_clausified_149) ).
fof(c_0_150,axiom,
( lhs_atom143
| ~ $true ),
file('<stdin>',to_be_clausified_148) ).
fof(c_0_151,axiom,
( lhs_atom142
| ~ $true ),
file('<stdin>',to_be_clausified_147) ).
fof(c_0_152,axiom,
( lhs_atom141
| ~ $true ),
file('<stdin>',to_be_clausified_146) ).
fof(c_0_153,axiom,
( lhs_atom140
| ~ $true ),
file('<stdin>',to_be_clausified_145) ).
fof(c_0_154,axiom,
( lhs_atom139
| ~ $true ),
file('<stdin>',to_be_clausified_144) ).
fof(c_0_155,axiom,
( lhs_atom138
| ~ $true ),
file('<stdin>',to_be_clausified_143) ).
fof(c_0_156,axiom,
( lhs_atom137
| ~ $true ),
file('<stdin>',to_be_clausified_142) ).
fof(c_0_157,axiom,
( lhs_atom136
| ~ $true ),
file('<stdin>',to_be_clausified_141) ).
fof(c_0_158,axiom,
( lhs_atom82
| ~ $true ),
file('<stdin>',to_be_clausified_140) ).
fof(c_0_159,axiom,
( lhs_atom136
| ~ $true ),
file('<stdin>',to_be_clausified_139) ).
fof(c_0_160,axiom,
( lhs_atom135
| ~ $true ),
file('<stdin>',to_be_clausified_138) ).
fof(c_0_161,axiom,
( lhs_atom133
| ~ $true ),
file('<stdin>',to_be_clausified_136) ).
fof(c_0_162,axiom,
( lhs_atom130
| ~ $true ),
file('<stdin>',to_be_clausified_133) ).
fof(c_0_163,axiom,
( lhs_atom128
| ~ $true ),
file('<stdin>',to_be_clausified_131) ).
fof(c_0_164,axiom,
( lhs_atom94
| ~ $true ),
file('<stdin>',to_be_clausified_97) ).
fof(c_0_165,axiom,
( lhs_atom91
| ~ $true ),
file('<stdin>',to_be_clausified_94) ).
fof(c_0_166,axiom,
( lhs_atom89
| ~ $true ),
file('<stdin>',to_be_clausified_92) ).
fof(c_0_167,axiom,
( lhs_atom82
| ~ $true ),
file('<stdin>',to_be_clausified_85) ).
fof(c_0_168,axiom,
( lhs_atom65
| ~ $true ),
file('<stdin>',to_be_clausified_68) ).
fof(c_0_169,axiom,
( lhs_atom64
| ~ $true ),
file('<stdin>',to_be_clausified_67) ).
fof(c_0_170,plain,
! [X11,X10,X13,X8,X14,X5] : lhs_atom123(X11,X10,X13,X8,X14,X5),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_171,plain,
! [X10,X9,X13,X8,X14,X5] : lhs_atom122(X10,X9,X13,X8,X14,X5),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_172,plain,
! [X1,X2,X3,X40,X41,X5] : lhs_atom110(X1,X2,X3,X40,X41,X5),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_173,plain,
! [X1,X2,X3,X40,X41,X5] : lhs_atom109(X1,X2,X3,X40,X41,X5),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_174,plain,
! [X10,X9,X13,X8,X14,X5] : lhs_atom72(X10,X9,X13,X8,X14,X5),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_175,plain,
! [X21,X22,X23,X24,X14,X5] : lhs_atom19(X21,X22,X23,X24,X14,X5),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_176,plain,
! [X11,X10,X13,X8,X14,X5] : lhs_atom10(X11,X10,X13,X8,X14,X5),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_177,plain,
! [X10,X12,X13,X14,X5] : lhs_atom81(X10,X12,X13,X14,X5),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_178,plain,
! [X1,X2,X3,X4,X5] : lhs_atom71(X1,X2,X3,X4,X5),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_179,plain,
! [X11,X10,X13,X14,X5] : lhs_atom48(X11,X10,X13,X14,X5),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_180,plain,
! [X16,X1,X2,X3,X5] : lhs_atom40(X16,X1,X2,X3,X5),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_181,plain,
! [X10,X9,X13,X14,X5] : lhs_atom33(X10,X9,X13,X14,X5),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_182,plain,
! [X30,X29,X13,X14,X5] : lhs_atom32(X30,X29,X13,X14,X5),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_183,plain,
! [X29,X9,X13,X14,X5] : lhs_atom31(X29,X9,X13,X14,X5),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_184,plain,
! [X16,X1,X2,X3,X5] : lhs_atom18(X16,X1,X2,X3,X5),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_185,plain,
! [X9,X12,X13,X14,X5] : lhs_atom8(X9,X12,X13,X14,X5),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_186,plain,
! [X1,X2,X3,X4,X5] : lhs_atom1(X1,X2,X3,X4,X5),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_187,plain,
! [X45,X36,X44,X20] : lhs_atom134(X45,X36,X44,X20),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_188,plain,
! [X45,X37,X36,X26] : lhs_atom124(X45,X37,X36,X26),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_189,plain,
! [X13,X8,X14,X5] : lhs_atom121(X13,X8,X14,X5),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_190,plain,
! [X36,X46,X44,X12] : lhs_atom120(X36,X46,X44,X12),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
fof(c_0_191,plain,
! [X37,X46,X7,X12] : lhs_atom115(X37,X46,X7,X12),
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_192,plain,
! [X45,X36,X44,X20] : lhs_atom112(X45,X36,X44,X20),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_193,plain,
! [X36,X44,X12,X20] : lhs_atom111(X36,X44,X12,X20),
inference(fof_simplification,[status(thm)],[c_0_23]) ).
fof(c_0_194,plain,
! [X10,X9,X37,X5] : lhs_atom87(X10,X9,X37,X5),
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_195,plain,
! [X28,X11,X9,X5] : lhs_atom86(X28,X11,X9,X5),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_196,plain,
! [X31,X10,X38,X5] : lhs_atom85(X31,X10,X38,X5),
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_197,plain,
! [X28,X11,X10,X5] : lhs_atom84(X28,X11,X10,X5),
inference(fof_simplification,[status(thm)],[c_0_27]) ).
fof(c_0_198,plain,
! [X10,X9,X12,X5] : lhs_atom80(X10,X9,X12,X5),
inference(fof_simplification,[status(thm)],[c_0_28]) ).
fof(c_0_199,plain,
! [X9,X20,X26,X5] : lhs_atom55(X9,X20,X26,X5),
inference(fof_simplification,[status(thm)],[c_0_29]) ).
fof(c_0_200,plain,
! [X9,X12,X15,X5] : lhs_atom53(X9,X12,X15,X5),
inference(fof_simplification,[status(thm)],[c_0_30]) ).
fof(c_0_201,plain,
! [X10,X12,X15,X5] : lhs_atom52(X10,X12,X15,X5),
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_202,plain,
! [X9,X12,X20,X5] : lhs_atom49(X9,X12,X20,X5),
inference(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_203,plain,
! [X9,X34,X35,X5] : lhs_atom38(X9,X34,X35,X5),
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_204,plain,
! [X28,X31,X9,X5] : lhs_atom35(X28,X31,X9,X5),
inference(fof_simplification,[status(thm)],[c_0_34]) ).
fof(c_0_205,plain,
! [X28,X29,X9,X5] : lhs_atom34(X28,X29,X9,X5),
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_206,plain,
! [X11,X10,X9,X5] : lhs_atom29(X11,X10,X9,X5),
inference(fof_simplification,[status(thm)],[c_0_36]) ).
fof(c_0_207,plain,
! [X28,X29,X9,X5] : lhs_atom28(X28,X29,X9,X5),
inference(fof_simplification,[status(thm)],[c_0_37]) ).
fof(c_0_208,plain,
! [X13,X8,X14,X5] : lhs_atom20(X13,X8,X14,X5),
inference(fof_simplification,[status(thm)],[c_0_38]) ).
fof(c_0_209,axiom,
! [X19,X9,X5] :
( lhs_atom99(X19,X9,X5)
| c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X9,X5) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X19,X5) ),
c_0_39 ).
fof(c_0_210,plain,
! [X36,X44,X20] : lhs_atom126(X36,X44,X20),
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_211,plain,
! [X36,X44,X12] : lhs_atom114(X36,X44,X12),
inference(fof_simplification,[status(thm)],[c_0_41]) ).
fof(c_0_212,plain,
! [X16,X42,X43] : lhs_atom113(X16,X42,X43),
inference(fof_simplification,[status(thm)],[c_0_42]) ).
fof(c_0_213,plain,
! [X36,X44,X20] : lhs_atom108(X36,X44,X20),
inference(fof_simplification,[status(thm)],[c_0_43]) ).
fof(c_0_214,plain,
! [X16,X42,X43] : lhs_atom107(X16,X42,X43),
inference(fof_simplification,[status(thm)],[c_0_44]) ).
fof(c_0_215,plain,
! [X17,X40,X41] : lhs_atom106(X17,X40,X41),
inference(fof_simplification,[status(thm)],[c_0_45]) ).
fof(c_0_216,plain,
! [X17,X40,X41] : lhs_atom105(X17,X40,X41),
inference(fof_simplification,[status(thm)],[c_0_46]) ).
fof(c_0_217,plain,
! [X10,X9,X5] : lhs_atom76(X10,X9,X5),
inference(fof_simplification,[status(thm)],[c_0_47]) ).
fof(c_0_218,plain,
! [X7,X14,X5] : lhs_atom73(X7,X14,X5),
inference(fof_simplification,[status(thm)],[c_0_48]) ).
fof(c_0_219,plain,
! [X2,X3,X5] : lhs_atom68(X2,X3,X5),
inference(fof_simplification,[status(thm)],[c_0_49]) ).
fof(c_0_220,plain,
! [X9,X13,X5] : lhs_atom67(X9,X13,X5),
inference(fof_simplification,[status(thm)],[c_0_50]) ).
fof(c_0_221,plain,
! [X9,X26,X5] : lhs_atom61(X9,X26,X5),
inference(fof_simplification,[status(thm)],[c_0_51]) ).
fof(c_0_222,plain,
! [X13,X14,X5] : lhs_atom21(X13,X14,X5),
inference(fof_simplification,[status(thm)],[c_0_52]) ).
fof(c_0_223,plain,
! [X10,X9,X5] : lhs_atom58(X10,X9,X5),
inference(fof_simplification,[status(thm)],[c_0_53]) ).
fof(c_0_224,plain,
! [X10,X9,X5] : lhs_atom57(X10,X9,X5),
inference(fof_simplification,[status(thm)],[c_0_54]) ).
fof(c_0_225,plain,
! [X9,X36,X5] : lhs_atom56(X9,X36,X5),
inference(fof_simplification,[status(thm)],[c_0_55]) ).
fof(c_0_226,plain,
! [X37,X36,X26] : lhs_atom54(X37,X36,X26),
inference(fof_simplification,[status(thm)],[c_0_56]) ).
fof(c_0_227,plain,
! [X32,X33,X5] : lhs_atom50(X32,X33,X5),
inference(fof_simplification,[status(thm)],[c_0_57]) ).
fof(c_0_228,plain,
! [X32,X33,X5] : lhs_atom37(X32,X33,X5),
inference(fof_simplification,[status(thm)],[c_0_58]) ).
fof(c_0_229,plain,
! [X29,X9,X5] : lhs_atom36(X29,X9,X5),
inference(fof_simplification,[status(thm)],[c_0_59]) ).
fof(c_0_230,plain,
! [X20,X25,X26] : lhs_atom30(X20,X25,X26),
inference(fof_simplification,[status(thm)],[c_0_60]) ).
fof(c_0_231,plain,
! [X12,X15,X20] : lhs_atom25(X12,X15,X20),
inference(fof_simplification,[status(thm)],[c_0_61]) ).
fof(c_0_232,plain,
! [X12,X15,X20] : lhs_atom24(X12,X15,X20),
inference(fof_simplification,[status(thm)],[c_0_62]) ).
fof(c_0_233,plain,
! [X20,X25,X26] : lhs_atom23(X20,X25,X26),
inference(fof_simplification,[status(thm)],[c_0_63]) ).
fof(c_0_234,plain,
! [X13,X14,X5] : lhs_atom21(X13,X14,X5),
inference(fof_simplification,[status(thm)],[c_0_64]) ).
fof(c_0_235,plain,
! [X10,X9,X5] : lhs_atom17(X10,X9,X5),
inference(fof_simplification,[status(thm)],[c_0_65]) ).
fof(c_0_236,plain,
! [X12,X15,X20] : lhs_atom16(X12,X15,X20),
inference(fof_simplification,[status(thm)],[c_0_66]) ).
fof(c_0_237,plain,
! [X18,X19,X9] : lhs_atom15(X18,X19,X9),
inference(fof_simplification,[status(thm)],[c_0_67]) ).
fof(c_0_238,plain,
! [X10,X7,X5] : lhs_atom14(X10,X7,X5),
inference(fof_simplification,[status(thm)],[c_0_68]) ).
fof(c_0_239,plain,
! [X10,X7,X5] : lhs_atom13(X10,X7,X5),
inference(fof_simplification,[status(thm)],[c_0_69]) ).
fof(c_0_240,plain,
! [X9,X7,X5] : lhs_atom4(X9,X7,X5),
inference(fof_simplification,[status(thm)],[c_0_70]) ).
fof(c_0_241,plain,
! [X7,X8,X5] : lhs_atom3(X7,X8,X5),
inference(fof_simplification,[status(thm)],[c_0_71]) ).
fof(c_0_242,plain,
! [X9,X5] : lhs_atom164(X9,X5),
inference(fof_simplification,[status(thm)],[c_0_72]) ).
fof(c_0_243,plain,
! [X44,X7] : lhs_atom132(X44,X7),
inference(fof_simplification,[status(thm)],[c_0_73]) ).
fof(c_0_244,plain,
! [X36,X44] : lhs_atom131(X36,X44),
inference(fof_simplification,[status(thm)],[c_0_74]) ).
fof(c_0_245,plain,
! [X36,X44] : lhs_atom129(X36,X44),
inference(fof_simplification,[status(thm)],[c_0_75]) ).
fof(c_0_246,plain,
! [X45,X20] : lhs_atom125(X45,X20),
inference(fof_simplification,[status(thm)],[c_0_76]) ).
fof(c_0_247,plain,
! [X10,X5] : lhs_atom95(X10,X5),
inference(fof_simplification,[status(thm)],[c_0_77]) ).
fof(c_0_248,plain,
! [X16,X17] : lhs_atom79(X16,X17),
inference(fof_simplification,[status(thm)],[c_0_78]) ).
fof(c_0_249,plain,
! [X25,X26] : lhs_atom75(X25,X26),
inference(fof_simplification,[status(thm)],[c_0_79]) ).
fof(c_0_250,plain,
! [X25,X26] : lhs_atom74(X25,X26),
inference(fof_simplification,[status(thm)],[c_0_80]) ).
fof(c_0_251,plain,
! [X36,X20] : lhs_atom66(X36,X20),
inference(fof_simplification,[status(thm)],[c_0_81]) ).
fof(c_0_252,plain,
! [X12,X15] : lhs_atom63(X12,X15),
inference(fof_simplification,[status(thm)],[c_0_82]) ).
fof(c_0_253,plain,
! [X12,X15] : lhs_atom62(X12,X15),
inference(fof_simplification,[status(thm)],[c_0_83]) ).
fof(c_0_254,plain,
! [X7,X5] : lhs_atom60(X7,X5),
inference(fof_simplification,[status(thm)],[c_0_84]) ).
fof(c_0_255,plain,
! [X9,X5] : lhs_atom41(X9,X5),
inference(fof_simplification,[status(thm)],[c_0_85]) ).
fof(c_0_256,plain,
! [X36,X26] : lhs_atom51(X36,X26),
inference(fof_simplification,[status(thm)],[c_0_86]) ).
fof(c_0_257,plain,
! [X12,X15] : lhs_atom47(X12,X15),
inference(fof_simplification,[status(thm)],[c_0_87]) ).
fof(c_0_258,plain,
! [X9,X15] : lhs_atom46(X9,X15),
inference(fof_simplification,[status(thm)],[c_0_88]) ).
fof(c_0_259,plain,
! [X12,X15] : lhs_atom45(X12,X15),
inference(fof_simplification,[status(thm)],[c_0_89]) ).
fof(c_0_260,plain,
! [X12,X15] : lhs_atom44(X12,X15),
inference(fof_simplification,[status(thm)],[c_0_90]) ).
fof(c_0_261,plain,
! [X9,X5] : lhs_atom41(X9,X5),
inference(fof_simplification,[status(thm)],[c_0_91]) ).
fof(c_0_262,plain,
! [X9,X27] : lhs_atom27(X9,X27),
inference(fof_simplification,[status(thm)],[c_0_92]) ).
fof(c_0_263,plain,
! [X12,X15] : lhs_atom26(X12,X15),
inference(fof_simplification,[status(thm)],[c_0_93]) ).
fof(c_0_264,plain,
! [X12,X15] : lhs_atom22(X12,X15),
inference(fof_simplification,[status(thm)],[c_0_94]) ).
fof(c_0_265,plain,
! [X16,X17] : lhs_atom12(X16,X17),
inference(fof_simplification,[status(thm)],[c_0_95]) ).
fof(c_0_266,plain,
! [X12,X5] : lhs_atom11(X12,X5),
inference(fof_simplification,[status(thm)],[c_0_96]) ).
fof(c_0_267,plain,
! [X12,X15] : lhs_atom9(X12,X15),
inference(fof_simplification,[status(thm)],[c_0_97]) ).
fof(c_0_268,plain,
! [X11,X5] : lhs_atom7(X11,X5),
inference(fof_simplification,[status(thm)],[c_0_98]) ).
fof(c_0_269,plain,
! [X11,X5] : lhs_atom7(X11,X5),
inference(fof_simplification,[status(thm)],[c_0_99]) ).
fof(c_0_270,plain,
! [X10,X5] : lhs_atom5(X10,X5),
inference(fof_simplification,[status(thm)],[c_0_100]) ).
fof(c_0_271,plain,
! [X9,X5] : lhs_atom6(X9,X5),
inference(fof_simplification,[status(thm)],[c_0_101]) ).
fof(c_0_272,plain,
! [X10,X5] : lhs_atom5(X10,X5),
inference(fof_simplification,[status(thm)],[c_0_102]) ).
fof(c_0_273,plain,
! [X6,X5] : lhs_atom2(X6,X5),
inference(fof_simplification,[status(thm)],[c_0_103]) ).
fof(c_0_274,plain,
! [X12] : lhs_atom127(X12),
inference(fof_simplification,[status(thm)],[c_0_104]) ).
fof(c_0_275,plain,
! [X7] : lhs_atom119(X7),
inference(fof_simplification,[status(thm)],[c_0_105]) ).
fof(c_0_276,plain,
! [X36] : lhs_atom118(X36),
inference(fof_simplification,[status(thm)],[c_0_106]) ).
fof(c_0_277,plain,
! [X7] : lhs_atom117(X7),
inference(fof_simplification,[status(thm)],[c_0_107]) ).
fof(c_0_278,plain,
! [X15] : lhs_atom116(X15),
inference(fof_simplification,[status(thm)],[c_0_108]) ).
fof(c_0_279,plain,
! [X15] : lhs_atom104(X15),
inference(fof_simplification,[status(thm)],[c_0_109]) ).
fof(c_0_280,plain,
! [X12] : lhs_atom103(X12),
inference(fof_simplification,[status(thm)],[c_0_110]) ).
fof(c_0_281,plain,
! [X9] : lhs_atom102(X9),
inference(fof_simplification,[status(thm)],[c_0_111]) ).
fof(c_0_282,plain,
! [X12] : lhs_atom101(X12),
inference(fof_simplification,[status(thm)],[c_0_112]) ).
fof(c_0_283,plain,
! [X12] : lhs_atom100(X12),
inference(fof_simplification,[status(thm)],[c_0_113]) ).
fof(c_0_284,plain,
! [X39] : lhs_atom98(X39),
inference(fof_simplification,[status(thm)],[c_0_114]) ).
fof(c_0_285,plain,
! [X12] : lhs_atom97(X12),
inference(fof_simplification,[status(thm)],[c_0_115]) ).
fof(c_0_286,plain,
! [X12] : lhs_atom96(X12),
inference(fof_simplification,[status(thm)],[c_0_116]) ).
fof(c_0_287,plain,
! [X12] : lhs_atom93(X12),
inference(fof_simplification,[status(thm)],[c_0_117]) ).
fof(c_0_288,plain,
! [X15] : lhs_atom92(X15),
inference(fof_simplification,[status(thm)],[c_0_118]) ).
fof(c_0_289,plain,
! [X39] : lhs_atom90(X39),
inference(fof_simplification,[status(thm)],[c_0_119]) ).
fof(c_0_290,plain,
! [X9] : lhs_atom88(X9),
inference(fof_simplification,[status(thm)],[c_0_120]) ).
fof(c_0_291,plain,
! [X5] : lhs_atom83(X5),
inference(fof_simplification,[status(thm)],[c_0_121]) ).
fof(c_0_292,plain,
! [X9] : lhs_atom78(X9),
inference(fof_simplification,[status(thm)],[c_0_122]) ).
fof(c_0_293,plain,
! [X12] : lhs_atom77(X12),
inference(fof_simplification,[status(thm)],[c_0_123]) ).
fof(c_0_294,plain,
! [X15] : lhs_atom70(X15),
inference(fof_simplification,[status(thm)],[c_0_124]) ).
fof(c_0_295,plain,
! [X15] : lhs_atom69(X15),
inference(fof_simplification,[status(thm)],[c_0_125]) ).
fof(c_0_296,plain,
! [X5] : lhs_atom59(X5),
inference(fof_simplification,[status(thm)],[c_0_126]) ).
fof(c_0_297,plain,
! [X12] : lhs_atom43(X12),
inference(fof_simplification,[status(thm)],[c_0_127]) ).
fof(c_0_298,plain,
! [X9] : lhs_atom42(X9),
inference(fof_simplification,[status(thm)],[c_0_128]) ).
fof(c_0_299,plain,
! [X5] : lhs_atom39(X5),
inference(fof_simplification,[status(thm)],[c_0_129]) ).
fof(c_0_300,plain,
lhs_atom163,
inference(fof_simplification,[status(thm)],[c_0_130]) ).
fof(c_0_301,plain,
lhs_atom162,
inference(fof_simplification,[status(thm)],[c_0_131]) ).
fof(c_0_302,plain,
lhs_atom161,
inference(fof_simplification,[status(thm)],[c_0_132]) ).
fof(c_0_303,plain,
lhs_atom160,
inference(fof_simplification,[status(thm)],[c_0_133]) ).
fof(c_0_304,plain,
lhs_atom159,
inference(fof_simplification,[status(thm)],[c_0_134]) ).
fof(c_0_305,plain,
lhs_atom158,
inference(fof_simplification,[status(thm)],[c_0_135]) ).
fof(c_0_306,plain,
lhs_atom157,
inference(fof_simplification,[status(thm)],[c_0_136]) ).
fof(c_0_307,plain,
lhs_atom156,
inference(fof_simplification,[status(thm)],[c_0_137]) ).
fof(c_0_308,plain,
lhs_atom155,
inference(fof_simplification,[status(thm)],[c_0_138]) ).
fof(c_0_309,plain,
lhs_atom154,
inference(fof_simplification,[status(thm)],[c_0_139]) ).
fof(c_0_310,plain,
lhs_atom153,
inference(fof_simplification,[status(thm)],[c_0_140]) ).
fof(c_0_311,plain,
lhs_atom152,
inference(fof_simplification,[status(thm)],[c_0_141]) ).
fof(c_0_312,plain,
lhs_atom151,
inference(fof_simplification,[status(thm)],[c_0_142]) ).
fof(c_0_313,plain,
lhs_atom150,
inference(fof_simplification,[status(thm)],[c_0_143]) ).
fof(c_0_314,plain,
lhs_atom149,
inference(fof_simplification,[status(thm)],[c_0_144]) ).
fof(c_0_315,plain,
lhs_atom148,
inference(fof_simplification,[status(thm)],[c_0_145]) ).
fof(c_0_316,plain,
lhs_atom147,
inference(fof_simplification,[status(thm)],[c_0_146]) ).
fof(c_0_317,plain,
lhs_atom146,
inference(fof_simplification,[status(thm)],[c_0_147]) ).
fof(c_0_318,plain,
lhs_atom145,
inference(fof_simplification,[status(thm)],[c_0_148]) ).
fof(c_0_319,plain,
lhs_atom144,
inference(fof_simplification,[status(thm)],[c_0_149]) ).
fof(c_0_320,plain,
lhs_atom143,
inference(fof_simplification,[status(thm)],[c_0_150]) ).
fof(c_0_321,plain,
lhs_atom142,
inference(fof_simplification,[status(thm)],[c_0_151]) ).
fof(c_0_322,plain,
lhs_atom141,
inference(fof_simplification,[status(thm)],[c_0_152]) ).
fof(c_0_323,plain,
lhs_atom140,
inference(fof_simplification,[status(thm)],[c_0_153]) ).
fof(c_0_324,plain,
lhs_atom139,
inference(fof_simplification,[status(thm)],[c_0_154]) ).
fof(c_0_325,plain,
lhs_atom138,
inference(fof_simplification,[status(thm)],[c_0_155]) ).
fof(c_0_326,plain,
lhs_atom137,
inference(fof_simplification,[status(thm)],[c_0_156]) ).
fof(c_0_327,plain,
lhs_atom136,
inference(fof_simplification,[status(thm)],[c_0_157]) ).
fof(c_0_328,plain,
lhs_atom82,
inference(fof_simplification,[status(thm)],[c_0_158]) ).
fof(c_0_329,plain,
lhs_atom136,
inference(fof_simplification,[status(thm)],[c_0_159]) ).
fof(c_0_330,plain,
lhs_atom135,
inference(fof_simplification,[status(thm)],[c_0_160]) ).
fof(c_0_331,plain,
lhs_atom133,
inference(fof_simplification,[status(thm)],[c_0_161]) ).
fof(c_0_332,plain,
lhs_atom130,
inference(fof_simplification,[status(thm)],[c_0_162]) ).
fof(c_0_333,plain,
lhs_atom128,
inference(fof_simplification,[status(thm)],[c_0_163]) ).
fof(c_0_334,plain,
lhs_atom94,
inference(fof_simplification,[status(thm)],[c_0_164]) ).
fof(c_0_335,plain,
lhs_atom91,
inference(fof_simplification,[status(thm)],[c_0_165]) ).
fof(c_0_336,plain,
lhs_atom89,
inference(fof_simplification,[status(thm)],[c_0_166]) ).
fof(c_0_337,plain,
lhs_atom82,
inference(fof_simplification,[status(thm)],[c_0_167]) ).
fof(c_0_338,plain,
lhs_atom65,
inference(fof_simplification,[status(thm)],[c_0_168]) ).
fof(c_0_339,plain,
lhs_atom64,
inference(fof_simplification,[status(thm)],[c_0_169]) ).
fof(c_0_340,plain,
! [X15,X16,X17,X18,X19,X20] : lhs_atom123(X15,X16,X17,X18,X19,X20),
inference(variable_rename,[status(thm)],[c_0_170]) ).
fof(c_0_341,plain,
! [X15,X16,X17,X18,X19,X20] : lhs_atom122(X15,X16,X17,X18,X19,X20),
inference(variable_rename,[status(thm)],[c_0_171]) ).
fof(c_0_342,plain,
! [X42,X43,X44,X45,X46,X47] : lhs_atom110(X42,X43,X44,X45,X46,X47),
inference(variable_rename,[status(thm)],[c_0_172]) ).
fof(c_0_343,plain,
! [X42,X43,X44,X45,X46,X47] : lhs_atom109(X42,X43,X44,X45,X46,X47),
inference(variable_rename,[status(thm)],[c_0_173]) ).
fof(c_0_344,plain,
! [X15,X16,X17,X18,X19,X20] : lhs_atom72(X15,X16,X17,X18,X19,X20),
inference(variable_rename,[status(thm)],[c_0_174]) ).
fof(c_0_345,plain,
! [X25,X26,X27,X28,X29,X30] : lhs_atom19(X25,X26,X27,X28,X29,X30),
inference(variable_rename,[status(thm)],[c_0_175]) ).
fof(c_0_346,plain,
! [X15,X16,X17,X18,X19,X20] : lhs_atom10(X15,X16,X17,X18,X19,X20),
inference(variable_rename,[status(thm)],[c_0_176]) ).
fof(c_0_347,plain,
! [X15,X16,X17,X18,X19] : lhs_atom81(X15,X16,X17,X18,X19),
inference(variable_rename,[status(thm)],[c_0_177]) ).
fof(c_0_348,plain,
! [X6,X7,X8,X9,X10] : lhs_atom71(X6,X7,X8,X9,X10),
inference(variable_rename,[status(thm)],[c_0_178]) ).
fof(c_0_349,plain,
! [X15,X16,X17,X18,X19] : lhs_atom48(X15,X16,X17,X18,X19),
inference(variable_rename,[status(thm)],[c_0_179]) ).
fof(c_0_350,plain,
! [X17,X18,X19,X20,X21] : lhs_atom40(X17,X18,X19,X20,X21),
inference(variable_rename,[status(thm)],[c_0_180]) ).
fof(c_0_351,plain,
! [X15,X16,X17,X18,X19] : lhs_atom33(X15,X16,X17,X18,X19),
inference(variable_rename,[status(thm)],[c_0_181]) ).
fof(c_0_352,plain,
! [X31,X32,X33,X34,X35] : lhs_atom32(X31,X32,X33,X34,X35),
inference(variable_rename,[status(thm)],[c_0_182]) ).
fof(c_0_353,plain,
! [X30,X31,X32,X33,X34] : lhs_atom31(X30,X31,X32,X33,X34),
inference(variable_rename,[status(thm)],[c_0_183]) ).
fof(c_0_354,plain,
! [X17,X18,X19,X20,X21] : lhs_atom18(X17,X18,X19,X20,X21),
inference(variable_rename,[status(thm)],[c_0_184]) ).
fof(c_0_355,plain,
! [X15,X16,X17,X18,X19] : lhs_atom8(X15,X16,X17,X18,X19),
inference(variable_rename,[status(thm)],[c_0_185]) ).
fof(c_0_356,plain,
! [X6,X7,X8,X9,X10] : lhs_atom1(X6,X7,X8,X9,X10),
inference(variable_rename,[status(thm)],[c_0_186]) ).
fof(c_0_357,plain,
! [X46,X47,X48,X49] : lhs_atom134(X46,X47,X48,X49),
inference(variable_rename,[status(thm)],[c_0_187]) ).
fof(c_0_358,plain,
! [X46,X47,X48,X49] : lhs_atom124(X46,X47,X48,X49),
inference(variable_rename,[status(thm)],[c_0_188]) ).
fof(c_0_359,plain,
! [X15,X16,X17,X18] : lhs_atom121(X15,X16,X17,X18),
inference(variable_rename,[status(thm)],[c_0_189]) ).
fof(c_0_360,plain,
! [X47,X48,X49,X50] : lhs_atom120(X47,X48,X49,X50),
inference(variable_rename,[status(thm)],[c_0_190]) ).
fof(c_0_361,plain,
! [X47,X48,X49,X50] : lhs_atom115(X47,X48,X49,X50),
inference(variable_rename,[status(thm)],[c_0_191]) ).
fof(c_0_362,plain,
! [X46,X47,X48,X49] : lhs_atom112(X46,X47,X48,X49),
inference(variable_rename,[status(thm)],[c_0_192]) ).
fof(c_0_363,plain,
! [X45,X46,X47,X48] : lhs_atom111(X45,X46,X47,X48),
inference(variable_rename,[status(thm)],[c_0_193]) ).
fof(c_0_364,plain,
! [X38,X39,X40,X41] : lhs_atom87(X38,X39,X40,X41),
inference(variable_rename,[status(thm)],[c_0_194]) ).
fof(c_0_365,plain,
! [X29,X30,X31,X32] : lhs_atom86(X29,X30,X31,X32),
inference(variable_rename,[status(thm)],[c_0_195]) ).
fof(c_0_366,plain,
! [X39,X40,X41,X42] : lhs_atom85(X39,X40,X41,X42),
inference(variable_rename,[status(thm)],[c_0_196]) ).
fof(c_0_367,plain,
! [X29,X30,X31,X32] : lhs_atom84(X29,X30,X31,X32),
inference(variable_rename,[status(thm)],[c_0_197]) ).
fof(c_0_368,plain,
! [X13,X14,X15,X16] : lhs_atom80(X13,X14,X15,X16),
inference(variable_rename,[status(thm)],[c_0_198]) ).
fof(c_0_369,plain,
! [X27,X28,X29,X30] : lhs_atom55(X27,X28,X29,X30),
inference(variable_rename,[status(thm)],[c_0_199]) ).
fof(c_0_370,plain,
! [X16,X17,X18,X19] : lhs_atom53(X16,X17,X18,X19),
inference(variable_rename,[status(thm)],[c_0_200]) ).
fof(c_0_371,plain,
! [X16,X17,X18,X19] : lhs_atom52(X16,X17,X18,X19),
inference(variable_rename,[status(thm)],[c_0_201]) ).
fof(c_0_372,plain,
! [X21,X22,X23,X24] : lhs_atom49(X21,X22,X23,X24),
inference(variable_rename,[status(thm)],[c_0_202]) ).
fof(c_0_373,plain,
! [X36,X37,X38,X39] : lhs_atom38(X36,X37,X38,X39),
inference(variable_rename,[status(thm)],[c_0_203]) ).
fof(c_0_374,plain,
! [X32,X33,X34,X35] : lhs_atom35(X32,X33,X34,X35),
inference(variable_rename,[status(thm)],[c_0_204]) ).
fof(c_0_375,plain,
! [X30,X31,X32,X33] : lhs_atom34(X30,X31,X32,X33),
inference(variable_rename,[status(thm)],[c_0_205]) ).
fof(c_0_376,plain,
! [X12,X13,X14,X15] : lhs_atom29(X12,X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_206]) ).
fof(c_0_377,plain,
! [X30,X31,X32,X33] : lhs_atom28(X30,X31,X32,X33),
inference(variable_rename,[status(thm)],[c_0_207]) ).
fof(c_0_378,plain,
! [X15,X16,X17,X18] : lhs_atom20(X15,X16,X17,X18),
inference(variable_rename,[status(thm)],[c_0_208]) ).
fof(c_0_379,plain,
! [X20,X21,X22] :
( lhs_atom99(X20,X21,X22)
| c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X21,X22) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X20,X22) ),
inference(variable_rename,[status(thm)],[c_0_209]) ).
fof(c_0_380,plain,
! [X45,X46,X47] : lhs_atom126(X45,X46,X47),
inference(variable_rename,[status(thm)],[c_0_210]) ).
fof(c_0_381,plain,
! [X45,X46,X47] : lhs_atom114(X45,X46,X47),
inference(variable_rename,[status(thm)],[c_0_211]) ).
fof(c_0_382,plain,
! [X44,X45,X46] : lhs_atom113(X44,X45,X46),
inference(variable_rename,[status(thm)],[c_0_212]) ).
fof(c_0_383,plain,
! [X45,X46,X47] : lhs_atom108(X45,X46,X47),
inference(variable_rename,[status(thm)],[c_0_213]) ).
fof(c_0_384,plain,
! [X44,X45,X46] : lhs_atom107(X44,X45,X46),
inference(variable_rename,[status(thm)],[c_0_214]) ).
fof(c_0_385,plain,
! [X42,X43,X44] : lhs_atom106(X42,X43,X44),
inference(variable_rename,[status(thm)],[c_0_215]) ).
fof(c_0_386,plain,
! [X42,X43,X44] : lhs_atom105(X42,X43,X44),
inference(variable_rename,[status(thm)],[c_0_216]) ).
fof(c_0_387,plain,
! [X11,X12,X13] : lhs_atom76(X11,X12,X13),
inference(variable_rename,[status(thm)],[c_0_217]) ).
fof(c_0_388,plain,
! [X15,X16,X17] : lhs_atom73(X15,X16,X17),
inference(variable_rename,[status(thm)],[c_0_218]) ).
fof(c_0_389,plain,
! [X6,X7,X8] : lhs_atom68(X6,X7,X8),
inference(variable_rename,[status(thm)],[c_0_219]) ).
fof(c_0_390,plain,
! [X14,X15,X16] : lhs_atom67(X14,X15,X16),
inference(variable_rename,[status(thm)],[c_0_220]) ).
fof(c_0_391,plain,
! [X27,X28,X29] : lhs_atom61(X27,X28,X29),
inference(variable_rename,[status(thm)],[c_0_221]) ).
fof(c_0_392,plain,
! [X15,X16,X17] : lhs_atom21(X15,X16,X17),
inference(variable_rename,[status(thm)],[c_0_222]) ).
fof(c_0_393,plain,
! [X11,X12,X13] : lhs_atom58(X11,X12,X13),
inference(variable_rename,[status(thm)],[c_0_223]) ).
fof(c_0_394,plain,
! [X11,X12,X13] : lhs_atom57(X11,X12,X13),
inference(variable_rename,[status(thm)],[c_0_224]) ).
fof(c_0_395,plain,
! [X37,X38,X39] : lhs_atom56(X37,X38,X39),
inference(variable_rename,[status(thm)],[c_0_225]) ).
fof(c_0_396,plain,
! [X38,X39,X40] : lhs_atom54(X38,X39,X40),
inference(variable_rename,[status(thm)],[c_0_226]) ).
fof(c_0_397,plain,
! [X34,X35,X36] : lhs_atom50(X34,X35,X36),
inference(variable_rename,[status(thm)],[c_0_227]) ).
fof(c_0_398,plain,
! [X34,X35,X36] : lhs_atom37(X34,X35,X36),
inference(variable_rename,[status(thm)],[c_0_228]) ).
fof(c_0_399,plain,
! [X30,X31,X32] : lhs_atom36(X30,X31,X32),
inference(variable_rename,[status(thm)],[c_0_229]) ).
fof(c_0_400,plain,
! [X27,X28,X29] : lhs_atom30(X27,X28,X29),
inference(variable_rename,[status(thm)],[c_0_230]) ).
fof(c_0_401,plain,
! [X21,X22,X23] : lhs_atom25(X21,X22,X23),
inference(variable_rename,[status(thm)],[c_0_231]) ).
fof(c_0_402,plain,
! [X21,X22,X23] : lhs_atom24(X21,X22,X23),
inference(variable_rename,[status(thm)],[c_0_232]) ).
fof(c_0_403,plain,
! [X27,X28,X29] : lhs_atom23(X27,X28,X29),
inference(variable_rename,[status(thm)],[c_0_233]) ).
fof(c_0_404,plain,
! [X15,X16,X17] : lhs_atom21(X15,X16,X17),
inference(variable_rename,[status(thm)],[c_0_234]) ).
fof(c_0_405,plain,
! [X11,X12,X13] : lhs_atom17(X11,X12,X13),
inference(variable_rename,[status(thm)],[c_0_235]) ).
fof(c_0_406,plain,
! [X21,X22,X23] : lhs_atom16(X21,X22,X23),
inference(variable_rename,[status(thm)],[c_0_236]) ).
fof(c_0_407,plain,
! [X20,X21,X22] : lhs_atom15(X20,X21,X22),
inference(variable_rename,[status(thm)],[c_0_237]) ).
fof(c_0_408,plain,
! [X11,X12,X13] : lhs_atom14(X11,X12,X13),
inference(variable_rename,[status(thm)],[c_0_238]) ).
fof(c_0_409,plain,
! [X11,X12,X13] : lhs_atom13(X11,X12,X13),
inference(variable_rename,[status(thm)],[c_0_239]) ).
fof(c_0_410,plain,
! [X10,X11,X12] : lhs_atom4(X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_240]) ).
fof(c_0_411,plain,
! [X9,X10,X11] : lhs_atom3(X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_241]) ).
fof(c_0_412,plain,
! [X10,X11] : lhs_atom164(X10,X11),
inference(variable_rename,[status(thm)],[c_0_242]) ).
fof(c_0_413,plain,
! [X45,X46] : lhs_atom132(X45,X46),
inference(variable_rename,[status(thm)],[c_0_243]) ).
fof(c_0_414,plain,
! [X45,X46] : lhs_atom131(X45,X46),
inference(variable_rename,[status(thm)],[c_0_244]) ).
fof(c_0_415,plain,
! [X45,X46] : lhs_atom129(X45,X46),
inference(variable_rename,[status(thm)],[c_0_245]) ).
fof(c_0_416,plain,
! [X46,X47] : lhs_atom125(X46,X47),
inference(variable_rename,[status(thm)],[c_0_246]) ).
fof(c_0_417,plain,
! [X11,X12] : lhs_atom95(X11,X12),
inference(variable_rename,[status(thm)],[c_0_247]) ).
fof(c_0_418,plain,
! [X18,X19] : lhs_atom79(X18,X19),
inference(variable_rename,[status(thm)],[c_0_248]) ).
fof(c_0_419,plain,
! [X27,X28] : lhs_atom75(X27,X28),
inference(variable_rename,[status(thm)],[c_0_249]) ).
fof(c_0_420,plain,
! [X27,X28] : lhs_atom74(X27,X28),
inference(variable_rename,[status(thm)],[c_0_250]) ).
fof(c_0_421,plain,
! [X37,X38] : lhs_atom66(X37,X38),
inference(variable_rename,[status(thm)],[c_0_251]) ).
fof(c_0_422,plain,
! [X16,X17] : lhs_atom63(X16,X17),
inference(variable_rename,[status(thm)],[c_0_252]) ).
fof(c_0_423,plain,
! [X16,X17] : lhs_atom62(X16,X17),
inference(variable_rename,[status(thm)],[c_0_253]) ).
fof(c_0_424,plain,
! [X8,X9] : lhs_atom60(X8,X9),
inference(variable_rename,[status(thm)],[c_0_254]) ).
fof(c_0_425,plain,
! [X10,X11] : lhs_atom41(X10,X11),
inference(variable_rename,[status(thm)],[c_0_255]) ).
fof(c_0_426,plain,
! [X37,X38] : lhs_atom51(X37,X38),
inference(variable_rename,[status(thm)],[c_0_256]) ).
fof(c_0_427,plain,
! [X16,X17] : lhs_atom47(X16,X17),
inference(variable_rename,[status(thm)],[c_0_257]) ).
fof(c_0_428,plain,
! [X16,X17] : lhs_atom46(X16,X17),
inference(variable_rename,[status(thm)],[c_0_258]) ).
fof(c_0_429,plain,
! [X16,X17] : lhs_atom45(X16,X17),
inference(variable_rename,[status(thm)],[c_0_259]) ).
fof(c_0_430,plain,
! [X16,X17] : lhs_atom44(X16,X17),
inference(variable_rename,[status(thm)],[c_0_260]) ).
fof(c_0_431,plain,
! [X10,X11] : lhs_atom41(X10,X11),
inference(variable_rename,[status(thm)],[c_0_261]) ).
fof(c_0_432,plain,
! [X28,X29] : lhs_atom27(X28,X29),
inference(variable_rename,[status(thm)],[c_0_262]) ).
fof(c_0_433,plain,
! [X16,X17] : lhs_atom26(X16,X17),
inference(variable_rename,[status(thm)],[c_0_263]) ).
fof(c_0_434,plain,
! [X16,X17] : lhs_atom22(X16,X17),
inference(variable_rename,[status(thm)],[c_0_264]) ).
fof(c_0_435,plain,
! [X18,X19] : lhs_atom12(X18,X19),
inference(variable_rename,[status(thm)],[c_0_265]) ).
fof(c_0_436,plain,
! [X13,X14] : lhs_atom11(X13,X14),
inference(variable_rename,[status(thm)],[c_0_266]) ).
fof(c_0_437,plain,
! [X16,X17] : lhs_atom9(X16,X17),
inference(variable_rename,[status(thm)],[c_0_267]) ).
fof(c_0_438,plain,
! [X12,X13] : lhs_atom7(X12,X13),
inference(variable_rename,[status(thm)],[c_0_268]) ).
fof(c_0_439,plain,
! [X12,X13] : lhs_atom7(X12,X13),
inference(variable_rename,[status(thm)],[c_0_269]) ).
fof(c_0_440,plain,
! [X11,X12] : lhs_atom5(X11,X12),
inference(variable_rename,[status(thm)],[c_0_270]) ).
fof(c_0_441,plain,
! [X10,X11] : lhs_atom6(X10,X11),
inference(variable_rename,[status(thm)],[c_0_271]) ).
fof(c_0_442,plain,
! [X11,X12] : lhs_atom5(X11,X12),
inference(variable_rename,[status(thm)],[c_0_272]) ).
fof(c_0_443,plain,
! [X7,X8] : lhs_atom2(X7,X8),
inference(variable_rename,[status(thm)],[c_0_273]) ).
fof(c_0_444,plain,
! [X13] : lhs_atom127(X13),
inference(variable_rename,[status(thm)],[c_0_274]) ).
fof(c_0_445,plain,
! [X8] : lhs_atom119(X8),
inference(variable_rename,[status(thm)],[c_0_275]) ).
fof(c_0_446,plain,
! [X37] : lhs_atom118(X37),
inference(variable_rename,[status(thm)],[c_0_276]) ).
fof(c_0_447,plain,
! [X8] : lhs_atom117(X8),
inference(variable_rename,[status(thm)],[c_0_277]) ).
fof(c_0_448,plain,
! [X16] : lhs_atom116(X16),
inference(variable_rename,[status(thm)],[c_0_278]) ).
fof(c_0_449,plain,
! [X16] : lhs_atom104(X16),
inference(variable_rename,[status(thm)],[c_0_279]) ).
fof(c_0_450,plain,
! [X13] : lhs_atom103(X13),
inference(variable_rename,[status(thm)],[c_0_280]) ).
fof(c_0_451,plain,
! [X10] : lhs_atom102(X10),
inference(variable_rename,[status(thm)],[c_0_281]) ).
fof(c_0_452,plain,
! [X13] : lhs_atom101(X13),
inference(variable_rename,[status(thm)],[c_0_282]) ).
fof(c_0_453,plain,
! [X13] : lhs_atom100(X13),
inference(variable_rename,[status(thm)],[c_0_283]) ).
fof(c_0_454,plain,
! [X40] : lhs_atom98(X40),
inference(variable_rename,[status(thm)],[c_0_284]) ).
fof(c_0_455,plain,
! [X13] : lhs_atom97(X13),
inference(variable_rename,[status(thm)],[c_0_285]) ).
fof(c_0_456,plain,
! [X13] : lhs_atom96(X13),
inference(variable_rename,[status(thm)],[c_0_286]) ).
fof(c_0_457,plain,
! [X13] : lhs_atom93(X13),
inference(variable_rename,[status(thm)],[c_0_287]) ).
fof(c_0_458,plain,
! [X16] : lhs_atom92(X16),
inference(variable_rename,[status(thm)],[c_0_288]) ).
fof(c_0_459,plain,
! [X40] : lhs_atom90(X40),
inference(variable_rename,[status(thm)],[c_0_289]) ).
fof(c_0_460,plain,
! [X10] : lhs_atom88(X10),
inference(variable_rename,[status(thm)],[c_0_290]) ).
fof(c_0_461,plain,
! [X6] : lhs_atom83(X6),
inference(variable_rename,[status(thm)],[c_0_291]) ).
fof(c_0_462,plain,
! [X10] : lhs_atom78(X10),
inference(variable_rename,[status(thm)],[c_0_292]) ).
fof(c_0_463,plain,
! [X13] : lhs_atom77(X13),
inference(variable_rename,[status(thm)],[c_0_293]) ).
fof(c_0_464,plain,
! [X16] : lhs_atom70(X16),
inference(variable_rename,[status(thm)],[c_0_294]) ).
fof(c_0_465,plain,
! [X16] : lhs_atom69(X16),
inference(variable_rename,[status(thm)],[c_0_295]) ).
fof(c_0_466,plain,
! [X6] : lhs_atom59(X6),
inference(variable_rename,[status(thm)],[c_0_296]) ).
fof(c_0_467,plain,
! [X13] : lhs_atom43(X13),
inference(variable_rename,[status(thm)],[c_0_297]) ).
fof(c_0_468,plain,
! [X10] : lhs_atom42(X10),
inference(variable_rename,[status(thm)],[c_0_298]) ).
fof(c_0_469,plain,
! [X6] : lhs_atom39(X6),
inference(variable_rename,[status(thm)],[c_0_299]) ).
fof(c_0_470,plain,
lhs_atom163,
c_0_300 ).
fof(c_0_471,plain,
lhs_atom162,
c_0_301 ).
fof(c_0_472,plain,
lhs_atom161,
c_0_302 ).
fof(c_0_473,plain,
lhs_atom160,
c_0_303 ).
fof(c_0_474,plain,
lhs_atom159,
c_0_304 ).
fof(c_0_475,plain,
lhs_atom158,
c_0_305 ).
fof(c_0_476,plain,
lhs_atom157,
c_0_306 ).
fof(c_0_477,plain,
lhs_atom156,
c_0_307 ).
fof(c_0_478,plain,
lhs_atom155,
c_0_308 ).
fof(c_0_479,plain,
lhs_atom154,
c_0_309 ).
fof(c_0_480,plain,
lhs_atom153,
c_0_310 ).
fof(c_0_481,plain,
lhs_atom152,
c_0_311 ).
fof(c_0_482,plain,
lhs_atom151,
c_0_312 ).
fof(c_0_483,plain,
lhs_atom150,
c_0_313 ).
fof(c_0_484,plain,
lhs_atom149,
c_0_314 ).
fof(c_0_485,plain,
lhs_atom148,
c_0_315 ).
fof(c_0_486,plain,
lhs_atom147,
c_0_316 ).
fof(c_0_487,plain,
lhs_atom146,
c_0_317 ).
fof(c_0_488,plain,
lhs_atom145,
c_0_318 ).
fof(c_0_489,plain,
lhs_atom144,
c_0_319 ).
fof(c_0_490,plain,
lhs_atom143,
c_0_320 ).
fof(c_0_491,plain,
lhs_atom142,
c_0_321 ).
fof(c_0_492,plain,
lhs_atom141,
c_0_322 ).
fof(c_0_493,plain,
lhs_atom140,
c_0_323 ).
fof(c_0_494,plain,
lhs_atom139,
c_0_324 ).
fof(c_0_495,plain,
lhs_atom138,
c_0_325 ).
fof(c_0_496,plain,
lhs_atom137,
c_0_326 ).
fof(c_0_497,plain,
lhs_atom136,
c_0_327 ).
fof(c_0_498,plain,
lhs_atom82,
c_0_328 ).
fof(c_0_499,plain,
lhs_atom136,
c_0_329 ).
fof(c_0_500,plain,
lhs_atom135,
c_0_330 ).
fof(c_0_501,plain,
lhs_atom133,
c_0_331 ).
fof(c_0_502,plain,
lhs_atom130,
c_0_332 ).
fof(c_0_503,plain,
lhs_atom128,
c_0_333 ).
fof(c_0_504,plain,
lhs_atom94,
c_0_334 ).
fof(c_0_505,plain,
lhs_atom91,
c_0_335 ).
fof(c_0_506,plain,
lhs_atom89,
c_0_336 ).
fof(c_0_507,plain,
lhs_atom82,
c_0_337 ).
fof(c_0_508,plain,
lhs_atom65,
c_0_338 ).
fof(c_0_509,plain,
lhs_atom64,
c_0_339 ).
cnf(c_0_510,plain,
lhs_atom123(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_340]) ).
cnf(c_0_511,plain,
lhs_atom122(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_341]) ).
cnf(c_0_512,plain,
lhs_atom110(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_342]) ).
cnf(c_0_513,plain,
lhs_atom109(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_343]) ).
cnf(c_0_514,plain,
lhs_atom72(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_344]) ).
cnf(c_0_515,plain,
lhs_atom19(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_345]) ).
cnf(c_0_516,plain,
lhs_atom10(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_346]) ).
cnf(c_0_517,plain,
lhs_atom81(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_347]) ).
cnf(c_0_518,plain,
lhs_atom71(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_348]) ).
cnf(c_0_519,plain,
lhs_atom48(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_349]) ).
cnf(c_0_520,plain,
lhs_atom40(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_350]) ).
cnf(c_0_521,plain,
lhs_atom33(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_351]) ).
cnf(c_0_522,plain,
lhs_atom32(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_352]) ).
cnf(c_0_523,plain,
lhs_atom31(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_353]) ).
cnf(c_0_524,plain,
lhs_atom18(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_354]) ).
cnf(c_0_525,plain,
lhs_atom8(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_355]) ).
cnf(c_0_526,plain,
lhs_atom1(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_356]) ).
cnf(c_0_527,plain,
lhs_atom134(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_528,plain,
lhs_atom124(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_358]) ).
cnf(c_0_529,plain,
lhs_atom121(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_530,plain,
lhs_atom120(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_360]) ).
cnf(c_0_531,plain,
lhs_atom115(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_361]) ).
cnf(c_0_532,plain,
lhs_atom112(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_362]) ).
cnf(c_0_533,plain,
lhs_atom111(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_363]) ).
cnf(c_0_534,plain,
lhs_atom87(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_364]) ).
cnf(c_0_535,plain,
lhs_atom86(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_365]) ).
cnf(c_0_536,plain,
lhs_atom85(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_366]) ).
cnf(c_0_537,plain,
lhs_atom84(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_367]) ).
cnf(c_0_538,plain,
lhs_atom80(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_368]) ).
cnf(c_0_539,plain,
lhs_atom55(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_369]) ).
cnf(c_0_540,plain,
lhs_atom53(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_370]) ).
cnf(c_0_541,plain,
lhs_atom52(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_371]) ).
cnf(c_0_542,plain,
lhs_atom49(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_372]) ).
cnf(c_0_543,plain,
lhs_atom38(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_373]) ).
cnf(c_0_544,plain,
lhs_atom35(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_374]) ).
cnf(c_0_545,plain,
lhs_atom34(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_375]) ).
cnf(c_0_546,plain,
lhs_atom29(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_376]) ).
cnf(c_0_547,plain,
lhs_atom28(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_377]) ).
cnf(c_0_548,plain,
lhs_atom20(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_378]) ).
cnf(c_0_549,plain,
( c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X3,X2)
| lhs_atom99(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_379]) ).
cnf(c_0_550,plain,
lhs_atom126(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_380]) ).
cnf(c_0_551,plain,
lhs_atom114(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_381]) ).
cnf(c_0_552,plain,
lhs_atom113(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_382]) ).
cnf(c_0_553,plain,
lhs_atom108(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_554,plain,
lhs_atom107(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_384]) ).
cnf(c_0_555,plain,
lhs_atom106(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_385]) ).
cnf(c_0_556,plain,
lhs_atom105(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_386]) ).
cnf(c_0_557,plain,
lhs_atom76(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_387]) ).
cnf(c_0_558,plain,
lhs_atom73(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_388]) ).
cnf(c_0_559,plain,
lhs_atom68(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_389]) ).
cnf(c_0_560,plain,
lhs_atom67(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_390]) ).
cnf(c_0_561,plain,
lhs_atom61(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_562,plain,
lhs_atom21(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_392]) ).
cnf(c_0_563,plain,
lhs_atom58(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_393]) ).
cnf(c_0_564,plain,
lhs_atom57(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_394]) ).
cnf(c_0_565,plain,
lhs_atom56(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_395]) ).
cnf(c_0_566,plain,
lhs_atom54(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_567,plain,
lhs_atom50(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_397]) ).
cnf(c_0_568,plain,
lhs_atom37(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_398]) ).
cnf(c_0_569,plain,
lhs_atom36(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_399]) ).
cnf(c_0_570,plain,
lhs_atom30(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_400]) ).
cnf(c_0_571,plain,
lhs_atom25(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_401]) ).
cnf(c_0_572,plain,
lhs_atom24(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_402]) ).
cnf(c_0_573,plain,
lhs_atom23(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_403]) ).
cnf(c_0_574,plain,
lhs_atom21(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_404]) ).
cnf(c_0_575,plain,
lhs_atom17(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_405]) ).
cnf(c_0_576,plain,
lhs_atom16(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_406]) ).
cnf(c_0_577,plain,
lhs_atom15(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_407]) ).
cnf(c_0_578,plain,
lhs_atom14(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_408]) ).
cnf(c_0_579,plain,
lhs_atom13(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_409]) ).
cnf(c_0_580,plain,
lhs_atom4(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_410]) ).
cnf(c_0_581,plain,
lhs_atom3(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_411]) ).
cnf(c_0_582,plain,
lhs_atom164(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_412]) ).
cnf(c_0_583,plain,
lhs_atom132(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_413]) ).
cnf(c_0_584,plain,
lhs_atom131(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_414]) ).
cnf(c_0_585,plain,
lhs_atom129(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_415]) ).
cnf(c_0_586,plain,
lhs_atom125(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_416]) ).
cnf(c_0_587,plain,
lhs_atom95(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_417]) ).
cnf(c_0_588,plain,
lhs_atom79(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_418]) ).
cnf(c_0_589,plain,
lhs_atom75(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_419]) ).
cnf(c_0_590,plain,
lhs_atom74(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_420]) ).
cnf(c_0_591,plain,
lhs_atom66(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_421]) ).
cnf(c_0_592,plain,
lhs_atom63(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_593,plain,
lhs_atom62(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_423]) ).
cnf(c_0_594,plain,
lhs_atom60(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_424]) ).
cnf(c_0_595,plain,
lhs_atom41(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_425]) ).
cnf(c_0_596,plain,
lhs_atom51(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_426]) ).
cnf(c_0_597,plain,
lhs_atom47(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_427]) ).
cnf(c_0_598,plain,
lhs_atom46(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_428]) ).
cnf(c_0_599,plain,
lhs_atom45(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_429]) ).
cnf(c_0_600,plain,
lhs_atom44(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_430]) ).
cnf(c_0_601,plain,
lhs_atom41(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_431]) ).
cnf(c_0_602,plain,
lhs_atom27(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_432]) ).
cnf(c_0_603,plain,
lhs_atom26(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_433]) ).
cnf(c_0_604,plain,
lhs_atom22(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_434]) ).
cnf(c_0_605,plain,
lhs_atom12(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_435]) ).
cnf(c_0_606,plain,
lhs_atom11(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_436]) ).
cnf(c_0_607,plain,
lhs_atom9(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_437]) ).
cnf(c_0_608,plain,
lhs_atom7(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_438]) ).
cnf(c_0_609,plain,
lhs_atom7(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_439]) ).
cnf(c_0_610,plain,
lhs_atom5(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_440]) ).
cnf(c_0_611,plain,
lhs_atom6(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_441]) ).
cnf(c_0_612,plain,
lhs_atom5(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_613,plain,
lhs_atom2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_614,plain,
lhs_atom127(X1),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_615,plain,
lhs_atom119(X1),
inference(split_conjunct,[status(thm)],[c_0_445]) ).
cnf(c_0_616,plain,
lhs_atom118(X1),
inference(split_conjunct,[status(thm)],[c_0_446]) ).
cnf(c_0_617,plain,
lhs_atom117(X1),
inference(split_conjunct,[status(thm)],[c_0_447]) ).
cnf(c_0_618,plain,
lhs_atom116(X1),
inference(split_conjunct,[status(thm)],[c_0_448]) ).
cnf(c_0_619,plain,
lhs_atom104(X1),
inference(split_conjunct,[status(thm)],[c_0_449]) ).
cnf(c_0_620,plain,
lhs_atom103(X1),
inference(split_conjunct,[status(thm)],[c_0_450]) ).
cnf(c_0_621,plain,
lhs_atom102(X1),
inference(split_conjunct,[status(thm)],[c_0_451]) ).
cnf(c_0_622,plain,
lhs_atom101(X1),
inference(split_conjunct,[status(thm)],[c_0_452]) ).
cnf(c_0_623,plain,
lhs_atom100(X1),
inference(split_conjunct,[status(thm)],[c_0_453]) ).
cnf(c_0_624,plain,
lhs_atom98(X1),
inference(split_conjunct,[status(thm)],[c_0_454]) ).
cnf(c_0_625,plain,
lhs_atom97(X1),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_626,plain,
lhs_atom96(X1),
inference(split_conjunct,[status(thm)],[c_0_456]) ).
cnf(c_0_627,plain,
lhs_atom93(X1),
inference(split_conjunct,[status(thm)],[c_0_457]) ).
cnf(c_0_628,plain,
lhs_atom92(X1),
inference(split_conjunct,[status(thm)],[c_0_458]) ).
cnf(c_0_629,plain,
lhs_atom90(X1),
inference(split_conjunct,[status(thm)],[c_0_459]) ).
cnf(c_0_630,plain,
lhs_atom88(X1),
inference(split_conjunct,[status(thm)],[c_0_460]) ).
cnf(c_0_631,plain,
lhs_atom83(X1),
inference(split_conjunct,[status(thm)],[c_0_461]) ).
cnf(c_0_632,plain,
lhs_atom78(X1),
inference(split_conjunct,[status(thm)],[c_0_462]) ).
cnf(c_0_633,plain,
lhs_atom77(X1),
inference(split_conjunct,[status(thm)],[c_0_463]) ).
cnf(c_0_634,plain,
lhs_atom70(X1),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_635,plain,
lhs_atom69(X1),
inference(split_conjunct,[status(thm)],[c_0_465]) ).
cnf(c_0_636,plain,
lhs_atom59(X1),
inference(split_conjunct,[status(thm)],[c_0_466]) ).
cnf(c_0_637,plain,
lhs_atom43(X1),
inference(split_conjunct,[status(thm)],[c_0_467]) ).
cnf(c_0_638,plain,
lhs_atom42(X1),
inference(split_conjunct,[status(thm)],[c_0_468]) ).
cnf(c_0_639,plain,
lhs_atom39(X1),
inference(split_conjunct,[status(thm)],[c_0_469]) ).
cnf(c_0_640,plain,
lhs_atom163,
inference(split_conjunct,[status(thm)],[c_0_470]) ).
cnf(c_0_641,plain,
lhs_atom162,
inference(split_conjunct,[status(thm)],[c_0_471]) ).
cnf(c_0_642,plain,
lhs_atom161,
inference(split_conjunct,[status(thm)],[c_0_472]) ).
cnf(c_0_643,plain,
lhs_atom160,
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_644,plain,
lhs_atom159,
inference(split_conjunct,[status(thm)],[c_0_474]) ).
cnf(c_0_645,plain,
lhs_atom158,
inference(split_conjunct,[status(thm)],[c_0_475]) ).
cnf(c_0_646,plain,
lhs_atom157,
inference(split_conjunct,[status(thm)],[c_0_476]) ).
cnf(c_0_647,plain,
lhs_atom156,
inference(split_conjunct,[status(thm)],[c_0_477]) ).
cnf(c_0_648,plain,
lhs_atom155,
inference(split_conjunct,[status(thm)],[c_0_478]) ).
cnf(c_0_649,plain,
lhs_atom154,
inference(split_conjunct,[status(thm)],[c_0_479]) ).
cnf(c_0_650,plain,
lhs_atom153,
inference(split_conjunct,[status(thm)],[c_0_480]) ).
cnf(c_0_651,plain,
lhs_atom152,
inference(split_conjunct,[status(thm)],[c_0_481]) ).
cnf(c_0_652,plain,
lhs_atom151,
inference(split_conjunct,[status(thm)],[c_0_482]) ).
cnf(c_0_653,plain,
lhs_atom150,
inference(split_conjunct,[status(thm)],[c_0_483]) ).
cnf(c_0_654,plain,
lhs_atom149,
inference(split_conjunct,[status(thm)],[c_0_484]) ).
cnf(c_0_655,plain,
lhs_atom148,
inference(split_conjunct,[status(thm)],[c_0_485]) ).
cnf(c_0_656,plain,
lhs_atom147,
inference(split_conjunct,[status(thm)],[c_0_486]) ).
cnf(c_0_657,plain,
lhs_atom146,
inference(split_conjunct,[status(thm)],[c_0_487]) ).
cnf(c_0_658,plain,
lhs_atom145,
inference(split_conjunct,[status(thm)],[c_0_488]) ).
cnf(c_0_659,plain,
lhs_atom144,
inference(split_conjunct,[status(thm)],[c_0_489]) ).
cnf(c_0_660,plain,
lhs_atom143,
inference(split_conjunct,[status(thm)],[c_0_490]) ).
cnf(c_0_661,plain,
lhs_atom142,
inference(split_conjunct,[status(thm)],[c_0_491]) ).
cnf(c_0_662,plain,
lhs_atom141,
inference(split_conjunct,[status(thm)],[c_0_492]) ).
cnf(c_0_663,plain,
lhs_atom140,
inference(split_conjunct,[status(thm)],[c_0_493]) ).
cnf(c_0_664,plain,
lhs_atom139,
inference(split_conjunct,[status(thm)],[c_0_494]) ).
cnf(c_0_665,plain,
lhs_atom138,
inference(split_conjunct,[status(thm)],[c_0_495]) ).
cnf(c_0_666,plain,
lhs_atom137,
inference(split_conjunct,[status(thm)],[c_0_496]) ).
cnf(c_0_667,plain,
lhs_atom136,
inference(split_conjunct,[status(thm)],[c_0_497]) ).
cnf(c_0_668,plain,
lhs_atom82,
inference(split_conjunct,[status(thm)],[c_0_498]) ).
cnf(c_0_669,plain,
lhs_atom136,
inference(split_conjunct,[status(thm)],[c_0_499]) ).
cnf(c_0_670,plain,
lhs_atom135,
inference(split_conjunct,[status(thm)],[c_0_500]) ).
cnf(c_0_671,plain,
lhs_atom133,
inference(split_conjunct,[status(thm)],[c_0_501]) ).
cnf(c_0_672,plain,
lhs_atom130,
inference(split_conjunct,[status(thm)],[c_0_502]) ).
cnf(c_0_673,plain,
lhs_atom128,
inference(split_conjunct,[status(thm)],[c_0_503]) ).
cnf(c_0_674,plain,
lhs_atom94,
inference(split_conjunct,[status(thm)],[c_0_504]) ).
cnf(c_0_675,plain,
lhs_atom91,
inference(split_conjunct,[status(thm)],[c_0_505]) ).
cnf(c_0_676,plain,
lhs_atom89,
inference(split_conjunct,[status(thm)],[c_0_506]) ).
cnf(c_0_677,plain,
lhs_atom82,
inference(split_conjunct,[status(thm)],[c_0_507]) ).
cnf(c_0_678,plain,
lhs_atom65,
inference(split_conjunct,[status(thm)],[c_0_508]) ).
cnf(c_0_679,plain,
lhs_atom64,
inference(split_conjunct,[status(thm)],[c_0_509]) ).
cnf(c_0_680,plain,
lhs_atom123(X1,X2,X3,X4,X5,X6),
c_0_510,
[final] ).
cnf(c_0_681,plain,
lhs_atom122(X1,X2,X3,X4,X5,X6),
c_0_511,
[final] ).
cnf(c_0_682,plain,
lhs_atom110(X1,X2,X3,X4,X5,X6),
c_0_512,
[final] ).
cnf(c_0_683,plain,
lhs_atom109(X1,X2,X3,X4,X5,X6),
c_0_513,
[final] ).
cnf(c_0_684,plain,
lhs_atom72(X1,X2,X3,X4,X5,X6),
c_0_514,
[final] ).
cnf(c_0_685,plain,
lhs_atom19(X1,X2,X3,X4,X5,X6),
c_0_515,
[final] ).
cnf(c_0_686,plain,
lhs_atom10(X1,X2,X3,X4,X5,X6),
c_0_516,
[final] ).
cnf(c_0_687,plain,
lhs_atom81(X1,X2,X3,X4,X5),
c_0_517,
[final] ).
cnf(c_0_688,plain,
lhs_atom71(X1,X2,X3,X4,X5),
c_0_518,
[final] ).
cnf(c_0_689,plain,
lhs_atom48(X1,X2,X3,X4,X5),
c_0_519,
[final] ).
cnf(c_0_690,plain,
lhs_atom40(X1,X2,X3,X4,X5),
c_0_520,
[final] ).
cnf(c_0_691,plain,
lhs_atom33(X1,X2,X3,X4,X5),
c_0_521,
[final] ).
cnf(c_0_692,plain,
lhs_atom32(X1,X2,X3,X4,X5),
c_0_522,
[final] ).
cnf(c_0_693,plain,
lhs_atom31(X1,X2,X3,X4,X5),
c_0_523,
[final] ).
cnf(c_0_694,plain,
lhs_atom18(X1,X2,X3,X4,X5),
c_0_524,
[final] ).
cnf(c_0_695,plain,
lhs_atom8(X1,X2,X3,X4,X5),
c_0_525,
[final] ).
cnf(c_0_696,plain,
lhs_atom1(X1,X2,X3,X4,X5),
c_0_526,
[final] ).
cnf(c_0_697,plain,
lhs_atom134(X1,X2,X3,X4),
c_0_527,
[final] ).
cnf(c_0_698,plain,
lhs_atom124(X1,X2,X3,X4),
c_0_528,
[final] ).
cnf(c_0_699,plain,
lhs_atom121(X1,X2,X3,X4),
c_0_529,
[final] ).
cnf(c_0_700,plain,
lhs_atom120(X1,X2,X3,X4),
c_0_530,
[final] ).
cnf(c_0_701,plain,
lhs_atom115(X1,X2,X3,X4),
c_0_531,
[final] ).
cnf(c_0_702,plain,
lhs_atom112(X1,X2,X3,X4),
c_0_532,
[final] ).
cnf(c_0_703,plain,
lhs_atom111(X1,X2,X3,X4),
c_0_533,
[final] ).
cnf(c_0_704,plain,
lhs_atom87(X1,X2,X3,X4),
c_0_534,
[final] ).
cnf(c_0_705,plain,
lhs_atom86(X1,X2,X3,X4),
c_0_535,
[final] ).
cnf(c_0_706,plain,
lhs_atom85(X1,X2,X3,X4),
c_0_536,
[final] ).
cnf(c_0_707,plain,
lhs_atom84(X1,X2,X3,X4),
c_0_537,
[final] ).
cnf(c_0_708,plain,
lhs_atom80(X1,X2,X3,X4),
c_0_538,
[final] ).
cnf(c_0_709,plain,
lhs_atom55(X1,X2,X3,X4),
c_0_539,
[final] ).
cnf(c_0_710,plain,
lhs_atom53(X1,X2,X3,X4),
c_0_540,
[final] ).
cnf(c_0_711,plain,
lhs_atom52(X1,X2,X3,X4),
c_0_541,
[final] ).
cnf(c_0_712,plain,
lhs_atom49(X1,X2,X3,X4),
c_0_542,
[final] ).
cnf(c_0_713,plain,
lhs_atom38(X1,X2,X3,X4),
c_0_543,
[final] ).
cnf(c_0_714,plain,
lhs_atom35(X1,X2,X3,X4),
c_0_544,
[final] ).
cnf(c_0_715,plain,
lhs_atom34(X1,X2,X3,X4),
c_0_545,
[final] ).
cnf(c_0_716,plain,
lhs_atom29(X1,X2,X3,X4),
c_0_546,
[final] ).
cnf(c_0_717,plain,
lhs_atom28(X1,X2,X3,X4),
c_0_547,
[final] ).
cnf(c_0_718,plain,
lhs_atom20(X1,X2,X3,X4),
c_0_548,
[final] ).
cnf(c_0_719,plain,
( c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X3,X2)
| lhs_atom99(X3,X1,X2) ),
c_0_549,
[final] ).
cnf(c_0_720,plain,
lhs_atom126(X1,X2,X3),
c_0_550,
[final] ).
cnf(c_0_721,plain,
lhs_atom114(X1,X2,X3),
c_0_551,
[final] ).
cnf(c_0_722,plain,
lhs_atom113(X1,X2,X3),
c_0_552,
[final] ).
cnf(c_0_723,plain,
lhs_atom108(X1,X2,X3),
c_0_553,
[final] ).
cnf(c_0_724,plain,
lhs_atom107(X1,X2,X3),
c_0_554,
[final] ).
cnf(c_0_725,plain,
lhs_atom106(X1,X2,X3),
c_0_555,
[final] ).
cnf(c_0_726,plain,
lhs_atom105(X1,X2,X3),
c_0_556,
[final] ).
cnf(c_0_727,plain,
lhs_atom76(X1,X2,X3),
c_0_557,
[final] ).
cnf(c_0_728,plain,
lhs_atom73(X1,X2,X3),
c_0_558,
[final] ).
cnf(c_0_729,plain,
lhs_atom68(X1,X2,X3),
c_0_559,
[final] ).
cnf(c_0_730,plain,
lhs_atom67(X1,X2,X3),
c_0_560,
[final] ).
cnf(c_0_731,plain,
lhs_atom61(X1,X2,X3),
c_0_561,
[final] ).
cnf(c_0_732,plain,
lhs_atom21(X1,X2,X3),
c_0_562,
[final] ).
cnf(c_0_733,plain,
lhs_atom58(X1,X2,X3),
c_0_563,
[final] ).
cnf(c_0_734,plain,
lhs_atom57(X1,X2,X3),
c_0_564,
[final] ).
cnf(c_0_735,plain,
lhs_atom56(X1,X2,X3),
c_0_565,
[final] ).
cnf(c_0_736,plain,
lhs_atom54(X1,X2,X3),
c_0_566,
[final] ).
cnf(c_0_737,plain,
lhs_atom50(X1,X2,X3),
c_0_567,
[final] ).
cnf(c_0_738,plain,
lhs_atom37(X1,X2,X3),
c_0_568,
[final] ).
cnf(c_0_739,plain,
lhs_atom36(X1,X2,X3),
c_0_569,
[final] ).
cnf(c_0_740,plain,
lhs_atom30(X1,X2,X3),
c_0_570,
[final] ).
cnf(c_0_741,plain,
lhs_atom25(X1,X2,X3),
c_0_571,
[final] ).
cnf(c_0_742,plain,
lhs_atom24(X1,X2,X3),
c_0_572,
[final] ).
cnf(c_0_743,plain,
lhs_atom23(X1,X2,X3),
c_0_573,
[final] ).
cnf(c_0_744,plain,
lhs_atom21(X1,X2,X3),
c_0_574,
[final] ).
cnf(c_0_745,plain,
lhs_atom17(X1,X2,X3),
c_0_575,
[final] ).
cnf(c_0_746,plain,
lhs_atom16(X1,X2,X3),
c_0_576,
[final] ).
cnf(c_0_747,plain,
lhs_atom15(X1,X2,X3),
c_0_577,
[final] ).
cnf(c_0_748,plain,
lhs_atom14(X1,X2,X3),
c_0_578,
[final] ).
cnf(c_0_749,plain,
lhs_atom13(X1,X2,X3),
c_0_579,
[final] ).
cnf(c_0_750,plain,
lhs_atom4(X1,X2,X3),
c_0_580,
[final] ).
cnf(c_0_751,plain,
lhs_atom3(X1,X2,X3),
c_0_581,
[final] ).
cnf(c_0_752,plain,
lhs_atom164(X1,X2),
c_0_582,
[final] ).
cnf(c_0_753,plain,
lhs_atom132(X1,X2),
c_0_583,
[final] ).
cnf(c_0_754,plain,
lhs_atom131(X1,X2),
c_0_584,
[final] ).
cnf(c_0_755,plain,
lhs_atom129(X1,X2),
c_0_585,
[final] ).
cnf(c_0_756,plain,
lhs_atom125(X1,X2),
c_0_586,
[final] ).
cnf(c_0_757,plain,
lhs_atom95(X1,X2),
c_0_587,
[final] ).
cnf(c_0_758,plain,
lhs_atom79(X1,X2),
c_0_588,
[final] ).
cnf(c_0_759,plain,
lhs_atom75(X1,X2),
c_0_589,
[final] ).
cnf(c_0_760,plain,
lhs_atom74(X1,X2),
c_0_590,
[final] ).
cnf(c_0_761,plain,
lhs_atom66(X1,X2),
c_0_591,
[final] ).
cnf(c_0_762,plain,
lhs_atom63(X1,X2),
c_0_592,
[final] ).
cnf(c_0_763,plain,
lhs_atom62(X1,X2),
c_0_593,
[final] ).
cnf(c_0_764,plain,
lhs_atom60(X1,X2),
c_0_594,
[final] ).
cnf(c_0_765,plain,
lhs_atom41(X1,X2),
c_0_595,
[final] ).
cnf(c_0_766,plain,
lhs_atom51(X1,X2),
c_0_596,
[final] ).
cnf(c_0_767,plain,
lhs_atom47(X1,X2),
c_0_597,
[final] ).
cnf(c_0_768,plain,
lhs_atom46(X1,X2),
c_0_598,
[final] ).
cnf(c_0_769,plain,
lhs_atom45(X1,X2),
c_0_599,
[final] ).
cnf(c_0_770,plain,
lhs_atom44(X1,X2),
c_0_600,
[final] ).
cnf(c_0_771,plain,
lhs_atom41(X1,X2),
c_0_601,
[final] ).
cnf(c_0_772,plain,
lhs_atom27(X1,X2),
c_0_602,
[final] ).
cnf(c_0_773,plain,
lhs_atom26(X1,X2),
c_0_603,
[final] ).
cnf(c_0_774,plain,
lhs_atom22(X1,X2),
c_0_604,
[final] ).
cnf(c_0_775,plain,
lhs_atom12(X1,X2),
c_0_605,
[final] ).
cnf(c_0_776,plain,
lhs_atom11(X1,X2),
c_0_606,
[final] ).
cnf(c_0_777,plain,
lhs_atom9(X1,X2),
c_0_607,
[final] ).
cnf(c_0_778,plain,
lhs_atom7(X1,X2),
c_0_608,
[final] ).
cnf(c_0_779,plain,
lhs_atom7(X1,X2),
c_0_609,
[final] ).
cnf(c_0_780,plain,
lhs_atom5(X1,X2),
c_0_610,
[final] ).
cnf(c_0_781,plain,
lhs_atom6(X1,X2),
c_0_611,
[final] ).
cnf(c_0_782,plain,
lhs_atom5(X1,X2),
c_0_612,
[final] ).
cnf(c_0_783,plain,
lhs_atom2(X1,X2),
c_0_613,
[final] ).
cnf(c_0_784,plain,
lhs_atom127(X1),
c_0_614,
[final] ).
cnf(c_0_785,plain,
lhs_atom119(X1),
c_0_615,
[final] ).
cnf(c_0_786,plain,
lhs_atom118(X1),
c_0_616,
[final] ).
cnf(c_0_787,plain,
lhs_atom117(X1),
c_0_617,
[final] ).
cnf(c_0_788,plain,
lhs_atom116(X1),
c_0_618,
[final] ).
cnf(c_0_789,plain,
lhs_atom104(X1),
c_0_619,
[final] ).
cnf(c_0_790,plain,
lhs_atom103(X1),
c_0_620,
[final] ).
cnf(c_0_791,plain,
lhs_atom102(X1),
c_0_621,
[final] ).
cnf(c_0_792,plain,
lhs_atom101(X1),
c_0_622,
[final] ).
cnf(c_0_793,plain,
lhs_atom100(X1),
c_0_623,
[final] ).
cnf(c_0_794,plain,
lhs_atom98(X1),
c_0_624,
[final] ).
cnf(c_0_795,plain,
lhs_atom97(X1),
c_0_625,
[final] ).
cnf(c_0_796,plain,
lhs_atom96(X1),
c_0_626,
[final] ).
cnf(c_0_797,plain,
lhs_atom93(X1),
c_0_627,
[final] ).
cnf(c_0_798,plain,
lhs_atom92(X1),
c_0_628,
[final] ).
cnf(c_0_799,plain,
lhs_atom90(X1),
c_0_629,
[final] ).
cnf(c_0_800,plain,
lhs_atom88(X1),
c_0_630,
[final] ).
cnf(c_0_801,plain,
lhs_atom83(X1),
c_0_631,
[final] ).
cnf(c_0_802,plain,
lhs_atom78(X1),
c_0_632,
[final] ).
cnf(c_0_803,plain,
lhs_atom77(X1),
c_0_633,
[final] ).
cnf(c_0_804,plain,
lhs_atom70(X1),
c_0_634,
[final] ).
cnf(c_0_805,plain,
lhs_atom69(X1),
c_0_635,
[final] ).
cnf(c_0_806,plain,
lhs_atom59(X1),
c_0_636,
[final] ).
cnf(c_0_807,plain,
lhs_atom43(X1),
c_0_637,
[final] ).
cnf(c_0_808,plain,
lhs_atom42(X1),
c_0_638,
[final] ).
cnf(c_0_809,plain,
lhs_atom39(X1),
c_0_639,
[final] ).
cnf(c_0_810,plain,
lhs_atom163,
c_0_640,
[final] ).
cnf(c_0_811,plain,
lhs_atom162,
c_0_641,
[final] ).
cnf(c_0_812,plain,
lhs_atom161,
c_0_642,
[final] ).
cnf(c_0_813,plain,
lhs_atom160,
c_0_643,
[final] ).
cnf(c_0_814,plain,
lhs_atom159,
c_0_644,
[final] ).
cnf(c_0_815,plain,
lhs_atom158,
c_0_645,
[final] ).
cnf(c_0_816,plain,
lhs_atom157,
c_0_646,
[final] ).
cnf(c_0_817,plain,
lhs_atom156,
c_0_647,
[final] ).
cnf(c_0_818,plain,
lhs_atom155,
c_0_648,
[final] ).
cnf(c_0_819,plain,
lhs_atom154,
c_0_649,
[final] ).
cnf(c_0_820,plain,
lhs_atom153,
c_0_650,
[final] ).
cnf(c_0_821,plain,
lhs_atom152,
c_0_651,
[final] ).
cnf(c_0_822,plain,
lhs_atom151,
c_0_652,
[final] ).
cnf(c_0_823,plain,
lhs_atom150,
c_0_653,
[final] ).
cnf(c_0_824,plain,
lhs_atom149,
c_0_654,
[final] ).
cnf(c_0_825,plain,
lhs_atom148,
c_0_655,
[final] ).
cnf(c_0_826,plain,
lhs_atom147,
c_0_656,
[final] ).
cnf(c_0_827,plain,
lhs_atom146,
c_0_657,
[final] ).
cnf(c_0_828,plain,
lhs_atom145,
c_0_658,
[final] ).
cnf(c_0_829,plain,
lhs_atom144,
c_0_659,
[final] ).
cnf(c_0_830,plain,
lhs_atom143,
c_0_660,
[final] ).
cnf(c_0_831,plain,
lhs_atom142,
c_0_661,
[final] ).
cnf(c_0_832,plain,
lhs_atom141,
c_0_662,
[final] ).
cnf(c_0_833,plain,
lhs_atom140,
c_0_663,
[final] ).
cnf(c_0_834,plain,
lhs_atom139,
c_0_664,
[final] ).
cnf(c_0_835,plain,
lhs_atom138,
c_0_665,
[final] ).
cnf(c_0_836,plain,
lhs_atom137,
c_0_666,
[final] ).
cnf(c_0_837,plain,
lhs_atom136,
c_0_667,
[final] ).
cnf(c_0_838,plain,
lhs_atom82,
c_0_668,
[final] ).
cnf(c_0_839,plain,
lhs_atom136,
c_0_669,
[final] ).
cnf(c_0_840,plain,
lhs_atom135,
c_0_670,
[final] ).
cnf(c_0_841,plain,
lhs_atom133,
c_0_671,
[final] ).
cnf(c_0_842,plain,
lhs_atom130,
c_0_672,
[final] ).
cnf(c_0_843,plain,
lhs_atom128,
c_0_673,
[final] ).
cnf(c_0_844,plain,
lhs_atom94,
c_0_674,
[final] ).
cnf(c_0_845,plain,
lhs_atom91,
c_0_675,
[final] ).
cnf(c_0_846,plain,
lhs_atom89,
c_0_676,
[final] ).
cnf(c_0_847,plain,
lhs_atom82,
c_0_677,
[final] ).
cnf(c_0_848,plain,
lhs_atom65,
c_0_678,
[final] ).
cnf(c_0_849,plain,
lhs_atom64,
c_0_679,
[final] ).
% End CNF derivation
cnf(c_0_719_0,axiom,
( c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X3,X2)
| c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X3,X2) ),
inference(unfold_definition,[status(thm)],[c_0_719,def_lhs_atom99]) ).
cnf(c_0_680_0,axiom,
c_List_Ofoldl(X3,X4,c_List_Oappend(X2,X1,X5),X6,X5) = c_List_Ofoldl(X3,c_List_Ofoldl(X3,X4,X2,X6,X5),X1,X6,X5),
inference(unfold_definition,[status(thm)],[c_0_680,def_lhs_atom123]) ).
cnf(c_0_681_0,axiom,
c_List_Ofoldl(X3,X4,c_List_Olist_OCons(X2,X1,X5),X6,X5) = c_List_Ofoldl(X3,hAPP(hAPP(X3,X4),X2),X1,X6,X5),
inference(unfold_definition,[status(thm)],[c_0_681,def_lhs_atom122]) ).
cnf(c_0_682_0,axiom,
c_Lambda_OdB_OdB__rec(X3,X2,X1,hAPP(hAPP(c_Lambda_OdB_OApp,X5),X4),X6) = hAPP(hAPP(hAPP(hAPP(X2,X5),X4),c_Lambda_OdB_OdB__rec(X3,X2,X1,X5,X6)),c_Lambda_OdB_OdB__rec(X3,X2,X1,X4,X6)),
inference(unfold_definition,[status(thm)],[c_0_682,def_lhs_atom110]) ).
cnf(c_0_683_0,axiom,
c_Lambda_OdB_OdB__case(X3,X2,X1,hAPP(hAPP(c_Lambda_OdB_OApp,X5),X4),X6) = hAPP(hAPP(X2,X5),X4),
inference(unfold_definition,[status(thm)],[c_0_683,def_lhs_atom109]) ).
cnf(c_0_684_0,axiom,
c_List_Ofoldr(X3,c_List_Olist_OCons(X2,X1,X5),X4,X5,X6) = hAPP(hAPP(X3,X2),c_List_Ofoldr(X3,X1,X4,X5,X6)),
inference(unfold_definition,[status(thm)],[c_0_684,def_lhs_atom72]) ).
cnf(c_0_685_0,axiom,
hAPP(c_COMBC(X3,X2,X5,X4,X6),X1) = hAPP(hAPP(X3,X1),X2),
inference(unfold_definition,[status(thm)],[c_0_685,def_lhs_atom19]) ).
cnf(c_0_686_0,axiom,
c_List_Ofoldr(X3,c_List_Oappend(X2,X1,X5),X4,X5,X6) = c_List_Ofoldr(X3,X2,c_List_Ofoldr(X3,X1,X4,X5,X6),X5,X6),
inference(unfold_definition,[status(thm)],[c_0_686,def_lhs_atom10]) ).
cnf(c_0_687_0,axiom,
c_List_Odrop(X2,c_List_Omap(X3,X1,X4,X5),X5) = c_List_Omap(X3,c_List_Odrop(X2,X1,X4),X4,X5),
inference(unfold_definition,[status(thm)],[c_0_687,def_lhs_atom81]) ).
cnf(c_0_688_0,axiom,
c_Lambda_OdB_OdB__rec(X3,X2,X1,c_Lambda_OdB_OAbs(X4),X5) = hAPP(hAPP(X1,X4),c_Lambda_OdB_OdB__rec(X3,X2,X1,X4,X5)),
inference(unfold_definition,[status(thm)],[c_0_688,def_lhs_atom71]) ).
cnf(c_0_689_0,axiom,
c_List_Omap(X3,c_List_Oappend(X2,X1,X4),X4,X5) = c_List_Oappend(c_List_Omap(X3,X2,X4,X5),c_List_Omap(X3,X1,X4,X5),X5),
inference(unfold_definition,[status(thm)],[c_0_689,def_lhs_atom48]) ).
cnf(c_0_690_0,axiom,
c_Lambda_OdB_OdB__rec(X4,X3,X2,c_Lambda_OdB_OVar(X1),X5) = hAPP(X4,X1),
inference(unfold_definition,[status(thm)],[c_0_690,def_lhs_atom40]) ).
cnf(c_0_691_0,axiom,
c_List_Omap(X3,c_List_Olist_OCons(X2,X1,X4),X4,X5) = c_List_Olist_OCons(hAPP(X3,X2),c_List_Omap(X3,X1,X4,X5),X5),
inference(unfold_definition,[status(thm)],[c_0_691,def_lhs_atom33]) ).
cnf(c_0_692_0,axiom,
c_List_Olist_OCons(hAPP(X3,X2),c_List_Omap(X3,X1,X4,X5),X5) = c_List_Omap(X3,c_List_Olist_OCons(X2,X1,X4),X4,X5),
inference(unfold_definition,[status(thm)],[c_0_692,def_lhs_atom32]) ).
cnf(c_0_693_0,axiom,
c_List_Omap(X3,c_List_Olist_OCons(X2,X1,X4),X4,X5) = c_List_Olist_OCons(hAPP(X3,X2),c_List_Omap(X3,X1,X4,X5),X5),
inference(unfold_definition,[status(thm)],[c_0_693,def_lhs_atom31]) ).
cnf(c_0_694_0,axiom,
c_Lambda_OdB_OdB__case(X4,X3,X2,c_Lambda_OdB_OVar(X1),X5) = hAPP(X4,X1),
inference(unfold_definition,[status(thm)],[c_0_694,def_lhs_atom18]) ).
cnf(c_0_695_0,axiom,
c_List_Omap(X3,c_List_Oreplicate(X2,X1,X4),X4,X5) = c_List_Oreplicate(X2,hAPP(X3,X1),X5),
inference(unfold_definition,[status(thm)],[c_0_695,def_lhs_atom8]) ).
cnf(c_0_696_0,axiom,
c_Lambda_OdB_OdB__case(X3,X2,X1,c_Lambda_OdB_OAbs(X4),X5) = hAPP(X1,X4),
inference(unfold_definition,[status(thm)],[c_0_696,def_lhs_atom1]) ).
cnf(c_0_697_0,axiom,
hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X1)),X3),X4) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4)),
inference(unfold_definition,[status(thm)],[c_0_697,def_lhs_atom134]) ).
cnf(c_0_698_0,axiom,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X1),X4) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X1),X4),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X1,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(unfold_definition,[status(thm)],[c_0_698,def_lhs_atom124]) ).
cnf(c_0_699_0,axiom,
c_List_Ofoldl(X1,X2,c_List_Olist_ONil(X3),X4,X3) = X2,
inference(unfold_definition,[status(thm)],[c_0_699,def_lhs_atom121]) ).
cnf(c_0_700_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3)),X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB),
inference(unfold_definition,[status(thm)],[c_0_700,def_lhs_atom120]) ).
cnf(c_0_701_0,axiom,
c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X2,tc_Lambda_OdB,tc_Lambda_OdB),
inference(unfold_definition,[status(thm)],[c_0_701,def_lhs_atom115]) ).
cnf(c_0_702_0,axiom,
c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,X2),X1),X3,X4) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(X2,X3,X4)),c_Lambda_Osubstn(X1,X3,X4)),
inference(unfold_definition,[status(thm)],[c_0_702,def_lhs_atom112]) ).
cnf(c_0_703_0,axiom,
c_Lambda_Oliftn(X3,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X1),X4) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(X3,X2,X4)),c_Lambda_Oliftn(X3,X1,X4)),
inference(unfold_definition,[status(thm)],[c_0_703,def_lhs_atom111]) ).
cnf(c_0_704_0,axiom,
c_List_Oappend(X1,c_List_Oappend(X2,X3,X4),X4) = c_List_Oappend(c_List_Oappend(X1,X2,X4),X3,X4),
inference(unfold_definition,[status(thm)],[c_0_704,def_lhs_atom87]) ).
cnf(c_0_705_0,axiom,
c_List_Oappend(c_List_Oappend(X1,X3,X4),X2,X4) = c_List_Oappend(X1,c_List_Oappend(X3,X2,X4),X4),
inference(unfold_definition,[status(thm)],[c_0_705,def_lhs_atom86]) ).
cnf(c_0_706_0,axiom,
c_List_Oappend(X2,c_List_Oappend(X1,X3,X4),X4) = c_List_Oappend(c_List_Oappend(X2,X1,X4),X3,X4),
inference(unfold_definition,[status(thm)],[c_0_706,def_lhs_atom85]) ).
cnf(c_0_707_0,axiom,
c_List_Oappend(c_List_Oappend(X3,X2,X4),X1,X4) = c_List_Oappend(X3,c_List_Oappend(X2,X1,X4),X4),
inference(unfold_definition,[status(thm)],[c_0_707,def_lhs_atom84]) ).
cnf(c_0_708_0,axiom,
c_List_Oappend(c_List_Oreplicate(X3,X2,X4),c_List_Olist_OCons(X2,X1,X4),X4) = c_List_Olist_OCons(X2,c_List_Oappend(c_List_Oreplicate(X3,X2,X4),X1,X4),X4),
inference(unfold_definition,[status(thm)],[c_0_708,def_lhs_atom80]) ).
cnf(c_0_709_0,axiom,
c_List_Odrop(X3,c_List_Oreplicate(X2,X1,X4),X4) = c_List_Oreplicate(c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),X1,X4),
inference(unfold_definition,[status(thm)],[c_0_709,def_lhs_atom55]) ).
cnf(c_0_710_0,axiom,
c_List_Oreplicate(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X1,X4) = c_List_Oappend(c_List_Oreplicate(X2,X1,X4),c_List_Oreplicate(X3,X1,X4),X4),
inference(unfold_definition,[status(thm)],[c_0_710,def_lhs_atom53]) ).
cnf(c_0_711_0,axiom,
c_List_Odrop(X2,c_List_Odrop(X3,X1,X4),X4) = c_List_Odrop(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X1,X4),
inference(unfold_definition,[status(thm)],[c_0_711,def_lhs_atom52]) ).
cnf(c_0_712_0,axiom,
c_List_Oappend(c_List_Oreplicate(X2,X1,X4),c_List_Oreplicate(X3,X1,X4),X4) = c_List_Oappend(c_List_Oreplicate(X3,X1,X4),c_List_Oreplicate(X2,X1,X4),X4),
inference(unfold_definition,[status(thm)],[c_0_712,def_lhs_atom49]) ).
cnf(c_0_713_0,axiom,
hAPP(c_Type_Oshift(X2,X1,X3,X4),X1) = X3,
inference(unfold_definition,[status(thm)],[c_0_713,def_lhs_atom38]) ).
cnf(c_0_714_0,axiom,
c_List_Olist_OCons(X3,c_List_Oappend(X2,X1,X4),X4) = c_List_Oappend(c_List_Olist_OCons(X3,X2,X4),X1,X4),
inference(unfold_definition,[status(thm)],[c_0_714,def_lhs_atom35]) ).
cnf(c_0_715_0,axiom,
c_List_Olist_OCons(X3,c_List_Oappend(X2,X1,X4),X4) = c_List_Oappend(c_List_Olist_OCons(X3,X2,X4),X1,X4),
inference(unfold_definition,[status(thm)],[c_0_715,def_lhs_atom34]) ).
cnf(c_0_716_0,axiom,
c_List_Oappend(c_List_Olist_OCons(X3,X2,X4),X1,X4) = c_List_Olist_OCons(X3,c_List_Oappend(X2,X1,X4),X4),
inference(unfold_definition,[status(thm)],[c_0_716,def_lhs_atom29]) ).
cnf(c_0_717_0,axiom,
c_List_Oappend(c_List_Olist_OCons(X3,X2,X4),X1,X4) = c_List_Olist_OCons(X3,c_List_Oappend(X2,X1,X4),X4),
inference(unfold_definition,[status(thm)],[c_0_717,def_lhs_atom28]) ).
cnf(c_0_718_0,axiom,
c_List_Ofoldr(X1,c_List_Olist_ONil(X3),X2,X3,X4) = X2,
inference(unfold_definition,[status(thm)],[c_0_718,def_lhs_atom20]) ).
cnf(c_0_720_0,axiom,
hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X1),X3)),X2),X3) = X1,
inference(unfold_definition,[status(thm)],[c_0_720,def_lhs_atom126]) ).
cnf(c_0_721_0,axiom,
c_Lambda_Osubstn(X1,X2,X3) = hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),c_Lambda_Oliftn(X3,X2,c_HOL_Ozero__class_Ozero(tc_nat))),X3),
inference(unfold_definition,[status(thm)],[c_0_721,def_lhs_atom114]) ).
cnf(c_0_722_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2) != c_Lambda_OdB_OVar(X1),
inference(unfold_definition,[status(thm)],[c_0_722,def_lhs_atom113]) ).
cnf(c_0_723_0,axiom,
hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X1)),X3) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X2),X3)),hAPP(hAPP(c_Lambda_Olift,X1),X3)),
inference(unfold_definition,[status(thm)],[c_0_723,def_lhs_atom108]) ).
cnf(c_0_724_0,axiom,
c_Lambda_OdB_OVar(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2),
inference(unfold_definition,[status(thm)],[c_0_724,def_lhs_atom107]) ).
cnf(c_0_725_0,axiom,
c_Lambda_OdB_OAbs(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2),
inference(unfold_definition,[status(thm)],[c_0_725,def_lhs_atom106]) ).
cnf(c_0_726_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2) != c_Lambda_OdB_OAbs(X1),
inference(unfold_definition,[status(thm)],[c_0_726,def_lhs_atom105]) ).
cnf(c_0_727_0,axiom,
c_List_Oappend(c_List_Olist_ONil(X3),c_List_Olist_OCons(X2,X1,X3),X3) = c_List_Olist_OCons(X2,X1,X3),
inference(unfold_definition,[status(thm)],[c_0_727,def_lhs_atom76]) ).
cnf(c_0_728_0,axiom,
c_Predicate_Oconversep(c_Predicate_Oconversep(X1,X3,X2),X2,X3) = X1,
inference(unfold_definition,[status(thm)],[c_0_728,def_lhs_atom73]) ).
cnf(c_0_729_0,axiom,
c_Nat_Onat_Onat__case(X2,X1,c_HOL_Ozero__class_Ozero(tc_nat),X3) = X2,
inference(unfold_definition,[status(thm)],[c_0_729,def_lhs_atom68]) ).
cnf(c_0_730_0,axiom,
c_Nat_Onat_Onat__case(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat),X3) = X1,
inference(unfold_definition,[status(thm)],[c_0_730,def_lhs_atom67]) ).
cnf(c_0_731_0,axiom,
c_List_Oappend(c_List_Oreplicate(X2,X1,X3),c_List_Olist_OCons(X1,c_List_Olist_ONil(X3),X3),X3) = c_List_Olist_OCons(X1,c_List_Oreplicate(X2,X1,X3),X3),
inference(unfold_definition,[status(thm)],[c_0_731,def_lhs_atom61]) ).
cnf(c_0_732_0,axiom,
c_List_Omap(X1,c_List_Olist_ONil(X2),X2,X3) = c_List_Olist_ONil(X3),
inference(unfold_definition,[status(thm)],[c_0_732,def_lhs_atom21]) ).
cnf(c_0_733_0,axiom,
c_List_Olist_OCons(X2,X1,X3) = c_List_Oappend(c_List_Olist_ONil(X3),c_List_Olist_OCons(X2,X1,X3),X3),
inference(unfold_definition,[status(thm)],[c_0_733,def_lhs_atom58]) ).
cnf(c_0_734_0,axiom,
X1 != c_List_Olist_OCons(X2,X1,X3),
inference(unfold_definition,[status(thm)],[c_0_734,def_lhs_atom57]) ).
cnf(c_0_735_0,axiom,
c_List_Olist_OCons(X1,X2,X3) != X2,
inference(unfold_definition,[status(thm)],[c_0_735,def_lhs_atom56]) ).
cnf(c_0_736_0,axiom,
hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X1,tc_Lambda_OdB,tc_Lambda_OdB)),X3) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X2),X3),c_List_Omap(c_COMBC(c_Lambda_Olift,X3,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(unfold_definition,[status(thm)],[c_0_736,def_lhs_atom54]) ).
cnf(c_0_737_0,axiom,
c_List_Olist_ONil(X3) != c_List_Olist_OCons(X2,X1,X3),
inference(unfold_definition,[status(thm)],[c_0_737,def_lhs_atom50]) ).
cnf(c_0_738_0,axiom,
c_List_Olist_OCons(X2,X1,X3) != c_List_Olist_ONil(X3),
inference(unfold_definition,[status(thm)],[c_0_738,def_lhs_atom37]) ).
cnf(c_0_739_0,axiom,
c_List_Olist_OCons(X2,X1,X3) != c_List_Olist_ONil(X3),
inference(unfold_definition,[status(thm)],[c_0_739,def_lhs_atom36]) ).
cnf(c_0_740_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),X1,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),X2,tc_nat),
inference(unfold_definition,[status(thm)],[c_0_740,def_lhs_atom30]) ).
cnf(c_0_741_0,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),tc_nat) = c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),
inference(unfold_definition,[status(thm)],[c_0_741,def_lhs_atom25]) ).
cnf(c_0_742_0,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),tc_nat) = c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),
inference(unfold_definition,[status(thm)],[c_0_742,def_lhs_atom24]) ).
cnf(c_0_743_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),X1,tc_nat) = c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat),
inference(unfold_definition,[status(thm)],[c_0_743,def_lhs_atom23]) ).
cnf(c_0_744_0,axiom,
c_List_Omap(X1,c_List_Olist_ONil(X2),X2,X3) = c_List_Olist_ONil(X3),
inference(unfold_definition,[status(thm)],[c_0_744,def_lhs_atom21]) ).
cnf(c_0_745_0,axiom,
c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),c_List_Olist_OCons(X2,X1,X3),X3) = c_List_Olist_OCons(X2,X1,X3),
inference(unfold_definition,[status(thm)],[c_0_745,def_lhs_atom17]) ).
cnf(c_0_746_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_746,def_lhs_atom16]) ).
cnf(c_0_747_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_747,def_lhs_atom15]) ).
cnf(c_0_748_0,axiom,
~ c_ListOrder_Ostep1(X2,X1,c_List_Olist_ONil(X3),X3),
inference(unfold_definition,[status(thm)],[c_0_748,def_lhs_atom14]) ).
cnf(c_0_749_0,axiom,
~ c_ListOrder_Ostep1(X2,c_List_Olist_ONil(X3),X1,X3),
inference(unfold_definition,[status(thm)],[c_0_749,def_lhs_atom13]) ).
cnf(c_0_750_0,axiom,
hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X2,X3),X1),X1)),
inference(unfold_definition,[status(thm)],[c_0_750,def_lhs_atom4]) ).
cnf(c_0_751_0,axiom,
hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X3),X2),X2)),
inference(unfold_definition,[status(thm)],[c_0_751,def_lhs_atom3]) ).
cnf(c_0_752_0,axiom,
hBOOL(hAPP(hAPP(c_fequal(X2),X1),X1)),
inference(unfold_definition,[status(thm)],[c_0_752,def_lhs_atom164]) ).
cnf(c_0_753_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,X2),X1) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(unfold_definition,[status(thm)],[c_0_753,def_lhs_atom132]) ).
cnf(c_0_754_0,axiom,
c_Lambda_Osubstn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),
inference(unfold_definition,[status(thm)],[c_0_754,def_lhs_atom131]) ).
cnf(c_0_755_0,axiom,
hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X2)),X1)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X1),c_HOL_Ozero__class_Ozero(tc_nat)))),
inference(unfold_definition,[status(thm)],[c_0_755,def_lhs_atom129]) ).
cnf(c_0_756_0,axiom,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X2)),X1),X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_756,def_lhs_atom125]) ).
cnf(c_0_757_0,axiom,
c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_757,def_lhs_atom95]) ).
cnf(c_0_758_0,axiom,
c_Lambda_OdB_OAbs(X2) != c_Lambda_OdB_OVar(X1),
inference(unfold_definition,[status(thm)],[c_0_758,def_lhs_atom79]) ).
cnf(c_0_759_0,axiom,
~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X2,tc_nat),
inference(unfold_definition,[status(thm)],[c_0_759,def_lhs_atom75]) ).
cnf(c_0_760_0,axiom,
~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),X2,tc_nat),
inference(unfold_definition,[status(thm)],[c_0_760,def_lhs_atom74]) ).
cnf(c_0_761_0,axiom,
c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_761,def_lhs_atom66]) ).
cnf(c_0_762_0,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X1,tc_nat) = X2,
inference(unfold_definition,[status(thm)],[c_0_762,def_lhs_atom63]) ).
cnf(c_0_763_0,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),X1,tc_nat) = X2,
inference(unfold_definition,[status(thm)],[c_0_763,def_lhs_atom62]) ).
cnf(c_0_764_0,axiom,
c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(X1,X2),X2) = c_Transitive__Closure_Ortranclp(X1,X2),
inference(unfold_definition,[status(thm)],[c_0_764,def_lhs_atom60]) ).
cnf(c_0_765_0,axiom,
c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = c_List_Olist_ONil(X2),
inference(unfold_definition,[status(thm)],[c_0_765,def_lhs_atom41]) ).
cnf(c_0_766_0,axiom,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X2)),X1)),
inference(unfold_definition,[status(thm)],[c_0_766,def_lhs_atom51]) ).
cnf(c_0_767_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)),X2) = c_Orderings_Oord__class_Omax(X1,X2,tc_nat),
inference(unfold_definition,[status(thm)],[c_0_767,def_lhs_atom47]) ).
cnf(c_0_768_0,axiom,
c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat),
inference(unfold_definition,[status(thm)],[c_0_768,def_lhs_atom46]) ).
cnf(c_0_769_0,axiom,
c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat),
inference(unfold_definition,[status(thm)],[c_0_769,def_lhs_atom45]) ).
cnf(c_0_770_0,axiom,
c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat),
inference(unfold_definition,[status(thm)],[c_0_770,def_lhs_atom44]) ).
cnf(c_0_771_0,axiom,
c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = c_List_Olist_ONil(X2),
inference(unfold_definition,[status(thm)],[c_0_771,def_lhs_atom41]) ).
cnf(c_0_772_0,axiom,
c_Type_Otyping(X2,c_Lambda_OdB_OVar(X1),hAPP(X2,X1)),
inference(unfold_definition,[status(thm)],[c_0_772,def_lhs_atom27]) ).
cnf(c_0_773_0,axiom,
c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X2,tc_nat),
inference(unfold_definition,[status(thm)],[c_0_773,def_lhs_atom26]) ).
cnf(c_0_774_0,axiom,
c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_774,def_lhs_atom22]) ).
cnf(c_0_775_0,axiom,
c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OAbs(X2),
inference(unfold_definition,[status(thm)],[c_0_775,def_lhs_atom12]) ).
cnf(c_0_776_0,axiom,
c_List_Odrop(X1,c_List_Olist_ONil(X2),X2) = c_List_Olist_ONil(X2),
inference(unfold_definition,[status(thm)],[c_0_776,def_lhs_atom11]) ).
cnf(c_0_777_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_777,def_lhs_atom9]) ).
cnf(c_0_778_0,axiom,
c_List_Oappend(c_List_Olist_ONil(X2),X1,X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_778,def_lhs_atom7]) ).
cnf(c_0_779_0,axiom,
c_List_Oappend(c_List_Olist_ONil(X2),X1,X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_779,def_lhs_atom7]) ).
cnf(c_0_780_0,axiom,
c_List_Oappend(X1,c_List_Olist_ONil(X2),X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_780,def_lhs_atom5]) ).
cnf(c_0_781_0,axiom,
c_List_Oappend(c_List_Olist_ONil(X2),X1,X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_781,def_lhs_atom6]) ).
cnf(c_0_782_0,axiom,
c_List_Oappend(X1,c_List_Olist_ONil(X2),X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_782,def_lhs_atom5]) ).
cnf(c_0_783_0,axiom,
c_List_Olistsp(X1,c_List_Olist_ONil(X2),X2),
inference(unfold_definition,[status(thm)],[c_0_783,def_lhs_atom2]) ).
cnf(c_0_784_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X1))),
inference(unfold_definition,[status(thm)],[c_0_784,def_lhs_atom127]) ).
cnf(c_0_785_0,axiom,
c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OAbs(X1),
inference(unfold_definition,[status(thm)],[c_0_785,def_lhs_atom119]) ).
cnf(c_0_786_0,axiom,
X1 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2(X1),c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1(X1),tc_Lambda_OdB,tc_Lambda_OdB),
inference(unfold_definition,[status(thm)],[c_0_786,def_lhs_atom118]) ).
cnf(c_0_787_0,axiom,
c_Lambda_OdB_OAbs(X1) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(unfold_definition,[status(thm)],[c_0_787,def_lhs_atom117]) ).
cnf(c_0_788_0,axiom,
c_Lambda_OdB_OVar(X1) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(unfold_definition,[status(thm)],[c_0_788,def_lhs_atom116]) ).
cnf(c_0_789_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_789,def_lhs_atom104]) ).
cnf(c_0_790_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_790,def_lhs_atom103]) ).
cnf(c_0_791_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_791,def_lhs_atom102]) ).
cnf(c_0_792_0,axiom,
c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1,
inference(unfold_definition,[status(thm)],[c_0_792,def_lhs_atom101]) ).
cnf(c_0_793_0,axiom,
c_Orderings_Oord__class_Omax(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
inference(unfold_definition,[status(thm)],[c_0_793,def_lhs_atom100]) ).
cnf(c_0_794_0,axiom,
c_Nat_Osize__class_Osize(X1,tc_String_Ochar) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_794,def_lhs_atom98]) ).
cnf(c_0_795_0,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),
inference(unfold_definition,[status(thm)],[c_0_795,def_lhs_atom97]) ).
cnf(c_0_796_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_796,def_lhs_atom96]) ).
cnf(c_0_797_0,axiom,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(unfold_definition,[status(thm)],[c_0_797,def_lhs_atom93]) ).
cnf(c_0_798_0,axiom,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(unfold_definition,[status(thm)],[c_0_798,def_lhs_atom92]) ).
cnf(c_0_799_0,axiom,
c_String_Ochar_Ochar__size(X1) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_799,def_lhs_atom90]) ).
cnf(c_0_800_0,axiom,
c_Nitpick_Onat__gcd(X1,c_HOL_Ozero__class_Ozero(tc_nat)) = X1,
inference(unfold_definition,[status(thm)],[c_0_800,def_lhs_atom88]) ).
cnf(c_0_801_0,axiom,
c_List_Oappend(c_List_Olist_ONil(X1),c_List_Olist_ONil(X1),X1) = c_List_Olist_ONil(X1),
inference(unfold_definition,[status(thm)],[c_0_801,def_lhs_atom83]) ).
cnf(c_0_802_0,axiom,
c_lessequals(X1,X1,tc_nat),
inference(unfold_definition,[status(thm)],[c_0_802,def_lhs_atom78]) ).
cnf(c_0_803_0,axiom,
c_lessequals(X1,X1,tc_nat),
inference(unfold_definition,[status(thm)],[c_0_803,def_lhs_atom77]) ).
cnf(c_0_804_0,axiom,
c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_804,def_lhs_atom70]) ).
cnf(c_0_805_0,axiom,
c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
inference(unfold_definition,[status(thm)],[c_0_805,def_lhs_atom69]) ).
cnf(c_0_806_0,axiom,
c_List_Olist_ONil(X1) = c_List_Oappend(c_List_Olist_ONil(X1),c_List_Olist_ONil(X1),X1),
inference(unfold_definition,[status(thm)],[c_0_806,def_lhs_atom59]) ).
cnf(c_0_807_0,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
inference(unfold_definition,[status(thm)],[c_0_807,def_lhs_atom43]) ).
cnf(c_0_808_0,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
inference(unfold_definition,[status(thm)],[c_0_808,def_lhs_atom42]) ).
cnf(c_0_809_0,axiom,
c_Predicate_Oconversep(c_fequal(X1),X1,X1) = c_fequal(X1),
inference(unfold_definition,[status(thm)],[c_0_809,def_lhs_atom39]) ).
cnf(c_0_810_0,axiom,
class_Orderings_Obot(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_810,def_lhs_atom163]) ).
cnf(c_0_811_0,axiom,
class_Orderings_Oorder(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_811,def_lhs_atom162]) ).
cnf(c_0_812_0,axiom,
class_Orderings_Opreorder(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_812,def_lhs_atom161]) ).
cnf(c_0_813_0,axiom,
class_Power_Opower(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_813,def_lhs_atom160]) ).
cnf(c_0_814_0,axiom,
class_Orderings_Obot(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_814,def_lhs_atom159]) ).
cnf(c_0_815_0,axiom,
class_Orderings_Oorder(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_815,def_lhs_atom158]) ).
cnf(c_0_816_0,axiom,
class_Orderings_Olinorder(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_816,def_lhs_atom157]) ).
cnf(c_0_817_0,axiom,
class_Orderings_Opreorder(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_817,def_lhs_atom156]) ).
cnf(c_0_818_0,axiom,
class_Nat_Osemiring__char__0(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_818,def_lhs_atom155]) ).
cnf(c_0_819_0,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_819,def_lhs_atom154]) ).
cnf(c_0_820_0,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_820,def_lhs_atom153]) ).
cnf(c_0_821_0,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_821,def_lhs_atom152]) ).
cnf(c_0_822_0,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_822,def_lhs_atom151]) ).
cnf(c_0_823_0,axiom,
class_OrderedGroup_Osemigroup__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_823,def_lhs_atom150]) ).
cnf(c_0_824_0,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_824,def_lhs_atom149]) ).
cnf(c_0_825_0,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_825,def_lhs_atom148]) ).
cnf(c_0_826_0,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_826,def_lhs_atom147]) ).
cnf(c_0_827_0,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_827,def_lhs_atom146]) ).
cnf(c_0_828_0,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_828,def_lhs_atom145]) ).
cnf(c_0_829_0,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_829,def_lhs_atom144]) ).
cnf(c_0_830_0,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_830,def_lhs_atom143]) ).
cnf(c_0_831_0,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_831,def_lhs_atom142]) ).
cnf(c_0_832_0,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_832,def_lhs_atom141]) ).
cnf(c_0_833_0,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_833,def_lhs_atom140]) ).
cnf(c_0_834_0,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_834,def_lhs_atom139]) ).
cnf(c_0_835_0,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_835,def_lhs_atom138]) ).
cnf(c_0_836_0,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
inference(unfold_definition,[status(thm)],[c_0_836,def_lhs_atom137]) ).
cnf(c_0_837_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
inference(unfold_definition,[status(thm)],[c_0_837,def_lhs_atom136]) ).
cnf(c_0_838_0,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
inference(unfold_definition,[status(thm)],[c_0_838,def_lhs_atom82]) ).
cnf(c_0_839_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
inference(unfold_definition,[status(thm)],[c_0_839,def_lhs_atom136]) ).
cnf(c_0_840_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))),
inference(unfold_definition,[status(thm)],[c_0_840,def_lhs_atom135]) ).
cnf(c_0_841_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_a____)),
inference(unfold_definition,[status(thm)],[c_0_841,def_lhs_atom133]) ).
cnf(c_0_842_0,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
inference(unfold_definition,[status(thm)],[c_0_842,def_lhs_atom130]) ).
cnf(c_0_843_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_ua______)),
inference(unfold_definition,[status(thm)],[c_0_843,def_lhs_atom128]) ).
cnf(c_0_844_0,axiom,
c_Orderings_Obot__class_Obot(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_844,def_lhs_atom94]) ).
cnf(c_0_845_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_845,def_lhs_atom91]) ).
cnf(c_0_846_0,axiom,
c_nat_Onat__size(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_846,def_lhs_atom89]) ).
cnf(c_0_847_0,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
inference(unfold_definition,[status(thm)],[c_0_847,def_lhs_atom82]) ).
cnf(c_0_848_0,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(unfold_definition,[status(thm)],[c_0_848,def_lhs_atom65]) ).
cnf(c_0_849_0,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(unfold_definition,[status(thm)],[c_0_849,def_lhs_atom64]) ).
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0_001,axiom,
! [X14,X15,X16,X17] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),X14),X15)))
| ~ c_Type_Otyping(X16,X14,v_T____)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X14))
| ~ c_Type_Otyping(c_Type_Oshift(X16,X15,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X17) ),
file('<stdin>',cls_SI1_0) ).
fof(c_0_1_002,axiom,
! [X13,X21,X8] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X8,X21,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X8,X13,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X21,X13,tc_Lambda_OdB) ),
file('<stdin>',cls_apps__preserves__betas_0) ).
fof(c_0_2_003,axiom,
! [X13,X7,X8] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X8,X13,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X13,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X8),X7)) ),
file('<stdin>',cls_apps__preserves__beta2_0) ).
fof(c_0_3_004,axiom,
! [X13,X7,X8] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X8,X13,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X13,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X8),X7)) ),
file('<stdin>',cls_apps__preserves__beta_0) ).
fof(c_0_4_005,axiom,
! [X13,X7,X8] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X8)),X7),X13,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X7))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X8),X7),c_HOL_Ozero__class_Ozero(tc_nat)),X13,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('<stdin>',cls_IT_OBeta_0) ).
fof(c_0_5_006,axiom,
! [X64,X65,X38,X39,X40,X41,X66,X67,X42,X3] :
( hAPP(hAPP(X41,hAPP(hAPP(X41,X67),X66)),hAPP(hAPP(X41,X65),X64)) = hAPP(hAPP(X41,X65),hAPP(hAPP(X41,hAPP(hAPP(X41,X67),X66)),X64))
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I15_J_0) ).
fof(c_0_6_007,axiom,
! [X38,X39,X40,X41,X57,X45,X44,X42,X25,X3] :
( hAPP(hAPP(X42,hAPP(hAPP(X42,X25),X44)),hAPP(hAPP(X42,X45),X57)) = hAPP(hAPP(X42,hAPP(hAPP(X42,X25),X45)),hAPP(hAPP(X42,X44),X57))
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I20_J_0) ).
fof(c_0_7_008,axiom,
! [X64,X65,X38,X39,X40,X41,X66,X67,X42,X3] :
( hAPP(hAPP(X41,hAPP(hAPP(X41,X67),X66)),hAPP(hAPP(X41,X65),X64)) = hAPP(hAPP(X41,X67),hAPP(hAPP(X41,X66),hAPP(hAPP(X41,X65),X64)))
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I14_J_0) ).
fof(c_0_8_009,axiom,
! [X64,X65,X38,X39,X40,X41,X66,X67,X42,X3] :
( hAPP(hAPP(X41,hAPP(hAPP(X41,X67),X66)),hAPP(hAPP(X41,X65),X64)) = hAPP(hAPP(X41,hAPP(hAPP(X41,X67),X65)),hAPP(hAPP(X41,X66),X64))
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I13_J_0) ).
fof(c_0_9_010,axiom,
! [X28,X24,X38,X39,X71,X40,X41,X42,X3] :
( hAPP(hAPP(X40,hAPP(hAPP(X41,X24),X28)),X71) = hAPP(hAPP(X41,hAPP(hAPP(X40,X24),X71)),hAPP(hAPP(X40,X28),X71))
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
file('<stdin>',cls_gb__semiring_Opwr__mul_0) ).
fof(c_0_10_011,axiom,
! [X38,X39,X40,X41,X45,X44,X42,X25,X3] :
( hAPP(hAPP(X41,hAPP(hAPP(X42,X25),X44)),X45) = hAPP(hAPP(X42,hAPP(hAPP(X41,X25),X45)),hAPP(hAPP(X41,X44),X45))
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I8_J_0) ).
fof(c_0_11_012,axiom,
! [X38,X39,X40,X41,X20,X44,X42,X25,X3] :
( hAPP(hAPP(X42,hAPP(hAPP(X41,X25),X20)),hAPP(hAPP(X41,X44),X20)) = hAPP(hAPP(X41,hAPP(hAPP(X42,X25),X44)),X20)
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I1_J_0) ).
fof(c_0_12_013,axiom,
! [X24,X38,X39,X71,X40,X74,X41,X42,X3] :
( hAPP(hAPP(X41,hAPP(hAPP(X40,X24),X74)),hAPP(hAPP(X40,X24),X71)) = hAPP(hAPP(X40,X24),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X74),X71))
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
file('<stdin>',cls_gb__semiring_Omul__pwr_0) ).
fof(c_0_13_014,axiom,
! [X58,X28,X24,X38,X39,X40,X41,X42,X3] :
( hAPP(hAPP(X41,X24),hAPP(hAPP(X42,X28),X58)) = hAPP(hAPP(X42,hAPP(hAPP(X41,X24),X28)),hAPP(hAPP(X41,X24),X58))
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
file('<stdin>',cls_gb__semiring_Omul__d_0) ).
fof(c_0_14_015,axiom,
! [X38,X39,X40,X41,X45,X44,X42,X25,X3] :
( hAPP(hAPP(X42,hAPP(hAPP(X42,X25),X44)),X45) = hAPP(hAPP(X42,hAPP(hAPP(X42,X25),X45)),X44)
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I23_J_0) ).
fof(c_0_15_016,axiom,
! [X65,X38,X39,X40,X41,X66,X67,X42,X3] :
( hAPP(hAPP(X41,hAPP(hAPP(X41,X67),X66)),X65) = hAPP(hAPP(X41,hAPP(hAPP(X41,X67),X65)),X66)
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I16_J_0) ).
fof(c_0_16_017,axiom,
! [X38,X39,X40,X41,X20,X42,X25,X3] :
( hAPP(hAPP(X42,hAPP(hAPP(X41,X25),X20)),X20) = hAPP(hAPP(X41,hAPP(hAPP(X42,X25),X38)),X20)
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I2_J_0) ).
fof(c_0_17_018,axiom,
! [X58,X28,X24,X38,X39,X40,X41,X42,X3] :
( hAPP(hAPP(X41,X24),hAPP(hAPP(X41,X28),X58)) = hAPP(hAPP(X41,hAPP(hAPP(X41,X24),X28)),X58)
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
file('<stdin>',cls_gb__semiring_Omul__a_0) ).
fof(c_0_18_019,axiom,
! [X58,X28,X24,X38,X39,X40,X41,X42,X3] :
( hAPP(hAPP(X42,X24),hAPP(hAPP(X42,X28),X58)) = hAPP(hAPP(X42,hAPP(hAPP(X42,X24),X28)),X58)
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
file('<stdin>',cls_gb__semiring_Oadd__a_0) ).
fof(c_0_19_020,axiom,
! [X38,X39,X40,X41,X57,X45,X42,X25,X3] :
( hAPP(hAPP(X42,X25),hAPP(hAPP(X42,X45),X57)) = hAPP(hAPP(X42,hAPP(hAPP(X42,X25),X45)),X57)
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I25_J_0) ).
fof(c_0_20_021,axiom,
! [X38,X39,X40,X41,X45,X44,X42,X25,X3] :
( hAPP(hAPP(X42,hAPP(hAPP(X42,X25),X44)),X45) = hAPP(hAPP(X42,X25),hAPP(hAPP(X42,X44),X45))
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I21_J_0) ).
fof(c_0_21_022,axiom,
! [X64,X65,X38,X39,X40,X41,X67,X42,X3] :
( hAPP(hAPP(X41,X67),hAPP(hAPP(X41,X65),X64)) = hAPP(hAPP(X41,hAPP(hAPP(X41,X67),X65)),X64)
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I18_J_0) ).
fof(c_0_22_023,axiom,
! [X65,X38,X39,X40,X41,X66,X67,X42,X3] :
( hAPP(hAPP(X41,hAPP(hAPP(X41,X67),X66)),X65) = hAPP(hAPP(X41,X67),hAPP(hAPP(X41,X66),X65))
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I17_J_0) ).
fof(c_0_23_024,axiom,
! [X38,X39,X40,X41,X20,X42,X25,X3] :
( hAPP(hAPP(X42,X20),hAPP(hAPP(X41,X25),X20)) = hAPP(hAPP(X41,hAPP(hAPP(X42,X25),X38)),X20)
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I3_J_0) ).
fof(c_0_24_025,axiom,
! [X38,X39,X40,X41,X57,X45,X42,X25,X3] :
( hAPP(hAPP(X42,X25),hAPP(hAPP(X42,X45),X57)) = hAPP(hAPP(X42,X45),hAPP(hAPP(X42,X25),X57))
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I22_J_0) ).
fof(c_0_25_026,axiom,
! [X64,X65,X38,X39,X40,X41,X67,X42,X3] :
( hAPP(hAPP(X41,X67),hAPP(hAPP(X41,X65),X64)) = hAPP(hAPP(X41,X65),hAPP(hAPP(X41,X67),X64))
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I19_J_0) ).
fof(c_0_26_027,axiom,
! [X38,X39,X40,X41,X20,X42,X3] :
( hAPP(hAPP(X42,X20),X20) = hAPP(hAPP(X41,hAPP(hAPP(X42,X38),X38)),X20)
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I4_J_0) ).
fof(c_0_27_028,axiom,
! [X28,X24,X38,X39,X40,X41,X42,X3] :
( hAPP(hAPP(X41,X24),X28) = hAPP(hAPP(X41,X28),X24)
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
file('<stdin>',cls_gb__semiring_Omul__c_0) ).
fof(c_0_28_029,axiom,
! [X28,X24,X38,X39,X40,X41,X42,X3] :
( hAPP(hAPP(X42,X24),X28) = hAPP(hAPP(X42,X28),X24)
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
file('<stdin>',cls_gb__semiring_Oadd__c_0) ).
fof(c_0_29_030,axiom,
! [X38,X39,X40,X41,X45,X42,X25,X3] :
( hAPP(hAPP(X42,X25),X45) = hAPP(hAPP(X42,X45),X25)
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I24_J_0) ).
fof(c_0_30_031,axiom,
! [X38,X39,X40,X41,X44,X42,X25,X3] :
( hAPP(hAPP(X41,X25),X44) = hAPP(hAPP(X41,X44),X25)
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I7_J_0) ).
fof(c_0_31_032,axiom,
! [X24,X38,X39,X40,X41,X42,X3] :
( hAPP(hAPP(X40,X24),c_HOL_Ozero__class_Ozero(tc_nat)) = X38
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
file('<stdin>',cls_gb__semiring_Opwr__0_0) ).
fof(c_0_32_033,axiom,
! [X24,X38,X39,X40,X41,X42,X3] :
( hAPP(hAPP(X41,X38),X24) = X24
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
file('<stdin>',cls_gb__semiring_Omul__1_0) ).
fof(c_0_33_034,axiom,
! [X24,X38,X39,X40,X41,X42,X3] :
( hAPP(hAPP(X41,X39),X24) = X39
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
file('<stdin>',cls_gb__semiring_Omul__0_0) ).
fof(c_0_34_035,axiom,
! [X24,X38,X39,X40,X41,X42,X3] :
( hAPP(hAPP(X42,X39),X24) = X24
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
file('<stdin>',cls_gb__semiring_Oadd__0_0) ).
fof(c_0_35_036,axiom,
! [X38,X39,X40,X41,X42,X25,X3] :
( hAPP(hAPP(X41,X25),X38) = X25
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I12_J_0) ).
fof(c_0_36_037,axiom,
! [X38,X39,X40,X41,X42,X25,X3] :
( hAPP(hAPP(X41,X38),X25) = X25
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I11_J_0) ).
fof(c_0_37_038,axiom,
! [X38,X39,X40,X41,X42,X25,X3] :
( hAPP(hAPP(X41,X25),X39) = X39
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I10_J_0) ).
fof(c_0_38_039,axiom,
! [X38,X39,X40,X41,X42,X25,X3] :
( hAPP(hAPP(X41,X39),X25) = X39
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I9_J_0) ).
fof(c_0_39_040,axiom,
! [X38,X39,X40,X41,X42,X25,X3] :
( hAPP(hAPP(X42,X25),X39) = X25
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I6_J_0) ).
fof(c_0_40_041,axiom,
! [X38,X39,X40,X41,X42,X25,X3] :
( hAPP(hAPP(X42,X39),X25) = X25
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I5_J_0) ).
fof(c_0_41_042,axiom,
! [X35,X36,X31,X32,X33,X34] :
( ~ hBOOL(hAPP(X34,c_Lambda_OdB_OdB__case(X33,X32,X31,hAPP(hAPP(c_Lambda_OdB_OApp,X36),X35),t_a)))
| hBOOL(hAPP(X34,hAPP(hAPP(X32,X36),X35))) ),
file('<stdin>',cls_dB_Osplit__asm_1) ).
fof(c_0_42_043,axiom,
! [X31,X32,X33,X10,X12,X34] :
( ~ hBOOL(hAPP(X34,c_Lambda_OdB_OdB__case(X33,X32,X31,hAPP(hAPP(c_Lambda_OdB_OApp,X12),X10),t_a)))
| hBOOL(hAPP(X34,hAPP(hAPP(X32,X12),X10))) ),
file('<stdin>',cls_dB_Osplit_1) ).
fof(c_0_43_044,axiom,
! [X6,X15,X16,X29,X30] :
( X30 = X29
| ~ c_Type_Otyping(X16,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X15),X6,tc_Lambda_OdB,tc_Lambda_OdB),X29)
| ~ c_Type_Otyping(X16,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X15),X6,tc_Lambda_OdB,tc_Lambda_OdB),X30) ),
file('<stdin>',cls_var__app__type__eq_0) ).
fof(c_0_44_045,axiom,
! [X31,X32,X33,X61,X34] :
( ~ hBOOL(hAPP(X34,c_Lambda_OdB_OdB__case(X33,X32,X31,c_Lambda_OdB_OAbs(X61),t_a)))
| hBOOL(hAPP(X34,hAPP(X31,X61))) ),
file('<stdin>',cls_dB_Osplit_2) ).
fof(c_0_45_046,axiom,
! [X60,X31,X32,X33,X34] :
( ~ hBOOL(hAPP(X34,c_Lambda_OdB_OdB__case(X33,X32,X31,c_Lambda_OdB_OAbs(X60),t_a)))
| hBOOL(hAPP(X34,hAPP(X31,X60))) ),
file('<stdin>',cls_dB_Osplit__asm_2) ).
fof(c_0_46_047,axiom,
! [X43,X31,X32,X33,X34] :
( ~ hBOOL(hAPP(X34,c_Lambda_OdB_OdB__case(X33,X32,X31,c_Lambda_OdB_OVar(X43),t_a)))
| hBOOL(hAPP(X34,hAPP(X33,X43))) ),
file('<stdin>',cls_dB_Osplit_0) ).
fof(c_0_47_048,axiom,
! [X52,X31,X32,X33,X34] :
( ~ hBOOL(hAPP(X34,c_Lambda_OdB_OdB__case(X33,X32,X31,c_Lambda_OdB_OVar(X52),t_a)))
| hBOOL(hAPP(X34,hAPP(X33,X52))) ),
file('<stdin>',cls_dB_Osplit__asm_0) ).
fof(c_0_48_049,axiom,
! [X13,X7,X8] :
( ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X8),X7),c_HOL_Ozero__class_Ozero(tc_nat)),X13,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X7,tc_Lambda_OdB)
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X8)),X7),X13,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
file('<stdin>',cls_double__induction__lemma_0) ).
fof(c_0_49_050,axiom,
! [X6] :
( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X6,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_List_Olistsp(c_InductTermi_OIT,X6,tc_Lambda_OdB) ),
file('<stdin>',cls_lifts__IT_0) ).
fof(c_0_50_051,axiom,
! [X21,X22] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X22),X21,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_List_Olistsp(c_InductTermi_OIT,X21,tc_Lambda_OdB) ),
file('<stdin>',cls_IT_OVar_0) ).
fof(c_0_51_052,axiom,
! [X13,X21,X22,X20] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X20),X21,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X22),X13,tc_Lambda_OdB,tc_Lambda_OdB)
| X20 = X22 ),
file('<stdin>',cls_Var__apps__eq__Var__apps__conv_0) ).
fof(c_0_52_053,axiom,
! [X13,X21,X22,X20] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X20),X21,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X22),X13,tc_Lambda_OdB,tc_Lambda_OdB)
| X21 = X13 ),
file('<stdin>',cls_Var__apps__eq__Var__apps__conv_1) ).
fof(c_0_53_054,axiom,
! [X13,X7,X21,X8] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X8),X21,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X7),X13,tc_Lambda_OdB,tc_Lambda_OdB)
| X8 = X7 ),
file('<stdin>',cls_Abs__apps__eq__Abs__apps__conv_0) ).
fof(c_0_54_055,axiom,
! [X13,X7,X21,X8] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X8),X21,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X7),X13,tc_Lambda_OdB,tc_Lambda_OdB)
| X21 = X13 ),
file('<stdin>',cls_Abs__apps__eq__Abs__apps__conv_1) ).
fof(c_0_55_056,axiom,
! [X23,X28,X24,X3] :
( ~ class_OrderedGroup_Osemigroup__add(X3)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X28),X23,X3,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X28,X23,X3,X3)) ),
file('<stdin>',cls_foldl__assoc_0) ).
fof(c_0_56_057,axiom,
! [X6,X7,X8] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X8,X6,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X6,tc_Lambda_OdB,tc_Lambda_OdB)
| X8 = X7 ),
file('<stdin>',cls_apps__eq__tail__conv_0) ).
fof(c_0_57_058,axiom,
! [X23,X28,X24,X27,X3] :
( c_List_Ofoldl(X27,hAPP(hAPP(X27,X24),X28),X23,X3,X3) = hAPP(hAPP(X27,X24),c_List_Ofoldl(X27,X28,X23,X3,X3))
| ~ c_OrderedGroup_Osemigroup__add(X27,X3) ),
file('<stdin>',cls_semigroup__add_Ofoldl__assoc_0) ).
fof(c_0_58_059,axiom,
! [X23,X26,X24,X27,X3] :
( hAPP(hAPP(X27,X24),c_List_Ofoldl(X27,X26,X23,X3,X3)) = c_List_Ofoldl(X27,X24,X23,X3,X3)
| ~ c_OrderedGroup_Omonoid__add(X26,X27,X3) ),
file('<stdin>',cls_monoid__add_Ofoldl__absorb0_0) ).
fof(c_0_59_060,axiom,
! [X37,X25,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X25,X37,X3,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X3),X37,c_HOL_Ozero__class_Ozero(X3),X3,X3)) ),
file('<stdin>',cls_foldl__foldr1__lemma_0) ).
fof(c_0_60_061,axiom,
! [X23,X24,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3),X23,X3,X3)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X24,X23,X3,X3) ),
file('<stdin>',cls_foldl__absorb0_0) ).
fof(c_0_61_062,axiom,
! [X6,X19,X7,X8] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X8),X7) != c_List_Ofoldl(c_Lambda_OdB_OApp,X19,X6,tc_Lambda_OdB,tc_Lambda_OdB)
| X8 = c_List_Ofoldl(c_Lambda_OdB_OApp,X19,c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X8,X7,X19,X6),tc_Lambda_OdB,tc_Lambda_OdB)
| X6 = c_List_Olist_ONil(tc_Lambda_OdB) ),
file('<stdin>',cls_App__eq__foldl__conv_2) ).
fof(c_0_62_063,axiom,
! [X37,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3),X37,X3,X3) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X3),X37,c_HOL_Ozero__class_Ozero(X3),X3,X3) ),
file('<stdin>',cls_foldl__foldr1_0) ).
fof(c_0_63_064,axiom,
! [X37,X25,X3] :
( ~ class_OrderedGroup_Oab__semigroup__add(X3)
| c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X3),X37,X25,X3,X3) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X25,X37,X3,X3) ),
file('<stdin>',cls_foldr__conv__foldl_0) ).
fof(c_0_64_065,axiom,
! [X19,X7,X8] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X8),X7) != c_List_Ofoldl(c_Lambda_OdB_OApp,X19,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,X8),X7) = X19 ),
file('<stdin>',cls_App__eq__foldl__conv_0) ).
fof(c_0_65_066,axiom,
! [X13,X7,X8] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X13,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X8)
| X7 = c_Lambda_OdB_OAbs(X8) ),
file('<stdin>',cls_apps__eq__Abs__conv_0) ).
fof(c_0_66_067,axiom,
! [X13,X7,X20] :
( c_Lambda_OdB_OVar(X20) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X13,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OVar(X20) = X7 ),
file('<stdin>',cls_Var__eq__apps__conv_0) ).
fof(c_0_67_068,axiom,
! [X13,X7,X8] :
( c_Lambda_OdB_OAbs(X8) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X13,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(X8) = X7 ),
file('<stdin>',cls_Abs__eq__apps__conv_0) ).
fof(c_0_68_069,axiom,
! [X13,X7,X8] :
( c_Lambda_OdB_OAbs(X8) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X13,tc_Lambda_OdB,tc_Lambda_OdB)
| X13 = c_List_Olist_ONil(tc_Lambda_OdB) ),
file('<stdin>',cls_Abs__eq__apps__conv_1) ).
fof(c_0_69_070,axiom,
! [X13,X7,X8] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X13,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X8)
| X13 = c_List_Olist_ONil(tc_Lambda_OdB) ),
file('<stdin>',cls_apps__eq__Abs__conv_1) ).
fof(c_0_70_071,axiom,
! [X13,X7,X20] :
( c_Lambda_OdB_OVar(X20) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X13,tc_Lambda_OdB,tc_Lambda_OdB)
| X13 = c_List_Olist_ONil(tc_Lambda_OdB) ),
file('<stdin>',cls_Var__eq__apps__conv_1) ).
fof(c_0_71_072,axiom,
! [X28,X24,X8,X3] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X28),X24))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X8,X3,X3),X3),X24),X28)) ),
file('<stdin>',cls_rtranclp__converseD_0) ).
fof(c_0_72_073,axiom,
! [X46,X28,X37,X24,X8,X3] :
( hBOOL(hAPP(hAPP(X8,X28),X24))
| c_ListOrder_Ostep1(X8,X46,X37,X3)
| ~ c_ListOrder_Ostep1(X8,c_List_Oappend(X46,c_List_Olist_OCons(X28,c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X37,c_List_Olist_OCons(X24,c_List_Olist_ONil(X3),X3),X3),X3) ),
file('<stdin>',cls_Snoc__step1__SnocD_1) ).
fof(c_0_73_074,axiom,
! [X46,X28,X37,X24,X8,X3] :
( X46 = X37
| c_ListOrder_Ostep1(X8,X46,X37,X3)
| ~ c_ListOrder_Ostep1(X8,c_List_Oappend(X46,c_List_Olist_OCons(X28,c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X37,c_List_Olist_OCons(X24,c_List_Olist_ONil(X3),X3),X3),X3) ),
file('<stdin>',cls_Snoc__step1__SnocD_0) ).
fof(c_0_74_075,axiom,
! [X32,X33,X34] :
( ~ hBOOL(hAPP(X34,c_Nat_Onat_Onat__case(X33,X32,c_HOL_Ozero__class_Ozero(tc_nat),t_a)))
| hBOOL(hAPP(X34,X33)) ),
file('<stdin>',cls_nat_Osplit_0) ).
fof(c_0_75_076,axiom,
! [X46,X28,X37,X24,X8,X3] :
( hBOOL(hAPP(hAPP(X8,X28),X24))
| X28 = X24
| ~ c_ListOrder_Ostep1(X8,c_List_Oappend(X46,c_List_Olist_OCons(X28,c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X37,c_List_Olist_OCons(X24,c_List_Olist_ONil(X3),X3),X3),X3) ),
file('<stdin>',cls_Snoc__step1__SnocD_3) ).
fof(c_0_76_077,axiom,
! [X46,X28,X37,X24,X8,X3] :
( X46 = X37
| X28 = X24
| ~ c_ListOrder_Ostep1(X8,c_List_Oappend(X46,c_List_Olist_OCons(X28,c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X37,c_List_Olist_OCons(X24,c_List_Olist_ONil(X3),X3),X3),X3) ),
file('<stdin>',cls_Snoc__step1__SnocD_2) ).
fof(c_0_77_078,axiom,
! [X19,X7,X8,X15] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X8),X19),X15)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X7),X19),X15)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X8),X7)) ),
file('<stdin>',cls_subst__preserves__beta_H_0) ).
fof(c_0_78_079,axiom,
! [X19,X7,X8,X15] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X19),X8),X15)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X19),X7),X15)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X8),X7)) ),
file('<stdin>',cls_subst__preserves__beta2_H_0) ).
fof(c_0_79_080,axiom,
! [X28,X24,X8,X3] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X8,X3,X3),X3),X24),X28))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X28),X24)) ),
file('<stdin>',cls_rtranclp__converseI_0) ).
fof(c_0_80_081,axiom,
! [X14,X15,X16,X17] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),X14),X15)))
| ~ c_Type_Otyping(X16,X14,v_T____)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X14))
| ~ c_Type_Otyping(c_Type_Oshift(X16,X15,v_T____,tc_Type_Otype),v_a____,X17) ),
file('<stdin>',cls_SI2_0) ).
fof(c_0_81_082,axiom,
! [X19,X7,X8,X15] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X19),X8),X15)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X19),X7),X15)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X8),X7)) ),
file('<stdin>',cls_subst__preserves__beta2_0) ).
fof(c_0_82_083,axiom,
! [X37,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| c_List_Olistsum(X37,X3) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X3),X37,c_HOL_Ozero__class_Ozero(X3),X3,X3) ),
file('<stdin>',cls_listsum__foldr_0) ).
fof(c_0_83_084,axiom,
! [X37,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| c_List_Olistsum(X37,X3) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3),X37,X3,X3) ),
file('<stdin>',cls_listsum_0) ).
fof(c_0_84_085,axiom,
! [X19,X7,X8,X15] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(hAPP(c_Lambda_Osubst,X8),X19),X15)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X7),X19),X15)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X8),X7)) ),
file('<stdin>',cls_subst__preserves__beta_0) ).
fof(c_0_85_086,axiom,
! [X14,X19,X15,X62,X29,X30] :
( ~ c_Type_Otyping(X62,X14,X29)
| ~ c_Type_Otyping(c_Type_Oshift(X62,X15,X29,tc_Type_Otype),X19,X30)
| c_Type_Otyping(X62,hAPP(hAPP(hAPP(c_Lambda_Osubst,X19),X14),X15),X30) ),
file('<stdin>',cls_subst__lemma_0) ).
fof(c_0_86_087,axiom,
! [X53,X19,X63,X7] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X7),X19)),hAPP(hAPP(c_Lambda_OdB_OApp,X63),X53)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X19),X53))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X7),X63)) ),
file('<stdin>',cls_rtrancl__beta__App_0) ).
fof(c_0_87_088,axiom,
! [X46,X28,X37,X24,X8,X3] :
( c_ListOrder_Ostep1(X8,X46,X37,X3)
| hBOOL(hAPP(hAPP(X8,X28),X24))
| ~ c_ListOrder_Ostep1(X8,c_List_Olist_OCons(X28,X46,X3),c_List_Olist_OCons(X24,X37,X3),X3) ),
file('<stdin>',cls_Cons__step1__Cons_1) ).
fof(c_0_88_089,axiom,
! [X46,X28,X37,X24,X8,X3] :
( c_ListOrder_Ostep1(X8,X46,X37,X3)
| X37 = X46
| ~ c_ListOrder_Ostep1(X8,c_List_Olist_OCons(X28,X46,X3),c_List_Olist_OCons(X24,X37,X3),X3) ),
file('<stdin>',cls_Cons__step1__Cons_3) ).
fof(c_0_89_090,axiom,
! [X57,X44,X34] :
( ~ hBOOL(hAPP(X34,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X44),X57),X44,tc_nat)))
| hBOOL(hAPP(X34,X57)) ),
file('<stdin>',cls_nat__diff__split_1) ).
fof(c_0_90_091,axiom,
! [X24,X44,X34] :
( ~ hBOOL(hAPP(X34,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X44),X24),X44,tc_nat)))
| hBOOL(hAPP(X34,X24)) ),
file('<stdin>',cls_nat__diff__split__asm_1) ).
fof(c_0_91_092,axiom,
! [X8,X72,X73,X48,X3] :
( hBOOL(hAPP(hAPP(X8,X72),X73))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X8,X3,X48),X73),X72)) ),
file('<stdin>',cls_conversep_Ocases_0) ).
fof(c_0_92_093,axiom,
! [X8,X44,X25,X48,X3] :
( hBOOL(hAPP(hAPP(X8,X44),X25))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X8,X3,X48),X25),X44)) ),
file('<stdin>',cls_conversepD_0) ).
fof(c_0_93_094,axiom,
! [X46,X37,X24,X8,X3] :
( ~ c_ListOrder_Ostep1(X8,X46,X37,X3)
| c_ListOrder_Ostep1(X8,c_List_Oappend(X46,X24,X3),c_List_Oappend(X37,X24,X3),X3) ),
file('<stdin>',cls_append__step1I_0) ).
fof(c_0_94_095,axiom,
! [X24,X75,X76,X8,X3] :
( c_ListOrder_Ostep1(X8,c_List_Oappend(X24,X75,X3),c_List_Oappend(X24,X76,X3),X3)
| ~ c_ListOrder_Ostep1(X8,X75,X76,X3) ),
file('<stdin>',cls_append__step1I_1) ).
fof(c_0_95_096,axiom,
! [X46,X37,X24,X8,X3] :
( c_ListOrder_Ostep1(X8,c_List_Olist_OCons(X24,X46,X3),c_List_Olist_OCons(X24,X37,X3),X3)
| ~ c_ListOrder_Ostep1(X8,X46,X37,X3) ),
file('<stdin>',cls_Cons__step1__Cons_5) ).
fof(c_0_96_097,axiom,
! [X53,X19,X7] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X7),X19)),hAPP(hAPP(c_Lambda_OdB_OApp,X7),X53)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X19),X53)) ),
file('<stdin>',cls_rtrancl__beta__AppR_0) ).
fof(c_0_97_098,axiom,
! [X19,X63,X7] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X7),X19)),hAPP(hAPP(c_Lambda_OdB_OApp,X63),X19)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X7),X63)) ),
file('<stdin>',cls_rtrancl__beta__AppL_0) ).
fof(c_0_98_099,axiom,
! [X7,X8,X15] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,X8),X15)),hAPP(hAPP(c_Lambda_Olift,X7),X15)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X8),X7)) ),
file('<stdin>',cls_lift__preserves__beta_H_0) ).
fof(c_0_99_100,axiom,
! [X46,X28,X37,X24,X8,X3] :
( X24 = X28
| hBOOL(hAPP(hAPP(X8,X28),X24))
| ~ c_ListOrder_Ostep1(X8,c_List_Olist_OCons(X28,X46,X3),c_List_Olist_OCons(X24,X37,X3),X3) ),
file('<stdin>',cls_Cons__step1__Cons_0) ).
fof(c_0_100_101,axiom,
! [X58,X28,X24,X8,X3] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X24),X58))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X28),X58))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X24),X28)) ),
file('<stdin>',cls_rtranclp__trans_0) ).
fof(c_0_101_102,axiom,
! [X46,X28,X37,X24,X8,X3] :
( X24 = X28
| X37 = X46
| ~ c_ListOrder_Ostep1(X8,c_List_Olist_OCons(X28,X46,X3),c_List_Olist_OCons(X24,X37,X3),X3) ),
file('<stdin>',cls_Cons__step1__Cons_2) ).
fof(c_0_102_103,axiom,
! [X57,X45,X44,X25,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),X25),X44)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X57)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X44),X57)) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I20_J_0) ).
fof(c_0_103_104,axiom,
! [X19,X15,X16,X29,X30] :
( c_Type_Otyping(c_Type_Oshift(X16,X15,X29,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X19),X15),X30)
| ~ c_Type_Otyping(X16,X19,X30) ),
file('<stdin>',cls_lift__type_0) ).
fof(c_0_104_105,axiom,
! [X8,X44,X25,X48,X3] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X8,X3,X48),X44),X25))
| ~ hBOOL(hAPP(hAPP(X8,X25),X44)) ),
file('<stdin>',cls_conversep_Ointros_0) ).
fof(c_0_105_106,axiom,
! [X8,X44,X25,X48,X3] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X8,X3,X48),X25),X44))
| ~ hBOOL(hAPP(hAPP(X8,X44),X25)) ),
file('<stdin>',cls_conversep__iff_1) ).
fof(c_0_106_107,axiom,
! [X22,X20,X59] :
( c_lessequals(X20,X22,tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X20,X59,tc_nat),c_HOL_Ominus__class_Ominus(X22,X59,tc_nat),tc_nat)
| ~ c_lessequals(X59,X22,tc_nat)
| ~ c_lessequals(X59,X20,tc_nat) ),
file('<stdin>',cls_le__diff__iff_0) ).
fof(c_0_107_108,axiom,
! [X22,X20,X59] :
( c_HOL_Oord__class_Oless(X20,X22,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X20,X59,tc_nat),c_HOL_Ominus__class_Ominus(X22,X59,tc_nat),tc_nat)
| ~ c_lessequals(X59,X22,tc_nat)
| ~ c_lessequals(X59,X20,tc_nat) ),
file('<stdin>',cls_less__diff__iff_0) ).
fof(c_0_108_109,axiom,
! [X7,X8,X15] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,X8),X15)),hAPP(hAPP(c_Lambda_Olift,X7),X15)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X8),X7)) ),
file('<stdin>',cls_lift__preserves__beta_0) ).
fof(c_0_109_110,axiom,
! [X14,X19,X7] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X14),X7)),hAPP(hAPP(c_Lambda_OdB_OApp,X14),X19)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X7),X19)) ),
file('<stdin>',cls_appR_0) ).
fof(c_0_110_111,axiom,
! [X14,X19,X7] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X7),X14)),hAPP(hAPP(c_Lambda_OdB_OApp,X19),X14)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X7),X19)) ),
file('<stdin>',cls_appL_0) ).
fof(c_0_111_112,axiom,
! [X8,X45,X44,X25,X3] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X25),X45))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X44),X45))
| ~ hBOOL(hAPP(hAPP(X8,X25),X44)) ),
file('<stdin>',cls_converse__rtranclp__into__rtranclp_0) ).
fof(c_0_112_113,axiom,
! [X8,X45,X44,X25,X3] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X25),X45))
| ~ hBOOL(hAPP(hAPP(X8,X44),X45))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X25),X44)) ),
file('<stdin>',cls_rtranclp_Ortrancl__into__rtrancl_0) ).
fof(c_0_113_114,axiom,
! [X18,X15,X16,X30,X3] :
( hAPP(c_Type_Oshift(X16,X15,X30,X3),X18) = hAPP(X16,X18)
| ~ c_HOL_Oord__class_Oless(X18,X15,tc_nat) ),
file('<stdin>',cls_shift__gt_0) ).
fof(c_0_114_115,axiom,
! [X28,X60,X24,X8,X3] :
( ~ hBOOL(hAPP(hAPP(X8,X28),X60))
| c_ListOrder_Ostep1(X8,c_List_Olist_OCons(X28,X24,X3),c_List_Olist_OCons(X60,X24,X3),X3) ),
file('<stdin>',cls_Cons__step1__Cons_4) ).
fof(c_0_115_116,axiom,
! [X22,X44,X25,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X25,X44,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X44,X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X25,X22,X3),c_Power_Opower__class_Opower(X44,X22,X3),X3) ),
file('<stdin>',cls_power__less__imp__less__base_0) ).
fof(c_0_116_117,axiom,
! [X46,X28,X37,X24,X3] :
( c_List_Oappend(X37,c_List_Olist_OCons(X24,c_List_Olist_ONil(X3),X3),X3) != c_List_Oappend(X46,c_List_Olist_OCons(X28,c_List_Olist_ONil(X3),X3),X3)
| X37 = X46 ),
file('<stdin>',cls_append1__eq__conv_0) ).
fof(c_0_117_118,axiom,
! [X46,X28,X37,X24,X3] :
( c_List_Oappend(X37,c_List_Olist_OCons(X24,c_List_Olist_ONil(X3),X3),X3) != c_List_Oappend(X46,c_List_Olist_OCons(X28,c_List_Olist_ONil(X3),X3),X3)
| X24 = X28 ),
file('<stdin>',cls_append1__eq__conv_1) ).
fof(c_0_118_119,axiom,
! [X22,X44,X25,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X25,X22,X3),c_Power_Opower__class_Opower(X44,X22,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X22,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X25,X3)
| ~ c_HOL_Oord__class_Oless(X25,X44,X3) ),
file('<stdin>',cls_power__strict__mono_0) ).
fof(c_0_119_120,axiom,
! [X58,X28,X24,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Orderings_Oord__class_Omax(X24,X28,X3)),X58) = c_Orderings_Oord__class_Omax(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X58),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X28),X58),X3) ),
file('<stdin>',cls_max__add__distrib__left_0) ).
fof(c_0_120_121,axiom,
! [X45,X44,X25,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),X25),X44)),X45) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45)),X44) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I23_J_0) ).
fof(c_0_121_122,axiom,
! [X22,X20,X59] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X20,X59,tc_nat),c_HOL_Ominus__class_Ominus(X22,X59,tc_nat),tc_nat)
| ~ c_lessequals(X20,X22,tc_nat)
| ~ c_lessequals(X59,X22,tc_nat)
| ~ c_lessequals(X59,X20,tc_nat) ),
file('<stdin>',cls_le__diff__iff_1) ).
fof(c_0_122_123,axiom,
! [X22,X20,X59] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X20,X59,tc_nat),c_HOL_Ominus__class_Ominus(X22,X59,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X20,X22,tc_nat)
| ~ c_lessequals(X59,X22,tc_nat)
| ~ c_lessequals(X59,X20,tc_nat) ),
file('<stdin>',cls_less__diff__iff_1) ).
fof(c_0_123_124,axiom,
! [X57,X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X25,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X44),X57),X3)
| ~ c_lessequals(X45,X57,X3)
| ~ c_lessequals(X25,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X44),X45),X3) ),
file('<stdin>',cls_le__add__right__mono_0) ).
fof(c_0_124_125,axiom,
! [X44,X25,X34] :
( hBOOL(hAPP(X34,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X25,X44,tc_nat)
| ~ hBOOL(hAPP(X34,c_HOL_Ominus__class_Ominus(X25,X44,tc_nat))) ),
file('<stdin>',cls_nat__diff__split_0) ).
fof(c_0_125_126,axiom,
! [X22,X20,X59] :
( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X20,X59,tc_nat),c_HOL_Ominus__class_Ominus(X22,X59,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X20,X22,tc_nat)
| ~ c_lessequals(X59,X22,tc_nat)
| ~ c_lessequals(X59,X20,tc_nat) ),
file('<stdin>',cls_Nat_Odiff__diff__eq_0) ).
fof(c_0_126_127,axiom,
! [X59,X18,X15] :
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X15),X59,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X18,X59,tc_nat)),X15)
| ~ c_lessequals(X59,X18,tc_nat) ),
file('<stdin>',cls_diff__add__assoc2_0) ).
fof(c_0_127_128,axiom,
! [X59,X18,X15] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X18,X59,tc_nat)),X15) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X15),X59,tc_nat)
| ~ c_lessequals(X59,X18,tc_nat) ),
file('<stdin>',cls_add__diff__assoc2_0) ).
fof(c_0_128_129,axiom,
! [X59,X18,X15] :
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X59),X18,tc_nat)
| ~ c_lessequals(X15,c_HOL_Ominus__class_Ominus(X18,X59,tc_nat),tc_nat)
| ~ c_lessequals(X59,X18,tc_nat) ),
file('<stdin>',cls_le__diff__conv2_0) ).
fof(c_0_129_130,axiom,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_lessequals(X25,X44,X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X44),X45),X3) ),
file('<stdin>',cls_add__le__cancel__right_0) ).
fof(c_0_130_131,axiom,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_lessequals(X25,X44,X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X44),X3) ),
file('<stdin>',cls_add__le__cancel__left_0) ).
fof(c_0_131_132,axiom,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(X25,X44,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X44),X45),X3) ),
file('<stdin>',cls_add__less__cancel__right_0) ).
fof(c_0_132_133,axiom,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(X25,X44,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X44),X3) ),
file('<stdin>',cls_add__less__cancel__left_0) ).
fof(c_0_133_134,axiom,
! [X59,X18,X15] :
( c_lessequals(X15,c_HOL_Ominus__class_Ominus(X18,X59,tc_nat),tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X59),X18,tc_nat)
| ~ c_lessequals(X59,X18,tc_nat) ),
file('<stdin>',cls_le__diff__conv2_1) ).
fof(c_0_134_135,axiom,
! [X22,X44,X25,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_Power_Opower__class_Opower(X25,X22,X3) != c_Power_Opower__class_Opower(X44,X22,X3)
| X25 = X44
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X22,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X44,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X25,X3) ),
file('<stdin>',cls_power__eq__imp__eq__base_0) ).
fof(c_0_135_136,axiom,
! [X8,X18,X15] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X8),c_Lambda_OdB_OVar(X15)),X18)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X8)) ),
file('<stdin>',cls_subst__Var__IT_0) ).
fof(c_0_136_137,axiom,
! [X22,X44,X25,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_Power_Opower__class_Opower(X25,X22,X3),c_Power_Opower__class_Opower(X44,X22,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X25,X3)
| ~ c_lessequals(X25,X44,X3) ),
file('<stdin>',cls_power__mono_0) ).
fof(c_0_137_138,axiom,
! [X63,X7] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X7)),c_Lambda_OdB_OAbs(X63)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X7),X63)) ),
file('<stdin>',cls_rtrancl__beta__Abs_0) ).
fof(c_0_138_139,axiom,
! [X57,X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X44),X57),X3)
| ~ c_lessequals(X45,X57,X3)
| ~ c_lessequals(X25,X44,X3) ),
file('<stdin>',cls_add__mono_0) ).
fof(c_0_139_140,axiom,
! [X57,X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X44),X57),X3)
| ~ c_HOL_Oord__class_Oless(X45,X57,X3)
| ~ c_HOL_Oord__class_Oless(X25,X44,X3) ),
file('<stdin>',cls_add__strict__mono_0) ).
fof(c_0_140_141,axiom,
! [X57,X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X44),X57),X3)
| ~ c_HOL_Oord__class_Oless(X45,X57,X3)
| ~ c_lessequals(X25,X44,X3) ),
file('<stdin>',cls_add__le__less__mono_0) ).
fof(c_0_141_142,axiom,
! [X57,X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X44),X57),X3)
| ~ c_lessequals(X45,X57,X3)
| ~ c_HOL_Oord__class_Oless(X25,X44,X3) ),
file('<stdin>',cls_add__less__le__mono_0) ).
fof(c_0_142_143,axiom,
! [X58,X28,X24,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(X24,X28,X3),X58,X3) = c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(X24,X58,X3),c_HOL_Ominus__class_Ominus(X28,X58,X3),X3) ),
file('<stdin>',cls_max__diff__distrib__left_0) ).
fof(c_0_143_144,axiom,
! [X8,X44,X25,X3] :
( c_Wellfounded_Oaccp(X8,X44,X3)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X44),X25))
| ~ c_Wellfounded_Oaccp(X8,X25,X3) ),
file('<stdin>',cls_accp__downwards_0) ).
fof(c_0_144_145,axiom,
! [X8,X44,X25,X3] :
( c_Wellfounded_Oaccp(X8,X44,X3)
| ~ c_Wellfounded_Oaccp(X8,X25,X3)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X44),X25)) ),
file('<stdin>',cls_accp__downwards__aux_0) ).
fof(c_0_145_146,axiom,
! [X22,X20,X69] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X69,X22,tc_nat),c_HOL_Ominus__class_Ominus(X69,X20,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X20,X69,tc_nat)
| ~ c_HOL_Oord__class_Oless(X20,X22,tc_nat) ),
file('<stdin>',cls_diff__less__mono2_0) ).
fof(c_0_146_147,axiom,
! [X45,X44,X25] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X25,X45,tc_nat),c_HOL_Ominus__class_Ominus(X44,X45,tc_nat),tc_nat)
| ~ c_lessequals(X45,X25,tc_nat)
| ~ c_HOL_Oord__class_Oless(X25,X44,tc_nat) ),
file('<stdin>',cls_diff__less__mono_0) ).
fof(c_0_147_148,axiom,
! [X22,X20,X59] :
( c_lessequals(X20,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X20),X59,tc_nat),tc_nat)
| ~ c_lessequals(X59,X22,tc_nat) ),
file('<stdin>',cls_le__add__diff_0) ).
fof(c_0_148_149,axiom,
! [X22,X20,X59] :
( c_lessequals(X20,X22,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X59),X20),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X59),X22),tc_nat) ),
file('<stdin>',cls_nat__add__left__cancel__le_0) ).
fof(c_0_149_150,axiom,
! [X22,X20,X59] :
( c_HOL_Oord__class_Oless(X20,X22,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X59),X20),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X59),X22),tc_nat) ),
file('<stdin>',cls_nat__add__left__cancel__less_0) ).
fof(c_0_150_151,axiom,
! [X58,X28,X24,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X28),X58)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X28)),X58) ),
file('<stdin>',cls_class__semiring_Oadd__a_0) ).
fof(c_0_151_152,axiom,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X44)),X45) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X44),X45)) ),
file('<stdin>',cls_comm__monoid__add_Omult__assoc_0) ).
fof(c_0_152_153,axiom,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Oab__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X44)),X45) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X44),X45)) ),
file('<stdin>',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
fof(c_0_153_154,axiom,
! [X57,X45,X25,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X57)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45)),X57) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I25_J_0) ).
fof(c_0_154_155,axiom,
! [X45,X44,X25,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),X25),X44)),X45) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X44),X45)) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I21_J_0) ).
fof(c_0_155_156,axiom,
! [X69,X59,X18,X15] :
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X59),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X69),tc_nat)
| ~ c_lessequals(X59,X69,tc_nat)
| ~ c_lessequals(X15,X18,tc_nat) ),
file('<stdin>',cls_add__le__mono_0) ).
fof(c_0_156_157,axiom,
! [X69,X59,X18,X15] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X59),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X69),tc_nat)
| ~ c_HOL_Oord__class_Oless(X59,X69,tc_nat)
| ~ c_HOL_Oord__class_Oless(X15,X18,tc_nat) ),
file('<stdin>',cls_add__less__mono_0) ).
fof(c_0_157_158,axiom,
! [X37,X47,X48,X3] :
( c_List_Olist_ONil(X3) != c_List_Omap(X47,X37,X48,X3)
| X37 = c_List_Olist_ONil(X48) ),
file('<stdin>',cls_Nil__is__map__conv_0) ).
fof(c_0_158_159,axiom,
! [X37,X47,X48,X3] :
( c_List_Omap(X47,X37,X48,X3) != c_List_Olist_ONil(X3)
| X37 = c_List_Olist_ONil(X48) ),
file('<stdin>',cls_map__is__Nil__conv_0) ).
fof(c_0_159_160,axiom,
! [X53,X19,X16,X30] :
( c_Type_Otyping(X16,X53,X30)
| ~ c_Type_Otyping(X16,X19,X30)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X19),X53)) ),
file('<stdin>',cls_subject__reduction_H_0) ).
fof(c_0_160_161,axiom,
! [X59,X18,X15] :
( c_lessequals(X18,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X59),tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X18,X59,tc_nat),X15,tc_nat) ),
file('<stdin>',cls_le__diff__conv_0) ).
fof(c_0_161_162,axiom,
! [X59,X18,X15] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X59),X18,tc_nat)
| ~ c_HOL_Oord__class_Oless(X15,c_HOL_Ominus__class_Ominus(X18,X59,tc_nat),tc_nat) ),
file('<stdin>',cls_less__diff__conv_0) ).
fof(c_0_162_163,axiom,
! [X58,X28,X24,X14,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X28),X58)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X28),X14)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X58) = X14 ),
file('<stdin>',cls_add__cancel__21_0) ).
fof(c_0_163_164,axiom,
! [X59,X18,X15] :
( c_HOL_Ominus__class_Ominus(X15,c_HOL_Ominus__class_Ominus(X18,X59,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X59),X18,tc_nat)
| ~ c_lessequals(X59,X18,tc_nat) ),
file('<stdin>',cls_diff__diff__right_0) ).
fof(c_0_164_165,axiom,
! [X59,X18,X15] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X18,X59,tc_nat),X15,tc_nat)
| ~ c_lessequals(X18,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X59),tc_nat) ),
file('<stdin>',cls_le__diff__conv_1) ).
fof(c_0_165_166,axiom,
! [X59,X18,X15] :
( c_HOL_Oord__class_Oless(X15,c_HOL_Ominus__class_Ominus(X18,X59,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X59),X18,tc_nat) ),
file('<stdin>',cls_less__diff__conv_1) ).
fof(c_0_166_167,axiom,
! [X59,X18,X15] :
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X18),X59,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Ominus__class_Ominus(X18,X59,tc_nat))
| ~ c_lessequals(X59,X18,tc_nat) ),
file('<stdin>',cls_diff__add__assoc_0) ).
fof(c_0_167_168,axiom,
! [X59,X18,X15] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Ominus__class_Ominus(X18,X59,tc_nat)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X18),X59,tc_nat)
| ~ c_lessequals(X59,X18,tc_nat) ),
file('<stdin>',cls_add__diff__assoc_0) ).
fof(c_0_168_169,axiom,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X58,X28,X3)
| c_lessequals(X58,X24,X3)
| ~ c_lessequals(X58,c_Orderings_Oord__class_Omax(X24,X28,X3),X3) ),
file('<stdin>',cls_le__max__iff__disj_0) ).
fof(c_0_169_170,axiom,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X58,X28,X3)
| c_HOL_Oord__class_Oless(X58,X24,X3)
| ~ c_HOL_Oord__class_Oless(X58,c_Orderings_Oord__class_Omax(X24,X28,X3),X3) ),
file('<stdin>',cls_less__max__iff__disj_0) ).
fof(c_0_170_171,axiom,
! [X59,X15] :
( ~ c_lessequals(X15,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X59),X15),tc_nat)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X59),X15),X15,tc_nat) = X59 ),
file('<stdin>',cls_le__imp__diff__is__add_1) ).
fof(c_0_171_172,axiom,
! [X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X44),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X44,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X25,X3) ),
file('<stdin>',cls_add__nonneg__nonneg_0) ).
fof(c_0_172_173,axiom,
! [X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X44),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X44,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X25,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_add__neg__neg_0) ).
fof(c_0_173_174,axiom,
! [X44,X25,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),X25),X44),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X44,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X25,X3) ),
file('<stdin>',cls_add__nonneg__pos_0) ).
fof(c_0_174_175,axiom,
! [X44,X25,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),X25),X44),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X44,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X25,X3) ),
file('<stdin>',cls_add__pos__nonneg_0) ).
fof(c_0_175_176,axiom,
! [X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X44),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X44,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X25,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_add__nonpos__neg_0) ).
fof(c_0_176_177,axiom,
! [X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X44),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X44,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X25,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_add__neg__nonpos_0) ).
fof(c_0_177_178,axiom,
! [X44,X25,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),X25),X44),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X44,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X25,X3) ),
file('<stdin>',cls_add__pos__pos_0) ).
fof(c_0_178_179,axiom,
! [X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X44),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X44,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X25,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_add__nonpos__nonpos_0) ).
fof(c_0_179_180,axiom,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oord__class_Oless(X44,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45),X3)
| ~ c_lessequals(X44,X45,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X25,X3) ),
file('<stdin>',cls_add__strict__increasing_0) ).
fof(c_0_180_181,axiom,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_lessequals(X44,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45),X3)
| ~ c_lessequals(X44,X45,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X25,X3) ),
file('<stdin>',cls_add__increasing_0) ).
fof(c_0_181_182,axiom,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_lessequals(X44,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45),X3)
| ~ c_lessequals(X44,X25,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X45,X3) ),
file('<stdin>',cls_add__increasing2_0) ).
fof(c_0_182_183,axiom,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oord__class_Oless(X44,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45),X3)
| ~ c_HOL_Oord__class_Oless(X44,X45,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X25,X3) ),
file('<stdin>',cls_add__strict__increasing2_0) ).
fof(c_0_183_184,axiom,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X44),X45),X3)
| ~ c_lessequals(X25,X44,X3) ),
file('<stdin>',cls_add__le__cancel__right_1) ).
fof(c_0_184_185,axiom,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X44),X3)
| ~ c_lessequals(X25,X44,X3) ),
file('<stdin>',cls_add__le__cancel__left_1) ).
fof(c_0_185_186,axiom,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X44),X45),X3)
| ~ c_lessequals(X25,X44,X3) ),
file('<stdin>',cls_add__right__mono_0) ).
fof(c_0_186_187,axiom,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X44),X3)
| ~ c_lessequals(X25,X44,X3) ),
file('<stdin>',cls_add__left__mono_0) ).
fof(c_0_187_188,axiom,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X44),X45),X3)
| ~ c_HOL_Oord__class_Oless(X25,X44,X3) ),
file('<stdin>',cls_add__strict__right__mono_0) ).
fof(c_0_188_189,axiom,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X44),X45),X3)
| ~ c_HOL_Oord__class_Oless(X25,X44,X3) ),
file('<stdin>',cls_add__less__cancel__right_1) ).
fof(c_0_189_190,axiom,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X44),X3)
| ~ c_HOL_Oord__class_Oless(X25,X44,X3) ),
file('<stdin>',cls_add__strict__left__mono_0) ).
fof(c_0_190_191,axiom,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X44),X3)
| ~ c_HOL_Oord__class_Oless(X25,X44,X3) ),
file('<stdin>',cls_add__less__cancel__left_1) ).
fof(c_0_191_192,axiom,
! [X45,X44,X25,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X44,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45),X3)
| ~ c_HOL_Oord__class_Oless(X44,X45,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X25,X3) ),
file('<stdin>',cls_pos__add__strict_0) ).
fof(c_0_192_193,axiom,
! [X22,X20,X69] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X69,X22,tc_nat),c_HOL_Ominus__class_Ominus(X69,X20,tc_nat),tc_nat)
| ~ c_lessequals(X20,X22,tc_nat) ),
file('<stdin>',cls_diff__le__mono2_0) ).
fof(c_0_193_194,axiom,
! [X22,X20,X69] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X20,X69,tc_nat),c_HOL_Ominus__class_Ominus(X22,X69,tc_nat),tc_nat)
| ~ c_lessequals(X20,X22,tc_nat) ),
file('<stdin>',cls_diff__le__mono_0) ).
fof(c_0_194_195,axiom,
! [X22,X20] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X22,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X22),tc_nat) ),
file('<stdin>',cls_add__gr__0_0) ).
fof(c_0_195_196,axiom,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X24,X28,X3),X58,X3)
| ~ c_HOL_Oord__class_Oless(X28,X58,X3)
| ~ c_HOL_Oord__class_Oless(X24,X58,X3) ),
file('<stdin>',cls_max__less__iff__conj_2) ).
fof(c_0_196_197,axiom,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(c_Orderings_Oord__class_Omax(X24,X28,X3),X58,X3)
| ~ c_lessequals(X28,X58,X3)
| ~ c_lessequals(X24,X58,X3) ),
file('<stdin>',cls_min__max_Ole__sup__iff_2) ).
fof(c_0_197_198,axiom,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(c_Orderings_Oord__class_Omax(X28,X58,X3),X24,X3)
| ~ c_lessequals(X58,X24,X3)
| ~ c_lessequals(X28,X24,X3) ),
file('<stdin>',cls_min__max_Osup__least_0) ).
fof(c_0_198_199,axiom,
! [X24,X44,X25,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(c_Orderings_Oord__class_Omax(X25,X44,X3),X24,X3)
| ~ c_lessequals(X44,X24,X3)
| ~ c_lessequals(X25,X24,X3) ),
file('<stdin>',cls_min__max_Ole__supI_0) ).
fof(c_0_199_200,axiom,
! [X18,X15] :
( ~ c_lessequals(X15,X18,tc_nat)
| X18 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X18,X15,tc_nat)),X15) ),
file('<stdin>',cls_le__imp__diff__is__add_0) ).
fof(c_0_200_201,axiom,
! [X22,X20] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X20,X22,tc_nat)),X22) = X20
| ~ c_lessequals(X22,X20,tc_nat) ),
file('<stdin>',cls_le__add__diff__inverse2_0) ).
fof(c_0_201_202,axiom,
! [X22,X20,X59] :
( c_HOL_Ominus__class_Ominus(X20,X59,tc_nat) != c_HOL_Ominus__class_Ominus(X22,X59,tc_nat)
| ~ c_lessequals(X59,X22,tc_nat)
| ~ c_lessequals(X59,X20,tc_nat)
| X20 = X22 ),
file('<stdin>',cls_eq__diff__iff_0) ).
fof(c_0_202_203,axiom,
! [X27,X45,X44,X25,X3] :
( hAPP(hAPP(X27,hAPP(hAPP(X27,X25),X44)),X45) = hAPP(hAPP(X27,X25),hAPP(hAPP(X27,X44),X45))
| ~ c_OrderedGroup_Osemigroup__add(X27,X3) ),
file('<stdin>',cls_semigroup__add_Oadd__assoc_0) ).
fof(c_0_203_204,axiom,
! [X22,X20] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X20,X22,tc_nat),X20,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X22,tc_nat) ),
file('<stdin>',cls_diff__less_0) ).
fof(c_0_204_205,axiom,
! [X46,X37,X68,X3] :
( c_List_Olistsp(X68,c_List_Oappend(X37,X46,X3),X3)
| ~ c_List_Olistsp(X68,X46,X3)
| ~ c_List_Olistsp(X68,X37,X3) ),
file('<stdin>',cls_append__in__listsp__conv_2) ).
fof(c_0_205_206,axiom,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X24,X28,X3),X58,X3) = c_Orderings_Oord__class_Omax(X24,c_Orderings_Oord__class_Omax(X28,X58,X3),X3) ),
file('<stdin>',cls_min__max_Osup__assoc_0) ).
fof(c_0_206_207,axiom,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Orderings_Oord__class_Omax(X24,c_Orderings_Oord__class_Omax(X28,X58,X3),X3) = c_Orderings_Oord__class_Omax(X28,c_Orderings_Oord__class_Omax(X24,X58,X3),X3) ),
file('<stdin>',cls_min__max_Osup__left__commute_0) ).
fof(c_0_207_208,axiom,
! [X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X25,X44,X3)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X25,X44,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_le__iff__diff__le__0_1) ).
fof(c_0_208_209,axiom,
! [X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X25,X44,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X25,X44,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_less__iff__diff__less__0_1) ).
fof(c_0_209_210,axiom,
! [X25,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X25,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X25),X3) ),
file('<stdin>',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
fof(c_0_210_211,axiom,
! [X25,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X25,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X25),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_double__add__less__zero__iff__single__less__zero_0) ).
fof(c_0_211_212,axiom,
! [X25,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X25,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X25),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_even__less__0__iff_0) ).
fof(c_0_212_213,axiom,
! [X25,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X25,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X25),X3) ),
file('<stdin>',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
fof(c_0_213_214,axiom,
! [X25,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(X25,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X25),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
fof(c_0_214_215,axiom,
! [X49,X28,X50,X24,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X24,X28,X3) != c_HOL_Ominus__class_Ominus(X50,X49,X3)
| c_lessequals(X49,X50,X3)
| ~ c_lessequals(X28,X24,X3) ),
file('<stdin>',cls_le__eqI_0) ).
fof(c_0_215_216,axiom,
! [X49,X28,X50,X24,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X24,X28,X3) != c_HOL_Ominus__class_Ominus(X50,X49,X3)
| c_lessequals(X28,X24,X3)
| ~ c_lessequals(X49,X50,X3) ),
file('<stdin>',cls_le__eqI_1) ).
fof(c_0_216_217,axiom,
! [X49,X28,X50,X24,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X24,X28,X3) != c_HOL_Ominus__class_Ominus(X50,X49,X3)
| c_HOL_Oord__class_Oless(X50,X49,X3)
| ~ c_HOL_Oord__class_Oless(X24,X28,X3) ),
file('<stdin>',cls_less__eqI_0) ).
fof(c_0_217_218,axiom,
! [X49,X28,X50,X24,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X24,X28,X3) != c_HOL_Ominus__class_Ominus(X50,X49,X3)
| c_HOL_Oord__class_Oless(X24,X28,X3)
| ~ c_HOL_Oord__class_Oless(X50,X49,X3) ),
file('<stdin>',cls_less__eqI_1) ).
fof(c_0_218_219,axiom,
! [X59,X18,X15] :
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X59),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X59),tc_nat)
| ~ c_lessequals(X15,X18,tc_nat) ),
file('<stdin>',cls_add__le__mono1_0) ).
fof(c_0_219_220,axiom,
! [X22,X20,X59] :
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X59),X20),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X59),X22),tc_nat)
| ~ c_lessequals(X20,X22,tc_nat) ),
file('<stdin>',cls_nat__add__left__cancel__le_1) ).
fof(c_0_220_221,axiom,
! [X59,X18,X15] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X59),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X59),tc_nat)
| ~ c_HOL_Oord__class_Oless(X15,X18,tc_nat) ),
file('<stdin>',cls_add__less__mono1_0) ).
fof(c_0_221_222,axiom,
! [X22,X20,X59] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X59),X20),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X59),X22),tc_nat)
| ~ c_HOL_Oord__class_Oless(X20,X22,tc_nat) ),
file('<stdin>',cls_nat__add__left__cancel__less_1) ).
fof(c_0_222_223,axiom,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X24,X58,X3)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X24,X28,X3),X58,X3) ),
file('<stdin>',cls_max__less__iff__conj_0) ).
fof(c_0_223_224,axiom,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X28,X58,X3)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X24,X28,X3),X58,X3) ),
file('<stdin>',cls_max__less__iff__conj_1) ).
fof(c_0_224_225,axiom,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X28,X58,X3)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X24,X28,X3),X58,X3) ),
file('<stdin>',cls_min__max_Ole__sup__iff_1) ).
fof(c_0_225_226,axiom,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X24,X58,X3)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X24,X28,X3),X58,X3) ),
file('<stdin>',cls_min__max_Ole__sup__iff_0) ).
fof(c_0_226_227,axiom,
! [X24,X44,X25,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X44,X24,X3)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X25,X44,X3),X24,X3) ),
file('<stdin>',cls_min__max_Ole__supE_1) ).
fof(c_0_227_228,axiom,
! [X24,X44,X25,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X25,X24,X3)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X25,X44,X3),X24,X3) ),
file('<stdin>',cls_min__max_Ole__supE_0) ).
fof(c_0_228_229,axiom,
! [X58,X28,X24,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X28),X58)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X28),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X58)) ),
file('<stdin>',cls_add__cancel__21_1) ).
fof(c_0_229_230,axiom,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X44),X45)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X44),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45)) ),
file('<stdin>',cls_comm__monoid__add_Omult__left__commute_0) ).
fof(c_0_230_231,axiom,
! [X57,X45,X25,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X57)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X57)) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I22_J_0) ).
fof(c_0_231_232,axiom,
! [X22,X20,X59] :
( c_HOL_Oord__class_Oless(X20,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X59),tc_nat)
| ~ c_lessequals(X20,X22,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X59,tc_nat) ),
file('<stdin>',cls_lem0_0) ).
fof(c_0_232_233,axiom,
! [X28,X24,X8,X3] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X24),X28))
| ~ hBOOL(hAPP(hAPP(X8,X24),X28)) ),
file('<stdin>',cls_r__into__rtranclp_0) ).
fof(c_0_233_234,axiom,
! [X22,X20,X3] :
( ~ class_Ring__and__Field_Oring__1(X3)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(X20,X22,tc_nat),X3) = c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(X20,X3),c_Nat_Osemiring__1__class_Oof__nat(X22,X3),X3)
| ~ c_lessequals(X22,X20,tc_nat) ),
file('<stdin>',cls_of__nat__diff_0) ).
fof(c_0_234_235,axiom,
! [X46,X37,X68,X3] :
( c_List_Olistsp(X68,X37,X3)
| ~ c_List_Olistsp(X68,c_List_Oappend(X37,X46,X3),X3) ),
file('<stdin>',cls_append__in__listsp__conv_0) ).
fof(c_0_235_236,axiom,
! [X46,X37,X68,X3] :
( c_List_Olistsp(X68,X46,X3)
| ~ c_List_Olistsp(X68,c_List_Oappend(X37,X46,X3),X3) ),
file('<stdin>',cls_append__in__listsp__conv_1) ).
fof(c_0_236_237,axiom,
! [X22,X20] :
( c_HOL_Oord__class_Oless(X20,X22,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X22,X20,tc_nat),tc_nat) ),
file('<stdin>',cls_zero__less__diff_0) ).
fof(c_0_237_238,axiom,
! [X28,X24,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X28) != c_HOL_Ozero__class_Ozero(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X28,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X24,X3)
| X28 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_add__nonneg__eq__0__iff_1) ).
fof(c_0_238_239,axiom,
! [X28,X24,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X28) != c_HOL_Ozero__class_Ozero(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X28,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X24,X3)
| X24 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_add__nonneg__eq__0__iff_0) ).
fof(c_0_239_240,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_240_241,axiom,
! [X22,X20,X69,X59] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X69) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X59),X22)
| ~ c_HOL_Oord__class_Oless(X59,X69,tc_nat)
| c_HOL_Oord__class_Oless(X20,X22,tc_nat) ),
file('<stdin>',cls_less__add__eq__less_0) ).
fof(c_0_241_242,axiom,
! [X59,X18,X15] :
( c_HOL_Oord__class_Oless(X15,X59,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X18),X59,tc_nat) ),
file('<stdin>',cls_add__lessD1_0) ).
fof(c_0_242_243,axiom,
! [X22,X20,X59] :
( c_lessequals(X59,X22,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X59),X22,tc_nat) ),
file('<stdin>',cls_add__leE_1) ).
fof(c_0_243_244,axiom,
! [X22,X20,X59] :
( c_lessequals(X20,X22,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X59),X22,tc_nat) ),
file('<stdin>',cls_add__leE_0) ).
fof(c_0_244_245,axiom,
! [X44,X25,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ominus__class_Ominus(X25,X44,X3)),X44) = X25 ),
file('<stdin>',cls_diff__add__cancel_0) ).
fof(c_0_245_246,axiom,
! [X22,X25,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X25,X22,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X25,X3) ),
file('<stdin>',cls_zero__le__power_0) ).
fof(c_0_246_247,axiom,
! [X22,X25,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X25,X22,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X25,X3) ),
file('<stdin>',cls_zero__less__power_0) ).
fof(c_0_247_248,axiom,
! [X28,X8,X25,X3] :
( c_Wellfounded_Oaccp(X8,X28,X3)
| ~ hBOOL(hAPP(hAPP(X8,X28),X25))
| ~ c_Wellfounded_Oaccp(X8,X25,X3) ),
file('<stdin>',cls_accp_Ocases_0) ).
fof(c_0_248_249,axiom,
! [X8,X44,X25,X3] :
( c_Wellfounded_Oaccp(X8,X25,X3)
| ~ hBOOL(hAPP(hAPP(X8,X25),X44))
| ~ c_Wellfounded_Oaccp(X8,X44,X3) ),
file('<stdin>',cls_accp__downward_0) ).
fof(c_0_249_250,axiom,
! [X25,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X25),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X25,X3) ),
file('<stdin>',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
fof(c_0_250_251,axiom,
! [X25,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X25),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X25,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_double__add__less__zero__iff__single__less__zero_1) ).
fof(c_0_251_252,axiom,
! [X25,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X25),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X25,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_even__less__0__iff_1) ).
fof(c_0_252_253,axiom,
! [X25,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),X25),X25),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X25,X3) ),
file('<stdin>',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
fof(c_0_253_254,axiom,
! [X25,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X25),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X25,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
fof(c_0_254_255,axiom,
! [X8] :
( hBOOL(hAPP(c_InductTermi_OIT,X8))
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X8,tc_Lambda_OdB) ),
file('<stdin>',cls_termi__implies__IT_0) ).
fof(c_0_255_256,axiom,
! [X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ominus__class_Ominus(X25,X44,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X25,X44,X3) ),
file('<stdin>',cls_le__iff__diff__le__0_0) ).
fof(c_0_256_257,axiom,
! [X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X25,X44,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X25,X44,X3) ),
file('<stdin>',cls_less__iff__diff__less__0_0) ).
fof(c_0_257_258,axiom,
! [X53,X19,X16,X30] :
( c_Type_Otyping(X16,X53,X30)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X19),X53))
| ~ c_Type_Otyping(X16,X19,X30) ),
file('<stdin>',cls_subject__reduction_0) ).
fof(c_0_258_259,axiom,
! [X46,X37,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| c_List_Olistsum(c_List_Oappend(X37,X46,X3),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_List_Olistsum(X37,X3)),c_List_Olistsum(X46,X3)) ),
file('<stdin>',cls_listsum__append_0) ).
fof(c_0_259_260,axiom,
! [X24,X44,X25,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X24,c_Orderings_Oord__class_Omax(X25,X44,X3),X3)
| ~ c_HOL_Oord__class_Oless(X24,X25,X3) ),
file('<stdin>',cls_min__max_Oless__supI1_0) ).
fof(c_0_260_261,axiom,
! [X24,X44,X25,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X24,c_Orderings_Oord__class_Omax(X25,X44,X3),X3)
| ~ c_HOL_Oord__class_Oless(X24,X44,X3) ),
file('<stdin>',cls_min__max_Oless__supI2_0) ).
fof(c_0_261_262,axiom,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X58,c_Orderings_Oord__class_Omax(X24,X28,X3),X3)
| ~ c_HOL_Oord__class_Oless(X58,X24,X3) ),
file('<stdin>',cls_less__max__iff__disj_1) ).
fof(c_0_262_263,axiom,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X58,c_Orderings_Oord__class_Omax(X24,X28,X3),X3)
| ~ c_HOL_Oord__class_Oless(X58,X28,X3) ),
file('<stdin>',cls_less__max__iff__disj_2) ).
fof(c_0_263_264,axiom,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X58,c_Orderings_Oord__class_Omax(X24,X28,X3),X3)
| ~ c_lessequals(X58,X28,X3) ),
file('<stdin>',cls_le__max__iff__disj_2) ).
fof(c_0_264_265,axiom,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X58,c_Orderings_Oord__class_Omax(X24,X28,X3),X3)
| ~ c_lessequals(X58,X24,X3) ),
file('<stdin>',cls_le__max__iff__disj_1) ).
fof(c_0_265_266,axiom,
! [X24,X44,X25,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X24,c_Orderings_Oord__class_Omax(X25,X44,X3),X3)
| ~ c_lessequals(X24,X44,X3) ),
file('<stdin>',cls_min__max_Ole__supI2_0) ).
fof(c_0_266_267,axiom,
! [X24,X44,X25,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X24,c_Orderings_Oord__class_Omax(X25,X44,X3),X3)
| ~ c_lessequals(X24,X25,X3) ),
file('<stdin>',cls_min__max_Ole__supI1_0) ).
fof(c_0_267_268,axiom,
! [X22,X20] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X22,X20,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X20,X22,tc_nat) ),
file('<stdin>',cls_zero__less__diff_1) ).
fof(c_0_268_269,axiom,
! [X22,X15] :
( c_HOL_Ominus__class_Ominus(X22,c_HOL_Ominus__class_Ominus(X22,X15,tc_nat),tc_nat) = X15
| ~ c_lessequals(X15,X22,tc_nat) ),
file('<stdin>',cls_diff__diff__cancel_0) ).
fof(c_0_269_270,axiom,
! [X22,X20,X3] :
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X22),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Nat_Osemiring__1__class_Oof__nat(X20,X3)),c_Nat_Osemiring__1__class_Oof__nat(X22,X3)) ),
file('<stdin>',cls_of__nat__add_0) ).
fof(c_0_270_271,axiom,
! [X22,X59,X18] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X18,X22,tc_nat),X59,tc_nat)
| ~ c_HOL_Oord__class_Oless(X18,X59,tc_nat) ),
file('<stdin>',cls_less__imp__diff__less_0) ).
fof(c_0_271_272,axiom,
! [X19,X15] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X19),c_Lambda_OdB_OVar(X15))))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X19)) ),
file('<stdin>',cls_app__Var__IT_0) ).
fof(c_0_272_273,axiom,
! [X22,X20] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X22),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X22,tc_nat) ),
file('<stdin>',cls_add__gr__0_2) ).
fof(c_0_273_274,axiom,
! [X22,X20] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X22),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat) ),
file('<stdin>',cls_add__gr__0_1) ).
fof(c_0_274_275,axiom,
! [X22,X20] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),c_HOL_Ominus__class_Ominus(X20,X22,tc_nat)) = X20
| ~ c_lessequals(X22,X20,tc_nat) ),
file('<stdin>',cls_le__add__diff__inverse_0) ).
fof(c_0_275_276,axiom,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X58,X24,X3)
| ~ c_HOL_Oord__class_Oless(X58,X28,X3)
| ~ c_HOL_Oord__class_Oless(X28,X24,X3) ),
file('<stdin>',cls_xt1_I10_J_0) ).
fof(c_0_276_277,axiom,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X24,X58,X3)
| ~ c_HOL_Oord__class_Oless(X28,X58,X3)
| ~ c_HOL_Oord__class_Oless(X24,X28,X3) ),
file('<stdin>',cls_order__less__trans_0) ).
fof(c_0_277_278,axiom,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X58,X24,X3)
| ~ c_lessequals(X58,X28,X3)
| ~ c_lessequals(X28,X24,X3) ),
file('<stdin>',cls_xt1_I6_J_0) ).
fof(c_0_278_279,axiom,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X58,X24,X3)
| ~ c_lessequals(X58,X28,X3)
| ~ c_HOL_Oord__class_Oless(X28,X24,X3) ),
file('<stdin>',cls_xt1_I7_J_0) ).
fof(c_0_279_280,axiom,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X58,X24,X3)
| ~ c_HOL_Oord__class_Oless(X58,X28,X3)
| ~ c_lessequals(X28,X24,X3) ),
file('<stdin>',cls_xt1_I8_J_0) ).
fof(c_0_280_281,axiom,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X24,X58,X3)
| ~ c_lessequals(X28,X58,X3)
| ~ c_lessequals(X24,X28,X3) ),
file('<stdin>',cls_order__trans_0) ).
fof(c_0_281_282,axiom,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X24,X58,X3)
| ~ c_HOL_Oord__class_Oless(X28,X58,X3)
| ~ c_lessequals(X24,X28,X3) ),
file('<stdin>',cls_order__le__less__trans_0) ).
fof(c_0_282_283,axiom,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X24,X58,X3)
| ~ c_lessequals(X28,X58,X3)
| ~ c_HOL_Oord__class_Oless(X24,X28,X3) ),
file('<stdin>',cls_order__less__le__trans_0) ).
fof(c_0_283_284,axiom,
! [X19,X7] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X7)),c_Lambda_OdB_OAbs(X19)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X7),X19)) ),
file('<stdin>',cls_abs_0) ).
fof(c_0_284_285,axiom,
! [X22,X20,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(X20,X22,tc_nat)
| ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X20,X3),c_Nat_Osemiring__1__class_Oof__nat(X22,X3),X3) ),
file('<stdin>',cls_of__nat__le__iff_0) ).
fof(c_0_285_286,axiom,
! [X22,X20,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X20,X22,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X20,X3),c_Nat_Osemiring__1__class_Oof__nat(X22,X3),X3) ),
file('<stdin>',cls_of__nat__less__iff_0) ).
fof(c_0_286_287,axiom,
! [X58,X28,X24] :
( c_HOL_Oord__class_Oless(X24,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X28),X58),tc_nat)
| ~ c_HOL_Oord__class_Oless(X24,X28,tc_nat) ),
file('<stdin>',cls_termination__basic__simps_I1_J_0) ).
fof(c_0_287_288,axiom,
! [X58,X28,X24] :
( c_HOL_Oord__class_Oless(X24,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X28),X58),tc_nat)
| ~ c_HOL_Oord__class_Oless(X24,X58,tc_nat) ),
file('<stdin>',cls_termination__basic__simps_I2_J_0) ).
fof(c_0_288_289,axiom,
! [X20,X18,X15] :
( c_HOL_Oord__class_Oless(X15,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X20),tc_nat)
| ~ c_HOL_Oord__class_Oless(X15,X18,tc_nat) ),
file('<stdin>',cls_trans__less__add1_0) ).
fof(c_0_289_290,axiom,
! [X20,X18,X15] :
( c_HOL_Oord__class_Oless(X15,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X18),tc_nat)
| ~ c_HOL_Oord__class_Oless(X15,X18,tc_nat) ),
file('<stdin>',cls_trans__less__add2_0) ).
fof(c_0_290_291,axiom,
! [X20,X18,X15] :
( c_lessequals(X15,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X18),tc_nat)
| ~ c_lessequals(X15,X18,tc_nat) ),
file('<stdin>',cls_trans__le__add2_0) ).
fof(c_0_291_292,axiom,
! [X20,X18,X15] :
( c_lessequals(X15,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X20),tc_nat)
| ~ c_lessequals(X15,X18,tc_nat) ),
file('<stdin>',cls_trans__le__add1_0) ).
fof(c_0_292_293,axiom,
! [X58,X28,X24] :
( c_lessequals(X24,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X28),X58),tc_nat)
| ~ c_lessequals(X24,X58,tc_nat) ),
file('<stdin>',cls_termination__basic__simps_I4_J_0) ).
fof(c_0_293_294,axiom,
! [X58,X28,X24] :
( c_lessequals(X24,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X28),X58),tc_nat)
| ~ c_lessequals(X24,X28,tc_nat) ),
file('<stdin>',cls_termination__basic__simps_I3_J_0) ).
fof(c_0_294_295,axiom,
! [X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Orderings_Oord__class_Omax(X24,c_Orderings_Oord__class_Omax(X24,X28,X3),X3) = c_Orderings_Oord__class_Omax(X24,X28,X3) ),
file('<stdin>',cls_min__max_Osup__left__idem_0) ).
fof(c_0_295_296,axiom,
! [X59,X18,X15] :
( c_lessequals(X15,X59,tc_nat)
| ~ c_lessequals(X18,X59,tc_nat)
| ~ c_lessequals(X15,X18,tc_nat) ),
file('<stdin>',cls_le__trans_0) ).
fof(c_0_296_297,axiom,
! [X19,X15] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X19),X15)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X19)) ),
file('<stdin>',cls_lift__IT_0) ).
fof(c_0_297_298,axiom,
! [X24,X22,X34] :
( hBOOL(hAPP(X34,X22))
| hBOOL(hAPP(X34,X24))
| ~ c_HOL_Oord__class_Oless(X24,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X34),tc_nat)
| ~ hBOOL(hAPP(X34,c_HOL_Ozero__class_Ozero(tc_nat))) ),
file('<stdin>',cls_infinite__descent0_2) ).
fof(c_0_298_299,axiom,
! [X22,X59,X15] :
( c_Lambda_Oliftn(X22,c_Lambda_OdB_OVar(X15),X59) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X22))
| c_HOL_Oord__class_Oless(X15,X59,tc_nat) ),
file('<stdin>',cls_liftn_Osimps_I1_J_1) ).
fof(c_0_299_300,axiom,
! [X37,X24,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| c_List_Olistsum(c_List_Olist_OCons(X24,X37,X3),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),c_List_Olistsum(X37,X3)) ),
file('<stdin>',cls_listsum_Osimps_I2_J_0) ).
fof(c_0_300_301,axiom,
! [X22,X20] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),c_HOL_Ominus__class_Ominus(X20,X22,tc_nat)) = X20
| c_HOL_Oord__class_Oless(X20,X22,tc_nat) ),
file('<stdin>',cls_add__diff__inverse_0) ).
fof(c_0_301_302,axiom,
! [X28,X24,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X24,X28,X3)
| c_lessequals(X28,X24,X3)
| ~ c_lessequals(X24,X28,X3) ),
file('<stdin>',cls_less__le__not__le_2) ).
fof(c_0_302_303,axiom,
! [X22,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X22,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X22,X3),X3) ),
file('<stdin>',cls_of__nat__0__less__iff_0) ).
fof(c_0_303_304,axiom,
! [X14,X18,X15] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X18)),X14),X15) = c_Lambda_OdB_OVar(X18)
| ~ c_HOL_Oord__class_Oless(X18,X15,tc_nat) ),
file('<stdin>',cls_subst__lt_0) ).
fof(c_0_304_305,axiom,
! [X22,X20,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X20,X3),c_Nat_Osemiring__1__class_Oof__nat(X22,X3),X3)
| ~ c_lessequals(X20,X22,tc_nat) ),
file('<stdin>',cls_of__nat__le__iff_1) ).
fof(c_0_305_306,axiom,
! [X22,X20,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X20,X3),c_Nat_Osemiring__1__class_Oof__nat(X22,X3),X3)
| ~ c_HOL_Oord__class_Oless(X20,X22,tc_nat) ),
file('<stdin>',cls_of__nat__less__iff_1) ).
fof(c_0_306_307,axiom,
! [X19] :
( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X19,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X19)) ),
file('<stdin>',cls_IT__implies__termi_0) ).
fof(c_0_307_308,axiom,
! [X22,X20,X34] :
( hBOOL(hAPP(hAPP(X34,X22),X20))
| c_HOL_Oord__class_Oless(X22,X20,tc_nat)
| X20 = X22
| c_HOL_Oord__class_Oless(X20,X22,tc_nat) ),
file('<stdin>',cls_nat__less__cases_0) ).
fof(c_0_308_309,axiom,
! [X22,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X22,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X22,tc_nat) ),
file('<stdin>',cls_of__nat__0__less__iff_1) ).
fof(c_0_309_310,axiom,
! [X28,X24,X3] :
( ~ class_Orderings_Oorder(X3)
| X24 = X28
| ~ c_lessequals(X28,X24,X3)
| ~ c_lessequals(X24,X28,X3) ),
file('<stdin>',cls_order__eq__iff_2) ).
fof(c_0_310_311,axiom,
! [X28,X24,X3] :
( ~ class_Orderings_Oorder(X3)
| X24 = X28
| ~ c_lessequals(X28,X24,X3)
| ~ c_lessequals(X24,X28,X3) ),
file('<stdin>',cls_order__antisym_0) ).
fof(c_0_311_312,axiom,
! [X28,X24,X3] :
( ~ class_Orderings_Oorder(X3)
| X24 = X28
| ~ c_lessequals(X24,X28,X3)
| ~ c_lessequals(X28,X24,X3) ),
file('<stdin>',cls_order__antisym__conv_0) ).
fof(c_0_312_313,axiom,
! [X28,X60,X24,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X60,X28,X3) != c_HOL_Ominus__class_Ominus(X24,X24,X3)
| X60 = X28 ),
file('<stdin>',cls_eq__eqI_1) ).
fof(c_0_313_314,axiom,
! [X49,X50,X24,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X24,X24,X3) != c_HOL_Ominus__class_Ominus(X50,X49,X3)
| X50 = X49 ),
file('<stdin>',cls_eq__eqI_0) ).
fof(c_0_314_315,axiom,
! [X58,X28,X24,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X28) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X58)
| X28 = X58 ),
file('<stdin>',cls_class__ringb_Oadd__cancel_0) ).
fof(c_0_315_316,axiom,
! [X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X24,X24,X3)
| ~ c_HOL_Oord__class_Oless(X24,X24,X3) ),
file('<stdin>',cls_linorder__antisym__conv2_1) ).
fof(c_0_316_317,axiom,
! [X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X24,X28,X3)
| ~ c_lessequals(X28,X24,X3) ),
file('<stdin>',cls_linorder__not__less_1) ).
fof(c_0_317_318,axiom,
! [X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X24,X28,X3)
| ~ c_HOL_Oord__class_Oless(X28,X24,X3) ),
file('<stdin>',cls_linorder__not__le_1) ).
fof(c_0_318_319,axiom,
! [X28,X24,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X28,X24,X3)
| ~ c_HOL_Oord__class_Oless(X24,X28,X3) ),
file('<stdin>',cls_less__le__not__le_1) ).
fof(c_0_319_320,axiom,
! [X44,X25,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X25,X44,X3)
| ~ c_HOL_Oord__class_Oless(X44,X25,X3) ),
file('<stdin>',cls_xt1_I9_J_0) ).
fof(c_0_320_321,axiom,
! [X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X24,X28,X3)
| ~ c_HOL_Oord__class_Oless(X28,X24,X3) ),
file('<stdin>',cls_not__less__iff__gr__or__eq_1) ).
fof(c_0_321_322,axiom,
! [X28,X24,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X28,X24,X3)
| ~ c_HOL_Oord__class_Oless(X24,X28,X3) ),
file('<stdin>',cls_order__less__asym_0) ).
fof(c_0_322_323,axiom,
! [X44,X25,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X44,X25,X3)
| ~ c_HOL_Oord__class_Oless(X25,X44,X3) ),
file('<stdin>',cls_order__less__asym_H_0) ).
fof(c_0_323_324,axiom,
! [X28,X24,X22,X20,X3] :
( c_List_Oreplicate(X20,X24,X3) != c_List_Oreplicate(X22,X28,X3)
| X24 = X28
| X20 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_replicate__eq__replicate_1) ).
fof(c_0_324_325,axiom,
! [X22,X20] :
( c_HOL_Ominus__class_Ominus(X22,X20,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X20,X22,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X20 = X22 ),
file('<stdin>',cls_diffs0__imp__equal_0) ).
fof(c_0_325_326,axiom,
! [X28,X24,X22,X20,X3] :
( c_List_Oreplicate(X20,X24,X3) != c_List_Oreplicate(X22,X28,X3)
| X20 = X22 ),
file('<stdin>',cls_replicate__eq__replicate_0) ).
fof(c_0_326_327,axiom,
! [X23,X46,X37,X3] :
( c_List_Oappend(X46,X37,X3) != c_List_Oappend(X23,X37,X3)
| X46 = X23 ),
file('<stdin>',cls_append__same__eq_0) ).
fof(c_0_327_328,axiom,
! [X23,X46,X37,X3] :
( c_List_Oappend(X37,X46,X3) != c_List_Oappend(X37,X23,X3)
| X46 = X23 ),
file('<stdin>',cls_same__append__eq_0) ).
fof(c_0_328_329,axiom,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X44) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45)
| X44 = X45 ),
file('<stdin>',cls_add__imp__eq_0) ).
fof(c_0_329_330,axiom,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X44) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45)
| X44 = X45 ),
file('<stdin>',cls_add__left__cancel_0) ).
fof(c_0_330_331,axiom,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X44),X25) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X25)
| X44 = X45 ),
file('<stdin>',cls_add__right__cancel_0) ).
fof(c_0_331_332,axiom,
! [X54,X55,X56,X25,X3] :
( c_List_Olist_OCons(X25,X55,X3) != c_List_Olist_OCons(X56,X54,X3)
| X25 = X56 ),
file('<stdin>',cls_list_Oinject_0) ).
fof(c_0_332_333,axiom,
! [X54,X55,X56,X25,X3] :
( c_List_Olist_OCons(X25,X55,X3) != c_List_Olist_OCons(X56,X54,X3)
| X55 = X54 ),
file('<stdin>',cls_list_Oinject_1) ).
fof(c_0_333_334,axiom,
! [X24,X7] :
( c_HOL_Oord__class_Oless(X24,X24,tc_nat)
| c_Lambda_Osubstn(c_Lambda_OdB_OVar(X24),X7,X24) = c_Lambda_Oliftn(X24,X7,c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('<stdin>',cls_substn_Osimps_I1_J_1) ).
fof(c_0_334_335,axiom,
! [X7,X59,X15] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X15)),X7),X59) = c_Lambda_OdB_OVar(X15)
| X15 = X59
| c_HOL_Oord__class_Oless(X59,X15,tc_nat) ),
file('<stdin>',cls_subst__Var_2) ).
fof(c_0_335_336,axiom,
! [X22,X20] :
( X20 = X22
| ~ c_lessequals(X22,X20,tc_nat)
| ~ c_lessequals(X20,X22,tc_nat) ),
file('<stdin>',cls_le__antisym_0) ).
fof(c_0_336_337,axiom,
! [X1,X2,X3] :
( X2 = X1
| ~ hBOOL(hAPP(hAPP(c_fequal(X3),X2),X1)) ),
file('<stdin>',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(c_0_337_338,axiom,
! [X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X24,c_Orderings_Oord__class_Omax(X24,X28,X3),X3) ),
file('<stdin>',cls_le__maxI1_0) ).
fof(c_0_338_339,axiom,
! [X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X28,c_Orderings_Oord__class_Omax(X24,X28,X3),X3) ),
file('<stdin>',cls_le__maxI2_0) ).
fof(c_0_339_340,axiom,
! [X44,X25,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X44),X44,X3) = X25 ),
file('<stdin>',cls_add__diff__cancel_0) ).
fof(c_0_340_341,axiom,
! [X24,X7] :
( c_HOL_Oord__class_Oless(X24,X24,tc_nat)
| hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X24)),X7),X24) = X7 ),
file('<stdin>',cls_subst__Var_1) ).
fof(c_0_341_342,axiom,
! [X22,X34] :
( hBOOL(hAPP(X34,X22))
| ~ hBOOL(hAPP(X34,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X34)))
| ~ hBOOL(hAPP(X34,c_HOL_Ozero__class_Ozero(tc_nat))) ),
file('<stdin>',cls_infinite__descent0_1) ).
fof(c_0_342_343,axiom,
! [X44,X25,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X44,X25,X3)
| X25 = X44
| ~ c_lessequals(X44,X25,X3) ),
file('<stdin>',cls_xt1_I11_J_0) ).
fof(c_0_343_344,axiom,
! [X44,X25,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X44,X25,X3)
| ~ c_lessequals(X44,X25,X3)
| X25 = X44 ),
file('<stdin>',cls_xt1_I12_J_0) ).
fof(c_0_344_345,axiom,
! [X28,X24,X3] :
( ~ class_Orderings_Oorder(X3)
| X24 = X28
| c_HOL_Oord__class_Oless(X24,X28,X3)
| ~ c_lessequals(X24,X28,X3) ),
file('<stdin>',cls_order__le__less_0) ).
fof(c_0_345_346,axiom,
! [X28,X24,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X24,X28,X3)
| X24 = X28
| ~ c_lessequals(X24,X28,X3) ),
file('<stdin>',cls_order__less__le_2) ).
fof(c_0_346_347,axiom,
! [X44,X25,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X25,X44,X3)
| X25 = X44
| ~ c_lessequals(X25,X44,X3) ),
file('<stdin>',cls_order__le__neq__trans_0) ).
fof(c_0_347_348,axiom,
! [X44,X25,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X25,X44,X3)
| ~ c_lessequals(X25,X44,X3)
| X25 = X44 ),
file('<stdin>',cls_order__neq__le__trans_0) ).
fof(c_0_348_349,axiom,
! [X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| X24 = X28
| ~ c_lessequals(X24,X28,X3)
| c_HOL_Oord__class_Oless(X24,X28,X3) ),
file('<stdin>',cls_linorder__antisym__conv1_0) ).
fof(c_0_349_350,axiom,
! [X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| X24 = X28
| c_HOL_Oord__class_Oless(X24,X28,X3)
| ~ c_lessequals(X24,X28,X3) ),
file('<stdin>',cls_linorder__antisym__conv2_0) ).
fof(c_0_350_351,axiom,
! [X22,X34] :
( hBOOL(hAPP(X34,X22))
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X34),tc_nat)
| ~ hBOOL(hAPP(X34,c_HOL_Ozero__class_Ozero(tc_nat))) ),
file('<stdin>',cls_infinite__descent0_0) ).
fof(c_0_351_352,axiom,
! [X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Orderings_Oord__class_Omax(X24,X28,X3) != X28
| c_lessequals(X24,X28,X3) ),
file('<stdin>',cls_min__max_Ole__iff__sup_1) ).
fof(c_0_352_353,axiom,
! [X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Orderings_Oord__class_Omax(X24,X28,X3) = X24
| ~ c_lessequals(X28,X24,X3) ),
file('<stdin>',cls_min__max_Osup__absorb1_0) ).
fof(c_0_353_354,axiom,
! [X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Orderings_Oord__class_Omax(X24,X28,X3) = X28
| ~ c_lessequals(X24,X28,X3) ),
file('<stdin>',cls_min__max_Ole__iff__sup_0) ).
fof(c_0_354_355,axiom,
! [X22,X59,X15] :
( c_Lambda_Oliftn(X22,c_Lambda_OdB_OVar(X15),X59) = c_Lambda_OdB_OVar(X15)
| ~ c_HOL_Oord__class_Oless(X15,X59,tc_nat) ),
file('<stdin>',cls_liftn_Osimps_I1_J_0) ).
fof(c_0_355_356,axiom,
! [X28,X24,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X24,X28,X3)
| ~ c_HOL_Oord__class_Oless(X24,X28,X3) ),
file('<stdin>',cls_order__le__less_1) ).
fof(c_0_356_357,axiom,
! [X28,X24,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X24,X28,X3)
| ~ c_HOL_Oord__class_Oless(X24,X28,X3) ),
file('<stdin>',cls_order__less__imp__le_0) ).
fof(c_0_357_358,axiom,
! [X58,X28,X24] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X28) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X58)
| X28 = X58 ),
file('<stdin>',cls_natgb_Oadd__cancel_0) ).
fof(c_0_358_359,axiom,
! [X22,X20,X59] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X59) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X59)
| X20 = X22 ),
file('<stdin>',cls_nat__add__right__cancel_0) ).
fof(c_0_359_360,axiom,
! [X22,X20,X59] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X59),X20) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X59),X22)
| X20 = X22 ),
file('<stdin>',cls_nat__add__left__cancel_0) ).
fof(c_0_360_361,axiom,
! [X20,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X20,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_of__nat__less__0__iff_0) ).
fof(c_0_361_362,axiom,
! [X22,X20] :
( c_HOL_Ominus__class_Ominus(X20,X22,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_lessequals(X20,X22,tc_nat) ),
file('<stdin>',cls_diff__is__0__eq_0) ).
fof(c_0_362_363,axiom,
! [X22,X20] :
( c_HOL_Ominus__class_Ominus(X20,X22,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(X20,X22,tc_nat) ),
file('<stdin>',cls_diff__is__0__eq_1) ).
fof(c_0_363_364,axiom,
! [X22,X20] :
( c_HOL_Oord__class_Oless(X20,X22,tc_nat)
| X20 = X22
| ~ c_lessequals(X20,X22,tc_nat) ),
file('<stdin>',cls_nat__less__le_2) ).
fof(c_0_364_365,axiom,
! [X22,X20] :
( X20 = X22
| c_HOL_Oord__class_Oless(X20,X22,tc_nat)
| ~ c_lessequals(X20,X22,tc_nat) ),
file('<stdin>',cls_le__eq__less__or__eq_0) ).
fof(c_0_365_366,axiom,
! [X22,X20] :
( c_HOL_Oord__class_Oless(X20,X22,tc_nat)
| X20 = X22
| ~ c_lessequals(X20,X22,tc_nat) ),
file('<stdin>',cls_le__neq__implies__less_0) ).
fof(c_0_366_367,axiom,
! [X28,X24] :
( c_lessequals(X24,X28,tc_nat)
| ~ c_HOL_Oord__class_Oless(X24,X28,tc_nat) ),
file('<stdin>',cls_termination__basic__simps_I5_J_0) ).
fof(c_0_367_368,axiom,
! [X22,X20] :
( c_lessequals(X20,X22,tc_nat)
| ~ c_HOL_Oord__class_Oless(X20,X22,tc_nat) ),
file('<stdin>',cls_nat__less__le_0) ).
fof(c_0_368_369,axiom,
! [X59,X15] :
( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X15)),X59) = c_Lambda_OdB_OVar(X15)
| ~ c_HOL_Oord__class_Oless(X15,X59,tc_nat) ),
file('<stdin>',cls_lift_Osimps_I1_J_0) ).
fof(c_0_369_370,axiom,
! [X43,X34] :
( hBOOL(hAPP(X34,X43))
| hBOOL(hAPP(X34,v_sko__Nat__Xnat__Xinducts__1(X34)))
| ~ hBOOL(hAPP(X34,c_HOL_Ozero__class_Ozero(tc_nat))) ),
file('<stdin>',cls_nat_Oinducts_0) ).
fof(c_0_370_371,axiom,
! [X43,X34] :
( hBOOL(hAPP(X34,X43))
| hBOOL(hAPP(X34,v_sko__Nat__Xnat__Xinduct__1(X34)))
| ~ hBOOL(hAPP(X34,c_HOL_Ozero__class_Ozero(tc_nat))) ),
file('<stdin>',cls_nat_Oinduct_0) ).
fof(c_0_371_372,axiom,
! [X43,X34] :
( hBOOL(hAPP(X34,X43))
| hBOOL(hAPP(X34,v_sko__List__Xupt__Xinduct__1(X34)))
| ~ hBOOL(hAPP(X34,c_HOL_Ozero__class_Ozero(tc_nat))) ),
file('<stdin>',cls_upt_Oinduct_0) ).
fof(c_0_372_373,axiom,
! [X26,X27,X25,X3] :
( hAPP(hAPP(X27,X25),X26) = X25
| ~ c_OrderedGroup_Omonoid__add(X26,X27,X3) ),
file('<stdin>',cls_monoid__add_Oadd__0__right_0) ).
fof(c_0_373_374,axiom,
! [X26,X27,X25,X3] :
( hAPP(hAPP(X27,X26),X25) = X25
| ~ c_OrderedGroup_Omonoid__add(X26,X27,X3) ),
file('<stdin>',cls_monoid__add_Oadd__0__left_0) ).
fof(c_0_374_375,axiom,
! [X22,X25,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)
| c_Power_Opower__class_Opower(X25,X22,X3) != c_HOL_Ozero__class_Ozero(X3)
| X25 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_power__eq__0__iff_0) ).
fof(c_0_375_376,axiom,
! [X25,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)
| c_Power_Opower__class_Opower(X25,c_HOL_Ozero__class_Ozero(tc_nat),X3) != c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_power__eq__0__iff_1) ).
fof(c_0_376_377,axiom,
! [X7,X59,X15] :
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X15),X7,X59) = c_Lambda_OdB_OVar(X15)
| X15 = X59
| c_HOL_Oord__class_Oless(X59,X15,tc_nat) ),
file('<stdin>',cls_substn_Osimps_I1_J_2) ).
fof(c_0_377_378,axiom,
! [X28,X24,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X28,X24,X3)
| c_HOL_Oord__class_Oless(X24,X28,X3)
| X24 = X28 ),
file('<stdin>',cls_linorder__neqE__ordered__idom_0) ).
fof(c_0_378_379,axiom,
! [X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| X24 = X28
| c_HOL_Oord__class_Oless(X28,X24,X3)
| c_HOL_Oord__class_Oless(X24,X28,X3) ),
file('<stdin>',cls_not__less__iff__gr__or__eq_0) ).
fof(c_0_379_380,axiom,
! [X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X28,X24,X3)
| c_HOL_Oord__class_Oless(X24,X28,X3)
| X24 = X28 ),
file('<stdin>',cls_linorder__neqE_0) ).
fof(c_0_380_381,axiom,
! [X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X28,X24,X3)
| X24 = X28
| c_HOL_Oord__class_Oless(X24,X28,X3) ),
file('<stdin>',cls_linorder__less__linear_0) ).
fof(c_0_381_382,axiom,
! [X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| X24 = X28
| c_HOL_Oord__class_Oless(X24,X28,X3)
| c_HOL_Oord__class_Oless(X28,X24,X3) ),
file('<stdin>',cls_linorder__antisym__conv3_0) ).
fof(c_0_382_383,axiom,
! [X9,X10,X11,X12] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X12),X10) != hAPP(hAPP(c_Lambda_OdB_OApp,X11),X9)
| X12 = X11 ),
file('<stdin>',cls_dB_Osimps_I2_J_0) ).
fof(c_0_383_384,axiom,
! [X9,X10,X11,X12] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X12),X10) != hAPP(hAPP(c_Lambda_OdB_OApp,X11),X9)
| X10 = X9 ),
file('<stdin>',cls_dB_Osimps_I2_J_1) ).
fof(c_0_384_385,axiom,
! [X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X24,X28,X3)
| c_lessequals(X28,X24,X3) ),
file('<stdin>',cls_not__leE_0) ).
fof(c_0_385_386,axiom,
! [X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X24,X24,X3)
| c_lessequals(X24,X24,X3) ),
file('<stdin>',cls_linorder__antisym__conv1_1) ).
fof(c_0_386_387,axiom,
! [X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X28,X24,X3)
| c_HOL_Oord__class_Oless(X24,X28,X3) ),
file('<stdin>',cls_linorder__not__less_0) ).
fof(c_0_387_388,axiom,
! [X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X28,X24,X3)
| c_lessequals(X24,X28,X3) ),
file('<stdin>',cls_linorder__not__le_0) ).
fof(c_0_388_389,axiom,
! [X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X28,X24,X3)
| c_lessequals(X24,X28,X3) ),
file('<stdin>',cls_linorder__linear_0) ).
fof(c_0_389_390,axiom,
! [X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Orderings_Oord__class_Omax(X24,X28,X3) = c_Orderings_Oord__class_Omax(X28,X24,X3) ),
file('<stdin>',cls_min__max_Osup__commute_0) ).
fof(c_0_390_391,axiom,
! [X45,X25,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X25) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I24_J_0) ).
fof(c_0_391_392,axiom,
! [X44,X25,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X44) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X44),X25) ),
file('<stdin>',cls_comm__monoid__add_Omult__commute_0) ).
fof(c_0_392_393,axiom,
! [X28,X24,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X28) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X28),X24) ),
file('<stdin>',cls_class__semiring_Oadd__c_0) ).
fof(c_0_393_394,axiom,
! [X15,X16,X30] :
( hAPP(X16,X15) = X30
| ~ c_Type_Otyping(X16,c_Lambda_OdB_OVar(X15),X30) ),
file('<stdin>',cls_typing__elims_I1_J_0) ).
fof(c_0_394_395,axiom,
! [X22,X20] :
( c_HOL_Oord__class_Oless(X22,X20,tc_nat)
| c_HOL_Oord__class_Oless(X20,X22,tc_nat)
| X20 = X22 ),
file('<stdin>',cls_nat__neq__iff_0) ).
fof(c_0_395_396,axiom,
! [X28,X24] :
( c_HOL_Oord__class_Oless(X28,X24,tc_nat)
| c_HOL_Oord__class_Oless(X24,X28,tc_nat)
| X24 = X28 ),
file('<stdin>',cls_linorder__neqE__nat_0) ).
fof(c_0_396_397,axiom,
! [X28,X24,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Ominus__class_Ominus(X24,X28,X3) != c_HOL_Ozero__class_Ozero(X3)
| X24 = X28 ),
file('<stdin>',cls_class__ringb_Osubr0__iff_0) ).
fof(c_0_397_398,axiom,
! [X22,X20] :
( c_lessequals(X22,X20,tc_nat)
| c_lessequals(X20,X22,tc_nat) ),
file('<stdin>',cls_nat__le__linear_0) ).
fof(c_0_398_399,axiom,
! [X22,X25,X3] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X3)
| c_Power_Opower__class_Opower(X25,X22,X3) != c_HOL_Ozero__class_Ozero(X3)
| X25 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_field__power__not__zero_0) ).
fof(c_0_399_400,axiom,
! [X24,X25,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| X24 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X25)
| X25 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_class__ringb_Oadd__r0__iff_0) ).
fof(c_0_400_401,axiom,
! [X44,X25,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X25,X44,X3) != c_HOL_Ozero__class_Ozero(X3)
| X25 = X44 ),
file('<stdin>',cls_right__minus__eq_0) ).
fof(c_0_401_402,axiom,
! [X44,X25,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X25,X44,X3) != c_HOL_Ozero__class_Ozero(X3)
| X25 = X44 ),
file('<stdin>',cls_eq__iff__diff__eq__0_1) ).
fof(c_0_402_403,axiom,
! [X25,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X25) != c_HOL_Ozero__class_Ozero(X3)
| X25 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_double__eq__0__iff_0) ).
fof(c_0_403_404,axiom,
! [X46,X37,X3] :
( c_List_Olist_ONil(X3) != c_List_Oappend(X37,X46,X3)
| X37 = c_List_Olist_ONil(X3) ),
file('<stdin>',cls_Nil__is__append__conv_0) ).
fof(c_0_404_405,axiom,
! [X46,X37,X3] :
( c_List_Olist_ONil(X3) != c_List_Oappend(X37,X46,X3)
| X46 = c_List_Olist_ONil(X3) ),
file('<stdin>',cls_Nil__is__append__conv_1) ).
fof(c_0_405_406,axiom,
! [X46,X37,X3] :
( c_List_Oappend(X37,X46,X3) != c_List_Olist_ONil(X3)
| X37 = c_List_Olist_ONil(X3) ),
file('<stdin>',cls_append__is__Nil__conv_0) ).
fof(c_0_406_407,axiom,
! [X46,X37,X3] :
( c_List_Oappend(X37,X46,X3) != c_List_Olist_ONil(X3)
| X46 = c_List_Olist_ONil(X3) ),
file('<stdin>',cls_append__is__Nil__conv_1) ).
fof(c_0_407_408,axiom,
! [X22,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)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X3),X22,X3) = c_HOL_Ozero__class_Ozero(X3)
| X22 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_power__eq__0__iff_2) ).
fof(c_0_408_409,axiom,
! [X24,X22,X3] :
( c_List_Oreplicate(X22,X24,X3) != c_List_Olist_ONil(X3)
| X22 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_replicate__empty_0) ).
fof(c_0_409_410,axiom,
! [X24,X22,X3] :
( c_List_Olist_ONil(X3) != c_List_Oreplicate(X22,X24,X3)
| X22 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_empty__replicate_0) ).
fof(c_0_410_411,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_of__nat__0__le__iff_0) ).
fof(c_0_411_412,axiom,
! [X20,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X20,X3),X3) ),
file('<stdin>',cls_zero__le__imp__of__nat_0) ).
fof(c_0_412_413,axiom,
! [X24,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X24,X24,X3) ),
file('<stdin>',cls_order__less__le_1) ).
fof(c_0_413_414,axiom,
! [X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X24,X24,X3) ),
file('<stdin>',cls_linorder__neq__iff_1) ).
fof(c_0_414_415,axiom,
! [X24,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X24,X24,X3) ),
file('<stdin>',cls_order__less__irrefl_0) ).
fof(c_0_415_416,axiom,
! [X46,X37,X3] :
( c_List_Oappend(X37,X46,X3) != X37
| X46 = c_List_Olist_ONil(X3) ),
file('<stdin>',cls_append__self__conv_0) ).
fof(c_0_416_417,axiom,
! [X46,X37,X3] :
( X37 != c_List_Oappend(X37,X46,X3)
| X46 = c_List_Olist_ONil(X3) ),
file('<stdin>',cls_self__append__conv_0) ).
fof(c_0_417_418,axiom,
! [X46,X37,X3] :
( c_List_Oappend(X37,X46,X3) != X46
| X37 = c_List_Olist_ONil(X3) ),
file('<stdin>',cls_append__self__conv2_0) ).
fof(c_0_418_419,axiom,
! [X46,X37,X3] :
( X46 != c_List_Oappend(X37,X46,X3)
| X37 = c_List_Olist_ONil(X3) ),
file('<stdin>',cls_self__append__conv2_0) ).
fof(c_0_419_420,axiom,
! [X22] :
( X22 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(X22,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
file('<stdin>',cls_le__0__eq_0) ).
fof(c_0_420_421,axiom,
! [X22,X3] :
( ~ class_Ring__and__Field_Osemiring__0(X3)
| ~ class_Power_Opower(X3)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X3),X22,X3) = c_HOL_Ozero__class_Ozero(X3)
| X22 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_power__0__left_1) ).
fof(c_0_421_422,axiom,
! [X8] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X8)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X8)) ),
file('<stdin>',cls_Lambda_0) ).
fof(c_0_422_423,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_423_424,axiom,
! [X22,X20] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X22) != c_HOL_Ozero__class_Ozero(tc_nat)
| X22 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_add__is__0_1) ).
fof(c_0_424_425,axiom,
! [X22,X20] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X22) != c_HOL_Ozero__class_Ozero(tc_nat)
| X20 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_add__is__0_0) ).
fof(c_0_425_426,axiom,
! [X24,X25] :
( X24 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X25)
| X25 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_natgb_Oadd__r0__iff_0) ).
fof(c_0_426_427,axiom,
! [X22,X20] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X22) != X20
| X22 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_add__eq__self__zero_0) ).
fof(c_0_427_428,axiom,
! [X24,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| X24 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),c_HOL_Ozero__class_Ozero(X3)) ),
file('<stdin>',cls_class__ringb_Oadd__r0__iff_1) ).
fof(c_0_428_429,axiom,
! [X24,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Ominus__class_Ominus(X24,X24,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_class__ringb_Osubr0__iff_1) ).
fof(c_0_429_430,axiom,
! [X24,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X24) = X24 ),
file('<stdin>',cls_class__semiring_Oadd__0_0) ).
fof(c_0_430_431,axiom,
! [X25,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X25) = X25 ),
file('<stdin>',cls_comm__monoid__add_Omult__1_0) ).
fof(c_0_431_432,axiom,
! [X25,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X25) = X25 ),
file('<stdin>',cls_add__0__left_0) ).
fof(c_0_432_433,axiom,
! [X25,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X25) = X25 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I5_J_0) ).
fof(c_0_433_434,axiom,
! [X25,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X25,c_HOL_Ozero__class_Ozero(X3),X3) = X25 ),
file('<stdin>',cls_diff__0__right_0) ).
fof(c_0_434_435,axiom,
! [X24,X3] :
( ~ class_Orderings_Obot(X3)
| c_lessequals(c_Orderings_Obot__class_Obot(X3),X24,X3) ),
file('<stdin>',cls_bot__least_0) ).
fof(c_0_435_436,axiom,
! [X25,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),c_HOL_Ozero__class_Ozero(X3)) = X25 ),
file('<stdin>',cls_comm__monoid__add_Omult__1__right_0) ).
fof(c_0_436_437,axiom,
! [X25,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),c_HOL_Ozero__class_Ozero(X3)) = X25 ),
file('<stdin>',cls_monoid__add__class_Oadd__0__right_0) ).
fof(c_0_437_438,axiom,
! [X25,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),c_HOL_Ozero__class_Ozero(X3)) = X25 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(c_0_438_439,axiom,
! [X25,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X25,X25,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_diff__self_0) ).
fof(c_0_439_440,axiom,
! [X24,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X24,X24,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_right__minus__eq_1) ).
fof(c_0_440_441,axiom,
! [X24,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X24,X24,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_eq__iff__diff__eq__0_0) ).
fof(c_0_441_442,axiom,
! [X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Orderings_Oord__class_Omax(X24,X24,X3) = X24 ),
file('<stdin>',cls_min__max_Osup__idem_0) ).
fof(c_0_442_443,axiom,
! [X24,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X24,X24,X3) ),
file('<stdin>',cls_order__eq__iff_0) ).
fof(c_0_443_444,axiom,
! [X24,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X24,X24,X3) ),
file('<stdin>',cls_order__eq__refl_0) ).
fof(c_0_444_445,axiom,
! [X22] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X22,tc_nat)
| X22 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_gr0I_0) ).
fof(c_0_445_446,axiom,
! [X22,X20,X3] :
( ~ class_Nat_Osemiring__char__0(X3)
| c_Nat_Osemiring__1__class_Oof__nat(X20,X3) != c_Nat_Osemiring__1__class_Oof__nat(X22,X3)
| X20 = X22 ),
file('<stdin>',cls_of__nat__eq__iff_0) ).
fof(c_0_446_447,axiom,
! [X4,X5] :
( class_Orderings_Opreorder(tc_fun(X4,X5))
| ~ class_Orderings_Opreorder(X5) ),
file('<stdin>',clsarity_fun__Orderings_Opreorder) ).
fof(c_0_447_448,axiom,
! [X4,X5] :
( class_Orderings_Oorder(tc_fun(X4,X5))
| ~ class_Orderings_Oorder(X5) ),
file('<stdin>',clsarity_fun__Orderings_Oorder) ).
fof(c_0_448_449,axiom,
! [X4,X5] :
( class_Orderings_Obot(tc_fun(X4,X5))
| ~ class_Orderings_Obot(X5) ),
file('<stdin>',clsarity_fun__Orderings_Obot) ).
fof(c_0_449_450,axiom,
! [X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| c_List_Olistsum(c_List_Olist_ONil(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_listsum_Osimps_I1_J_0) ).
fof(c_0_450_451,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_451_452,axiom,
! [X3] :
( ~ class_OrderedGroup_Osemigroup__add(X3)
| c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(X3),X3) ),
file('<stdin>',cls_semigroup__add__class_Oaxioms_0) ).
fof(c_0_452_453,axiom,
! [X70,X61] :
( c_Lambda_OdB_OAbs(X61) != c_Lambda_OdB_OAbs(X70)
| X61 = X70 ),
file('<stdin>',cls_dB_Osimps_I3_J_0) ).
fof(c_0_453_454,axiom,
! [X51,X43] :
( c_Lambda_OdB_OVar(X43) != c_Lambda_OdB_OVar(X51)
| X43 = X51 ),
file('<stdin>',cls_dB_Osimps_I1_J_0) ).
fof(c_0_454_455,plain,
! [X14,X15,X16,X17] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),X14),X15)))
| ~ c_Type_Otyping(X16,X14,v_T____)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X14))
| ~ c_Type_Otyping(c_Type_Oshift(X16,X15,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X17) ),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_455_456,plain,
! [X13,X21,X8] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X8,X21,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X8,X13,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X21,X13,tc_Lambda_OdB) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_456_457,plain,
! [X13,X7,X8] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X8,X13,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X13,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X8),X7)) ),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_457_458,plain,
! [X13,X7,X8] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X8,X13,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X13,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X8),X7)) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_458_459,plain,
! [X13,X7,X8] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X8)),X7),X13,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X7))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X8),X7),c_HOL_Ozero__class_Ozero(tc_nat)),X13,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_459_460,plain,
! [X64,X65,X38,X39,X40,X41,X66,X67,X42,X3] :
( hAPP(hAPP(X41,hAPP(hAPP(X41,X67),X66)),hAPP(hAPP(X41,X65),X64)) = hAPP(hAPP(X41,X65),hAPP(hAPP(X41,hAPP(hAPP(X41,X67),X66)),X64))
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_460_461,plain,
! [X38,X39,X40,X41,X57,X45,X44,X42,X25,X3] :
( hAPP(hAPP(X42,hAPP(hAPP(X42,X25),X44)),hAPP(hAPP(X42,X45),X57)) = hAPP(hAPP(X42,hAPP(hAPP(X42,X25),X45)),hAPP(hAPP(X42,X44),X57))
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_461_462,plain,
! [X64,X65,X38,X39,X40,X41,X66,X67,X42,X3] :
( hAPP(hAPP(X41,hAPP(hAPP(X41,X67),X66)),hAPP(hAPP(X41,X65),X64)) = hAPP(hAPP(X41,X67),hAPP(hAPP(X41,X66),hAPP(hAPP(X41,X65),X64)))
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_462_463,plain,
! [X64,X65,X38,X39,X40,X41,X66,X67,X42,X3] :
( hAPP(hAPP(X41,hAPP(hAPP(X41,X67),X66)),hAPP(hAPP(X41,X65),X64)) = hAPP(hAPP(X41,hAPP(hAPP(X41,X67),X65)),hAPP(hAPP(X41,X66),X64))
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_463_464,plain,
! [X28,X24,X38,X39,X71,X40,X41,X42,X3] :
( hAPP(hAPP(X40,hAPP(hAPP(X41,X24),X28)),X71) = hAPP(hAPP(X41,hAPP(hAPP(X40,X24),X71)),hAPP(hAPP(X40,X28),X71))
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_464_465,plain,
! [X38,X39,X40,X41,X45,X44,X42,X25,X3] :
( hAPP(hAPP(X41,hAPP(hAPP(X42,X25),X44)),X45) = hAPP(hAPP(X42,hAPP(hAPP(X41,X25),X45)),hAPP(hAPP(X41,X44),X45))
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_465_466,plain,
! [X38,X39,X40,X41,X20,X44,X42,X25,X3] :
( hAPP(hAPP(X42,hAPP(hAPP(X41,X25),X20)),hAPP(hAPP(X41,X44),X20)) = hAPP(hAPP(X41,hAPP(hAPP(X42,X25),X44)),X20)
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_466_467,plain,
! [X24,X38,X39,X71,X40,X74,X41,X42,X3] :
( hAPP(hAPP(X41,hAPP(hAPP(X40,X24),X74)),hAPP(hAPP(X40,X24),X71)) = hAPP(hAPP(X40,X24),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X74),X71))
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_467_468,plain,
! [X58,X28,X24,X38,X39,X40,X41,X42,X3] :
( hAPP(hAPP(X41,X24),hAPP(hAPP(X42,X28),X58)) = hAPP(hAPP(X42,hAPP(hAPP(X41,X24),X28)),hAPP(hAPP(X41,X24),X58))
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_468_469,plain,
! [X38,X39,X40,X41,X45,X44,X42,X25,X3] :
( hAPP(hAPP(X42,hAPP(hAPP(X42,X25),X44)),X45) = hAPP(hAPP(X42,hAPP(hAPP(X42,X25),X45)),X44)
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_469_470,plain,
! [X65,X38,X39,X40,X41,X66,X67,X42,X3] :
( hAPP(hAPP(X41,hAPP(hAPP(X41,X67),X66)),X65) = hAPP(hAPP(X41,hAPP(hAPP(X41,X67),X65)),X66)
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_470_471,plain,
! [X38,X39,X40,X41,X20,X42,X25,X3] :
( hAPP(hAPP(X42,hAPP(hAPP(X41,X25),X20)),X20) = hAPP(hAPP(X41,hAPP(hAPP(X42,X25),X38)),X20)
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_471_472,plain,
! [X58,X28,X24,X38,X39,X40,X41,X42,X3] :
( hAPP(hAPP(X41,X24),hAPP(hAPP(X41,X28),X58)) = hAPP(hAPP(X41,hAPP(hAPP(X41,X24),X28)),X58)
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_472_473,plain,
! [X58,X28,X24,X38,X39,X40,X41,X42,X3] :
( hAPP(hAPP(X42,X24),hAPP(hAPP(X42,X28),X58)) = hAPP(hAPP(X42,hAPP(hAPP(X42,X24),X28)),X58)
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_473_474,plain,
! [X38,X39,X40,X41,X57,X45,X42,X25,X3] :
( hAPP(hAPP(X42,X25),hAPP(hAPP(X42,X45),X57)) = hAPP(hAPP(X42,hAPP(hAPP(X42,X25),X45)),X57)
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_474_475,plain,
! [X38,X39,X40,X41,X45,X44,X42,X25,X3] :
( hAPP(hAPP(X42,hAPP(hAPP(X42,X25),X44)),X45) = hAPP(hAPP(X42,X25),hAPP(hAPP(X42,X44),X45))
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
fof(c_0_475_476,plain,
! [X64,X65,X38,X39,X40,X41,X67,X42,X3] :
( hAPP(hAPP(X41,X67),hAPP(hAPP(X41,X65),X64)) = hAPP(hAPP(X41,hAPP(hAPP(X41,X67),X65)),X64)
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_476_477,plain,
! [X65,X38,X39,X40,X41,X66,X67,X42,X3] :
( hAPP(hAPP(X41,hAPP(hAPP(X41,X67),X66)),X65) = hAPP(hAPP(X41,X67),hAPP(hAPP(X41,X66),X65))
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_477_478,plain,
! [X38,X39,X40,X41,X20,X42,X25,X3] :
( hAPP(hAPP(X42,X20),hAPP(hAPP(X41,X25),X20)) = hAPP(hAPP(X41,hAPP(hAPP(X42,X25),X38)),X20)
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
inference(fof_simplification,[status(thm)],[c_0_23]) ).
fof(c_0_478_479,plain,
! [X38,X39,X40,X41,X57,X45,X42,X25,X3] :
( hAPP(hAPP(X42,X25),hAPP(hAPP(X42,X45),X57)) = hAPP(hAPP(X42,X45),hAPP(hAPP(X42,X25),X57))
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_479_480,plain,
! [X64,X65,X38,X39,X40,X41,X67,X42,X3] :
( hAPP(hAPP(X41,X67),hAPP(hAPP(X41,X65),X64)) = hAPP(hAPP(X41,X65),hAPP(hAPP(X41,X67),X64))
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_480_481,plain,
! [X38,X39,X40,X41,X20,X42,X3] :
( hAPP(hAPP(X42,X20),X20) = hAPP(hAPP(X41,hAPP(hAPP(X42,X38),X38)),X20)
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_481_482,plain,
! [X28,X24,X38,X39,X40,X41,X42,X3] :
( hAPP(hAPP(X41,X24),X28) = hAPP(hAPP(X41,X28),X24)
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
inference(fof_simplification,[status(thm)],[c_0_27]) ).
fof(c_0_482_483,plain,
! [X28,X24,X38,X39,X40,X41,X42,X3] :
( hAPP(hAPP(X42,X24),X28) = hAPP(hAPP(X42,X28),X24)
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
inference(fof_simplification,[status(thm)],[c_0_28]) ).
fof(c_0_483_484,plain,
! [X38,X39,X40,X41,X45,X42,X25,X3] :
( hAPP(hAPP(X42,X25),X45) = hAPP(hAPP(X42,X45),X25)
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
inference(fof_simplification,[status(thm)],[c_0_29]) ).
fof(c_0_484_485,plain,
! [X38,X39,X40,X41,X44,X42,X25,X3] :
( hAPP(hAPP(X41,X25),X44) = hAPP(hAPP(X41,X44),X25)
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
inference(fof_simplification,[status(thm)],[c_0_30]) ).
fof(c_0_485_486,plain,
! [X24,X38,X39,X40,X41,X42,X3] :
( hAPP(hAPP(X40,X24),c_HOL_Ozero__class_Ozero(tc_nat)) = X38
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_486_487,plain,
! [X24,X38,X39,X40,X41,X42,X3] :
( hAPP(hAPP(X41,X38),X24) = X24
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
inference(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_487_488,plain,
! [X24,X38,X39,X40,X41,X42,X3] :
( hAPP(hAPP(X41,X39),X24) = X39
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_488_489,plain,
! [X24,X38,X39,X40,X41,X42,X3] :
( hAPP(hAPP(X42,X39),X24) = X24
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
inference(fof_simplification,[status(thm)],[c_0_34]) ).
fof(c_0_489_490,plain,
! [X38,X39,X40,X41,X42,X25,X3] :
( hAPP(hAPP(X41,X25),X38) = X25
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_490_491,plain,
! [X38,X39,X40,X41,X42,X25,X3] :
( hAPP(hAPP(X41,X38),X25) = X25
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
inference(fof_simplification,[status(thm)],[c_0_36]) ).
fof(c_0_491_492,plain,
! [X38,X39,X40,X41,X42,X25,X3] :
( hAPP(hAPP(X41,X25),X39) = X39
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
inference(fof_simplification,[status(thm)],[c_0_37]) ).
fof(c_0_492_493,plain,
! [X38,X39,X40,X41,X42,X25,X3] :
( hAPP(hAPP(X41,X39),X25) = X39
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
inference(fof_simplification,[status(thm)],[c_0_38]) ).
fof(c_0_493_494,plain,
! [X38,X39,X40,X41,X42,X25,X3] :
( hAPP(hAPP(X42,X25),X39) = X25
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
inference(fof_simplification,[status(thm)],[c_0_39]) ).
fof(c_0_494_495,plain,
! [X38,X39,X40,X41,X42,X25,X3] :
( hAPP(hAPP(X42,X39),X25) = X25
| ~ c_Groebner__Basis_Ogb__semiring(X42,X41,X40,X39,X38,X3) ),
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_495_496,plain,
! [X35,X36,X31,X32,X33,X34] :
( ~ hBOOL(hAPP(X34,c_Lambda_OdB_OdB__case(X33,X32,X31,hAPP(hAPP(c_Lambda_OdB_OApp,X36),X35),t_a)))
| hBOOL(hAPP(X34,hAPP(hAPP(X32,X36),X35))) ),
inference(fof_simplification,[status(thm)],[c_0_41]) ).
fof(c_0_496_497,plain,
! [X31,X32,X33,X10,X12,X34] :
( ~ hBOOL(hAPP(X34,c_Lambda_OdB_OdB__case(X33,X32,X31,hAPP(hAPP(c_Lambda_OdB_OApp,X12),X10),t_a)))
| hBOOL(hAPP(X34,hAPP(hAPP(X32,X12),X10))) ),
inference(fof_simplification,[status(thm)],[c_0_42]) ).
fof(c_0_497_498,plain,
! [X6,X15,X16,X29,X30] :
( X30 = X29
| ~ c_Type_Otyping(X16,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X15),X6,tc_Lambda_OdB,tc_Lambda_OdB),X29)
| ~ c_Type_Otyping(X16,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X15),X6,tc_Lambda_OdB,tc_Lambda_OdB),X30) ),
inference(fof_simplification,[status(thm)],[c_0_43]) ).
fof(c_0_498_499,plain,
! [X31,X32,X33,X61,X34] :
( ~ hBOOL(hAPP(X34,c_Lambda_OdB_OdB__case(X33,X32,X31,c_Lambda_OdB_OAbs(X61),t_a)))
| hBOOL(hAPP(X34,hAPP(X31,X61))) ),
inference(fof_simplification,[status(thm)],[c_0_44]) ).
fof(c_0_499_500,plain,
! [X60,X31,X32,X33,X34] :
( ~ hBOOL(hAPP(X34,c_Lambda_OdB_OdB__case(X33,X32,X31,c_Lambda_OdB_OAbs(X60),t_a)))
| hBOOL(hAPP(X34,hAPP(X31,X60))) ),
inference(fof_simplification,[status(thm)],[c_0_45]) ).
fof(c_0_500_501,plain,
! [X43,X31,X32,X33,X34] :
( ~ hBOOL(hAPP(X34,c_Lambda_OdB_OdB__case(X33,X32,X31,c_Lambda_OdB_OVar(X43),t_a)))
| hBOOL(hAPP(X34,hAPP(X33,X43))) ),
inference(fof_simplification,[status(thm)],[c_0_46]) ).
fof(c_0_501_502,plain,
! [X52,X31,X32,X33,X34] :
( ~ hBOOL(hAPP(X34,c_Lambda_OdB_OdB__case(X33,X32,X31,c_Lambda_OdB_OVar(X52),t_a)))
| hBOOL(hAPP(X34,hAPP(X33,X52))) ),
inference(fof_simplification,[status(thm)],[c_0_47]) ).
fof(c_0_502_503,plain,
! [X13,X7,X8] :
( ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X8),X7),c_HOL_Ozero__class_Ozero(tc_nat)),X13,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X7,tc_Lambda_OdB)
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X8)),X7),X13,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(fof_simplification,[status(thm)],[c_0_48]) ).
fof(c_0_503_504,plain,
! [X6] :
( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X6,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_List_Olistsp(c_InductTermi_OIT,X6,tc_Lambda_OdB) ),
inference(fof_simplification,[status(thm)],[c_0_49]) ).
fof(c_0_504_505,plain,
! [X21,X22] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X22),X21,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_List_Olistsp(c_InductTermi_OIT,X21,tc_Lambda_OdB) ),
inference(fof_simplification,[status(thm)],[c_0_50]) ).
fof(c_0_505_506,axiom,
! [X13,X21,X22,X20] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X20),X21,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X22),X13,tc_Lambda_OdB,tc_Lambda_OdB)
| X20 = X22 ),
c_0_51 ).
fof(c_0_506_507,axiom,
! [X13,X21,X22,X20] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X20),X21,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X22),X13,tc_Lambda_OdB,tc_Lambda_OdB)
| X21 = X13 ),
c_0_52 ).
fof(c_0_507_508,axiom,
! [X13,X7,X21,X8] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X8),X21,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X7),X13,tc_Lambda_OdB,tc_Lambda_OdB)
| X8 = X7 ),
c_0_53 ).
fof(c_0_508_509,axiom,
! [X13,X7,X21,X8] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X8),X21,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X7),X13,tc_Lambda_OdB,tc_Lambda_OdB)
| X21 = X13 ),
c_0_54 ).
fof(c_0_509_510,plain,
! [X23,X28,X24,X3] :
( ~ class_OrderedGroup_Osemigroup__add(X3)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X28),X23,X3,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X28,X23,X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_55]) ).
fof(c_0_510_511,axiom,
! [X6,X7,X8] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X8,X6,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X6,tc_Lambda_OdB,tc_Lambda_OdB)
| X8 = X7 ),
c_0_56 ).
fof(c_0_511_512,plain,
! [X23,X28,X24,X27,X3] :
( c_List_Ofoldl(X27,hAPP(hAPP(X27,X24),X28),X23,X3,X3) = hAPP(hAPP(X27,X24),c_List_Ofoldl(X27,X28,X23,X3,X3))
| ~ c_OrderedGroup_Osemigroup__add(X27,X3) ),
inference(fof_simplification,[status(thm)],[c_0_57]) ).
fof(c_0_512_513,plain,
! [X23,X26,X24,X27,X3] :
( hAPP(hAPP(X27,X24),c_List_Ofoldl(X27,X26,X23,X3,X3)) = c_List_Ofoldl(X27,X24,X23,X3,X3)
| ~ c_OrderedGroup_Omonoid__add(X26,X27,X3) ),
inference(fof_simplification,[status(thm)],[c_0_58]) ).
fof(c_0_513_514,plain,
! [X37,X25,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X25,X37,X3,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X3),X37,c_HOL_Ozero__class_Ozero(X3),X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_59]) ).
fof(c_0_514_515,plain,
! [X23,X24,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3),X23,X3,X3)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X24,X23,X3,X3) ),
inference(fof_simplification,[status(thm)],[c_0_60]) ).
fof(c_0_515_516,axiom,
! [X6,X19,X7,X8] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X8),X7) != c_List_Ofoldl(c_Lambda_OdB_OApp,X19,X6,tc_Lambda_OdB,tc_Lambda_OdB)
| X8 = c_List_Ofoldl(c_Lambda_OdB_OApp,X19,c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X8,X7,X19,X6),tc_Lambda_OdB,tc_Lambda_OdB)
| X6 = c_List_Olist_ONil(tc_Lambda_OdB) ),
c_0_61 ).
fof(c_0_516_517,plain,
! [X37,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3),X37,X3,X3) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X3),X37,c_HOL_Ozero__class_Ozero(X3),X3,X3) ),
inference(fof_simplification,[status(thm)],[c_0_62]) ).
fof(c_0_517_518,plain,
! [X37,X25,X3] :
( ~ class_OrderedGroup_Oab__semigroup__add(X3)
| c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X3),X37,X25,X3,X3) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X25,X37,X3,X3) ),
inference(fof_simplification,[status(thm)],[c_0_63]) ).
fof(c_0_518_519,axiom,
! [X19,X7,X8] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X8),X7) != c_List_Ofoldl(c_Lambda_OdB_OApp,X19,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,X8),X7) = X19 ),
c_0_64 ).
fof(c_0_519_520,axiom,
! [X13,X7,X8] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X13,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X8)
| X7 = c_Lambda_OdB_OAbs(X8) ),
c_0_65 ).
fof(c_0_520_521,axiom,
! [X13,X7,X20] :
( c_Lambda_OdB_OVar(X20) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X13,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OVar(X20) = X7 ),
c_0_66 ).
fof(c_0_521_522,axiom,
! [X13,X7,X8] :
( c_Lambda_OdB_OAbs(X8) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X13,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(X8) = X7 ),
c_0_67 ).
fof(c_0_522_523,axiom,
! [X13,X7,X8] :
( c_Lambda_OdB_OAbs(X8) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X13,tc_Lambda_OdB,tc_Lambda_OdB)
| X13 = c_List_Olist_ONil(tc_Lambda_OdB) ),
c_0_68 ).
fof(c_0_523_524,axiom,
! [X13,X7,X8] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X13,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X8)
| X13 = c_List_Olist_ONil(tc_Lambda_OdB) ),
c_0_69 ).
fof(c_0_524_525,axiom,
! [X13,X7,X20] :
( c_Lambda_OdB_OVar(X20) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X13,tc_Lambda_OdB,tc_Lambda_OdB)
| X13 = c_List_Olist_ONil(tc_Lambda_OdB) ),
c_0_70 ).
fof(c_0_525_526,plain,
! [X28,X24,X8,X3] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X28),X24))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X8,X3,X3),X3),X24),X28)) ),
inference(fof_simplification,[status(thm)],[c_0_71]) ).
fof(c_0_526_527,plain,
! [X46,X28,X37,X24,X8,X3] :
( hBOOL(hAPP(hAPP(X8,X28),X24))
| c_ListOrder_Ostep1(X8,X46,X37,X3)
| ~ c_ListOrder_Ostep1(X8,c_List_Oappend(X46,c_List_Olist_OCons(X28,c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X37,c_List_Olist_OCons(X24,c_List_Olist_ONil(X3),X3),X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_72]) ).
fof(c_0_527_528,plain,
! [X46,X28,X37,X24,X8,X3] :
( X46 = X37
| c_ListOrder_Ostep1(X8,X46,X37,X3)
| ~ c_ListOrder_Ostep1(X8,c_List_Oappend(X46,c_List_Olist_OCons(X28,c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X37,c_List_Olist_OCons(X24,c_List_Olist_ONil(X3),X3),X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_73]) ).
fof(c_0_528_529,plain,
! [X32,X33,X34] :
( ~ hBOOL(hAPP(X34,c_Nat_Onat_Onat__case(X33,X32,c_HOL_Ozero__class_Ozero(tc_nat),t_a)))
| hBOOL(hAPP(X34,X33)) ),
inference(fof_simplification,[status(thm)],[c_0_74]) ).
fof(c_0_529_530,plain,
! [X46,X28,X37,X24,X8,X3] :
( hBOOL(hAPP(hAPP(X8,X28),X24))
| X28 = X24
| ~ c_ListOrder_Ostep1(X8,c_List_Oappend(X46,c_List_Olist_OCons(X28,c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X37,c_List_Olist_OCons(X24,c_List_Olist_ONil(X3),X3),X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_75]) ).
fof(c_0_530_531,plain,
! [X46,X28,X37,X24,X8,X3] :
( X46 = X37
| X28 = X24
| ~ c_ListOrder_Ostep1(X8,c_List_Oappend(X46,c_List_Olist_OCons(X28,c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X37,c_List_Olist_OCons(X24,c_List_Olist_ONil(X3),X3),X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_76]) ).
fof(c_0_531_532,plain,
! [X19,X7,X8,X15] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X8),X19),X15)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X7),X19),X15)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X8),X7)) ),
inference(fof_simplification,[status(thm)],[c_0_77]) ).
fof(c_0_532_533,plain,
! [X19,X7,X8,X15] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X19),X8),X15)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X19),X7),X15)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X8),X7)) ),
inference(fof_simplification,[status(thm)],[c_0_78]) ).
fof(c_0_533_534,plain,
! [X28,X24,X8,X3] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X8,X3,X3),X3),X24),X28))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X28),X24)) ),
inference(fof_simplification,[status(thm)],[c_0_79]) ).
fof(c_0_534_535,plain,
! [X14,X15,X16,X17] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),X14),X15)))
| ~ c_Type_Otyping(X16,X14,v_T____)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X14))
| ~ c_Type_Otyping(c_Type_Oshift(X16,X15,v_T____,tc_Type_Otype),v_a____,X17) ),
inference(fof_simplification,[status(thm)],[c_0_80]) ).
fof(c_0_535_536,plain,
! [X19,X7,X8,X15] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X19),X8),X15)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X19),X7),X15)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X8),X7)) ),
inference(fof_simplification,[status(thm)],[c_0_81]) ).
fof(c_0_536_537,plain,
! [X37,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| c_List_Olistsum(X37,X3) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X3),X37,c_HOL_Ozero__class_Ozero(X3),X3,X3) ),
inference(fof_simplification,[status(thm)],[c_0_82]) ).
fof(c_0_537_538,plain,
! [X37,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| c_List_Olistsum(X37,X3) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3),X37,X3,X3) ),
inference(fof_simplification,[status(thm)],[c_0_83]) ).
fof(c_0_538_539,plain,
! [X19,X7,X8,X15] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(hAPP(c_Lambda_Osubst,X8),X19),X15)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X7),X19),X15)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X8),X7)) ),
inference(fof_simplification,[status(thm)],[c_0_84]) ).
fof(c_0_539_540,plain,
! [X14,X19,X15,X62,X29,X30] :
( ~ c_Type_Otyping(X62,X14,X29)
| ~ c_Type_Otyping(c_Type_Oshift(X62,X15,X29,tc_Type_Otype),X19,X30)
| c_Type_Otyping(X62,hAPP(hAPP(hAPP(c_Lambda_Osubst,X19),X14),X15),X30) ),
inference(fof_simplification,[status(thm)],[c_0_85]) ).
fof(c_0_540_541,plain,
! [X53,X19,X63,X7] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X7),X19)),hAPP(hAPP(c_Lambda_OdB_OApp,X63),X53)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X19),X53))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X7),X63)) ),
inference(fof_simplification,[status(thm)],[c_0_86]) ).
fof(c_0_541_542,plain,
! [X46,X28,X37,X24,X8,X3] :
( c_ListOrder_Ostep1(X8,X46,X37,X3)
| hBOOL(hAPP(hAPP(X8,X28),X24))
| ~ c_ListOrder_Ostep1(X8,c_List_Olist_OCons(X28,X46,X3),c_List_Olist_OCons(X24,X37,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_87]) ).
fof(c_0_542_543,plain,
! [X46,X28,X37,X24,X8,X3] :
( c_ListOrder_Ostep1(X8,X46,X37,X3)
| X37 = X46
| ~ c_ListOrder_Ostep1(X8,c_List_Olist_OCons(X28,X46,X3),c_List_Olist_OCons(X24,X37,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_88]) ).
fof(c_0_543_544,plain,
! [X57,X44,X34] :
( ~ hBOOL(hAPP(X34,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X44),X57),X44,tc_nat)))
| hBOOL(hAPP(X34,X57)) ),
inference(fof_simplification,[status(thm)],[c_0_89]) ).
fof(c_0_544_545,plain,
! [X24,X44,X34] :
( ~ hBOOL(hAPP(X34,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X44),X24),X44,tc_nat)))
| hBOOL(hAPP(X34,X24)) ),
inference(fof_simplification,[status(thm)],[c_0_90]) ).
fof(c_0_545_546,plain,
! [X8,X72,X73,X48,X3] :
( hBOOL(hAPP(hAPP(X8,X72),X73))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X8,X3,X48),X73),X72)) ),
inference(fof_simplification,[status(thm)],[c_0_91]) ).
fof(c_0_546_547,plain,
! [X8,X44,X25,X48,X3] :
( hBOOL(hAPP(hAPP(X8,X44),X25))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X8,X3,X48),X25),X44)) ),
inference(fof_simplification,[status(thm)],[c_0_92]) ).
fof(c_0_547_548,plain,
! [X46,X37,X24,X8,X3] :
( ~ c_ListOrder_Ostep1(X8,X46,X37,X3)
| c_ListOrder_Ostep1(X8,c_List_Oappend(X46,X24,X3),c_List_Oappend(X37,X24,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_93]) ).
fof(c_0_548_549,plain,
! [X24,X75,X76,X8,X3] :
( c_ListOrder_Ostep1(X8,c_List_Oappend(X24,X75,X3),c_List_Oappend(X24,X76,X3),X3)
| ~ c_ListOrder_Ostep1(X8,X75,X76,X3) ),
inference(fof_simplification,[status(thm)],[c_0_94]) ).
fof(c_0_549_550,plain,
! [X46,X37,X24,X8,X3] :
( c_ListOrder_Ostep1(X8,c_List_Olist_OCons(X24,X46,X3),c_List_Olist_OCons(X24,X37,X3),X3)
| ~ c_ListOrder_Ostep1(X8,X46,X37,X3) ),
inference(fof_simplification,[status(thm)],[c_0_95]) ).
fof(c_0_550_551,plain,
! [X53,X19,X7] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X7),X19)),hAPP(hAPP(c_Lambda_OdB_OApp,X7),X53)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X19),X53)) ),
inference(fof_simplification,[status(thm)],[c_0_96]) ).
fof(c_0_551_552,plain,
! [X19,X63,X7] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X7),X19)),hAPP(hAPP(c_Lambda_OdB_OApp,X63),X19)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X7),X63)) ),
inference(fof_simplification,[status(thm)],[c_0_97]) ).
fof(c_0_552_553,plain,
! [X7,X8,X15] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,X8),X15)),hAPP(hAPP(c_Lambda_Olift,X7),X15)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X8),X7)) ),
inference(fof_simplification,[status(thm)],[c_0_98]) ).
fof(c_0_553_554,plain,
! [X46,X28,X37,X24,X8,X3] :
( X24 = X28
| hBOOL(hAPP(hAPP(X8,X28),X24))
| ~ c_ListOrder_Ostep1(X8,c_List_Olist_OCons(X28,X46,X3),c_List_Olist_OCons(X24,X37,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_99]) ).
fof(c_0_554_555,plain,
! [X58,X28,X24,X8,X3] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X24),X58))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X28),X58))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X24),X28)) ),
inference(fof_simplification,[status(thm)],[c_0_100]) ).
fof(c_0_555_556,plain,
! [X46,X28,X37,X24,X8,X3] :
( X24 = X28
| X37 = X46
| ~ c_ListOrder_Ostep1(X8,c_List_Olist_OCons(X28,X46,X3),c_List_Olist_OCons(X24,X37,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_101]) ).
fof(c_0_556_557,plain,
! [X57,X45,X44,X25,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),X25),X44)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X57)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X44),X57)) ),
inference(fof_simplification,[status(thm)],[c_0_102]) ).
fof(c_0_557_558,plain,
! [X19,X15,X16,X29,X30] :
( c_Type_Otyping(c_Type_Oshift(X16,X15,X29,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X19),X15),X30)
| ~ c_Type_Otyping(X16,X19,X30) ),
inference(fof_simplification,[status(thm)],[c_0_103]) ).
fof(c_0_558_559,plain,
! [X8,X44,X25,X48,X3] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X8,X3,X48),X44),X25))
| ~ hBOOL(hAPP(hAPP(X8,X25),X44)) ),
inference(fof_simplification,[status(thm)],[c_0_104]) ).
fof(c_0_559_560,plain,
! [X8,X44,X25,X48,X3] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X8,X3,X48),X25),X44))
| ~ hBOOL(hAPP(hAPP(X8,X44),X25)) ),
inference(fof_simplification,[status(thm)],[c_0_105]) ).
fof(c_0_560_561,plain,
! [X22,X20,X59] :
( c_lessequals(X20,X22,tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X20,X59,tc_nat),c_HOL_Ominus__class_Ominus(X22,X59,tc_nat),tc_nat)
| ~ c_lessequals(X59,X22,tc_nat)
| ~ c_lessequals(X59,X20,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_106]) ).
fof(c_0_561_562,plain,
! [X22,X20,X59] :
( c_HOL_Oord__class_Oless(X20,X22,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X20,X59,tc_nat),c_HOL_Ominus__class_Ominus(X22,X59,tc_nat),tc_nat)
| ~ c_lessequals(X59,X22,tc_nat)
| ~ c_lessequals(X59,X20,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_107]) ).
fof(c_0_562_563,plain,
! [X7,X8,X15] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,X8),X15)),hAPP(hAPP(c_Lambda_Olift,X7),X15)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X8),X7)) ),
inference(fof_simplification,[status(thm)],[c_0_108]) ).
fof(c_0_563_564,plain,
! [X14,X19,X7] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X14),X7)),hAPP(hAPP(c_Lambda_OdB_OApp,X14),X19)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X7),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_109]) ).
fof(c_0_564_565,plain,
! [X14,X19,X7] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X7),X14)),hAPP(hAPP(c_Lambda_OdB_OApp,X19),X14)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X7),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_110]) ).
fof(c_0_565_566,plain,
! [X8,X45,X44,X25,X3] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X25),X45))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X44),X45))
| ~ hBOOL(hAPP(hAPP(X8,X25),X44)) ),
inference(fof_simplification,[status(thm)],[c_0_111]) ).
fof(c_0_566_567,plain,
! [X8,X45,X44,X25,X3] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X25),X45))
| ~ hBOOL(hAPP(hAPP(X8,X44),X45))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X25),X44)) ),
inference(fof_simplification,[status(thm)],[c_0_112]) ).
fof(c_0_567_568,plain,
! [X18,X15,X16,X30,X3] :
( hAPP(c_Type_Oshift(X16,X15,X30,X3),X18) = hAPP(X16,X18)
| ~ c_HOL_Oord__class_Oless(X18,X15,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_113]) ).
fof(c_0_568_569,plain,
! [X28,X60,X24,X8,X3] :
( ~ hBOOL(hAPP(hAPP(X8,X28),X60))
| c_ListOrder_Ostep1(X8,c_List_Olist_OCons(X28,X24,X3),c_List_Olist_OCons(X60,X24,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_114]) ).
fof(c_0_569_570,plain,
! [X22,X44,X25,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X25,X44,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X44,X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X25,X22,X3),c_Power_Opower__class_Opower(X44,X22,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_115]) ).
fof(c_0_570_571,axiom,
! [X46,X28,X37,X24,X3] :
( c_List_Oappend(X37,c_List_Olist_OCons(X24,c_List_Olist_ONil(X3),X3),X3) != c_List_Oappend(X46,c_List_Olist_OCons(X28,c_List_Olist_ONil(X3),X3),X3)
| X37 = X46 ),
c_0_116 ).
fof(c_0_571_572,axiom,
! [X46,X28,X37,X24,X3] :
( c_List_Oappend(X37,c_List_Olist_OCons(X24,c_List_Olist_ONil(X3),X3),X3) != c_List_Oappend(X46,c_List_Olist_OCons(X28,c_List_Olist_ONil(X3),X3),X3)
| X24 = X28 ),
c_0_117 ).
fof(c_0_572_573,plain,
! [X22,X44,X25,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X25,X22,X3),c_Power_Opower__class_Opower(X44,X22,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X22,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X25,X3)
| ~ c_HOL_Oord__class_Oless(X25,X44,X3) ),
inference(fof_simplification,[status(thm)],[c_0_118]) ).
fof(c_0_573_574,plain,
! [X58,X28,X24,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Orderings_Oord__class_Omax(X24,X28,X3)),X58) = c_Orderings_Oord__class_Omax(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X58),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X28),X58),X3) ),
inference(fof_simplification,[status(thm)],[c_0_119]) ).
fof(c_0_574_575,plain,
! [X45,X44,X25,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),X25),X44)),X45) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45)),X44) ),
inference(fof_simplification,[status(thm)],[c_0_120]) ).
fof(c_0_575_576,plain,
! [X22,X20,X59] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X20,X59,tc_nat),c_HOL_Ominus__class_Ominus(X22,X59,tc_nat),tc_nat)
| ~ c_lessequals(X20,X22,tc_nat)
| ~ c_lessequals(X59,X22,tc_nat)
| ~ c_lessequals(X59,X20,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_121]) ).
fof(c_0_576_577,plain,
! [X22,X20,X59] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X20,X59,tc_nat),c_HOL_Ominus__class_Ominus(X22,X59,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X20,X22,tc_nat)
| ~ c_lessequals(X59,X22,tc_nat)
| ~ c_lessequals(X59,X20,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_122]) ).
fof(c_0_577_578,plain,
! [X57,X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X25,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X44),X57),X3)
| ~ c_lessequals(X45,X57,X3)
| ~ c_lessequals(X25,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X44),X45),X3) ),
inference(fof_simplification,[status(thm)],[c_0_123]) ).
fof(c_0_578_579,plain,
! [X44,X25,X34] :
( hBOOL(hAPP(X34,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X25,X44,tc_nat)
| ~ hBOOL(hAPP(X34,c_HOL_Ominus__class_Ominus(X25,X44,tc_nat))) ),
inference(fof_simplification,[status(thm)],[c_0_124]) ).
fof(c_0_579_580,plain,
! [X22,X20,X59] :
( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X20,X59,tc_nat),c_HOL_Ominus__class_Ominus(X22,X59,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X20,X22,tc_nat)
| ~ c_lessequals(X59,X22,tc_nat)
| ~ c_lessequals(X59,X20,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_125]) ).
fof(c_0_580_581,plain,
! [X59,X18,X15] :
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X15),X59,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X18,X59,tc_nat)),X15)
| ~ c_lessequals(X59,X18,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_126]) ).
fof(c_0_581_582,plain,
! [X59,X18,X15] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X18,X59,tc_nat)),X15) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X15),X59,tc_nat)
| ~ c_lessequals(X59,X18,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_127]) ).
fof(c_0_582_583,plain,
! [X59,X18,X15] :
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X59),X18,tc_nat)
| ~ c_lessequals(X15,c_HOL_Ominus__class_Ominus(X18,X59,tc_nat),tc_nat)
| ~ c_lessequals(X59,X18,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_128]) ).
fof(c_0_583_584,plain,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_lessequals(X25,X44,X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X44),X45),X3) ),
inference(fof_simplification,[status(thm)],[c_0_129]) ).
fof(c_0_584_585,plain,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_lessequals(X25,X44,X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X44),X3) ),
inference(fof_simplification,[status(thm)],[c_0_130]) ).
fof(c_0_585_586,plain,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(X25,X44,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X44),X45),X3) ),
inference(fof_simplification,[status(thm)],[c_0_131]) ).
fof(c_0_586_587,plain,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(X25,X44,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X44),X3) ),
inference(fof_simplification,[status(thm)],[c_0_132]) ).
fof(c_0_587_588,plain,
! [X59,X18,X15] :
( c_lessequals(X15,c_HOL_Ominus__class_Ominus(X18,X59,tc_nat),tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X59),X18,tc_nat)
| ~ c_lessequals(X59,X18,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_133]) ).
fof(c_0_588_589,plain,
! [X22,X44,X25,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_Power_Opower__class_Opower(X25,X22,X3) != c_Power_Opower__class_Opower(X44,X22,X3)
| X25 = X44
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X22,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X44,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X25,X3) ),
inference(fof_simplification,[status(thm)],[c_0_134]) ).
fof(c_0_589_590,plain,
! [X8,X18,X15] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X8),c_Lambda_OdB_OVar(X15)),X18)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X8)) ),
inference(fof_simplification,[status(thm)],[c_0_135]) ).
fof(c_0_590_591,plain,
! [X22,X44,X25,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_Power_Opower__class_Opower(X25,X22,X3),c_Power_Opower__class_Opower(X44,X22,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X25,X3)
| ~ c_lessequals(X25,X44,X3) ),
inference(fof_simplification,[status(thm)],[c_0_136]) ).
fof(c_0_591_592,plain,
! [X63,X7] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X7)),c_Lambda_OdB_OAbs(X63)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X7),X63)) ),
inference(fof_simplification,[status(thm)],[c_0_137]) ).
fof(c_0_592_593,plain,
! [X57,X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X44),X57),X3)
| ~ c_lessequals(X45,X57,X3)
| ~ c_lessequals(X25,X44,X3) ),
inference(fof_simplification,[status(thm)],[c_0_138]) ).
fof(c_0_593_594,plain,
! [X57,X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X44),X57),X3)
| ~ c_HOL_Oord__class_Oless(X45,X57,X3)
| ~ c_HOL_Oord__class_Oless(X25,X44,X3) ),
inference(fof_simplification,[status(thm)],[c_0_139]) ).
fof(c_0_594_595,plain,
! [X57,X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X44),X57),X3)
| ~ c_HOL_Oord__class_Oless(X45,X57,X3)
| ~ c_lessequals(X25,X44,X3) ),
inference(fof_simplification,[status(thm)],[c_0_140]) ).
fof(c_0_595_596,plain,
! [X57,X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X44),X57),X3)
| ~ c_lessequals(X45,X57,X3)
| ~ c_HOL_Oord__class_Oless(X25,X44,X3) ),
inference(fof_simplification,[status(thm)],[c_0_141]) ).
fof(c_0_596_597,plain,
! [X58,X28,X24,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(X24,X28,X3),X58,X3) = c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(X24,X58,X3),c_HOL_Ominus__class_Ominus(X28,X58,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_142]) ).
fof(c_0_597_598,plain,
! [X8,X44,X25,X3] :
( c_Wellfounded_Oaccp(X8,X44,X3)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X44),X25))
| ~ c_Wellfounded_Oaccp(X8,X25,X3) ),
inference(fof_simplification,[status(thm)],[c_0_143]) ).
fof(c_0_598_599,plain,
! [X8,X44,X25,X3] :
( c_Wellfounded_Oaccp(X8,X44,X3)
| ~ c_Wellfounded_Oaccp(X8,X25,X3)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X44),X25)) ),
inference(fof_simplification,[status(thm)],[c_0_144]) ).
fof(c_0_599_600,plain,
! [X22,X20,X69] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X69,X22,tc_nat),c_HOL_Ominus__class_Ominus(X69,X20,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X20,X69,tc_nat)
| ~ c_HOL_Oord__class_Oless(X20,X22,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_145]) ).
fof(c_0_600_601,plain,
! [X45,X44,X25] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X25,X45,tc_nat),c_HOL_Ominus__class_Ominus(X44,X45,tc_nat),tc_nat)
| ~ c_lessequals(X45,X25,tc_nat)
| ~ c_HOL_Oord__class_Oless(X25,X44,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_146]) ).
fof(c_0_601_602,plain,
! [X22,X20,X59] :
( c_lessequals(X20,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X20),X59,tc_nat),tc_nat)
| ~ c_lessequals(X59,X22,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_147]) ).
fof(c_0_602_603,plain,
! [X22,X20,X59] :
( c_lessequals(X20,X22,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X59),X20),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X59),X22),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_148]) ).
fof(c_0_603_604,plain,
! [X22,X20,X59] :
( c_HOL_Oord__class_Oless(X20,X22,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X59),X20),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X59),X22),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_149]) ).
fof(c_0_604_605,plain,
! [X58,X28,X24,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X28),X58)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X28)),X58) ),
inference(fof_simplification,[status(thm)],[c_0_150]) ).
fof(c_0_605_606,plain,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X44)),X45) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X44),X45)) ),
inference(fof_simplification,[status(thm)],[c_0_151]) ).
fof(c_0_606_607,plain,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Oab__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X44)),X45) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X44),X45)) ),
inference(fof_simplification,[status(thm)],[c_0_152]) ).
fof(c_0_607_608,plain,
! [X57,X45,X25,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X57)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45)),X57) ),
inference(fof_simplification,[status(thm)],[c_0_153]) ).
fof(c_0_608_609,plain,
! [X45,X44,X25,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),X25),X44)),X45) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X44),X45)) ),
inference(fof_simplification,[status(thm)],[c_0_154]) ).
fof(c_0_609_610,plain,
! [X69,X59,X18,X15] :
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X59),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X69),tc_nat)
| ~ c_lessequals(X59,X69,tc_nat)
| ~ c_lessequals(X15,X18,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_155]) ).
fof(c_0_610_611,plain,
! [X69,X59,X18,X15] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X59),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X69),tc_nat)
| ~ c_HOL_Oord__class_Oless(X59,X69,tc_nat)
| ~ c_HOL_Oord__class_Oless(X15,X18,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_156]) ).
fof(c_0_611_612,axiom,
! [X37,X47,X48,X3] :
( c_List_Olist_ONil(X3) != c_List_Omap(X47,X37,X48,X3)
| X37 = c_List_Olist_ONil(X48) ),
c_0_157 ).
fof(c_0_612_613,axiom,
! [X37,X47,X48,X3] :
( c_List_Omap(X47,X37,X48,X3) != c_List_Olist_ONil(X3)
| X37 = c_List_Olist_ONil(X48) ),
c_0_158 ).
fof(c_0_613_614,plain,
! [X53,X19,X16,X30] :
( c_Type_Otyping(X16,X53,X30)
| ~ c_Type_Otyping(X16,X19,X30)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X19),X53)) ),
inference(fof_simplification,[status(thm)],[c_0_159]) ).
fof(c_0_614_615,plain,
! [X59,X18,X15] :
( c_lessequals(X18,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X59),tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X18,X59,tc_nat),X15,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_160]) ).
fof(c_0_615_616,plain,
! [X59,X18,X15] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X59),X18,tc_nat)
| ~ c_HOL_Oord__class_Oless(X15,c_HOL_Ominus__class_Ominus(X18,X59,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_161]) ).
fof(c_0_616_617,plain,
! [X58,X28,X24,X14,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X28),X58)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X28),X14)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X58) = X14 ),
inference(fof_simplification,[status(thm)],[c_0_162]) ).
fof(c_0_617_618,plain,
! [X59,X18,X15] :
( c_HOL_Ominus__class_Ominus(X15,c_HOL_Ominus__class_Ominus(X18,X59,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X59),X18,tc_nat)
| ~ c_lessequals(X59,X18,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_163]) ).
fof(c_0_618_619,plain,
! [X59,X18,X15] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X18,X59,tc_nat),X15,tc_nat)
| ~ c_lessequals(X18,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X59),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_164]) ).
fof(c_0_619_620,plain,
! [X59,X18,X15] :
( c_HOL_Oord__class_Oless(X15,c_HOL_Ominus__class_Ominus(X18,X59,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X59),X18,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_165]) ).
fof(c_0_620_621,plain,
! [X59,X18,X15] :
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X18),X59,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Ominus__class_Ominus(X18,X59,tc_nat))
| ~ c_lessequals(X59,X18,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_166]) ).
fof(c_0_621_622,plain,
! [X59,X18,X15] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Ominus__class_Ominus(X18,X59,tc_nat)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X18),X59,tc_nat)
| ~ c_lessequals(X59,X18,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_167]) ).
fof(c_0_622_623,plain,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X58,X28,X3)
| c_lessequals(X58,X24,X3)
| ~ c_lessequals(X58,c_Orderings_Oord__class_Omax(X24,X28,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_168]) ).
fof(c_0_623_624,plain,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X58,X28,X3)
| c_HOL_Oord__class_Oless(X58,X24,X3)
| ~ c_HOL_Oord__class_Oless(X58,c_Orderings_Oord__class_Omax(X24,X28,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_169]) ).
fof(c_0_624_625,plain,
! [X59,X15] :
( ~ c_lessequals(X15,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X59),X15),tc_nat)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X59),X15),X15,tc_nat) = X59 ),
inference(fof_simplification,[status(thm)],[c_0_170]) ).
fof(c_0_625_626,plain,
! [X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X44),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X44,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X25,X3) ),
inference(fof_simplification,[status(thm)],[c_0_171]) ).
fof(c_0_626_627,plain,
! [X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X44),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X44,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X25,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_172]) ).
fof(c_0_627_628,plain,
! [X44,X25,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),X25),X44),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X44,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X25,X3) ),
inference(fof_simplification,[status(thm)],[c_0_173]) ).
fof(c_0_628_629,plain,
! [X44,X25,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),X25),X44),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X44,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X25,X3) ),
inference(fof_simplification,[status(thm)],[c_0_174]) ).
fof(c_0_629_630,plain,
! [X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X44),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X44,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X25,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_175]) ).
fof(c_0_630_631,plain,
! [X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X44),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X44,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X25,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_176]) ).
fof(c_0_631_632,plain,
! [X44,X25,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),X25),X44),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X44,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X25,X3) ),
inference(fof_simplification,[status(thm)],[c_0_177]) ).
fof(c_0_632_633,plain,
! [X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X44),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X44,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X25,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_178]) ).
fof(c_0_633_634,plain,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oord__class_Oless(X44,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45),X3)
| ~ c_lessequals(X44,X45,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X25,X3) ),
inference(fof_simplification,[status(thm)],[c_0_179]) ).
fof(c_0_634_635,plain,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_lessequals(X44,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45),X3)
| ~ c_lessequals(X44,X45,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X25,X3) ),
inference(fof_simplification,[status(thm)],[c_0_180]) ).
fof(c_0_635_636,plain,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_lessequals(X44,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45),X3)
| ~ c_lessequals(X44,X25,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X45,X3) ),
inference(fof_simplification,[status(thm)],[c_0_181]) ).
fof(c_0_636_637,plain,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oord__class_Oless(X44,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45),X3)
| ~ c_HOL_Oord__class_Oless(X44,X45,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X25,X3) ),
inference(fof_simplification,[status(thm)],[c_0_182]) ).
fof(c_0_637_638,plain,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X44),X45),X3)
| ~ c_lessequals(X25,X44,X3) ),
inference(fof_simplification,[status(thm)],[c_0_183]) ).
fof(c_0_638_639,plain,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X44),X3)
| ~ c_lessequals(X25,X44,X3) ),
inference(fof_simplification,[status(thm)],[c_0_184]) ).
fof(c_0_639_640,plain,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X44),X45),X3)
| ~ c_lessequals(X25,X44,X3) ),
inference(fof_simplification,[status(thm)],[c_0_185]) ).
fof(c_0_640_641,plain,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X44),X3)
| ~ c_lessequals(X25,X44,X3) ),
inference(fof_simplification,[status(thm)],[c_0_186]) ).
fof(c_0_641_642,plain,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X44),X45),X3)
| ~ c_HOL_Oord__class_Oless(X25,X44,X3) ),
inference(fof_simplification,[status(thm)],[c_0_187]) ).
fof(c_0_642_643,plain,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X44),X45),X3)
| ~ c_HOL_Oord__class_Oless(X25,X44,X3) ),
inference(fof_simplification,[status(thm)],[c_0_188]) ).
fof(c_0_643_644,plain,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X44),X3)
| ~ c_HOL_Oord__class_Oless(X25,X44,X3) ),
inference(fof_simplification,[status(thm)],[c_0_189]) ).
fof(c_0_644_645,plain,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X44),X3)
| ~ c_HOL_Oord__class_Oless(X25,X44,X3) ),
inference(fof_simplification,[status(thm)],[c_0_190]) ).
fof(c_0_645_646,plain,
! [X45,X44,X25,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X44,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45),X3)
| ~ c_HOL_Oord__class_Oless(X44,X45,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X25,X3) ),
inference(fof_simplification,[status(thm)],[c_0_191]) ).
fof(c_0_646_647,plain,
! [X22,X20,X69] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X69,X22,tc_nat),c_HOL_Ominus__class_Ominus(X69,X20,tc_nat),tc_nat)
| ~ c_lessequals(X20,X22,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_192]) ).
fof(c_0_647_648,plain,
! [X22,X20,X69] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X20,X69,tc_nat),c_HOL_Ominus__class_Ominus(X22,X69,tc_nat),tc_nat)
| ~ c_lessequals(X20,X22,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_193]) ).
fof(c_0_648_649,plain,
! [X22,X20] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X22,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X22),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_194]) ).
fof(c_0_649_650,plain,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X24,X28,X3),X58,X3)
| ~ c_HOL_Oord__class_Oless(X28,X58,X3)
| ~ c_HOL_Oord__class_Oless(X24,X58,X3) ),
inference(fof_simplification,[status(thm)],[c_0_195]) ).
fof(c_0_650_651,plain,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(c_Orderings_Oord__class_Omax(X24,X28,X3),X58,X3)
| ~ c_lessequals(X28,X58,X3)
| ~ c_lessequals(X24,X58,X3) ),
inference(fof_simplification,[status(thm)],[c_0_196]) ).
fof(c_0_651_652,plain,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(c_Orderings_Oord__class_Omax(X28,X58,X3),X24,X3)
| ~ c_lessequals(X58,X24,X3)
| ~ c_lessequals(X28,X24,X3) ),
inference(fof_simplification,[status(thm)],[c_0_197]) ).
fof(c_0_652_653,plain,
! [X24,X44,X25,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(c_Orderings_Oord__class_Omax(X25,X44,X3),X24,X3)
| ~ c_lessequals(X44,X24,X3)
| ~ c_lessequals(X25,X24,X3) ),
inference(fof_simplification,[status(thm)],[c_0_198]) ).
fof(c_0_653_654,plain,
! [X18,X15] :
( ~ c_lessequals(X15,X18,tc_nat)
| X18 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X18,X15,tc_nat)),X15) ),
inference(fof_simplification,[status(thm)],[c_0_199]) ).
fof(c_0_654_655,plain,
! [X22,X20] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X20,X22,tc_nat)),X22) = X20
| ~ c_lessequals(X22,X20,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_200]) ).
fof(c_0_655_656,plain,
! [X22,X20,X59] :
( c_HOL_Ominus__class_Ominus(X20,X59,tc_nat) != c_HOL_Ominus__class_Ominus(X22,X59,tc_nat)
| ~ c_lessequals(X59,X22,tc_nat)
| ~ c_lessequals(X59,X20,tc_nat)
| X20 = X22 ),
inference(fof_simplification,[status(thm)],[c_0_201]) ).
fof(c_0_656_657,plain,
! [X27,X45,X44,X25,X3] :
( hAPP(hAPP(X27,hAPP(hAPP(X27,X25),X44)),X45) = hAPP(hAPP(X27,X25),hAPP(hAPP(X27,X44),X45))
| ~ c_OrderedGroup_Osemigroup__add(X27,X3) ),
inference(fof_simplification,[status(thm)],[c_0_202]) ).
fof(c_0_657_658,plain,
! [X22,X20] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X20,X22,tc_nat),X20,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X22,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_203]) ).
fof(c_0_658_659,plain,
! [X46,X37,X68,X3] :
( c_List_Olistsp(X68,c_List_Oappend(X37,X46,X3),X3)
| ~ c_List_Olistsp(X68,X46,X3)
| ~ c_List_Olistsp(X68,X37,X3) ),
inference(fof_simplification,[status(thm)],[c_0_204]) ).
fof(c_0_659_660,plain,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X24,X28,X3),X58,X3) = c_Orderings_Oord__class_Omax(X24,c_Orderings_Oord__class_Omax(X28,X58,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_205]) ).
fof(c_0_660_661,plain,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Orderings_Oord__class_Omax(X24,c_Orderings_Oord__class_Omax(X28,X58,X3),X3) = c_Orderings_Oord__class_Omax(X28,c_Orderings_Oord__class_Omax(X24,X58,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_206]) ).
fof(c_0_661_662,plain,
! [X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X25,X44,X3)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X25,X44,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_207]) ).
fof(c_0_662_663,plain,
! [X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X25,X44,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X25,X44,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_208]) ).
fof(c_0_663_664,plain,
! [X25,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X25,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X25),X3) ),
inference(fof_simplification,[status(thm)],[c_0_209]) ).
fof(c_0_664_665,plain,
! [X25,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X25,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X25),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_210]) ).
fof(c_0_665_666,plain,
! [X25,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X25,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X25),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_211]) ).
fof(c_0_666_667,plain,
! [X25,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X25,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X25),X3) ),
inference(fof_simplification,[status(thm)],[c_0_212]) ).
fof(c_0_667_668,plain,
! [X25,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(X25,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X25),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_213]) ).
fof(c_0_668_669,plain,
! [X49,X28,X50,X24,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X24,X28,X3) != c_HOL_Ominus__class_Ominus(X50,X49,X3)
| c_lessequals(X49,X50,X3)
| ~ c_lessequals(X28,X24,X3) ),
inference(fof_simplification,[status(thm)],[c_0_214]) ).
fof(c_0_669_670,plain,
! [X49,X28,X50,X24,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X24,X28,X3) != c_HOL_Ominus__class_Ominus(X50,X49,X3)
| c_lessequals(X28,X24,X3)
| ~ c_lessequals(X49,X50,X3) ),
inference(fof_simplification,[status(thm)],[c_0_215]) ).
fof(c_0_670_671,plain,
! [X49,X28,X50,X24,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X24,X28,X3) != c_HOL_Ominus__class_Ominus(X50,X49,X3)
| c_HOL_Oord__class_Oless(X50,X49,X3)
| ~ c_HOL_Oord__class_Oless(X24,X28,X3) ),
inference(fof_simplification,[status(thm)],[c_0_216]) ).
fof(c_0_671_672,plain,
! [X49,X28,X50,X24,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X24,X28,X3) != c_HOL_Ominus__class_Ominus(X50,X49,X3)
| c_HOL_Oord__class_Oless(X24,X28,X3)
| ~ c_HOL_Oord__class_Oless(X50,X49,X3) ),
inference(fof_simplification,[status(thm)],[c_0_217]) ).
fof(c_0_672_673,plain,
! [X59,X18,X15] :
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X59),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X59),tc_nat)
| ~ c_lessequals(X15,X18,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_218]) ).
fof(c_0_673_674,plain,
! [X22,X20,X59] :
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X59),X20),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X59),X22),tc_nat)
| ~ c_lessequals(X20,X22,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_219]) ).
fof(c_0_674_675,plain,
! [X59,X18,X15] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X59),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X59),tc_nat)
| ~ c_HOL_Oord__class_Oless(X15,X18,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_220]) ).
fof(c_0_675_676,plain,
! [X22,X20,X59] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X59),X20),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X59),X22),tc_nat)
| ~ c_HOL_Oord__class_Oless(X20,X22,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_221]) ).
fof(c_0_676_677,plain,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X24,X58,X3)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X24,X28,X3),X58,X3) ),
inference(fof_simplification,[status(thm)],[c_0_222]) ).
fof(c_0_677_678,plain,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X28,X58,X3)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X24,X28,X3),X58,X3) ),
inference(fof_simplification,[status(thm)],[c_0_223]) ).
fof(c_0_678_679,plain,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X28,X58,X3)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X24,X28,X3),X58,X3) ),
inference(fof_simplification,[status(thm)],[c_0_224]) ).
fof(c_0_679_680,plain,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X24,X58,X3)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X24,X28,X3),X58,X3) ),
inference(fof_simplification,[status(thm)],[c_0_225]) ).
fof(c_0_680_681,plain,
! [X24,X44,X25,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X44,X24,X3)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X25,X44,X3),X24,X3) ),
inference(fof_simplification,[status(thm)],[c_0_226]) ).
fof(c_0_681_682,plain,
! [X24,X44,X25,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X25,X24,X3)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X25,X44,X3),X24,X3) ),
inference(fof_simplification,[status(thm)],[c_0_227]) ).
fof(c_0_682_683,plain,
! [X58,X28,X24,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X28),X58)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X28),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X58)) ),
inference(fof_simplification,[status(thm)],[c_0_228]) ).
fof(c_0_683_684,plain,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X44),X45)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X44),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45)) ),
inference(fof_simplification,[status(thm)],[c_0_229]) ).
fof(c_0_684_685,plain,
! [X57,X45,X25,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X57)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X57)) ),
inference(fof_simplification,[status(thm)],[c_0_230]) ).
fof(c_0_685_686,plain,
! [X22,X20,X59] :
( c_HOL_Oord__class_Oless(X20,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X59),tc_nat)
| ~ c_lessequals(X20,X22,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X59,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_231]) ).
fof(c_0_686_687,plain,
! [X28,X24,X8,X3] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X24),X28))
| ~ hBOOL(hAPP(hAPP(X8,X24),X28)) ),
inference(fof_simplification,[status(thm)],[c_0_232]) ).
fof(c_0_687_688,plain,
! [X22,X20,X3] :
( ~ class_Ring__and__Field_Oring__1(X3)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(X20,X22,tc_nat),X3) = c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(X20,X3),c_Nat_Osemiring__1__class_Oof__nat(X22,X3),X3)
| ~ c_lessequals(X22,X20,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_233]) ).
fof(c_0_688_689,plain,
! [X46,X37,X68,X3] :
( c_List_Olistsp(X68,X37,X3)
| ~ c_List_Olistsp(X68,c_List_Oappend(X37,X46,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_234]) ).
fof(c_0_689_690,plain,
! [X46,X37,X68,X3] :
( c_List_Olistsp(X68,X46,X3)
| ~ c_List_Olistsp(X68,c_List_Oappend(X37,X46,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_235]) ).
fof(c_0_690_691,plain,
! [X22,X20] :
( c_HOL_Oord__class_Oless(X20,X22,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X22,X20,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_236]) ).
fof(c_0_691_692,plain,
! [X28,X24,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X28) != c_HOL_Ozero__class_Ozero(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X28,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X24,X3)
| X28 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_237]) ).
fof(c_0_692_693,plain,
! [X28,X24,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X28) != c_HOL_Ozero__class_Ozero(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X28,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X24,X3)
| X24 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_238]) ).
fof(c_0_693_694,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_239]) ).
fof(c_0_694_695,plain,
! [X22,X20,X69,X59] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X69) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X59),X22)
| ~ c_HOL_Oord__class_Oless(X59,X69,tc_nat)
| c_HOL_Oord__class_Oless(X20,X22,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_240]) ).
fof(c_0_695_696,plain,
! [X59,X18,X15] :
( c_HOL_Oord__class_Oless(X15,X59,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X18),X59,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_241]) ).
fof(c_0_696_697,plain,
! [X22,X20,X59] :
( c_lessequals(X59,X22,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X59),X22,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_242]) ).
fof(c_0_697_698,plain,
! [X22,X20,X59] :
( c_lessequals(X20,X22,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X59),X22,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_243]) ).
fof(c_0_698_699,plain,
! [X44,X25,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ominus__class_Ominus(X25,X44,X3)),X44) = X25 ),
inference(fof_simplification,[status(thm)],[c_0_244]) ).
fof(c_0_699_700,plain,
! [X22,X25,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X25,X22,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X25,X3) ),
inference(fof_simplification,[status(thm)],[c_0_245]) ).
fof(c_0_700_701,plain,
! [X22,X25,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X25,X22,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X25,X3) ),
inference(fof_simplification,[status(thm)],[c_0_246]) ).
fof(c_0_701_702,plain,
! [X28,X8,X25,X3] :
( c_Wellfounded_Oaccp(X8,X28,X3)
| ~ hBOOL(hAPP(hAPP(X8,X28),X25))
| ~ c_Wellfounded_Oaccp(X8,X25,X3) ),
inference(fof_simplification,[status(thm)],[c_0_247]) ).
fof(c_0_702_703,plain,
! [X8,X44,X25,X3] :
( c_Wellfounded_Oaccp(X8,X25,X3)
| ~ hBOOL(hAPP(hAPP(X8,X25),X44))
| ~ c_Wellfounded_Oaccp(X8,X44,X3) ),
inference(fof_simplification,[status(thm)],[c_0_248]) ).
fof(c_0_703_704,plain,
! [X25,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X25),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X25,X3) ),
inference(fof_simplification,[status(thm)],[c_0_249]) ).
fof(c_0_704_705,plain,
! [X25,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X25),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X25,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_250]) ).
fof(c_0_705_706,plain,
! [X25,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X25),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X25,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_251]) ).
fof(c_0_706_707,plain,
! [X25,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),X25),X25),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X25,X3) ),
inference(fof_simplification,[status(thm)],[c_0_252]) ).
fof(c_0_707_708,plain,
! [X25,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X25),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X25,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_253]) ).
fof(c_0_708_709,plain,
! [X8] :
( hBOOL(hAPP(c_InductTermi_OIT,X8))
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X8,tc_Lambda_OdB) ),
inference(fof_simplification,[status(thm)],[c_0_254]) ).
fof(c_0_709_710,plain,
! [X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ominus__class_Ominus(X25,X44,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X25,X44,X3) ),
inference(fof_simplification,[status(thm)],[c_0_255]) ).
fof(c_0_710_711,plain,
! [X44,X25,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X25,X44,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X25,X44,X3) ),
inference(fof_simplification,[status(thm)],[c_0_256]) ).
fof(c_0_711_712,plain,
! [X53,X19,X16,X30] :
( c_Type_Otyping(X16,X53,X30)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X19),X53))
| ~ c_Type_Otyping(X16,X19,X30) ),
inference(fof_simplification,[status(thm)],[c_0_257]) ).
fof(c_0_712_713,plain,
! [X46,X37,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| c_List_Olistsum(c_List_Oappend(X37,X46,X3),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_List_Olistsum(X37,X3)),c_List_Olistsum(X46,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_258]) ).
fof(c_0_713_714,plain,
! [X24,X44,X25,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X24,c_Orderings_Oord__class_Omax(X25,X44,X3),X3)
| ~ c_HOL_Oord__class_Oless(X24,X25,X3) ),
inference(fof_simplification,[status(thm)],[c_0_259]) ).
fof(c_0_714_715,plain,
! [X24,X44,X25,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X24,c_Orderings_Oord__class_Omax(X25,X44,X3),X3)
| ~ c_HOL_Oord__class_Oless(X24,X44,X3) ),
inference(fof_simplification,[status(thm)],[c_0_260]) ).
fof(c_0_715_716,plain,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X58,c_Orderings_Oord__class_Omax(X24,X28,X3),X3)
| ~ c_HOL_Oord__class_Oless(X58,X24,X3) ),
inference(fof_simplification,[status(thm)],[c_0_261]) ).
fof(c_0_716_717,plain,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X58,c_Orderings_Oord__class_Omax(X24,X28,X3),X3)
| ~ c_HOL_Oord__class_Oless(X58,X28,X3) ),
inference(fof_simplification,[status(thm)],[c_0_262]) ).
fof(c_0_717_718,plain,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X58,c_Orderings_Oord__class_Omax(X24,X28,X3),X3)
| ~ c_lessequals(X58,X28,X3) ),
inference(fof_simplification,[status(thm)],[c_0_263]) ).
fof(c_0_718_719,plain,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X58,c_Orderings_Oord__class_Omax(X24,X28,X3),X3)
| ~ c_lessequals(X58,X24,X3) ),
inference(fof_simplification,[status(thm)],[c_0_264]) ).
fof(c_0_719_720,plain,
! [X24,X44,X25,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X24,c_Orderings_Oord__class_Omax(X25,X44,X3),X3)
| ~ c_lessequals(X24,X44,X3) ),
inference(fof_simplification,[status(thm)],[c_0_265]) ).
fof(c_0_720_721,plain,
! [X24,X44,X25,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X24,c_Orderings_Oord__class_Omax(X25,X44,X3),X3)
| ~ c_lessequals(X24,X25,X3) ),
inference(fof_simplification,[status(thm)],[c_0_266]) ).
fof(c_0_721_722,plain,
! [X22,X20] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X22,X20,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X20,X22,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_267]) ).
fof(c_0_722_723,plain,
! [X22,X15] :
( c_HOL_Ominus__class_Ominus(X22,c_HOL_Ominus__class_Ominus(X22,X15,tc_nat),tc_nat) = X15
| ~ c_lessequals(X15,X22,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_268]) ).
fof(c_0_723_724,plain,
! [X22,X20,X3] :
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X22),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Nat_Osemiring__1__class_Oof__nat(X20,X3)),c_Nat_Osemiring__1__class_Oof__nat(X22,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_269]) ).
fof(c_0_724_725,plain,
! [X22,X59,X18] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X18,X22,tc_nat),X59,tc_nat)
| ~ c_HOL_Oord__class_Oless(X18,X59,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_270]) ).
fof(c_0_725_726,plain,
! [X19,X15] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X19),c_Lambda_OdB_OVar(X15))))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X19)) ),
inference(fof_simplification,[status(thm)],[c_0_271]) ).
fof(c_0_726_727,plain,
! [X22,X20] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X22),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X22,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_272]) ).
fof(c_0_727_728,plain,
! [X22,X20] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X22),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_273]) ).
fof(c_0_728_729,plain,
! [X22,X20] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),c_HOL_Ominus__class_Ominus(X20,X22,tc_nat)) = X20
| ~ c_lessequals(X22,X20,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_274]) ).
fof(c_0_729_730,plain,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X58,X24,X3)
| ~ c_HOL_Oord__class_Oless(X58,X28,X3)
| ~ c_HOL_Oord__class_Oless(X28,X24,X3) ),
inference(fof_simplification,[status(thm)],[c_0_275]) ).
fof(c_0_730_731,plain,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X24,X58,X3)
| ~ c_HOL_Oord__class_Oless(X28,X58,X3)
| ~ c_HOL_Oord__class_Oless(X24,X28,X3) ),
inference(fof_simplification,[status(thm)],[c_0_276]) ).
fof(c_0_731_732,plain,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X58,X24,X3)
| ~ c_lessequals(X58,X28,X3)
| ~ c_lessequals(X28,X24,X3) ),
inference(fof_simplification,[status(thm)],[c_0_277]) ).
fof(c_0_732_733,plain,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X58,X24,X3)
| ~ c_lessequals(X58,X28,X3)
| ~ c_HOL_Oord__class_Oless(X28,X24,X3) ),
inference(fof_simplification,[status(thm)],[c_0_278]) ).
fof(c_0_733_734,plain,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X58,X24,X3)
| ~ c_HOL_Oord__class_Oless(X58,X28,X3)
| ~ c_lessequals(X28,X24,X3) ),
inference(fof_simplification,[status(thm)],[c_0_279]) ).
fof(c_0_734_735,plain,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X24,X58,X3)
| ~ c_lessequals(X28,X58,X3)
| ~ c_lessequals(X24,X28,X3) ),
inference(fof_simplification,[status(thm)],[c_0_280]) ).
fof(c_0_735_736,plain,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X24,X58,X3)
| ~ c_HOL_Oord__class_Oless(X28,X58,X3)
| ~ c_lessequals(X24,X28,X3) ),
inference(fof_simplification,[status(thm)],[c_0_281]) ).
fof(c_0_736_737,plain,
! [X58,X28,X24,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X24,X58,X3)
| ~ c_lessequals(X28,X58,X3)
| ~ c_HOL_Oord__class_Oless(X24,X28,X3) ),
inference(fof_simplification,[status(thm)],[c_0_282]) ).
fof(c_0_737_738,plain,
! [X19,X7] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X7)),c_Lambda_OdB_OAbs(X19)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X7),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_283]) ).
fof(c_0_738_739,plain,
! [X22,X20,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(X20,X22,tc_nat)
| ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X20,X3),c_Nat_Osemiring__1__class_Oof__nat(X22,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_284]) ).
fof(c_0_739_740,plain,
! [X22,X20,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X20,X22,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X20,X3),c_Nat_Osemiring__1__class_Oof__nat(X22,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_285]) ).
fof(c_0_740_741,plain,
! [X58,X28,X24] :
( c_HOL_Oord__class_Oless(X24,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X28),X58),tc_nat)
| ~ c_HOL_Oord__class_Oless(X24,X28,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_286]) ).
fof(c_0_741_742,plain,
! [X58,X28,X24] :
( c_HOL_Oord__class_Oless(X24,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X28),X58),tc_nat)
| ~ c_HOL_Oord__class_Oless(X24,X58,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_287]) ).
fof(c_0_742_743,plain,
! [X20,X18,X15] :
( c_HOL_Oord__class_Oless(X15,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X20),tc_nat)
| ~ c_HOL_Oord__class_Oless(X15,X18,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_288]) ).
fof(c_0_743_744,plain,
! [X20,X18,X15] :
( c_HOL_Oord__class_Oless(X15,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X18),tc_nat)
| ~ c_HOL_Oord__class_Oless(X15,X18,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_289]) ).
fof(c_0_744_745,plain,
! [X20,X18,X15] :
( c_lessequals(X15,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X18),tc_nat)
| ~ c_lessequals(X15,X18,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_290]) ).
fof(c_0_745_746,plain,
! [X20,X18,X15] :
( c_lessequals(X15,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X20),tc_nat)
| ~ c_lessequals(X15,X18,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_291]) ).
fof(c_0_746_747,plain,
! [X58,X28,X24] :
( c_lessequals(X24,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X28),X58),tc_nat)
| ~ c_lessequals(X24,X58,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_292]) ).
fof(c_0_747_748,plain,
! [X58,X28,X24] :
( c_lessequals(X24,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X28),X58),tc_nat)
| ~ c_lessequals(X24,X28,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_293]) ).
fof(c_0_748_749,plain,
! [X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Orderings_Oord__class_Omax(X24,c_Orderings_Oord__class_Omax(X24,X28,X3),X3) = c_Orderings_Oord__class_Omax(X24,X28,X3) ),
inference(fof_simplification,[status(thm)],[c_0_294]) ).
fof(c_0_749_750,plain,
! [X59,X18,X15] :
( c_lessequals(X15,X59,tc_nat)
| ~ c_lessequals(X18,X59,tc_nat)
| ~ c_lessequals(X15,X18,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_295]) ).
fof(c_0_750_751,plain,
! [X19,X15] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X19),X15)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X19)) ),
inference(fof_simplification,[status(thm)],[c_0_296]) ).
fof(c_0_751_752,plain,
! [X24,X22,X34] :
( hBOOL(hAPP(X34,X22))
| hBOOL(hAPP(X34,X24))
| ~ c_HOL_Oord__class_Oless(X24,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X34),tc_nat)
| ~ hBOOL(hAPP(X34,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(fof_simplification,[status(thm)],[c_0_297]) ).
fof(c_0_752_753,axiom,
! [X22,X59,X15] :
( c_Lambda_Oliftn(X22,c_Lambda_OdB_OVar(X15),X59) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X22))
| c_HOL_Oord__class_Oless(X15,X59,tc_nat) ),
c_0_298 ).
fof(c_0_753_754,plain,
! [X37,X24,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| c_List_Olistsum(c_List_Olist_OCons(X24,X37,X3),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),c_List_Olistsum(X37,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_299]) ).
fof(c_0_754_755,axiom,
! [X22,X20] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),c_HOL_Ominus__class_Ominus(X20,X22,tc_nat)) = X20
| c_HOL_Oord__class_Oless(X20,X22,tc_nat) ),
c_0_300 ).
fof(c_0_755_756,plain,
! [X28,X24,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X24,X28,X3)
| c_lessequals(X28,X24,X3)
| ~ c_lessequals(X24,X28,X3) ),
inference(fof_simplification,[status(thm)],[c_0_301]) ).
fof(c_0_756_757,plain,
! [X22,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X22,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X22,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_302]) ).
fof(c_0_757_758,plain,
! [X14,X18,X15] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X18)),X14),X15) = c_Lambda_OdB_OVar(X18)
| ~ c_HOL_Oord__class_Oless(X18,X15,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_303]) ).
fof(c_0_758_759,plain,
! [X22,X20,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X20,X3),c_Nat_Osemiring__1__class_Oof__nat(X22,X3),X3)
| ~ c_lessequals(X20,X22,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_304]) ).
fof(c_0_759_760,plain,
! [X22,X20,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X20,X3),c_Nat_Osemiring__1__class_Oof__nat(X22,X3),X3)
| ~ c_HOL_Oord__class_Oless(X20,X22,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_305]) ).
fof(c_0_760_761,plain,
! [X19] :
( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X19,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X19)) ),
inference(fof_simplification,[status(thm)],[c_0_306]) ).
fof(c_0_761_762,axiom,
! [X22,X20,X34] :
( hBOOL(hAPP(hAPP(X34,X22),X20))
| c_HOL_Oord__class_Oless(X22,X20,tc_nat)
| X20 = X22
| c_HOL_Oord__class_Oless(X20,X22,tc_nat) ),
c_0_307 ).
fof(c_0_762_763,plain,
! [X22,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X22,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X22,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_308]) ).
fof(c_0_763_764,plain,
! [X28,X24,X3] :
( ~ class_Orderings_Oorder(X3)
| X24 = X28
| ~ c_lessequals(X28,X24,X3)
| ~ c_lessequals(X24,X28,X3) ),
inference(fof_simplification,[status(thm)],[c_0_309]) ).
fof(c_0_764_765,plain,
! [X28,X24,X3] :
( ~ class_Orderings_Oorder(X3)
| X24 = X28
| ~ c_lessequals(X28,X24,X3)
| ~ c_lessequals(X24,X28,X3) ),
inference(fof_simplification,[status(thm)],[c_0_310]) ).
fof(c_0_765_766,plain,
! [X28,X24,X3] :
( ~ class_Orderings_Oorder(X3)
| X24 = X28
| ~ c_lessequals(X24,X28,X3)
| ~ c_lessequals(X28,X24,X3) ),
inference(fof_simplification,[status(thm)],[c_0_311]) ).
fof(c_0_766_767,plain,
! [X28,X60,X24,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X60,X28,X3) != c_HOL_Ominus__class_Ominus(X24,X24,X3)
| X60 = X28 ),
inference(fof_simplification,[status(thm)],[c_0_312]) ).
fof(c_0_767_768,plain,
! [X49,X50,X24,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X24,X24,X3) != c_HOL_Ominus__class_Ominus(X50,X49,X3)
| X50 = X49 ),
inference(fof_simplification,[status(thm)],[c_0_313]) ).
fof(c_0_768_769,plain,
! [X58,X28,X24,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X28) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X58)
| X28 = X58 ),
inference(fof_simplification,[status(thm)],[c_0_314]) ).
fof(c_0_769_770,plain,
! [X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X24,X24,X3)
| ~ c_HOL_Oord__class_Oless(X24,X24,X3) ),
inference(fof_simplification,[status(thm)],[c_0_315]) ).
fof(c_0_770_771,plain,
! [X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X24,X28,X3)
| ~ c_lessequals(X28,X24,X3) ),
inference(fof_simplification,[status(thm)],[c_0_316]) ).
fof(c_0_771_772,plain,
! [X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X24,X28,X3)
| ~ c_HOL_Oord__class_Oless(X28,X24,X3) ),
inference(fof_simplification,[status(thm)],[c_0_317]) ).
fof(c_0_772_773,plain,
! [X28,X24,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X28,X24,X3)
| ~ c_HOL_Oord__class_Oless(X24,X28,X3) ),
inference(fof_simplification,[status(thm)],[c_0_318]) ).
fof(c_0_773_774,plain,
! [X44,X25,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X25,X44,X3)
| ~ c_HOL_Oord__class_Oless(X44,X25,X3) ),
inference(fof_simplification,[status(thm)],[c_0_319]) ).
fof(c_0_774_775,plain,
! [X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X24,X28,X3)
| ~ c_HOL_Oord__class_Oless(X28,X24,X3) ),
inference(fof_simplification,[status(thm)],[c_0_320]) ).
fof(c_0_775_776,plain,
! [X28,X24,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X28,X24,X3)
| ~ c_HOL_Oord__class_Oless(X24,X28,X3) ),
inference(fof_simplification,[status(thm)],[c_0_321]) ).
fof(c_0_776_777,plain,
! [X44,X25,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X44,X25,X3)
| ~ c_HOL_Oord__class_Oless(X25,X44,X3) ),
inference(fof_simplification,[status(thm)],[c_0_322]) ).
fof(c_0_777_778,axiom,
! [X28,X24,X22,X20,X3] :
( c_List_Oreplicate(X20,X24,X3) != c_List_Oreplicate(X22,X28,X3)
| X24 = X28
| X20 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_323 ).
fof(c_0_778_779,axiom,
! [X22,X20] :
( c_HOL_Ominus__class_Ominus(X22,X20,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X20,X22,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X20 = X22 ),
c_0_324 ).
fof(c_0_779_780,axiom,
! [X28,X24,X22,X20,X3] :
( c_List_Oreplicate(X20,X24,X3) != c_List_Oreplicate(X22,X28,X3)
| X20 = X22 ),
c_0_325 ).
fof(c_0_780_781,axiom,
! [X23,X46,X37,X3] :
( c_List_Oappend(X46,X37,X3) != c_List_Oappend(X23,X37,X3)
| X46 = X23 ),
c_0_326 ).
fof(c_0_781_782,axiom,
! [X23,X46,X37,X3] :
( c_List_Oappend(X37,X46,X3) != c_List_Oappend(X37,X23,X3)
| X46 = X23 ),
c_0_327 ).
fof(c_0_782_783,plain,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X44) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45)
| X44 = X45 ),
inference(fof_simplification,[status(thm)],[c_0_328]) ).
fof(c_0_783_784,plain,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X44) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45)
| X44 = X45 ),
inference(fof_simplification,[status(thm)],[c_0_329]) ).
fof(c_0_784_785,plain,
! [X45,X44,X25,X3] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X44),X25) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X25)
| X44 = X45 ),
inference(fof_simplification,[status(thm)],[c_0_330]) ).
fof(c_0_785_786,axiom,
! [X54,X55,X56,X25,X3] :
( c_List_Olist_OCons(X25,X55,X3) != c_List_Olist_OCons(X56,X54,X3)
| X25 = X56 ),
c_0_331 ).
fof(c_0_786_787,axiom,
! [X54,X55,X56,X25,X3] :
( c_List_Olist_OCons(X25,X55,X3) != c_List_Olist_OCons(X56,X54,X3)
| X55 = X54 ),
c_0_332 ).
fof(c_0_787_788,axiom,
! [X24,X7] :
( c_HOL_Oord__class_Oless(X24,X24,tc_nat)
| c_Lambda_Osubstn(c_Lambda_OdB_OVar(X24),X7,X24) = c_Lambda_Oliftn(X24,X7,c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_333 ).
fof(c_0_788_789,axiom,
! [X7,X59,X15] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X15)),X7),X59) = c_Lambda_OdB_OVar(X15)
| X15 = X59
| c_HOL_Oord__class_Oless(X59,X15,tc_nat) ),
c_0_334 ).
fof(c_0_789_790,plain,
! [X22,X20] :
( X20 = X22
| ~ c_lessequals(X22,X20,tc_nat)
| ~ c_lessequals(X20,X22,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_335]) ).
fof(c_0_790_791,plain,
! [X1,X2,X3] :
( X2 = X1
| ~ hBOOL(hAPP(hAPP(c_fequal(X3),X2),X1)) ),
inference(fof_simplification,[status(thm)],[c_0_336]) ).
fof(c_0_791_792,plain,
! [X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X24,c_Orderings_Oord__class_Omax(X24,X28,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_337]) ).
fof(c_0_792_793,plain,
! [X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X28,c_Orderings_Oord__class_Omax(X24,X28,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_338]) ).
fof(c_0_793_794,plain,
! [X44,X25,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X44),X44,X3) = X25 ),
inference(fof_simplification,[status(thm)],[c_0_339]) ).
fof(c_0_794_795,axiom,
! [X24,X7] :
( c_HOL_Oord__class_Oless(X24,X24,tc_nat)
| hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X24)),X7),X24) = X7 ),
c_0_340 ).
fof(c_0_795_796,plain,
! [X22,X34] :
( hBOOL(hAPP(X34,X22))
| ~ hBOOL(hAPP(X34,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X34)))
| ~ hBOOL(hAPP(X34,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(fof_simplification,[status(thm)],[c_0_341]) ).
fof(c_0_796_797,plain,
! [X44,X25,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X44,X25,X3)
| X25 = X44
| ~ c_lessequals(X44,X25,X3) ),
inference(fof_simplification,[status(thm)],[c_0_342]) ).
fof(c_0_797_798,plain,
! [X44,X25,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X44,X25,X3)
| ~ c_lessequals(X44,X25,X3)
| X25 = X44 ),
inference(fof_simplification,[status(thm)],[c_0_343]) ).
fof(c_0_798_799,plain,
! [X28,X24,X3] :
( ~ class_Orderings_Oorder(X3)
| X24 = X28
| c_HOL_Oord__class_Oless(X24,X28,X3)
| ~ c_lessequals(X24,X28,X3) ),
inference(fof_simplification,[status(thm)],[c_0_344]) ).
fof(c_0_799_800,plain,
! [X28,X24,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X24,X28,X3)
| X24 = X28
| ~ c_lessequals(X24,X28,X3) ),
inference(fof_simplification,[status(thm)],[c_0_345]) ).
fof(c_0_800_801,plain,
! [X44,X25,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X25,X44,X3)
| X25 = X44
| ~ c_lessequals(X25,X44,X3) ),
inference(fof_simplification,[status(thm)],[c_0_346]) ).
fof(c_0_801_802,plain,
! [X44,X25,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X25,X44,X3)
| ~ c_lessequals(X25,X44,X3)
| X25 = X44 ),
inference(fof_simplification,[status(thm)],[c_0_347]) ).
fof(c_0_802_803,plain,
! [X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| X24 = X28
| ~ c_lessequals(X24,X28,X3)
| c_HOL_Oord__class_Oless(X24,X28,X3) ),
inference(fof_simplification,[status(thm)],[c_0_348]) ).
fof(c_0_803_804,plain,
! [X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| X24 = X28
| c_HOL_Oord__class_Oless(X24,X28,X3)
| ~ c_lessequals(X24,X28,X3) ),
inference(fof_simplification,[status(thm)],[c_0_349]) ).
fof(c_0_804_805,plain,
! [X22,X34] :
( hBOOL(hAPP(X34,X22))
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X34),tc_nat)
| ~ hBOOL(hAPP(X34,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(fof_simplification,[status(thm)],[c_0_350]) ).
fof(c_0_805_806,plain,
! [X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Orderings_Oord__class_Omax(X24,X28,X3) != X28
| c_lessequals(X24,X28,X3) ),
inference(fof_simplification,[status(thm)],[c_0_351]) ).
fof(c_0_806_807,plain,
! [X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Orderings_Oord__class_Omax(X24,X28,X3) = X24
| ~ c_lessequals(X28,X24,X3) ),
inference(fof_simplification,[status(thm)],[c_0_352]) ).
fof(c_0_807_808,plain,
! [X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Orderings_Oord__class_Omax(X24,X28,X3) = X28
| ~ c_lessequals(X24,X28,X3) ),
inference(fof_simplification,[status(thm)],[c_0_353]) ).
fof(c_0_808_809,plain,
! [X22,X59,X15] :
( c_Lambda_Oliftn(X22,c_Lambda_OdB_OVar(X15),X59) = c_Lambda_OdB_OVar(X15)
| ~ c_HOL_Oord__class_Oless(X15,X59,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_354]) ).
fof(c_0_809_810,plain,
! [X28,X24,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X24,X28,X3)
| ~ c_HOL_Oord__class_Oless(X24,X28,X3) ),
inference(fof_simplification,[status(thm)],[c_0_355]) ).
fof(c_0_810_811,plain,
! [X28,X24,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X24,X28,X3)
| ~ c_HOL_Oord__class_Oless(X24,X28,X3) ),
inference(fof_simplification,[status(thm)],[c_0_356]) ).
fof(c_0_811_812,axiom,
! [X58,X28,X24] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X28) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X58)
| X28 = X58 ),
c_0_357 ).
fof(c_0_812_813,axiom,
! [X22,X20,X59] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X59) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X59)
| X20 = X22 ),
c_0_358 ).
fof(c_0_813_814,axiom,
! [X22,X20,X59] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X59),X20) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X59),X22)
| X20 = X22 ),
c_0_359 ).
fof(c_0_814_815,plain,
! [X20,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X20,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_360]) ).
fof(c_0_815_816,axiom,
! [X22,X20] :
( c_HOL_Ominus__class_Ominus(X20,X22,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_lessequals(X20,X22,tc_nat) ),
c_0_361 ).
fof(c_0_816_817,plain,
! [X22,X20] :
( c_HOL_Ominus__class_Ominus(X20,X22,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(X20,X22,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_362]) ).
fof(c_0_817_818,plain,
! [X22,X20] :
( c_HOL_Oord__class_Oless(X20,X22,tc_nat)
| X20 = X22
| ~ c_lessequals(X20,X22,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_363]) ).
fof(c_0_818_819,plain,
! [X22,X20] :
( X20 = X22
| c_HOL_Oord__class_Oless(X20,X22,tc_nat)
| ~ c_lessequals(X20,X22,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_364]) ).
fof(c_0_819_820,plain,
! [X22,X20] :
( c_HOL_Oord__class_Oless(X20,X22,tc_nat)
| X20 = X22
| ~ c_lessequals(X20,X22,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_365]) ).
fof(c_0_820_821,plain,
! [X28,X24] :
( c_lessequals(X24,X28,tc_nat)
| ~ c_HOL_Oord__class_Oless(X24,X28,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_366]) ).
fof(c_0_821_822,plain,
! [X22,X20] :
( c_lessequals(X20,X22,tc_nat)
| ~ c_HOL_Oord__class_Oless(X20,X22,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_367]) ).
fof(c_0_822_823,plain,
! [X59,X15] :
( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X15)),X59) = c_Lambda_OdB_OVar(X15)
| ~ c_HOL_Oord__class_Oless(X15,X59,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_368]) ).
fof(c_0_823_824,plain,
! [X43,X34] :
( hBOOL(hAPP(X34,X43))
| hBOOL(hAPP(X34,v_sko__Nat__Xnat__Xinducts__1(X34)))
| ~ hBOOL(hAPP(X34,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(fof_simplification,[status(thm)],[c_0_369]) ).
fof(c_0_824_825,plain,
! [X43,X34] :
( hBOOL(hAPP(X34,X43))
| hBOOL(hAPP(X34,v_sko__Nat__Xnat__Xinduct__1(X34)))
| ~ hBOOL(hAPP(X34,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(fof_simplification,[status(thm)],[c_0_370]) ).
fof(c_0_825_826,plain,
! [X43,X34] :
( hBOOL(hAPP(X34,X43))
| hBOOL(hAPP(X34,v_sko__List__Xupt__Xinduct__1(X34)))
| ~ hBOOL(hAPP(X34,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(fof_simplification,[status(thm)],[c_0_371]) ).
fof(c_0_826_827,plain,
! [X26,X27,X25,X3] :
( hAPP(hAPP(X27,X25),X26) = X25
| ~ c_OrderedGroup_Omonoid__add(X26,X27,X3) ),
inference(fof_simplification,[status(thm)],[c_0_372]) ).
fof(c_0_827_828,plain,
! [X26,X27,X25,X3] :
( hAPP(hAPP(X27,X26),X25) = X25
| ~ c_OrderedGroup_Omonoid__add(X26,X27,X3) ),
inference(fof_simplification,[status(thm)],[c_0_373]) ).
fof(c_0_828_829,plain,
! [X22,X25,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)
| c_Power_Opower__class_Opower(X25,X22,X3) != c_HOL_Ozero__class_Ozero(X3)
| X25 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_374]) ).
fof(c_0_829_830,plain,
! [X25,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)
| c_Power_Opower__class_Opower(X25,c_HOL_Ozero__class_Ozero(tc_nat),X3) != c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_375]) ).
fof(c_0_830_831,axiom,
! [X7,X59,X15] :
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X15),X7,X59) = c_Lambda_OdB_OVar(X15)
| X15 = X59
| c_HOL_Oord__class_Oless(X59,X15,tc_nat) ),
c_0_376 ).
fof(c_0_831_832,plain,
! [X28,X24,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X28,X24,X3)
| c_HOL_Oord__class_Oless(X24,X28,X3)
| X24 = X28 ),
inference(fof_simplification,[status(thm)],[c_0_377]) ).
fof(c_0_832_833,plain,
! [X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| X24 = X28
| c_HOL_Oord__class_Oless(X28,X24,X3)
| c_HOL_Oord__class_Oless(X24,X28,X3) ),
inference(fof_simplification,[status(thm)],[c_0_378]) ).
fof(c_0_833_834,plain,
! [X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X28,X24,X3)
| c_HOL_Oord__class_Oless(X24,X28,X3)
| X24 = X28 ),
inference(fof_simplification,[status(thm)],[c_0_379]) ).
fof(c_0_834_835,plain,
! [X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X28,X24,X3)
| X24 = X28
| c_HOL_Oord__class_Oless(X24,X28,X3) ),
inference(fof_simplification,[status(thm)],[c_0_380]) ).
fof(c_0_835_836,plain,
! [X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| X24 = X28
| c_HOL_Oord__class_Oless(X24,X28,X3)
| c_HOL_Oord__class_Oless(X28,X24,X3) ),
inference(fof_simplification,[status(thm)],[c_0_381]) ).
fof(c_0_836_837,axiom,
! [X9,X10,X11,X12] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X12),X10) != hAPP(hAPP(c_Lambda_OdB_OApp,X11),X9)
| X12 = X11 ),
c_0_382 ).
fof(c_0_837_838,axiom,
! [X9,X10,X11,X12] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X12),X10) != hAPP(hAPP(c_Lambda_OdB_OApp,X11),X9)
| X10 = X9 ),
c_0_383 ).
fof(c_0_838_839,plain,
! [X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X24,X28,X3)
| c_lessequals(X28,X24,X3) ),
inference(fof_simplification,[status(thm)],[c_0_384]) ).
fof(c_0_839_840,plain,
! [X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X24,X24,X3)
| c_lessequals(X24,X24,X3) ),
inference(fof_simplification,[status(thm)],[c_0_385]) ).
fof(c_0_840_841,plain,
! [X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X28,X24,X3)
| c_HOL_Oord__class_Oless(X24,X28,X3) ),
inference(fof_simplification,[status(thm)],[c_0_386]) ).
fof(c_0_841_842,plain,
! [X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X28,X24,X3)
| c_lessequals(X24,X28,X3) ),
inference(fof_simplification,[status(thm)],[c_0_387]) ).
fof(c_0_842_843,plain,
! [X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X28,X24,X3)
| c_lessequals(X24,X28,X3) ),
inference(fof_simplification,[status(thm)],[c_0_388]) ).
fof(c_0_843_844,plain,
! [X28,X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Orderings_Oord__class_Omax(X24,X28,X3) = c_Orderings_Oord__class_Omax(X28,X24,X3) ),
inference(fof_simplification,[status(thm)],[c_0_389]) ).
fof(c_0_844_845,plain,
! [X45,X25,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X45) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X25) ),
inference(fof_simplification,[status(thm)],[c_0_390]) ).
fof(c_0_845_846,plain,
! [X44,X25,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X44) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X44),X25) ),
inference(fof_simplification,[status(thm)],[c_0_391]) ).
fof(c_0_846_847,plain,
! [X28,X24,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X28) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X28),X24) ),
inference(fof_simplification,[status(thm)],[c_0_392]) ).
fof(c_0_847_848,plain,
! [X15,X16,X30] :
( hAPP(X16,X15) = X30
| ~ c_Type_Otyping(X16,c_Lambda_OdB_OVar(X15),X30) ),
inference(fof_simplification,[status(thm)],[c_0_393]) ).
fof(c_0_848_849,axiom,
! [X22,X20] :
( c_HOL_Oord__class_Oless(X22,X20,tc_nat)
| c_HOL_Oord__class_Oless(X20,X22,tc_nat)
| X20 = X22 ),
c_0_394 ).
fof(c_0_849_850,axiom,
! [X28,X24] :
( c_HOL_Oord__class_Oless(X28,X24,tc_nat)
| c_HOL_Oord__class_Oless(X24,X28,tc_nat)
| X24 = X28 ),
c_0_395 ).
fof(c_0_850,plain,
! [X28,X24,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Ominus__class_Ominus(X24,X28,X3) != c_HOL_Ozero__class_Ozero(X3)
| X24 = X28 ),
inference(fof_simplification,[status(thm)],[c_0_396]) ).
fof(c_0_851,axiom,
! [X22,X20] :
( c_lessequals(X22,X20,tc_nat)
| c_lessequals(X20,X22,tc_nat) ),
c_0_397 ).
fof(c_0_852,plain,
! [X22,X25,X3] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X3)
| c_Power_Opower__class_Opower(X25,X22,X3) != c_HOL_Ozero__class_Ozero(X3)
| X25 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_398]) ).
fof(c_0_853,plain,
! [X24,X25,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| X24 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X25)
| X25 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_399]) ).
fof(c_0_854,plain,
! [X44,X25,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X25,X44,X3) != c_HOL_Ozero__class_Ozero(X3)
| X25 = X44 ),
inference(fof_simplification,[status(thm)],[c_0_400]) ).
fof(c_0_855,plain,
! [X44,X25,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X25,X44,X3) != c_HOL_Ozero__class_Ozero(X3)
| X25 = X44 ),
inference(fof_simplification,[status(thm)],[c_0_401]) ).
fof(c_0_856,plain,
! [X25,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),X25) != c_HOL_Ozero__class_Ozero(X3)
| X25 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_402]) ).
fof(c_0_857,axiom,
! [X46,X37,X3] :
( c_List_Olist_ONil(X3) != c_List_Oappend(X37,X46,X3)
| X37 = c_List_Olist_ONil(X3) ),
c_0_403 ).
fof(c_0_858,axiom,
! [X46,X37,X3] :
( c_List_Olist_ONil(X3) != c_List_Oappend(X37,X46,X3)
| X46 = c_List_Olist_ONil(X3) ),
c_0_404 ).
fof(c_0_859,axiom,
! [X46,X37,X3] :
( c_List_Oappend(X37,X46,X3) != c_List_Olist_ONil(X3)
| X37 = c_List_Olist_ONil(X3) ),
c_0_405 ).
fof(c_0_860,axiom,
! [X46,X37,X3] :
( c_List_Oappend(X37,X46,X3) != c_List_Olist_ONil(X3)
| X46 = c_List_Olist_ONil(X3) ),
c_0_406 ).
fof(c_0_861,plain,
! [X22,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)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X3),X22,X3) = c_HOL_Ozero__class_Ozero(X3)
| X22 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_407]) ).
fof(c_0_862,axiom,
! [X24,X22,X3] :
( c_List_Oreplicate(X22,X24,X3) != c_List_Olist_ONil(X3)
| X22 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_408 ).
fof(c_0_863,axiom,
! [X24,X22,X3] :
( c_List_Olist_ONil(X3) != c_List_Oreplicate(X22,X24,X3)
| X22 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_409 ).
fof(c_0_864,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_410]) ).
fof(c_0_865,plain,
! [X20,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X20,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_411]) ).
fof(c_0_866,plain,
! [X24,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X24,X24,X3) ),
inference(fof_simplification,[status(thm)],[c_0_412]) ).
fof(c_0_867,plain,
! [X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X24,X24,X3) ),
inference(fof_simplification,[status(thm)],[c_0_413]) ).
fof(c_0_868,plain,
! [X24,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X24,X24,X3) ),
inference(fof_simplification,[status(thm)],[c_0_414]) ).
fof(c_0_869,axiom,
! [X46,X37,X3] :
( c_List_Oappend(X37,X46,X3) != X37
| X46 = c_List_Olist_ONil(X3) ),
c_0_415 ).
fof(c_0_870,axiom,
! [X46,X37,X3] :
( X37 != c_List_Oappend(X37,X46,X3)
| X46 = c_List_Olist_ONil(X3) ),
c_0_416 ).
fof(c_0_871,axiom,
! [X46,X37,X3] :
( c_List_Oappend(X37,X46,X3) != X46
| X37 = c_List_Olist_ONil(X3) ),
c_0_417 ).
fof(c_0_872,axiom,
! [X46,X37,X3] :
( X46 != c_List_Oappend(X37,X46,X3)
| X37 = c_List_Olist_ONil(X3) ),
c_0_418 ).
fof(c_0_873,plain,
! [X22] :
( X22 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(X22,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_419]) ).
fof(c_0_874,plain,
! [X22,X3] :
( ~ class_Ring__and__Field_Osemiring__0(X3)
| ~ class_Power_Opower(X3)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X3),X22,X3) = c_HOL_Ozero__class_Ozero(X3)
| X22 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_420]) ).
fof(c_0_875,plain,
! [X8] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X8)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X8)) ),
inference(fof_simplification,[status(thm)],[c_0_421]) ).
fof(c_0_876,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_422]) ).
fof(c_0_877,axiom,
! [X22,X20] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X22) != c_HOL_Ozero__class_Ozero(tc_nat)
| X22 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_423 ).
fof(c_0_878,axiom,
! [X22,X20] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X22) != c_HOL_Ozero__class_Ozero(tc_nat)
| X20 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_424 ).
fof(c_0_879,axiom,
! [X24,X25] :
( X24 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X25)
| X25 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_425 ).
fof(c_0_880,axiom,
! [X22,X20] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X22) != X20
| X22 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_426 ).
fof(c_0_881,plain,
! [X24,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| X24 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),c_HOL_Ozero__class_Ozero(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_427]) ).
fof(c_0_882,plain,
! [X24,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Ominus__class_Ominus(X24,X24,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_428]) ).
fof(c_0_883,plain,
! [X24,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X24) = X24 ),
inference(fof_simplification,[status(thm)],[c_0_429]) ).
fof(c_0_884,plain,
! [X25,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X25) = X25 ),
inference(fof_simplification,[status(thm)],[c_0_430]) ).
fof(c_0_885,plain,
! [X25,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X25) = X25 ),
inference(fof_simplification,[status(thm)],[c_0_431]) ).
fof(c_0_886,plain,
! [X25,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X25) = X25 ),
inference(fof_simplification,[status(thm)],[c_0_432]) ).
fof(c_0_887,plain,
! [X25,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X25,c_HOL_Ozero__class_Ozero(X3),X3) = X25 ),
inference(fof_simplification,[status(thm)],[c_0_433]) ).
fof(c_0_888,plain,
! [X24,X3] :
( ~ class_Orderings_Obot(X3)
| c_lessequals(c_Orderings_Obot__class_Obot(X3),X24,X3) ),
inference(fof_simplification,[status(thm)],[c_0_434]) ).
fof(c_0_889,plain,
! [X25,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),c_HOL_Ozero__class_Ozero(X3)) = X25 ),
inference(fof_simplification,[status(thm)],[c_0_435]) ).
fof(c_0_890,plain,
! [X25,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),c_HOL_Ozero__class_Ozero(X3)) = X25 ),
inference(fof_simplification,[status(thm)],[c_0_436]) ).
fof(c_0_891,plain,
! [X25,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X25),c_HOL_Ozero__class_Ozero(X3)) = X25 ),
inference(fof_simplification,[status(thm)],[c_0_437]) ).
fof(c_0_892,plain,
! [X25,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X25,X25,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_438]) ).
fof(c_0_893,plain,
! [X24,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X24,X24,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_439]) ).
fof(c_0_894,plain,
! [X24,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X24,X24,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_440]) ).
fof(c_0_895,plain,
! [X24,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Orderings_Oord__class_Omax(X24,X24,X3) = X24 ),
inference(fof_simplification,[status(thm)],[c_0_441]) ).
fof(c_0_896,plain,
! [X24,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X24,X24,X3) ),
inference(fof_simplification,[status(thm)],[c_0_442]) ).
fof(c_0_897,plain,
! [X24,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X24,X24,X3) ),
inference(fof_simplification,[status(thm)],[c_0_443]) ).
fof(c_0_898,axiom,
! [X22] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X22,tc_nat)
| X22 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_444 ).
fof(c_0_899,plain,
! [X22,X20,X3] :
( ~ class_Nat_Osemiring__char__0(X3)
| c_Nat_Osemiring__1__class_Oof__nat(X20,X3) != c_Nat_Osemiring__1__class_Oof__nat(X22,X3)
| X20 = X22 ),
inference(fof_simplification,[status(thm)],[c_0_445]) ).
fof(c_0_900,plain,
! [X4,X5] :
( class_Orderings_Opreorder(tc_fun(X4,X5))
| ~ class_Orderings_Opreorder(X5) ),
inference(fof_simplification,[status(thm)],[c_0_446]) ).
fof(c_0_901,plain,
! [X4,X5] :
( class_Orderings_Oorder(tc_fun(X4,X5))
| ~ class_Orderings_Oorder(X5) ),
inference(fof_simplification,[status(thm)],[c_0_447]) ).
fof(c_0_902,plain,
! [X4,X5] :
( class_Orderings_Obot(tc_fun(X4,X5))
| ~ class_Orderings_Obot(X5) ),
inference(fof_simplification,[status(thm)],[c_0_448]) ).
fof(c_0_903,plain,
! [X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| c_List_Olistsum(c_List_Olist_ONil(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_449]) ).
fof(c_0_904,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_450]) ).
fof(c_0_905,plain,
! [X3] :
( ~ class_OrderedGroup_Osemigroup__add(X3)
| c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_451]) ).
fof(c_0_906,axiom,
! [X70,X61] :
( c_Lambda_OdB_OAbs(X61) != c_Lambda_OdB_OAbs(X70)
| X61 = X70 ),
c_0_452 ).
fof(c_0_907,axiom,
! [X51,X43] :
( c_Lambda_OdB_OVar(X43) != c_Lambda_OdB_OVar(X51)
| X43 = X51 ),
c_0_453 ).
fof(c_0_908,plain,
! [X18,X19,X20,X21] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),X18),X19)))
| ~ c_Type_Otyping(X20,X18,v_T____)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X18))
| ~ c_Type_Otyping(c_Type_Oshift(X20,X19,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X21) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_454])])]) ).
fof(c_0_909,plain,
! [X22,X23,X24] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X24,X23,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X24,X22,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X23,X22,tc_Lambda_OdB) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_455])])]) ).
fof(c_0_910,plain,
! [X14,X15,X16] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X16,X14,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X15,X14,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_456]) ).
fof(c_0_911,plain,
! [X14,X15,X16] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X16,X14,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X15,X14,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_457]) ).
fof(c_0_912,plain,
! [X14,X15,X16] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X16)),X15),X14,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X15))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X16),X15),c_HOL_Ozero__class_Ozero(tc_nat)),X14,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(variable_rename,[status(thm)],[c_0_458]) ).
fof(c_0_913,plain,
! [X68,X69,X70,X71,X72,X73,X74,X75,X76,X77] :
( hAPP(hAPP(X73,hAPP(hAPP(X73,X75),X74)),hAPP(hAPP(X73,X69),X68)) = hAPP(hAPP(X73,X69),hAPP(hAPP(X73,hAPP(hAPP(X73,X75),X74)),X68))
| ~ c_Groebner__Basis_Ogb__semiring(X76,X73,X72,X71,X70,X77) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_459])])]) ).
fof(c_0_914,plain,
! [X58,X59,X60,X61,X62,X63,X64,X65,X66,X67] :
( hAPP(hAPP(X65,hAPP(hAPP(X65,X66),X64)),hAPP(hAPP(X65,X63),X62)) = hAPP(hAPP(X65,hAPP(hAPP(X65,X66),X63)),hAPP(hAPP(X65,X64),X62))
| ~ c_Groebner__Basis_Ogb__semiring(X65,X61,X60,X59,X58,X67) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_460])])]) ).
fof(c_0_915,plain,
! [X68,X69,X70,X71,X72,X73,X74,X75,X76,X77] :
( hAPP(hAPP(X73,hAPP(hAPP(X73,X75),X74)),hAPP(hAPP(X73,X69),X68)) = hAPP(hAPP(X73,X75),hAPP(hAPP(X73,X74),hAPP(hAPP(X73,X69),X68)))
| ~ c_Groebner__Basis_Ogb__semiring(X76,X73,X72,X71,X70,X77) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_461])])]) ).
fof(c_0_916,plain,
! [X68,X69,X70,X71,X72,X73,X74,X75,X76,X77] :
( hAPP(hAPP(X73,hAPP(hAPP(X73,X75),X74)),hAPP(hAPP(X73,X69),X68)) = hAPP(hAPP(X73,hAPP(hAPP(X73,X75),X69)),hAPP(hAPP(X73,X74),X68))
| ~ c_Groebner__Basis_Ogb__semiring(X76,X73,X72,X71,X70,X77) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_462])])]) ).
fof(c_0_917,plain,
! [X72,X73,X74,X75,X76,X77,X78,X79,X80] :
( hAPP(hAPP(X77,hAPP(hAPP(X78,X73),X72)),X76) = hAPP(hAPP(X78,hAPP(hAPP(X77,X73),X76)),hAPP(hAPP(X77,X72),X76))
| ~ c_Groebner__Basis_Ogb__semiring(X79,X78,X77,X75,X74,X80) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_463])])]) ).
fof(c_0_918,plain,
! [X46,X47,X48,X49,X50,X51,X52,X53,X54] :
( hAPP(hAPP(X49,hAPP(hAPP(X52,X53),X51)),X50) = hAPP(hAPP(X52,hAPP(hAPP(X49,X53),X50)),hAPP(hAPP(X49,X51),X50))
| ~ c_Groebner__Basis_Ogb__semiring(X52,X49,X48,X47,X46,X54) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_464])])]) ).
fof(c_0_919,plain,
! [X45,X46,X47,X48,X49,X50,X51,X52,X53] :
( hAPP(hAPP(X51,hAPP(hAPP(X48,X52),X49)),hAPP(hAPP(X48,X50),X49)) = hAPP(hAPP(X48,hAPP(hAPP(X51,X52),X50)),X49)
| ~ c_Groebner__Basis_Ogb__semiring(X51,X48,X47,X46,X45,X53) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_465])])]) ).
fof(c_0_920,plain,
! [X75,X76,X77,X78,X79,X80,X81,X82,X83] :
( hAPP(hAPP(X81,hAPP(hAPP(X79,X75),X80)),hAPP(hAPP(X79,X75),X78)) = hAPP(hAPP(X79,X75),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X80),X78))
| ~ c_Groebner__Basis_Ogb__semiring(X82,X81,X79,X77,X76,X83) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_466])])]) ).
fof(c_0_921,plain,
! [X59,X60,X61,X62,X63,X64,X65,X66,X67] :
( hAPP(hAPP(X65,X61),hAPP(hAPP(X66,X60),X59)) = hAPP(hAPP(X66,hAPP(hAPP(X65,X61),X60)),hAPP(hAPP(X65,X61),X59))
| ~ c_Groebner__Basis_Ogb__semiring(X66,X65,X64,X63,X62,X67) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_467])])]) ).
fof(c_0_922,plain,
! [X46,X47,X48,X49,X50,X51,X52,X53,X54] :
( hAPP(hAPP(X52,hAPP(hAPP(X52,X53),X51)),X50) = hAPP(hAPP(X52,hAPP(hAPP(X52,X53),X50)),X51)
| ~ c_Groebner__Basis_Ogb__semiring(X52,X49,X48,X47,X46,X54) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_468])])]) ).
fof(c_0_923,plain,
! [X68,X69,X70,X71,X72,X73,X74,X75,X76] :
( hAPP(hAPP(X72,hAPP(hAPP(X72,X74),X73)),X68) = hAPP(hAPP(X72,hAPP(hAPP(X72,X74),X68)),X73)
| ~ c_Groebner__Basis_Ogb__semiring(X75,X72,X71,X70,X69,X76) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_469])])]) ).
fof(c_0_924,plain,
! [X43,X44,X45,X46,X47,X48,X49,X50] :
( hAPP(hAPP(X48,hAPP(hAPP(X46,X49),X47)),X47) = hAPP(hAPP(X46,hAPP(hAPP(X48,X49),X43)),X47)
| ~ c_Groebner__Basis_Ogb__semiring(X48,X46,X45,X44,X43,X50) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_470])])]) ).
fof(c_0_925,plain,
! [X59,X60,X61,X62,X63,X64,X65,X66,X67] :
( hAPP(hAPP(X65,X61),hAPP(hAPP(X65,X60),X59)) = hAPP(hAPP(X65,hAPP(hAPP(X65,X61),X60)),X59)
| ~ c_Groebner__Basis_Ogb__semiring(X66,X65,X64,X63,X62,X67) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_471])])]) ).
fof(c_0_926,plain,
! [X59,X60,X61,X62,X63,X64,X65,X66,X67] :
( hAPP(hAPP(X66,X61),hAPP(hAPP(X66,X60),X59)) = hAPP(hAPP(X66,hAPP(hAPP(X66,X61),X60)),X59)
| ~ c_Groebner__Basis_Ogb__semiring(X66,X65,X64,X63,X62,X67) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_472])])]) ).
fof(c_0_927,plain,
! [X58,X59,X60,X61,X62,X63,X64,X65,X66] :
( hAPP(hAPP(X64,X65),hAPP(hAPP(X64,X63),X62)) = hAPP(hAPP(X64,hAPP(hAPP(X64,X65),X63)),X62)
| ~ c_Groebner__Basis_Ogb__semiring(X64,X61,X60,X59,X58,X66) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_473])])]) ).
fof(c_0_928,plain,
! [X46,X47,X48,X49,X50,X51,X52,X53,X54] :
( hAPP(hAPP(X52,hAPP(hAPP(X52,X53),X51)),X50) = hAPP(hAPP(X52,X53),hAPP(hAPP(X52,X51),X50))
| ~ c_Groebner__Basis_Ogb__semiring(X52,X49,X48,X47,X46,X54) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_474])])]) ).
fof(c_0_929,plain,
! [X68,X69,X70,X71,X72,X73,X74,X75,X76] :
( hAPP(hAPP(X73,X74),hAPP(hAPP(X73,X69),X68)) = hAPP(hAPP(X73,hAPP(hAPP(X73,X74),X69)),X68)
| ~ c_Groebner__Basis_Ogb__semiring(X75,X73,X72,X71,X70,X76) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_475])])]) ).
fof(c_0_930,plain,
! [X68,X69,X70,X71,X72,X73,X74,X75,X76] :
( hAPP(hAPP(X72,hAPP(hAPP(X72,X74),X73)),X68) = hAPP(hAPP(X72,X74),hAPP(hAPP(X72,X73),X68))
| ~ c_Groebner__Basis_Ogb__semiring(X75,X72,X71,X70,X69,X76) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_476])])]) ).
fof(c_0_931,plain,
! [X43,X44,X45,X46,X47,X48,X49,X50] :
( hAPP(hAPP(X48,X47),hAPP(hAPP(X46,X49),X47)) = hAPP(hAPP(X46,hAPP(hAPP(X48,X49),X43)),X47)
| ~ c_Groebner__Basis_Ogb__semiring(X48,X46,X45,X44,X43,X50) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_477])])]) ).
fof(c_0_932,plain,
! [X58,X59,X60,X61,X62,X63,X64,X65,X66] :
( hAPP(hAPP(X64,X65),hAPP(hAPP(X64,X63),X62)) = hAPP(hAPP(X64,X63),hAPP(hAPP(X64,X65),X62))
| ~ c_Groebner__Basis_Ogb__semiring(X64,X61,X60,X59,X58,X66) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_478])])]) ).
fof(c_0_933,plain,
! [X68,X69,X70,X71,X72,X73,X74,X75,X76] :
( hAPP(hAPP(X73,X74),hAPP(hAPP(X73,X69),X68)) = hAPP(hAPP(X73,X69),hAPP(hAPP(X73,X74),X68))
| ~ c_Groebner__Basis_Ogb__semiring(X75,X73,X72,X71,X70,X76) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_479])])]) ).
fof(c_0_934,plain,
! [X43,X44,X45,X46,X47,X48,X49] :
( hAPP(hAPP(X48,X47),X47) = hAPP(hAPP(X46,hAPP(hAPP(X48,X43),X43)),X47)
| ~ c_Groebner__Basis_Ogb__semiring(X48,X46,X45,X44,X43,X49) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_480])])]) ).
fof(c_0_935,plain,
! [X43,X44,X45,X46,X47,X48,X49,X50] :
( hAPP(hAPP(X48,X44),X43) = hAPP(hAPP(X48,X43),X44)
| ~ c_Groebner__Basis_Ogb__semiring(X49,X48,X47,X46,X45,X50) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_481])])]) ).
fof(c_0_936,plain,
! [X43,X44,X45,X46,X47,X48,X49,X50] :
( hAPP(hAPP(X49,X44),X43) = hAPP(hAPP(X49,X43),X44)
| ~ c_Groebner__Basis_Ogb__semiring(X49,X48,X47,X46,X45,X50) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_482])])]) ).
fof(c_0_937,plain,
! [X46,X47,X48,X49,X50,X51,X52,X53] :
( hAPP(hAPP(X51,X52),X50) = hAPP(hAPP(X51,X50),X52)
| ~ c_Groebner__Basis_Ogb__semiring(X51,X49,X48,X47,X46,X53) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_483])])]) ).
fof(c_0_938,plain,
! [X45,X46,X47,X48,X49,X50,X51,X52] :
( hAPP(hAPP(X48,X50),X49) = hAPP(hAPP(X48,X49),X50)
| ~ c_Groebner__Basis_Ogb__semiring(X51,X48,X47,X46,X45,X52) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_484])])]) ).
fof(c_0_939,plain,
! [X43,X44,X45,X46,X47,X48,X49] :
( hAPP(hAPP(X46,X43),c_HOL_Ozero__class_Ozero(tc_nat)) = X44
| ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X49) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_485])])]) ).
fof(c_0_940,plain,
! [X43,X44,X45,X46,X47,X48,X49] :
( hAPP(hAPP(X47,X44),X43) = X43
| ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X49) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_486])])]) ).
fof(c_0_941,plain,
! [X43,X44,X45,X46,X47,X48,X49] :
( hAPP(hAPP(X47,X45),X43) = X45
| ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X49) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_487])])]) ).
fof(c_0_942,plain,
! [X43,X44,X45,X46,X47,X48,X49] :
( hAPP(hAPP(X48,X45),X43) = X43
| ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X49) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_488])])]) ).
fof(c_0_943,plain,
! [X43,X44,X45,X46,X47,X48,X49] :
( hAPP(hAPP(X46,X47),X43) = X47
| ~ c_Groebner__Basis_Ogb__semiring(X48,X46,X45,X44,X43,X49) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_489])])]) ).
fof(c_0_944,plain,
! [X43,X44,X45,X46,X47,X48,X49] :
( hAPP(hAPP(X46,X43),X47) = X47
| ~ c_Groebner__Basis_Ogb__semiring(X48,X46,X45,X44,X43,X49) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_490])])]) ).
fof(c_0_945,plain,
! [X43,X44,X45,X46,X47,X48,X49] :
( hAPP(hAPP(X46,X47),X44) = X44
| ~ c_Groebner__Basis_Ogb__semiring(X48,X46,X45,X44,X43,X49) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_491])])]) ).
fof(c_0_946,plain,
! [X43,X44,X45,X46,X47,X48,X49] :
( hAPP(hAPP(X46,X44),X47) = X44
| ~ c_Groebner__Basis_Ogb__semiring(X48,X46,X45,X44,X43,X49) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_492])])]) ).
fof(c_0_947,plain,
! [X43,X44,X45,X46,X47,X48,X49] :
( hAPP(hAPP(X47,X48),X44) = X48
| ~ c_Groebner__Basis_Ogb__semiring(X47,X46,X45,X44,X43,X49) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_493])])]) ).
fof(c_0_948,plain,
! [X43,X44,X45,X46,X47,X48,X49] :
( hAPP(hAPP(X47,X44),X48) = X48
| ~ c_Groebner__Basis_Ogb__semiring(X47,X46,X45,X44,X43,X49) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_494])])]) ).
fof(c_0_949,plain,
! [X37,X38,X39,X40,X41,X42] :
( ~ hBOOL(hAPP(X42,c_Lambda_OdB_OdB__case(X41,X40,X39,hAPP(hAPP(c_Lambda_OdB_OApp,X38),X37),t_a)))
| hBOOL(hAPP(X42,hAPP(hAPP(X40,X38),X37))) ),
inference(variable_rename,[status(thm)],[c_0_495]) ).
fof(c_0_950,plain,
! [X35,X36,X37,X38,X39,X40] :
( ~ hBOOL(hAPP(X40,c_Lambda_OdB_OdB__case(X37,X36,X35,hAPP(hAPP(c_Lambda_OdB_OApp,X39),X38),t_a)))
| hBOOL(hAPP(X40,hAPP(hAPP(X36,X39),X38))) ),
inference(variable_rename,[status(thm)],[c_0_496]) ).
fof(c_0_951,plain,
! [X31,X32,X33,X34,X35] :
( X35 = X34
| ~ c_Type_Otyping(X33,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X32),X31,tc_Lambda_OdB,tc_Lambda_OdB),X34)
| ~ c_Type_Otyping(X33,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X32),X31,tc_Lambda_OdB,tc_Lambda_OdB),X35) ),
inference(variable_rename,[status(thm)],[c_0_497]) ).
fof(c_0_952,plain,
! [X62,X63,X64,X65,X66] :
( ~ hBOOL(hAPP(X66,c_Lambda_OdB_OdB__case(X64,X63,X62,c_Lambda_OdB_OAbs(X65),t_a)))
| hBOOL(hAPP(X66,hAPP(X62,X65))) ),
inference(variable_rename,[status(thm)],[c_0_498]) ).
fof(c_0_953,plain,
! [X61,X62,X63,X64,X65] :
( ~ hBOOL(hAPP(X65,c_Lambda_OdB_OdB__case(X64,X63,X62,c_Lambda_OdB_OAbs(X61),t_a)))
| hBOOL(hAPP(X65,hAPP(X62,X61))) ),
inference(variable_rename,[status(thm)],[c_0_499]) ).
fof(c_0_954,plain,
! [X44,X45,X46,X47,X48] :
( ~ hBOOL(hAPP(X48,c_Lambda_OdB_OdB__case(X47,X46,X45,c_Lambda_OdB_OVar(X44),t_a)))
| hBOOL(hAPP(X48,hAPP(X47,X44))) ),
inference(variable_rename,[status(thm)],[c_0_500]) ).
fof(c_0_955,plain,
! [X53,X54,X55,X56,X57] :
( ~ hBOOL(hAPP(X57,c_Lambda_OdB_OdB__case(X56,X55,X54,c_Lambda_OdB_OVar(X53),t_a)))
| hBOOL(hAPP(X57,hAPP(X56,X53))) ),
inference(variable_rename,[status(thm)],[c_0_501]) ).
fof(c_0_956,plain,
! [X14,X15,X16] :
( ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X16),X15),c_HOL_Ozero__class_Ozero(tc_nat)),X14,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X15,tc_Lambda_OdB)
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X16)),X15),X14,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(variable_rename,[status(thm)],[c_0_502]) ).
fof(c_0_957,plain,
! [X7] :
( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X7,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_List_Olistsp(c_InductTermi_OIT,X7,tc_Lambda_OdB) ),
inference(variable_rename,[status(thm)],[c_0_503]) ).
fof(c_0_958,plain,
! [X23,X24] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X24),X23,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_List_Olistsp(c_InductTermi_OIT,X23,tc_Lambda_OdB) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_504])])]) ).
fof(c_0_959,plain,
! [X23,X24,X25,X26] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X26),X24,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X25),X23,tc_Lambda_OdB,tc_Lambda_OdB)
| X26 = X25 ),
inference(variable_rename,[status(thm)],[c_0_505]) ).
fof(c_0_960,plain,
! [X23,X24,X25,X26] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X26),X24,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X25),X23,tc_Lambda_OdB,tc_Lambda_OdB)
| X24 = X23 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_506])])]) ).
fof(c_0_961,plain,
! [X22,X23,X24,X25] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X25),X24,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X23),X22,tc_Lambda_OdB,tc_Lambda_OdB)
| X25 = X23 ),
inference(variable_rename,[status(thm)],[c_0_507]) ).
fof(c_0_962,plain,
! [X22,X23,X24,X25] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X25),X24,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X23),X22,tc_Lambda_OdB,tc_Lambda_OdB)
| X24 = X22 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_508])])]) ).
fof(c_0_963,plain,
! [X29,X30,X31,X32] :
( ~ class_OrderedGroup_Osemigroup__add(X32)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X32),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X32),X31),X30),X29,X32,X32) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X32),X31),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X32),X30,X29,X32,X32)) ),
inference(variable_rename,[status(thm)],[c_0_509]) ).
fof(c_0_964,plain,
! [X9,X10,X11] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X11,X9,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X10,X9,tc_Lambda_OdB,tc_Lambda_OdB)
| X11 = X10 ),
inference(variable_rename,[status(thm)],[c_0_510]) ).
fof(c_0_965,plain,
! [X29,X30,X31,X32,X33] :
( c_List_Ofoldl(X32,hAPP(hAPP(X32,X31),X30),X29,X33,X33) = hAPP(hAPP(X32,X31),c_List_Ofoldl(X32,X30,X29,X33,X33))
| ~ c_OrderedGroup_Osemigroup__add(X32,X33) ),
inference(variable_rename,[status(thm)],[c_0_511]) ).
fof(c_0_966,plain,
! [X28,X29,X30,X31,X32] :
( hAPP(hAPP(X31,X30),c_List_Ofoldl(X31,X29,X28,X32,X32)) = c_List_Ofoldl(X31,X30,X28,X32,X32)
| ~ c_OrderedGroup_Omonoid__add(X29,X31,X32) ),
inference(variable_rename,[status(thm)],[c_0_512]) ).
fof(c_0_967,plain,
! [X38,X39,X40] :
( ~ class_OrderedGroup_Omonoid__add(X40)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X40),X39,X38,X40,X40) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X40),X39),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X40),X38,c_HOL_Ozero__class_Ozero(X40),X40,X40)) ),
inference(variable_rename,[status(thm)],[c_0_513]) ).
fof(c_0_968,plain,
! [X25,X26,X27] :
( ~ class_OrderedGroup_Omonoid__add(X27)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X27),c_HOL_Ozero__class_Ozero(X27),X25,X27,X27)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X27),X26,X25,X27,X27) ),
inference(variable_rename,[status(thm)],[c_0_514]) ).
fof(c_0_969,plain,
! [X20,X21,X22,X23] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X23),X22) != c_List_Ofoldl(c_Lambda_OdB_OApp,X21,X20,tc_Lambda_OdB,tc_Lambda_OdB)
| X23 = c_List_Ofoldl(c_Lambda_OdB_OApp,X21,c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X23,X22,X21,X20),tc_Lambda_OdB,tc_Lambda_OdB)
| X20 = c_List_Olist_ONil(tc_Lambda_OdB) ),
inference(variable_rename,[status(thm)],[c_0_515]) ).
fof(c_0_970,plain,
! [X38,X39] :
( ~ class_OrderedGroup_Omonoid__add(X39)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X39),c_HOL_Ozero__class_Ozero(X39),X38,X39,X39) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X39),X38,c_HOL_Ozero__class_Ozero(X39),X39,X39) ),
inference(variable_rename,[status(thm)],[c_0_516]) ).
fof(c_0_971,plain,
! [X38,X39,X40] :
( ~ class_OrderedGroup_Oab__semigroup__add(X40)
| c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X40),X38,X39,X40,X40) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X40),X39,X38,X40,X40) ),
inference(variable_rename,[status(thm)],[c_0_517]) ).
fof(c_0_972,plain,
! [X20,X21,X22] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X22),X21) != c_List_Ofoldl(c_Lambda_OdB_OApp,X20,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,X22),X21) = X20 ),
inference(variable_rename,[status(thm)],[c_0_518]) ).
fof(c_0_973,plain,
! [X14,X15,X16] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X15,X14,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X16)
| X15 = c_Lambda_OdB_OAbs(X16) ),
inference(variable_rename,[status(thm)],[c_0_519]) ).
fof(c_0_974,plain,
! [X21,X22,X23] :
( c_Lambda_OdB_OVar(X23) != c_List_Ofoldl(c_Lambda_OdB_OApp,X22,X21,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OVar(X23) = X22 ),
inference(variable_rename,[status(thm)],[c_0_520]) ).
fof(c_0_975,plain,
! [X14,X15,X16] :
( c_Lambda_OdB_OAbs(X16) != c_List_Ofoldl(c_Lambda_OdB_OApp,X15,X14,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(X16) = X15 ),
inference(variable_rename,[status(thm)],[c_0_521]) ).
fof(c_0_976,plain,
! [X14,X15,X16] :
( c_Lambda_OdB_OAbs(X16) != c_List_Ofoldl(c_Lambda_OdB_OApp,X15,X14,tc_Lambda_OdB,tc_Lambda_OdB)
| X14 = c_List_Olist_ONil(tc_Lambda_OdB) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_522])])]) ).
fof(c_0_977,plain,
! [X14,X15,X16] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X15,X14,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X16)
| X14 = c_List_Olist_ONil(tc_Lambda_OdB) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_523])])]) ).
fof(c_0_978,plain,
! [X21,X22,X23] :
( c_Lambda_OdB_OVar(X23) != c_List_Ofoldl(c_Lambda_OdB_OApp,X22,X21,tc_Lambda_OdB,tc_Lambda_OdB)
| X21 = c_List_Olist_ONil(tc_Lambda_OdB) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_524])])]) ).
fof(c_0_979,plain,
! [X29,X30,X31,X32] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X31,X32),X29),X30))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X31,X32,X32),X32),X30),X29)) ),
inference(variable_rename,[status(thm)],[c_0_525]) ).
fof(c_0_980,plain,
! [X47,X48,X49,X50,X51,X52] :
( hBOOL(hAPP(hAPP(X51,X48),X50))
| c_ListOrder_Ostep1(X51,X47,X49,X52)
| ~ c_ListOrder_Ostep1(X51,c_List_Oappend(X47,c_List_Olist_OCons(X48,c_List_Olist_ONil(X52),X52),X52),c_List_Oappend(X49,c_List_Olist_OCons(X50,c_List_Olist_ONil(X52),X52),X52),X52) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_526])])]) ).
fof(c_0_981,plain,
! [X47,X48,X49,X50,X51,X52] :
( X47 = X49
| c_ListOrder_Ostep1(X51,X47,X49,X52)
| ~ c_ListOrder_Ostep1(X51,c_List_Oappend(X47,c_List_Olist_OCons(X48,c_List_Olist_ONil(X52),X52),X52),c_List_Oappend(X49,c_List_Olist_OCons(X50,c_List_Olist_ONil(X52),X52),X52),X52) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_527])])]) ).
fof(c_0_982,plain,
! [X35,X36,X37] :
( ~ hBOOL(hAPP(X37,c_Nat_Onat_Onat__case(X36,X35,c_HOL_Ozero__class_Ozero(tc_nat),t_a)))
| hBOOL(hAPP(X37,X36)) ),
inference(variable_rename,[status(thm)],[c_0_528]) ).
fof(c_0_983,plain,
! [X47,X48,X49,X50,X51,X52] :
( hBOOL(hAPP(hAPP(X51,X48),X50))
| X48 = X50
| ~ c_ListOrder_Ostep1(X51,c_List_Oappend(X47,c_List_Olist_OCons(X48,c_List_Olist_ONil(X52),X52),X52),c_List_Oappend(X49,c_List_Olist_OCons(X50,c_List_Olist_ONil(X52),X52),X52),X52) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_529])])]) ).
fof(c_0_984,plain,
! [X47,X48,X49,X50,X51,X52] :
( X47 = X49
| X48 = X50
| ~ c_ListOrder_Ostep1(X51,c_List_Oappend(X47,c_List_Olist_OCons(X48,c_List_Olist_ONil(X52),X52),X52),c_List_Oappend(X49,c_List_Olist_OCons(X50,c_List_Olist_ONil(X52),X52),X52),X52) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_530])])]) ).
fof(c_0_985,plain,
! [X20,X21,X22,X23] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X22),X20),X23)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X21),X20),X23)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X22),X21)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_531])])]) ).
fof(c_0_986,plain,
! [X20,X21,X22,X23] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X20),X22),X23)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X20),X21),X23)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X22),X21)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_532])])]) ).
fof(c_0_987,plain,
! [X29,X30,X31,X32] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X31,X32,X32),X32),X30),X29))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X31,X32),X29),X30)) ),
inference(variable_rename,[status(thm)],[c_0_533]) ).
fof(c_0_988,plain,
! [X18,X19,X20,X21] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),X18),X19)))
| ~ c_Type_Otyping(X20,X18,v_T____)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X18))
| ~ c_Type_Otyping(c_Type_Oshift(X20,X19,v_T____,tc_Type_Otype),v_a____,X21) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_534])])]) ).
fof(c_0_989,plain,
! [X20,X21,X22,X23] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X20),X22),X23)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X20),X21),X23)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X22),X21)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_535])])]) ).
fof(c_0_990,plain,
! [X38,X39] :
( ~ class_OrderedGroup_Omonoid__add(X39)
| c_List_Olistsum(X38,X39) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X39),X38,c_HOL_Ozero__class_Ozero(X39),X39,X39) ),
inference(variable_rename,[status(thm)],[c_0_536]) ).
fof(c_0_991,plain,
! [X38,X39] :
( ~ class_OrderedGroup_Omonoid__add(X39)
| c_List_Olistsum(X38,X39) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X39),c_HOL_Ozero__class_Ozero(X39),X38,X39,X39) ),
inference(variable_rename,[status(thm)],[c_0_537]) ).
fof(c_0_992,plain,
! [X20,X21,X22,X23] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(hAPP(c_Lambda_Osubst,X22),X20),X23)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X21),X20),X23)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X22),X21)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_538])])]) ).
fof(c_0_993,plain,
! [X63,X64,X65,X66,X67,X68] :
( ~ c_Type_Otyping(X66,X63,X67)
| ~ c_Type_Otyping(c_Type_Oshift(X66,X65,X67,tc_Type_Otype),X64,X68)
| c_Type_Otyping(X66,hAPP(hAPP(hAPP(c_Lambda_Osubst,X64),X63),X65),X68) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_539])])]) ).
fof(c_0_994,plain,
! [X64,X65,X66,X67] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X67),X65)),hAPP(hAPP(c_Lambda_OdB_OApp,X66),X64)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X65),X64))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X67),X66)) ),
inference(variable_rename,[status(thm)],[c_0_540]) ).
fof(c_0_995,plain,
! [X47,X48,X49,X50,X51,X52] :
( c_ListOrder_Ostep1(X51,X47,X49,X52)
| hBOOL(hAPP(hAPP(X51,X48),X50))
| ~ c_ListOrder_Ostep1(X51,c_List_Olist_OCons(X48,X47,X52),c_List_Olist_OCons(X50,X49,X52),X52) ),
inference(variable_rename,[status(thm)],[c_0_541]) ).
fof(c_0_996,plain,
! [X47,X48,X49,X50,X51,X52] :
( c_ListOrder_Ostep1(X51,X47,X49,X52)
| X49 = X47
| ~ c_ListOrder_Ostep1(X51,c_List_Olist_OCons(X48,X47,X52),c_List_Olist_OCons(X50,X49,X52),X52) ),
inference(variable_rename,[status(thm)],[c_0_542]) ).
fof(c_0_997,plain,
! [X58,X59,X60] :
( ~ hBOOL(hAPP(X60,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X59),X58),X59,tc_nat)))
| hBOOL(hAPP(X60,X58)) ),
inference(variable_rename,[status(thm)],[c_0_543]) ).
fof(c_0_998,plain,
! [X45,X46,X47] :
( ~ hBOOL(hAPP(X47,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X46),X45),X46,tc_nat)))
| hBOOL(hAPP(X47,X45)) ),
inference(variable_rename,[status(thm)],[c_0_544]) ).
fof(c_0_999,plain,
! [X74,X75,X76,X77,X78] :
( hBOOL(hAPP(hAPP(X74,X75),X76))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X74,X78,X77),X76),X75)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_545])])]) ).
fof(c_0_1000,plain,
! [X49,X50,X51,X52,X53] :
( hBOOL(hAPP(hAPP(X49,X50),X51))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X49,X53,X52),X51),X50)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_546])])]) ).
fof(c_0_1001,plain,
! [X47,X48,X49,X50,X51] :
( ~ c_ListOrder_Ostep1(X50,X47,X48,X51)
| c_ListOrder_Ostep1(X50,c_List_Oappend(X47,X49,X51),c_List_Oappend(X48,X49,X51),X51) ),
inference(variable_rename,[status(thm)],[c_0_547]) ).
fof(c_0_1002,plain,
! [X77,X78,X79,X80,X81] :
( c_ListOrder_Ostep1(X80,c_List_Oappend(X77,X78,X81),c_List_Oappend(X77,X79,X81),X81)
| ~ c_ListOrder_Ostep1(X80,X78,X79,X81) ),
inference(variable_rename,[status(thm)],[c_0_548]) ).
fof(c_0_1003,plain,
! [X47,X48,X49,X50,X51] :
( c_ListOrder_Ostep1(X50,c_List_Olist_OCons(X49,X47,X51),c_List_Olist_OCons(X49,X48,X51),X51)
| ~ c_ListOrder_Ostep1(X50,X47,X48,X51) ),
inference(variable_rename,[status(thm)],[c_0_549]) ).
fof(c_0_1004,plain,
! [X54,X55,X56] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X56),X55)),hAPP(hAPP(c_Lambda_OdB_OApp,X56),X54)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X55),X54)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_550])])]) ).
fof(c_0_1005,plain,
! [X64,X65,X66] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X66),X64)),hAPP(hAPP(c_Lambda_OdB_OApp,X65),X64)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X66),X65)) ),
inference(variable_rename,[status(thm)],[c_0_551]) ).
fof(c_0_1006,plain,
! [X16,X17,X18] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,X17),X18)),hAPP(hAPP(c_Lambda_Olift,X16),X18)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X17),X16)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_552])])]) ).
fof(c_0_1007,plain,
! [X47,X48,X49,X50,X51,X52] :
( X50 = X48
| hBOOL(hAPP(hAPP(X51,X48),X50))
| ~ c_ListOrder_Ostep1(X51,c_List_Olist_OCons(X48,X47,X52),c_List_Olist_OCons(X50,X49,X52),X52) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_553])])]) ).
fof(c_0_1008,plain,
! [X59,X60,X61,X62,X63] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X62,X63),X61),X59))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X62,X63),X60),X59))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X62,X63),X61),X60)) ),
inference(variable_rename,[status(thm)],[c_0_554]) ).
fof(c_0_1009,plain,
! [X47,X48,X49,X50,X51,X52] :
( X50 = X48
| X49 = X47
| ~ c_ListOrder_Ostep1(X51,c_List_Olist_OCons(X48,X47,X52),c_List_Olist_OCons(X50,X49,X52),X52) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_555])])]) ).
fof(c_0_1010,plain,
! [X58,X59,X60,X61,X62] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X62)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X62),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X62),X61),X60)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X62),X59),X58)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X62),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X62),X61),X59)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X62),X60),X58)) ),
inference(variable_rename,[status(thm)],[c_0_556]) ).
fof(c_0_1011,plain,
! [X31,X32,X33,X34,X35] :
( c_Type_Otyping(c_Type_Oshift(X33,X32,X34,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X31),X32),X35)
| ~ c_Type_Otyping(X33,X31,X35) ),
inference(variable_rename,[status(thm)],[c_0_557]) ).
fof(c_0_1012,plain,
! [X49,X50,X51,X52,X53] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X49,X53,X52),X50),X51))
| ~ hBOOL(hAPP(hAPP(X49,X51),X50)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_558])])]) ).
fof(c_0_1013,plain,
! [X49,X50,X51,X52,X53] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X49,X53,X52),X51),X50))
| ~ hBOOL(hAPP(hAPP(X49,X50),X51)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_559])])]) ).
fof(c_0_1014,plain,
! [X60,X61,X62] :
( c_lessequals(X61,X60,tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X61,X62,tc_nat),c_HOL_Ominus__class_Ominus(X60,X62,tc_nat),tc_nat)
| ~ c_lessequals(X62,X60,tc_nat)
| ~ c_lessequals(X62,X61,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_560])])]) ).
fof(c_0_1015,plain,
! [X60,X61,X62] :
( c_HOL_Oord__class_Oless(X61,X60,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X61,X62,tc_nat),c_HOL_Ominus__class_Ominus(X60,X62,tc_nat),tc_nat)
| ~ c_lessequals(X62,X60,tc_nat)
| ~ c_lessequals(X62,X61,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_561])])]) ).
fof(c_0_1016,plain,
! [X16,X17,X18] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,X17),X18)),hAPP(hAPP(c_Lambda_Olift,X16),X18)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X17),X16)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_562])])]) ).
fof(c_0_1017,plain,
! [X20,X21,X22] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X20),X22)),hAPP(hAPP(c_Lambda_OdB_OApp,X20),X21)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X22),X21)) ),
inference(variable_rename,[status(thm)],[c_0_563]) ).
fof(c_0_1018,plain,
! [X20,X21,X22] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X22),X20)),hAPP(hAPP(c_Lambda_OdB_OApp,X21),X20)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X22),X21)) ),
inference(variable_rename,[status(thm)],[c_0_564]) ).
fof(c_0_1019,plain,
! [X46,X47,X48,X49,X50] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X46,X50),X49),X47))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X46,X50),X48),X47))
| ~ hBOOL(hAPP(hAPP(X46,X49),X48)) ),
inference(variable_rename,[status(thm)],[c_0_565]) ).
fof(c_0_1020,plain,
! [X46,X47,X48,X49,X50] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X46,X50),X49),X47))
| ~ hBOOL(hAPP(hAPP(X46,X48),X47))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X46,X50),X49),X48)) ),
inference(variable_rename,[status(thm)],[c_0_566]) ).
fof(c_0_1021,plain,
! [X31,X32,X33,X34,X35] :
( hAPP(c_Type_Oshift(X33,X32,X34,X35),X31) = hAPP(X33,X31)
| ~ c_HOL_Oord__class_Oless(X31,X32,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_567])])]) ).
fof(c_0_1022,plain,
! [X61,X62,X63,X64,X65] :
( ~ hBOOL(hAPP(hAPP(X64,X61),X62))
| c_ListOrder_Ostep1(X64,c_List_Olist_OCons(X61,X63,X65),c_List_Olist_OCons(X62,X63,X65),X65) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_568])])]) ).
fof(c_0_1023,plain,
! [X45,X46,X47,X48] :
( ~ class_Ring__and__Field_Oordered__semidom(X48)
| c_HOL_Oord__class_Oless(X47,X46,X48)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X48),X46,X48)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X47,X45,X48),c_Power_Opower__class_Opower(X46,X45,X48),X48) ),
inference(variable_rename,[status(thm)],[c_0_569]) ).
fof(c_0_1024,plain,
! [X47,X48,X49,X50,X51] :
( c_List_Oappend(X49,c_List_Olist_OCons(X50,c_List_Olist_ONil(X51),X51),X51) != c_List_Oappend(X47,c_List_Olist_OCons(X48,c_List_Olist_ONil(X51),X51),X51)
| X49 = X47 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_570])])]) ).
fof(c_0_1025,plain,
! [X47,X48,X49,X50,X51] :
( c_List_Oappend(X49,c_List_Olist_OCons(X50,c_List_Olist_ONil(X51),X51),X51) != c_List_Oappend(X47,c_List_Olist_OCons(X48,c_List_Olist_ONil(X51),X51),X51)
| X50 = X48 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_571])])]) ).
fof(c_0_1026,plain,
! [X45,X46,X47,X48] :
( ~ class_Ring__and__Field_Oordered__semidom(X48)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X47,X45,X48),c_Power_Opower__class_Opower(X46,X45,X48),X48)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X45,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X48),X47,X48)
| ~ c_HOL_Oord__class_Oless(X47,X46,X48) ),
inference(variable_rename,[status(thm)],[c_0_572]) ).
fof(c_0_1027,plain,
! [X59,X60,X61,X62] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X62)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X62),c_Orderings_Oord__class_Omax(X61,X60,X62)),X59) = c_Orderings_Oord__class_Omax(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X62),X61),X59),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X62),X60),X59),X62) ),
inference(variable_rename,[status(thm)],[c_0_573]) ).
fof(c_0_1028,plain,
! [X46,X47,X48,X49] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X49)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X48),X47)),X46) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X48),X46)),X47) ),
inference(variable_rename,[status(thm)],[c_0_574]) ).
fof(c_0_1029,plain,
! [X60,X61,X62] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X61,X62,tc_nat),c_HOL_Ominus__class_Ominus(X60,X62,tc_nat),tc_nat)
| ~ c_lessequals(X61,X60,tc_nat)
| ~ c_lessequals(X62,X60,tc_nat)
| ~ c_lessequals(X62,X61,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_575]) ).
fof(c_0_1030,plain,
! [X60,X61,X62] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X61,X62,tc_nat),c_HOL_Ominus__class_Ominus(X60,X62,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X61,X60,tc_nat)
| ~ c_lessequals(X62,X60,tc_nat)
| ~ c_lessequals(X62,X61,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_576]) ).
fof(c_0_1031,plain,
! [X58,X59,X60,X61,X62] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X62)
| c_lessequals(X61,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X62),X60),X58),X62)
| ~ c_lessequals(X59,X58,X62)
| ~ c_lessequals(X61,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X62),X60),X59),X62) ),
inference(variable_rename,[status(thm)],[c_0_577]) ).
fof(c_0_1032,plain,
! [X45,X46,X47] :
( hBOOL(hAPP(X47,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X46,X45,tc_nat)
| ~ hBOOL(hAPP(X47,c_HOL_Ominus__class_Ominus(X46,X45,tc_nat))) ),
inference(variable_rename,[status(thm)],[c_0_578]) ).
fof(c_0_1033,plain,
! [X60,X61,X62] :
( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X61,X62,tc_nat),c_HOL_Ominus__class_Ominus(X60,X62,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X61,X60,tc_nat)
| ~ c_lessequals(X62,X60,tc_nat)
| ~ c_lessequals(X62,X61,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_579]) ).
fof(c_0_1034,plain,
! [X60,X61,X62] :
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X61),X62),X60,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X61,X60,tc_nat)),X62)
| ~ c_lessequals(X60,X61,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_580])])]) ).
fof(c_0_1035,plain,
! [X60,X61,X62] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X61,X60,tc_nat)),X62) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X61),X62),X60,tc_nat)
| ~ c_lessequals(X60,X61,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_581])])]) ).
fof(c_0_1036,plain,
! [X60,X61,X62] :
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X62),X60),X61,tc_nat)
| ~ c_lessequals(X62,c_HOL_Ominus__class_Ominus(X61,X60,tc_nat),tc_nat)
| ~ c_lessequals(X60,X61,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_582]) ).
fof(c_0_1037,plain,
! [X46,X47,X48,X49] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X49)
| c_lessequals(X48,X47,X49)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X48),X46),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X47),X46),X49) ),
inference(variable_rename,[status(thm)],[c_0_583]) ).
fof(c_0_1038,plain,
! [X46,X47,X48,X49] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X49)
| c_lessequals(X48,X47,X49)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X46),X48),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X46),X47),X49) ),
inference(variable_rename,[status(thm)],[c_0_584]) ).
fof(c_0_1039,plain,
! [X46,X47,X48,X49] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X49)
| c_HOL_Oord__class_Oless(X48,X47,X49)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X48),X46),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X47),X46),X49) ),
inference(variable_rename,[status(thm)],[c_0_585]) ).
fof(c_0_1040,plain,
! [X46,X47,X48,X49] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X49)
| c_HOL_Oord__class_Oless(X48,X47,X49)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X46),X48),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X46),X47),X49) ),
inference(variable_rename,[status(thm)],[c_0_586]) ).
fof(c_0_1041,plain,
! [X60,X61,X62] :
( c_lessequals(X62,c_HOL_Ominus__class_Ominus(X61,X60,tc_nat),tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X62),X60),X61,tc_nat)
| ~ c_lessequals(X60,X61,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_587]) ).
fof(c_0_1042,plain,
! [X45,X46,X47,X48] :
( ~ class_Ring__and__Field_Oordered__semidom(X48)
| c_Power_Opower__class_Opower(X47,X45,X48) != c_Power_Opower__class_Opower(X46,X45,X48)
| X47 = X46
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X45,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X48),X46,X48)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X48),X47,X48) ),
inference(variable_rename,[status(thm)],[c_0_588]) ).
fof(c_0_1043,plain,
! [X19,X20,X21] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X19),c_Lambda_OdB_OVar(X21)),X20)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X19)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_589])])]) ).
fof(c_0_1044,plain,
! [X45,X46,X47,X48] :
( ~ class_Ring__and__Field_Oordered__semidom(X48)
| c_lessequals(c_Power_Opower__class_Opower(X47,X45,X48),c_Power_Opower__class_Opower(X46,X45,X48),X48)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X48),X47,X48)
| ~ c_lessequals(X47,X46,X48) ),
inference(variable_rename,[status(thm)],[c_0_590]) ).
fof(c_0_1045,plain,
! [X64,X65] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X65)),c_Lambda_OdB_OAbs(X64)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X65),X64)) ),
inference(variable_rename,[status(thm)],[c_0_591]) ).
fof(c_0_1046,plain,
! [X58,X59,X60,X61,X62] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X62)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X62),X61),X59),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X62),X60),X58),X62)
| ~ c_lessequals(X59,X58,X62)
| ~ c_lessequals(X61,X60,X62) ),
inference(variable_rename,[status(thm)],[c_0_592]) ).
fof(c_0_1047,plain,
! [X58,X59,X60,X61,X62] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X62)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X62),X61),X59),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X62),X60),X58),X62)
| ~ c_HOL_Oord__class_Oless(X59,X58,X62)
| ~ c_HOL_Oord__class_Oless(X61,X60,X62) ),
inference(variable_rename,[status(thm)],[c_0_593]) ).
fof(c_0_1048,plain,
! [X58,X59,X60,X61,X62] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X62)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X62),X61),X59),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X62),X60),X58),X62)
| ~ c_HOL_Oord__class_Oless(X59,X58,X62)
| ~ c_lessequals(X61,X60,X62) ),
inference(variable_rename,[status(thm)],[c_0_594]) ).
fof(c_0_1049,plain,
! [X58,X59,X60,X61,X62] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X62)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X62),X61),X59),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X62),X60),X58),X62)
| ~ c_lessequals(X59,X58,X62)
| ~ c_HOL_Oord__class_Oless(X61,X60,X62) ),
inference(variable_rename,[status(thm)],[c_0_595]) ).
fof(c_0_1050,plain,
! [X59,X60,X61,X62] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X62)
| c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(X61,X60,X62),X59,X62) = c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(X61,X59,X62),c_HOL_Ominus__class_Ominus(X60,X59,X62),X62) ),
inference(variable_rename,[status(thm)],[c_0_596]) ).
fof(c_0_1051,plain,
! [X45,X46,X47,X48] :
( c_Wellfounded_Oaccp(X45,X46,X48)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X45,X48),X46),X47))
| ~ c_Wellfounded_Oaccp(X45,X47,X48) ),
inference(variable_rename,[status(thm)],[c_0_597]) ).
fof(c_0_1052,plain,
! [X45,X46,X47,X48] :
( c_Wellfounded_Oaccp(X45,X46,X48)
| ~ c_Wellfounded_Oaccp(X45,X47,X48)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X45,X48),X46),X47)) ),
inference(variable_rename,[status(thm)],[c_0_598]) ).
fof(c_0_1053,plain,
! [X70,X71,X72] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X72,X70,tc_nat),c_HOL_Ominus__class_Ominus(X72,X71,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X71,X72,tc_nat)
| ~ c_HOL_Oord__class_Oless(X71,X70,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_599]) ).
fof(c_0_1054,plain,
! [X46,X47,X48] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X48,X46,tc_nat),c_HOL_Ominus__class_Ominus(X47,X46,tc_nat),tc_nat)
| ~ c_lessequals(X46,X48,tc_nat)
| ~ c_HOL_Oord__class_Oless(X48,X47,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_600]) ).
fof(c_0_1055,plain,
! [X60,X61,X62] :
( c_lessequals(X61,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X60),X61),X62,tc_nat),tc_nat)
| ~ c_lessequals(X62,X60,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_601]) ).
fof(c_0_1056,plain,
! [X60,X61,X62] :
( c_lessequals(X61,X60,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X62),X61),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X62),X60),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_602])])]) ).
fof(c_0_1057,plain,
! [X60,X61,X62] :
( c_HOL_Oord__class_Oless(X61,X60,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X62),X61),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X62),X60),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_603])])]) ).
fof(c_0_1058,plain,
! [X59,X60,X61,X62] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X62)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X62),X61),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X62),X60),X59)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X62),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X62),X61),X60)),X59) ),
inference(variable_rename,[status(thm)],[c_0_604]) ).
fof(c_0_1059,plain,
! [X46,X47,X48,X49] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X49)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X48),X47)),X46) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X48),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X47),X46)) ),
inference(variable_rename,[status(thm)],[c_0_605]) ).
fof(c_0_1060,plain,
! [X46,X47,X48,X49] :
( ~ class_OrderedGroup_Oab__semigroup__add(X49)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X48),X47)),X46) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X48),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X47),X46)) ),
inference(variable_rename,[status(thm)],[c_0_606]) ).
fof(c_0_1061,plain,
! [X58,X59,X60,X61] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X61)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X61),X60),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X61),X59),X58)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X61),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X61),X60),X59)),X58) ),
inference(variable_rename,[status(thm)],[c_0_607]) ).
fof(c_0_1062,plain,
! [X46,X47,X48,X49] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X49)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X48),X47)),X46) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X48),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X47),X46)) ),
inference(variable_rename,[status(thm)],[c_0_608]) ).
fof(c_0_1063,plain,
! [X70,X71,X72,X73] :
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X73),X71),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X72),X70),tc_nat)
| ~ c_lessequals(X71,X70,tc_nat)
| ~ c_lessequals(X73,X72,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_609]) ).
fof(c_0_1064,plain,
! [X70,X71,X72,X73] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X73),X71),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X72),X70),tc_nat)
| ~ c_HOL_Oord__class_Oless(X71,X70,tc_nat)
| ~ c_HOL_Oord__class_Oless(X73,X72,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_610]) ).
fof(c_0_1065,plain,
! [X49,X50,X51,X52] :
( c_List_Olist_ONil(X52) != c_List_Omap(X50,X49,X51,X52)
| X49 = c_List_Olist_ONil(X51) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_611])])]) ).
fof(c_0_1066,plain,
! [X49,X50,X51,X52] :
( c_List_Omap(X50,X49,X51,X52) != c_List_Olist_ONil(X52)
| X49 = c_List_Olist_ONil(X51) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_612])])]) ).
fof(c_0_1067,plain,
! [X54,X55,X56,X57] :
( c_Type_Otyping(X56,X54,X57)
| ~ c_Type_Otyping(X56,X55,X57)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X55),X54)) ),
inference(variable_rename,[status(thm)],[c_0_613]) ).
fof(c_0_1068,plain,
! [X60,X61,X62] :
( c_lessequals(X61,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X62),X60),tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X61,X60,tc_nat),X62,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_614]) ).
fof(c_0_1069,plain,
! [X60,X61,X62] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X62),X60),X61,tc_nat)
| ~ c_HOL_Oord__class_Oless(X62,c_HOL_Ominus__class_Ominus(X61,X60,tc_nat),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_615]) ).
fof(c_0_1070,plain,
! [X59,X60,X61,X62,X63] :
( ~ class_OrderedGroup_Oab__group__add(X63)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X63),X61),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X63),X60),X59)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X63),X60),X62)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X63),X61),X59) = X62 ),
inference(variable_rename,[status(thm)],[c_0_616]) ).
fof(c_0_1071,plain,
! [X60,X61,X62] :
( c_HOL_Ominus__class_Ominus(X62,c_HOL_Ominus__class_Ominus(X61,X60,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X62),X60),X61,tc_nat)
| ~ c_lessequals(X60,X61,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_617])])]) ).
fof(c_0_1072,plain,
! [X60,X61,X62] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X61,X60,tc_nat),X62,tc_nat)
| ~ c_lessequals(X61,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X62),X60),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_618]) ).
fof(c_0_1073,plain,
! [X60,X61,X62] :
( c_HOL_Oord__class_Oless(X62,c_HOL_Ominus__class_Ominus(X61,X60,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X62),X60),X61,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_619]) ).
fof(c_0_1074,plain,
! [X60,X61,X62] :
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X62),X61),X60,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X62),c_HOL_Ominus__class_Ominus(X61,X60,tc_nat))
| ~ c_lessequals(X60,X61,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_620])])]) ).
fof(c_0_1075,plain,
! [X60,X61,X62] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X62),c_HOL_Ominus__class_Ominus(X61,X60,tc_nat)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X62),X61),X60,tc_nat)
| ~ c_lessequals(X60,X61,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_621])])]) ).
fof(c_0_1076,plain,
! [X59,X60,X61,X62] :
( ~ class_Orderings_Olinorder(X62)
| c_lessequals(X59,X60,X62)
| c_lessequals(X59,X61,X62)
| ~ c_lessequals(X59,c_Orderings_Oord__class_Omax(X61,X60,X62),X62) ),
inference(variable_rename,[status(thm)],[c_0_622]) ).
fof(c_0_1077,plain,
! [X59,X60,X61,X62] :
( ~ class_Orderings_Olinorder(X62)
| c_HOL_Oord__class_Oless(X59,X60,X62)
| c_HOL_Oord__class_Oless(X59,X61,X62)
| ~ c_HOL_Oord__class_Oless(X59,c_Orderings_Oord__class_Omax(X61,X60,X62),X62) ),
inference(variable_rename,[status(thm)],[c_0_623]) ).
fof(c_0_1078,plain,
! [X60,X61] :
( ~ c_lessequals(X61,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X60),X61),tc_nat)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X60),X61),X61,tc_nat) = X60 ),
inference(variable_rename,[status(thm)],[c_0_624]) ).
fof(c_0_1079,plain,
! [X45,X46,X47] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X47)
| c_lessequals(c_HOL_Ozero__class_Ozero(X47),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X47),X46),X45),X47)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X47),X45,X47)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X47),X46,X47) ),
inference(variable_rename,[status(thm)],[c_0_625]) ).
fof(c_0_1080,plain,
! [X45,X46,X47] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X47)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X47),X46),X45),c_HOL_Ozero__class_Ozero(X47),X47)
| ~ c_HOL_Oord__class_Oless(X45,c_HOL_Ozero__class_Ozero(X47),X47)
| ~ c_HOL_Oord__class_Oless(X46,c_HOL_Ozero__class_Ozero(X47),X47) ),
inference(variable_rename,[status(thm)],[c_0_626]) ).
fof(c_0_1081,plain,
! [X45,X46,X47] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X47)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X47),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X47),X46),X45),X47)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X47),X45,X47)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X47),X46,X47) ),
inference(variable_rename,[status(thm)],[c_0_627]) ).
fof(c_0_1082,plain,
! [X45,X46,X47] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X47)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X47),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X47),X46),X45),X47)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X47),X45,X47)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X47),X46,X47) ),
inference(variable_rename,[status(thm)],[c_0_628]) ).
fof(c_0_1083,plain,
! [X45,X46,X47] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X47)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X47),X46),X45),c_HOL_Ozero__class_Ozero(X47),X47)
| ~ c_HOL_Oord__class_Oless(X45,c_HOL_Ozero__class_Ozero(X47),X47)
| ~ c_lessequals(X46,c_HOL_Ozero__class_Ozero(X47),X47) ),
inference(variable_rename,[status(thm)],[c_0_629]) ).
fof(c_0_1084,plain,
! [X45,X46,X47] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X47)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X47),X46),X45),c_HOL_Ozero__class_Ozero(X47),X47)
| ~ c_lessequals(X45,c_HOL_Ozero__class_Ozero(X47),X47)
| ~ c_HOL_Oord__class_Oless(X46,c_HOL_Ozero__class_Ozero(X47),X47) ),
inference(variable_rename,[status(thm)],[c_0_630]) ).
fof(c_0_1085,plain,
! [X45,X46,X47] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X47)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X47),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X47),X46),X45),X47)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X47),X45,X47)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X47),X46,X47) ),
inference(variable_rename,[status(thm)],[c_0_631]) ).
fof(c_0_1086,plain,
! [X45,X46,X47] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X47)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X47),X46),X45),c_HOL_Ozero__class_Ozero(X47),X47)
| ~ c_lessequals(X45,c_HOL_Ozero__class_Ozero(X47),X47)
| ~ c_lessequals(X46,c_HOL_Ozero__class_Ozero(X47),X47) ),
inference(variable_rename,[status(thm)],[c_0_632]) ).
fof(c_0_1087,plain,
! [X46,X47,X48,X49] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X49)
| ~ class_OrderedGroup_Ocomm__monoid__add(X49)
| c_HOL_Oord__class_Oless(X47,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X48),X46),X49)
| ~ c_lessequals(X47,X46,X49)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X49),X48,X49) ),
inference(variable_rename,[status(thm)],[c_0_633]) ).
fof(c_0_1088,plain,
! [X46,X47,X48,X49] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X49)
| ~ class_OrderedGroup_Ocomm__monoid__add(X49)
| c_lessequals(X47,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X48),X46),X49)
| ~ c_lessequals(X47,X46,X49)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X49),X48,X49) ),
inference(variable_rename,[status(thm)],[c_0_634]) ).
fof(c_0_1089,plain,
! [X46,X47,X48,X49] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X49)
| ~ class_OrderedGroup_Ocomm__monoid__add(X49)
| c_lessequals(X47,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X48),X46),X49)
| ~ c_lessequals(X47,X48,X49)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X49),X46,X49) ),
inference(variable_rename,[status(thm)],[c_0_635]) ).
fof(c_0_1090,plain,
! [X46,X47,X48,X49] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X49)
| ~ class_OrderedGroup_Ocomm__monoid__add(X49)
| c_HOL_Oord__class_Oless(X47,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X48),X46),X49)
| ~ c_HOL_Oord__class_Oless(X47,X46,X49)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X49),X48,X49) ),
inference(variable_rename,[status(thm)],[c_0_636]) ).
fof(c_0_1091,plain,
! [X46,X47,X48,X49] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X49)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X48),X46),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X47),X46),X49)
| ~ c_lessequals(X48,X47,X49) ),
inference(variable_rename,[status(thm)],[c_0_637]) ).
fof(c_0_1092,plain,
! [X46,X47,X48,X49] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X49)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X46),X48),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X46),X47),X49)
| ~ c_lessequals(X48,X47,X49) ),
inference(variable_rename,[status(thm)],[c_0_638]) ).
fof(c_0_1093,plain,
! [X46,X47,X48,X49] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X49)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X48),X46),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X47),X46),X49)
| ~ c_lessequals(X48,X47,X49) ),
inference(variable_rename,[status(thm)],[c_0_639]) ).
fof(c_0_1094,plain,
! [X46,X47,X48,X49] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X49)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X46),X48),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X46),X47),X49)
| ~ c_lessequals(X48,X47,X49) ),
inference(variable_rename,[status(thm)],[c_0_640]) ).
fof(c_0_1095,plain,
! [X46,X47,X48,X49] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X49)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X48),X46),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X47),X46),X49)
| ~ c_HOL_Oord__class_Oless(X48,X47,X49) ),
inference(variable_rename,[status(thm)],[c_0_641]) ).
fof(c_0_1096,plain,
! [X46,X47,X48,X49] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X49)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X48),X46),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X47),X46),X49)
| ~ c_HOL_Oord__class_Oless(X48,X47,X49) ),
inference(variable_rename,[status(thm)],[c_0_642]) ).
fof(c_0_1097,plain,
! [X46,X47,X48,X49] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X49)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X46),X48),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X46),X47),X49)
| ~ c_HOL_Oord__class_Oless(X48,X47,X49) ),
inference(variable_rename,[status(thm)],[c_0_643]) ).
fof(c_0_1098,plain,
! [X46,X47,X48,X49] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X49)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X46),X48),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X46),X47),X49)
| ~ c_HOL_Oord__class_Oless(X48,X47,X49) ),
inference(variable_rename,[status(thm)],[c_0_644]) ).
fof(c_0_1099,plain,
! [X46,X47,X48,X49] :
( ~ class_Ring__and__Field_Oordered__semidom(X49)
| c_HOL_Oord__class_Oless(X47,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X48),X46),X49)
| ~ c_HOL_Oord__class_Oless(X47,X46,X49)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X49),X48,X49) ),
inference(variable_rename,[status(thm)],[c_0_645]) ).
fof(c_0_1100,plain,
! [X70,X71,X72] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X72,X70,tc_nat),c_HOL_Ominus__class_Ominus(X72,X71,tc_nat),tc_nat)
| ~ c_lessequals(X71,X70,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_646])])]) ).
fof(c_0_1101,plain,
! [X70,X71,X72] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X71,X72,tc_nat),c_HOL_Ominus__class_Ominus(X70,X72,tc_nat),tc_nat)
| ~ c_lessequals(X71,X70,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_647])])]) ).
fof(c_0_1102,plain,
! [X23,X24] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X23,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X24,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X23),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_648])])]) ).
fof(c_0_1103,plain,
! [X59,X60,X61,X62] :
( ~ class_Orderings_Olinorder(X62)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X61,X60,X62),X59,X62)
| ~ c_HOL_Oord__class_Oless(X60,X59,X62)
| ~ c_HOL_Oord__class_Oless(X61,X59,X62) ),
inference(variable_rename,[status(thm)],[c_0_649]) ).
fof(c_0_1104,plain,
! [X59,X60,X61,X62] :
( ~ class_Orderings_Olinorder(X62)
| c_lessequals(c_Orderings_Oord__class_Omax(X61,X60,X62),X59,X62)
| ~ c_lessequals(X60,X59,X62)
| ~ c_lessequals(X61,X59,X62) ),
inference(variable_rename,[status(thm)],[c_0_650]) ).
fof(c_0_1105,plain,
! [X59,X60,X61,X62] :
( ~ class_Orderings_Olinorder(X62)
| c_lessequals(c_Orderings_Oord__class_Omax(X60,X59,X62),X61,X62)
| ~ c_lessequals(X59,X61,X62)
| ~ c_lessequals(X60,X61,X62) ),
inference(variable_rename,[status(thm)],[c_0_651]) ).
fof(c_0_1106,plain,
! [X45,X46,X47,X48] :
( ~ class_Orderings_Olinorder(X48)
| c_lessequals(c_Orderings_Oord__class_Omax(X47,X46,X48),X45,X48)
| ~ c_lessequals(X46,X45,X48)
| ~ c_lessequals(X47,X45,X48) ),
inference(variable_rename,[status(thm)],[c_0_652]) ).
fof(c_0_1107,plain,
! [X19,X20] :
( ~ c_lessequals(X20,X19,tc_nat)
| X19 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X19,X20,tc_nat)),X20) ),
inference(variable_rename,[status(thm)],[c_0_653]) ).
fof(c_0_1108,plain,
! [X23,X24] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X24,X23,tc_nat)),X23) = X24
| ~ c_lessequals(X23,X24,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_654]) ).
fof(c_0_1109,plain,
! [X60,X61,X62] :
( c_HOL_Ominus__class_Ominus(X61,X62,tc_nat) != c_HOL_Ominus__class_Ominus(X60,X62,tc_nat)
| ~ c_lessequals(X62,X60,tc_nat)
| ~ c_lessequals(X62,X61,tc_nat)
| X61 = X60 ),
inference(variable_rename,[status(thm)],[c_0_655]) ).
fof(c_0_1110,plain,
! [X46,X47,X48,X49,X50] :
( hAPP(hAPP(X46,hAPP(hAPP(X46,X49),X48)),X47) = hAPP(hAPP(X46,X49),hAPP(hAPP(X46,X48),X47))
| ~ c_OrderedGroup_Osemigroup__add(X46,X50) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_656])])]) ).
fof(c_0_1111,plain,
! [X23,X24] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X24,X23,tc_nat),X24,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X24,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X23,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_657]) ).
fof(c_0_1112,plain,
! [X69,X70,X71,X72] :
( c_List_Olistsp(X71,c_List_Oappend(X70,X69,X72),X72)
| ~ c_List_Olistsp(X71,X69,X72)
| ~ c_List_Olistsp(X71,X70,X72) ),
inference(variable_rename,[status(thm)],[c_0_658]) ).
fof(c_0_1113,plain,
! [X59,X60,X61,X62] :
( ~ class_Orderings_Olinorder(X62)
| c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X61,X60,X62),X59,X62) = c_Orderings_Oord__class_Omax(X61,c_Orderings_Oord__class_Omax(X60,X59,X62),X62) ),
inference(variable_rename,[status(thm)],[c_0_659]) ).
fof(c_0_1114,plain,
! [X59,X60,X61,X62] :
( ~ class_Orderings_Olinorder(X62)
| c_Orderings_Oord__class_Omax(X61,c_Orderings_Oord__class_Omax(X60,X59,X62),X62) = c_Orderings_Oord__class_Omax(X60,c_Orderings_Oord__class_Omax(X61,X59,X62),X62) ),
inference(variable_rename,[status(thm)],[c_0_660]) ).
fof(c_0_1115,plain,
! [X45,X46,X47] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X47)
| c_lessequals(X46,X45,X47)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X46,X45,X47),c_HOL_Ozero__class_Ozero(X47),X47) ),
inference(variable_rename,[status(thm)],[c_0_661]) ).
fof(c_0_1116,plain,
! [X45,X46,X47] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X47)
| c_HOL_Oord__class_Oless(X46,X45,X47)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X46,X45,X47),c_HOL_Ozero__class_Ozero(X47),X47) ),
inference(variable_rename,[status(thm)],[c_0_662]) ).
fof(c_0_1117,plain,
! [X26,X27] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X27)
| c_lessequals(c_HOL_Ozero__class_Ozero(X27),X26,X27)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X26),X27) ),
inference(variable_rename,[status(thm)],[c_0_663]) ).
fof(c_0_1118,plain,
! [X26,X27] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X27)
| c_HOL_Oord__class_Oless(X26,c_HOL_Ozero__class_Ozero(X27),X27)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X26),c_HOL_Ozero__class_Ozero(X27),X27) ),
inference(variable_rename,[status(thm)],[c_0_664]) ).
fof(c_0_1119,plain,
! [X26,X27] :
( ~ class_Ring__and__Field_Oordered__idom(X27)
| c_HOL_Oord__class_Oless(X26,c_HOL_Ozero__class_Ozero(X27),X27)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X26),c_HOL_Ozero__class_Ozero(X27),X27) ),
inference(variable_rename,[status(thm)],[c_0_665]) ).
fof(c_0_1120,plain,
! [X26,X27] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X27)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X27),X26,X27)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X26),X27) ),
inference(variable_rename,[status(thm)],[c_0_666]) ).
fof(c_0_1121,plain,
! [X26,X27] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X27)
| c_lessequals(X26,c_HOL_Ozero__class_Ozero(X27),X27)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X26),c_HOL_Ozero__class_Ozero(X27),X27) ),
inference(variable_rename,[status(thm)],[c_0_667]) ).
fof(c_0_1122,plain,
! [X51,X52,X53,X54,X55] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X55)
| c_HOL_Ominus__class_Ominus(X54,X52,X55) != c_HOL_Ominus__class_Ominus(X53,X51,X55)
| c_lessequals(X51,X53,X55)
| ~ c_lessequals(X52,X54,X55) ),
inference(variable_rename,[status(thm)],[c_0_668]) ).
fof(c_0_1123,plain,
! [X51,X52,X53,X54,X55] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X55)
| c_HOL_Ominus__class_Ominus(X54,X52,X55) != c_HOL_Ominus__class_Ominus(X53,X51,X55)
| c_lessequals(X52,X54,X55)
| ~ c_lessequals(X51,X53,X55) ),
inference(variable_rename,[status(thm)],[c_0_669]) ).
fof(c_0_1124,plain,
! [X51,X52,X53,X54,X55] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X55)
| c_HOL_Ominus__class_Ominus(X54,X52,X55) != c_HOL_Ominus__class_Ominus(X53,X51,X55)
| c_HOL_Oord__class_Oless(X53,X51,X55)
| ~ c_HOL_Oord__class_Oless(X54,X52,X55) ),
inference(variable_rename,[status(thm)],[c_0_670]) ).
fof(c_0_1125,plain,
! [X51,X52,X53,X54,X55] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X55)
| c_HOL_Ominus__class_Ominus(X54,X52,X55) != c_HOL_Ominus__class_Ominus(X53,X51,X55)
| c_HOL_Oord__class_Oless(X54,X52,X55)
| ~ c_HOL_Oord__class_Oless(X53,X51,X55) ),
inference(variable_rename,[status(thm)],[c_0_671]) ).
fof(c_0_1126,plain,
! [X60,X61,X62] :
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X62),X60),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X61),X60),tc_nat)
| ~ c_lessequals(X62,X61,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_672]) ).
fof(c_0_1127,plain,
! [X60,X61,X62] :
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X62),X61),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X62),X60),tc_nat)
| ~ c_lessequals(X61,X60,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_673])])]) ).
fof(c_0_1128,plain,
! [X60,X61,X62] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X62),X60),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X61),X60),tc_nat)
| ~ c_HOL_Oord__class_Oless(X62,X61,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_674]) ).
fof(c_0_1129,plain,
! [X60,X61,X62] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X62),X61),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X62),X60),tc_nat)
| ~ c_HOL_Oord__class_Oless(X61,X60,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_675])])]) ).
fof(c_0_1130,plain,
! [X59,X60,X61,X62] :
( ~ class_Orderings_Olinorder(X62)
| c_HOL_Oord__class_Oless(X61,X59,X62)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X61,X60,X62),X59,X62) ),
inference(variable_rename,[status(thm)],[c_0_676]) ).
fof(c_0_1131,plain,
! [X59,X60,X61,X62] :
( ~ class_Orderings_Olinorder(X62)
| c_HOL_Oord__class_Oless(X60,X59,X62)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X61,X60,X62),X59,X62) ),
inference(variable_rename,[status(thm)],[c_0_677]) ).
fof(c_0_1132,plain,
! [X59,X60,X61,X62] :
( ~ class_Orderings_Olinorder(X62)
| c_lessequals(X60,X59,X62)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X61,X60,X62),X59,X62) ),
inference(variable_rename,[status(thm)],[c_0_678]) ).
fof(c_0_1133,plain,
! [X59,X60,X61,X62] :
( ~ class_Orderings_Olinorder(X62)
| c_lessequals(X61,X59,X62)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X61,X60,X62),X59,X62) ),
inference(variable_rename,[status(thm)],[c_0_679]) ).
fof(c_0_1134,plain,
! [X45,X46,X47,X48] :
( ~ class_Orderings_Olinorder(X48)
| c_lessequals(X46,X45,X48)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X47,X46,X48),X45,X48) ),
inference(variable_rename,[status(thm)],[c_0_680]) ).
fof(c_0_1135,plain,
! [X45,X46,X47,X48] :
( ~ class_Orderings_Olinorder(X48)
| c_lessequals(X47,X45,X48)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X47,X46,X48),X45,X48) ),
inference(variable_rename,[status(thm)],[c_0_681]) ).
fof(c_0_1136,plain,
! [X59,X60,X61,X62] :
( ~ class_OrderedGroup_Oab__group__add(X62)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X62),X61),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X62),X60),X59)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X62),X60),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X62),X61),X59)) ),
inference(variable_rename,[status(thm)],[c_0_682]) ).
fof(c_0_1137,plain,
! [X46,X47,X48,X49] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X49)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X48),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X47),X46)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X47),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X48),X46)) ),
inference(variable_rename,[status(thm)],[c_0_683]) ).
fof(c_0_1138,plain,
! [X58,X59,X60,X61] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X61)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X61),X60),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X61),X59),X58)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X61),X59),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X61),X60),X58)) ),
inference(variable_rename,[status(thm)],[c_0_684]) ).
fof(c_0_1139,plain,
! [X60,X61,X62] :
( c_HOL_Oord__class_Oless(X61,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X60),X62),tc_nat)
| ~ c_lessequals(X61,X60,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X62,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_685]) ).
fof(c_0_1140,plain,
! [X29,X30,X31,X32] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X31,X32),X30),X29))
| ~ hBOOL(hAPP(hAPP(X31,X30),X29)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_686])])]) ).
fof(c_0_1141,plain,
! [X23,X24,X25] :
( ~ class_Ring__and__Field_Oring__1(X25)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(X24,X23,tc_nat),X25) = c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(X24,X25),c_Nat_Osemiring__1__class_Oof__nat(X23,X25),X25)
| ~ c_lessequals(X23,X24,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_687]) ).
fof(c_0_1142,plain,
! [X69,X70,X71,X72] :
( c_List_Olistsp(X71,X70,X72)
| ~ c_List_Olistsp(X71,c_List_Oappend(X70,X69,X72),X72) ),
inference(variable_rename,[status(thm)],[c_0_688]) ).
fof(c_0_1143,plain,
! [X69,X70,X71,X72] :
( c_List_Olistsp(X71,X69,X72)
| ~ c_List_Olistsp(X71,c_List_Oappend(X70,X69,X72),X72) ),
inference(variable_rename,[status(thm)],[c_0_689]) ).
fof(c_0_1144,plain,
! [X23,X24] :
( c_HOL_Oord__class_Oless(X24,X23,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X23,X24,tc_nat),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_690]) ).
fof(c_0_1145,plain,
! [X29,X30,X31] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X31)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X31),X30),X29) != c_HOL_Ozero__class_Ozero(X31)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X31),X29,X31)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X31),X30,X31)
| X29 = c_HOL_Ozero__class_Ozero(X31) ),
inference(variable_rename,[status(thm)],[c_0_691]) ).
fof(c_0_1146,plain,
! [X29,X30,X31] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X31)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X31),X30),X29) != c_HOL_Ozero__class_Ozero(X31)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X31),X29,X31)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X31),X30,X31)
| X30 = c_HOL_Ozero__class_Ozero(X31) ),
inference(variable_rename,[status(thm)],[c_0_692]) ).
fof(c_0_1147,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_693]) ).
fof(c_0_1148,plain,
! [X70,X71,X72,X73] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X71),X72) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X73),X70)
| ~ c_HOL_Oord__class_Oless(X73,X72,tc_nat)
| c_HOL_Oord__class_Oless(X71,X70,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_694]) ).
fof(c_0_1149,plain,
! [X60,X61,X62] :
( c_HOL_Oord__class_Oless(X62,X60,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X62),X61),X60,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_695]) ).
fof(c_0_1150,plain,
! [X60,X61,X62] :
( c_lessequals(X62,X60,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X61),X62),X60,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_696]) ).
fof(c_0_1151,plain,
! [X60,X61,X62] :
( c_lessequals(X61,X60,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X61),X62),X60,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_697])])]) ).
fof(c_0_1152,plain,
! [X45,X46,X47] :
( ~ class_OrderedGroup_Ogroup__add(X47)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X47),c_HOL_Ominus__class_Ominus(X46,X45,X47)),X45) = X46 ),
inference(variable_rename,[status(thm)],[c_0_698]) ).
fof(c_0_1153,plain,
! [X26,X27,X28] :
( ~ class_Ring__and__Field_Oordered__semidom(X28)
| c_lessequals(c_HOL_Ozero__class_Ozero(X28),c_Power_Opower__class_Opower(X27,X26,X28),X28)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X28),X27,X28) ),
inference(variable_rename,[status(thm)],[c_0_699]) ).
fof(c_0_1154,plain,
! [X26,X27,X28] :
( ~ class_Ring__and__Field_Oordered__semidom(X28)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X28),c_Power_Opower__class_Opower(X27,X26,X28),X28)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X28),X27,X28) ),
inference(variable_rename,[status(thm)],[c_0_700]) ).
fof(c_0_1155,plain,
! [X29,X30,X31,X32] :
( c_Wellfounded_Oaccp(X30,X29,X32)
| ~ hBOOL(hAPP(hAPP(X30,X29),X31))
| ~ c_Wellfounded_Oaccp(X30,X31,X32) ),
inference(variable_rename,[status(thm)],[c_0_701]) ).
fof(c_0_1156,plain,
! [X45,X46,X47,X48] :
( c_Wellfounded_Oaccp(X45,X47,X48)
| ~ hBOOL(hAPP(hAPP(X45,X47),X46))
| ~ c_Wellfounded_Oaccp(X45,X46,X48) ),
inference(variable_rename,[status(thm)],[c_0_702]) ).
fof(c_0_1157,plain,
! [X26,X27] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X27)
| c_lessequals(c_HOL_Ozero__class_Ozero(X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X26),X27)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X27),X26,X27) ),
inference(variable_rename,[status(thm)],[c_0_703]) ).
fof(c_0_1158,plain,
! [X26,X27] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X27)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X26),c_HOL_Ozero__class_Ozero(X27),X27)
| ~ c_HOL_Oord__class_Oless(X26,c_HOL_Ozero__class_Ozero(X27),X27) ),
inference(variable_rename,[status(thm)],[c_0_704]) ).
fof(c_0_1159,plain,
! [X26,X27] :
( ~ class_Ring__and__Field_Oordered__idom(X27)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X26),c_HOL_Ozero__class_Ozero(X27),X27)
| ~ c_HOL_Oord__class_Oless(X26,c_HOL_Ozero__class_Ozero(X27),X27) ),
inference(variable_rename,[status(thm)],[c_0_705]) ).
fof(c_0_1160,plain,
! [X26,X27] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X27)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X26),X27)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X27),X26,X27) ),
inference(variable_rename,[status(thm)],[c_0_706]) ).
fof(c_0_1161,plain,
! [X26,X27] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X27)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X26),c_HOL_Ozero__class_Ozero(X27),X27)
| ~ c_lessequals(X26,c_HOL_Ozero__class_Ozero(X27),X27) ),
inference(variable_rename,[status(thm)],[c_0_707]) ).
fof(c_0_1162,plain,
! [X9] :
( hBOOL(hAPP(c_InductTermi_OIT,X9))
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X9,tc_Lambda_OdB) ),
inference(variable_rename,[status(thm)],[c_0_708]) ).
fof(c_0_1163,plain,
! [X45,X46,X47] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X47)
| c_lessequals(c_HOL_Ominus__class_Ominus(X46,X45,X47),c_HOL_Ozero__class_Ozero(X47),X47)
| ~ c_lessequals(X46,X45,X47) ),
inference(variable_rename,[status(thm)],[c_0_709]) ).
fof(c_0_1164,plain,
! [X45,X46,X47] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X47)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X46,X45,X47),c_HOL_Ozero__class_Ozero(X47),X47)
| ~ c_HOL_Oord__class_Oless(X46,X45,X47) ),
inference(variable_rename,[status(thm)],[c_0_710]) ).
fof(c_0_1165,plain,
! [X54,X55,X56,X57] :
( c_Type_Otyping(X56,X54,X57)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X55),X54))
| ~ c_Type_Otyping(X56,X55,X57) ),
inference(variable_rename,[status(thm)],[c_0_711]) ).
fof(c_0_1166,plain,
! [X47,X48,X49] :
( ~ class_OrderedGroup_Omonoid__add(X49)
| c_List_Olistsum(c_List_Oappend(X48,X47,X49),X49) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),c_List_Olistsum(X48,X49)),c_List_Olistsum(X47,X49)) ),
inference(variable_rename,[status(thm)],[c_0_712]) ).
fof(c_0_1167,plain,
! [X45,X46,X47,X48] :
( ~ class_Orderings_Olinorder(X48)
| c_HOL_Oord__class_Oless(X45,c_Orderings_Oord__class_Omax(X47,X46,X48),X48)
| ~ c_HOL_Oord__class_Oless(X45,X47,X48) ),
inference(variable_rename,[status(thm)],[c_0_713]) ).
fof(c_0_1168,plain,
! [X45,X46,X47,X48] :
( ~ class_Orderings_Olinorder(X48)
| c_HOL_Oord__class_Oless(X45,c_Orderings_Oord__class_Omax(X47,X46,X48),X48)
| ~ c_HOL_Oord__class_Oless(X45,X46,X48) ),
inference(variable_rename,[status(thm)],[c_0_714]) ).
fof(c_0_1169,plain,
! [X59,X60,X61,X62] :
( ~ class_Orderings_Olinorder(X62)
| c_HOL_Oord__class_Oless(X59,c_Orderings_Oord__class_Omax(X61,X60,X62),X62)
| ~ c_HOL_Oord__class_Oless(X59,X61,X62) ),
inference(variable_rename,[status(thm)],[c_0_715]) ).
fof(c_0_1170,plain,
! [X59,X60,X61,X62] :
( ~ class_Orderings_Olinorder(X62)
| c_HOL_Oord__class_Oless(X59,c_Orderings_Oord__class_Omax(X61,X60,X62),X62)
| ~ c_HOL_Oord__class_Oless(X59,X60,X62) ),
inference(variable_rename,[status(thm)],[c_0_716]) ).
fof(c_0_1171,plain,
! [X59,X60,X61,X62] :
( ~ class_Orderings_Olinorder(X62)
| c_lessequals(X59,c_Orderings_Oord__class_Omax(X61,X60,X62),X62)
| ~ c_lessequals(X59,X60,X62) ),
inference(variable_rename,[status(thm)],[c_0_717]) ).
fof(c_0_1172,plain,
! [X59,X60,X61,X62] :
( ~ class_Orderings_Olinorder(X62)
| c_lessequals(X59,c_Orderings_Oord__class_Omax(X61,X60,X62),X62)
| ~ c_lessequals(X59,X61,X62) ),
inference(variable_rename,[status(thm)],[c_0_718]) ).
fof(c_0_1173,plain,
! [X45,X46,X47,X48] :
( ~ class_Orderings_Olinorder(X48)
| c_lessequals(X45,c_Orderings_Oord__class_Omax(X47,X46,X48),X48)
| ~ c_lessequals(X45,X46,X48) ),
inference(variable_rename,[status(thm)],[c_0_719]) ).
fof(c_0_1174,plain,
! [X45,X46,X47,X48] :
( ~ class_Orderings_Olinorder(X48)
| c_lessequals(X45,c_Orderings_Oord__class_Omax(X47,X46,X48),X48)
| ~ c_lessequals(X45,X47,X48) ),
inference(variable_rename,[status(thm)],[c_0_720]) ).
fof(c_0_1175,plain,
! [X23,X24] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X23,X24,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X24,X23,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_721]) ).
fof(c_0_1176,plain,
! [X23,X24] :
( c_HOL_Ominus__class_Ominus(X23,c_HOL_Ominus__class_Ominus(X23,X24,tc_nat),tc_nat) = X24
| ~ c_lessequals(X24,X23,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_722]) ).
fof(c_0_1177,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_723]) ).
fof(c_0_1178,plain,
! [X60,X61,X62] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X62,X60,tc_nat),X61,tc_nat)
| ~ c_HOL_Oord__class_Oless(X62,X61,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_724]) ).
fof(c_0_1179,plain,
! [X20,X21] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X20),c_Lambda_OdB_OVar(X21))))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X20)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_725])])]) ).
fof(c_0_1180,plain,
! [X23,X24] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X23),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X23,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_726])])]) ).
fof(c_0_1181,plain,
! [X23,X24] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X23),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X24,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_727]) ).
fof(c_0_1182,plain,
! [X23,X24] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X23),c_HOL_Ominus__class_Ominus(X24,X23,tc_nat)) = X24
| ~ c_lessequals(X23,X24,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_728]) ).
fof(c_0_1183,plain,
! [X59,X60,X61,X62] :
( ~ class_Orderings_Oorder(X62)
| c_HOL_Oord__class_Oless(X59,X61,X62)
| ~ c_HOL_Oord__class_Oless(X59,X60,X62)
| ~ c_HOL_Oord__class_Oless(X60,X61,X62) ),
inference(variable_rename,[status(thm)],[c_0_729]) ).
fof(c_0_1184,plain,
! [X59,X60,X61,X62] :
( ~ class_Orderings_Opreorder(X62)
| c_HOL_Oord__class_Oless(X61,X59,X62)
| ~ c_HOL_Oord__class_Oless(X60,X59,X62)
| ~ c_HOL_Oord__class_Oless(X61,X60,X62) ),
inference(variable_rename,[status(thm)],[c_0_730]) ).
fof(c_0_1185,plain,
! [X59,X60,X61,X62] :
( ~ class_Orderings_Oorder(X62)
| c_lessequals(X59,X61,X62)
| ~ c_lessequals(X59,X60,X62)
| ~ c_lessequals(X60,X61,X62) ),
inference(variable_rename,[status(thm)],[c_0_731]) ).
fof(c_0_1186,plain,
! [X59,X60,X61,X62] :
( ~ class_Orderings_Oorder(X62)
| c_HOL_Oord__class_Oless(X59,X61,X62)
| ~ c_lessequals(X59,X60,X62)
| ~ c_HOL_Oord__class_Oless(X60,X61,X62) ),
inference(variable_rename,[status(thm)],[c_0_732]) ).
fof(c_0_1187,plain,
! [X59,X60,X61,X62] :
( ~ class_Orderings_Oorder(X62)
| c_HOL_Oord__class_Oless(X59,X61,X62)
| ~ c_HOL_Oord__class_Oless(X59,X60,X62)
| ~ c_lessequals(X60,X61,X62) ),
inference(variable_rename,[status(thm)],[c_0_733]) ).
fof(c_0_1188,plain,
! [X59,X60,X61,X62] :
( ~ class_Orderings_Opreorder(X62)
| c_lessequals(X61,X59,X62)
| ~ c_lessequals(X60,X59,X62)
| ~ c_lessequals(X61,X60,X62) ),
inference(variable_rename,[status(thm)],[c_0_734]) ).
fof(c_0_1189,plain,
! [X59,X60,X61,X62] :
( ~ class_Orderings_Opreorder(X62)
| c_HOL_Oord__class_Oless(X61,X59,X62)
| ~ c_HOL_Oord__class_Oless(X60,X59,X62)
| ~ c_lessequals(X61,X60,X62) ),
inference(variable_rename,[status(thm)],[c_0_735]) ).
fof(c_0_1190,plain,
! [X59,X60,X61,X62] :
( ~ class_Orderings_Opreorder(X62)
| c_HOL_Oord__class_Oless(X61,X59,X62)
| ~ c_lessequals(X60,X59,X62)
| ~ c_HOL_Oord__class_Oless(X61,X60,X62) ),
inference(variable_rename,[status(thm)],[c_0_736]) ).
fof(c_0_1191,plain,
! [X20,X21] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X21)),c_Lambda_OdB_OAbs(X20)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X21),X20)) ),
inference(variable_rename,[status(thm)],[c_0_737]) ).
fof(c_0_1192,plain,
! [X23,X24,X25] :
( ~ class_Ring__and__Field_Oordered__semidom(X25)
| c_lessequals(X24,X23,tc_nat)
| ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X24,X25),c_Nat_Osemiring__1__class_Oof__nat(X23,X25),X25) ),
inference(variable_rename,[status(thm)],[c_0_738]) ).
fof(c_0_1193,plain,
! [X23,X24,X25] :
( ~ class_Ring__and__Field_Oordered__semidom(X25)
| c_HOL_Oord__class_Oless(X24,X23,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X24,X25),c_Nat_Osemiring__1__class_Oof__nat(X23,X25),X25) ),
inference(variable_rename,[status(thm)],[c_0_739]) ).
fof(c_0_1194,plain,
! [X59,X60,X61] :
( c_HOL_Oord__class_Oless(X61,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X60),X59),tc_nat)
| ~ c_HOL_Oord__class_Oless(X61,X60,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_740]) ).
fof(c_0_1195,plain,
! [X59,X60,X61] :
( c_HOL_Oord__class_Oless(X61,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X60),X59),tc_nat)
| ~ c_HOL_Oord__class_Oless(X61,X59,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_741]) ).
fof(c_0_1196,plain,
! [X21,X22,X23] :
( c_HOL_Oord__class_Oless(X23,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X21),tc_nat)
| ~ c_HOL_Oord__class_Oless(X23,X22,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_742]) ).
fof(c_0_1197,plain,
! [X21,X22,X23] :
( c_HOL_Oord__class_Oless(X23,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X21),X22),tc_nat)
| ~ c_HOL_Oord__class_Oless(X23,X22,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_743]) ).
fof(c_0_1198,plain,
! [X21,X22,X23] :
( c_lessequals(X23,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X21),X22),tc_nat)
| ~ c_lessequals(X23,X22,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_744]) ).
fof(c_0_1199,plain,
! [X21,X22,X23] :
( c_lessequals(X23,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X21),tc_nat)
| ~ c_lessequals(X23,X22,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_745]) ).
fof(c_0_1200,plain,
! [X59,X60,X61] :
( c_lessequals(X61,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X60),X59),tc_nat)
| ~ c_lessequals(X61,X59,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_746]) ).
fof(c_0_1201,plain,
! [X59,X60,X61] :
( c_lessequals(X61,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X60),X59),tc_nat)
| ~ c_lessequals(X61,X60,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_747]) ).
fof(c_0_1202,plain,
! [X29,X30,X31] :
( ~ class_Orderings_Olinorder(X31)
| c_Orderings_Oord__class_Omax(X30,c_Orderings_Oord__class_Omax(X30,X29,X31),X31) = c_Orderings_Oord__class_Omax(X30,X29,X31) ),
inference(variable_rename,[status(thm)],[c_0_748]) ).
fof(c_0_1203,plain,
! [X60,X61,X62] :
( c_lessequals(X62,X60,tc_nat)
| ~ c_lessequals(X61,X60,tc_nat)
| ~ c_lessequals(X62,X61,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_749]) ).
fof(c_0_1204,plain,
! [X20,X21] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X20),X21)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X20)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_750])])]) ).
fof(c_0_1205,plain,
! [X35,X36,X37] :
( hBOOL(hAPP(X37,X36))
| hBOOL(hAPP(X37,X35))
| ~ c_HOL_Oord__class_Oless(X35,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X37),tc_nat)
| ~ hBOOL(hAPP(X37,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(variable_rename,[status(thm)],[c_0_751]) ).
fof(c_0_1206,plain,
! [X60,X61,X62] :
( c_Lambda_Oliftn(X60,c_Lambda_OdB_OVar(X62),X61) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X62),X60))
| c_HOL_Oord__class_Oless(X62,X61,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_752]) ).
fof(c_0_1207,plain,
! [X38,X39,X40] :
( ~ class_OrderedGroup_Omonoid__add(X40)
| c_List_Olistsum(c_List_Olist_OCons(X39,X38,X40),X40) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X40),X39),c_List_Olistsum(X38,X40)) ),
inference(variable_rename,[status(thm)],[c_0_753]) ).
fof(c_0_1208,plain,
! [X23,X24] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X23),c_HOL_Ominus__class_Ominus(X24,X23,tc_nat)) = X24
| c_HOL_Oord__class_Oless(X24,X23,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_754]) ).
fof(c_0_1209,plain,
! [X29,X30,X31] :
( ~ class_Orderings_Opreorder(X31)
| c_HOL_Oord__class_Oless(X30,X29,X31)
| c_lessequals(X29,X30,X31)
| ~ c_lessequals(X30,X29,X31) ),
inference(variable_rename,[status(thm)],[c_0_755]) ).
fof(c_0_1210,plain,
! [X23,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X24)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X23,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X24),c_Nat_Osemiring__1__class_Oof__nat(X23,X24),X24) ),
inference(variable_rename,[status(thm)],[c_0_756]) ).
fof(c_0_1211,plain,
! [X19,X20,X21] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X20)),X19),X21) = c_Lambda_OdB_OVar(X20)
| ~ c_HOL_Oord__class_Oless(X20,X21,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_757]) ).
fof(c_0_1212,plain,
! [X23,X24,X25] :
( ~ class_Ring__and__Field_Oordered__semidom(X25)
| c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X24,X25),c_Nat_Osemiring__1__class_Oof__nat(X23,X25),X25)
| ~ c_lessequals(X24,X23,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_758]) ).
fof(c_0_1213,plain,
! [X23,X24,X25] :
( ~ class_Ring__and__Field_Oordered__semidom(X25)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X24,X25),c_Nat_Osemiring__1__class_Oof__nat(X23,X25),X25)
| ~ c_HOL_Oord__class_Oless(X24,X23,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_759]) ).
fof(c_0_1214,plain,
! [X20] :
( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X20,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X20)) ),
inference(variable_rename,[status(thm)],[c_0_760]) ).
fof(c_0_1215,plain,
! [X35,X36,X37] :
( hBOOL(hAPP(hAPP(X37,X35),X36))
| c_HOL_Oord__class_Oless(X35,X36,tc_nat)
| X36 = X35
| c_HOL_Oord__class_Oless(X36,X35,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_761])])]) ).
fof(c_0_1216,plain,
! [X23,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X24)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X24),c_Nat_Osemiring__1__class_Oof__nat(X23,X24),X24)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X23,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_762]) ).
fof(c_0_1217,plain,
! [X29,X30,X31] :
( ~ class_Orderings_Oorder(X31)
| X30 = X29
| ~ c_lessequals(X29,X30,X31)
| ~ c_lessequals(X30,X29,X31) ),
inference(variable_rename,[status(thm)],[c_0_763]) ).
fof(c_0_1218,plain,
! [X29,X30,X31] :
( ~ class_Orderings_Oorder(X31)
| X30 = X29
| ~ c_lessequals(X29,X30,X31)
| ~ c_lessequals(X30,X29,X31) ),
inference(variable_rename,[status(thm)],[c_0_764]) ).
fof(c_0_1219,plain,
! [X29,X30,X31] :
( ~ class_Orderings_Oorder(X31)
| X30 = X29
| ~ c_lessequals(X30,X29,X31)
| ~ c_lessequals(X29,X30,X31) ),
inference(variable_rename,[status(thm)],[c_0_765]) ).
fof(c_0_1220,plain,
! [X61,X62,X63,X64] :
( ~ class_OrderedGroup_Oab__group__add(X64)
| c_HOL_Ominus__class_Ominus(X62,X61,X64) != c_HOL_Ominus__class_Ominus(X63,X63,X64)
| X62 = X61 ),
inference(variable_rename,[status(thm)],[c_0_766]) ).
fof(c_0_1221,plain,
! [X51,X52,X53,X54] :
( ~ class_OrderedGroup_Oab__group__add(X54)
| c_HOL_Ominus__class_Ominus(X53,X53,X54) != c_HOL_Ominus__class_Ominus(X52,X51,X54)
| X52 = X51 ),
inference(variable_rename,[status(thm)],[c_0_767]) ).
fof(c_0_1222,plain,
! [X59,X60,X61,X62] :
( ~ class_Ring__and__Field_Oidom(X62)
| ~ class_Int_Onumber__ring(X62)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X62),X61),X60) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X62),X61),X59)
| X60 = X59 ),
inference(variable_rename,[status(thm)],[c_0_768]) ).
fof(c_0_1223,plain,
! [X25,X26] :
( ~ class_Orderings_Olinorder(X26)
| ~ c_lessequals(X25,X25,X26)
| ~ c_HOL_Oord__class_Oless(X25,X25,X26) ),
inference(variable_rename,[status(thm)],[c_0_769]) ).
fof(c_0_1224,plain,
! [X29,X30,X31] :
( ~ class_Orderings_Olinorder(X31)
| ~ c_HOL_Oord__class_Oless(X30,X29,X31)
| ~ c_lessequals(X29,X30,X31) ),
inference(variable_rename,[status(thm)],[c_0_770]) ).
fof(c_0_1225,plain,
! [X29,X30,X31] :
( ~ class_Orderings_Olinorder(X31)
| ~ c_lessequals(X30,X29,X31)
| ~ c_HOL_Oord__class_Oless(X29,X30,X31) ),
inference(variable_rename,[status(thm)],[c_0_771]) ).
fof(c_0_1226,plain,
! [X29,X30,X31] :
( ~ class_Orderings_Opreorder(X31)
| ~ c_lessequals(X29,X30,X31)
| ~ c_HOL_Oord__class_Oless(X30,X29,X31) ),
inference(variable_rename,[status(thm)],[c_0_772]) ).
fof(c_0_1227,plain,
! [X45,X46,X47] :
( ~ class_Orderings_Oorder(X47)
| ~ c_HOL_Oord__class_Oless(X46,X45,X47)
| ~ c_HOL_Oord__class_Oless(X45,X46,X47) ),
inference(variable_rename,[status(thm)],[c_0_773]) ).
fof(c_0_1228,plain,
! [X29,X30,X31] :
( ~ class_Orderings_Olinorder(X31)
| ~ c_HOL_Oord__class_Oless(X30,X29,X31)
| ~ c_HOL_Oord__class_Oless(X29,X30,X31) ),
inference(variable_rename,[status(thm)],[c_0_774]) ).
fof(c_0_1229,plain,
! [X29,X30,X31] :
( ~ class_Orderings_Opreorder(X31)
| ~ c_HOL_Oord__class_Oless(X29,X30,X31)
| ~ c_HOL_Oord__class_Oless(X30,X29,X31) ),
inference(variable_rename,[status(thm)],[c_0_775]) ).
fof(c_0_1230,plain,
! [X45,X46,X47] :
( ~ class_Orderings_Opreorder(X47)
| ~ c_HOL_Oord__class_Oless(X45,X46,X47)
| ~ c_HOL_Oord__class_Oless(X46,X45,X47) ),
inference(variable_rename,[status(thm)],[c_0_776]) ).
fof(c_0_1231,plain,
! [X29,X30,X31,X32,X33] :
( c_List_Oreplicate(X32,X30,X33) != c_List_Oreplicate(X31,X29,X33)
| X30 = X29
| X32 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_777])])]) ).
fof(c_0_1232,plain,
! [X23,X24] :
( c_HOL_Ominus__class_Ominus(X23,X24,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X24,X23,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X24 = X23 ),
inference(variable_rename,[status(thm)],[c_0_778]) ).
fof(c_0_1233,plain,
! [X29,X30,X31,X32,X33] :
( c_List_Oreplicate(X32,X30,X33) != c_List_Oreplicate(X31,X29,X33)
| X32 = X31 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_779])])]) ).
fof(c_0_1234,plain,
! [X47,X48,X49,X50] :
( c_List_Oappend(X48,X49,X50) != c_List_Oappend(X47,X49,X50)
| X48 = X47 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_780])])]) ).
fof(c_0_1235,plain,
! [X47,X48,X49,X50] :
( c_List_Oappend(X49,X48,X50) != c_List_Oappend(X49,X47,X50)
| X48 = X47 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_781])])]) ).
fof(c_0_1236,plain,
! [X46,X47,X48,X49] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X49)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X48),X47) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X48),X46)
| X47 = X46 ),
inference(variable_rename,[status(thm)],[c_0_782]) ).
fof(c_0_1237,plain,
! [X46,X47,X48,X49] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X49)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X48),X47) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X48),X46)
| X47 = X46 ),
inference(variable_rename,[status(thm)],[c_0_783]) ).
fof(c_0_1238,plain,
! [X46,X47,X48,X49] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X49)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X47),X48) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X46),X48)
| X47 = X46 ),
inference(variable_rename,[status(thm)],[c_0_784]) ).
fof(c_0_1239,plain,
! [X57,X58,X59,X60,X61] :
( c_List_Olist_OCons(X60,X58,X61) != c_List_Olist_OCons(X59,X57,X61)
| X60 = X59 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_785])])]) ).
fof(c_0_1240,plain,
! [X57,X58,X59,X60,X61] :
( c_List_Olist_OCons(X60,X58,X61) != c_List_Olist_OCons(X59,X57,X61)
| X58 = X57 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_786])])]) ).
fof(c_0_1241,plain,
! [X25,X26] :
( c_HOL_Oord__class_Oless(X25,X25,tc_nat)
| c_Lambda_Osubstn(c_Lambda_OdB_OVar(X25),X26,X25) = c_Lambda_Oliftn(X25,X26,c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_787])])]) ).
fof(c_0_1242,plain,
! [X60,X61,X62] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X62)),X60),X61) = c_Lambda_OdB_OVar(X62)
| X62 = X61
| c_HOL_Oord__class_Oless(X61,X62,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_788]) ).
fof(c_0_1243,plain,
! [X23,X24] :
( X24 = X23
| ~ c_lessequals(X23,X24,tc_nat)
| ~ c_lessequals(X24,X23,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_789]) ).
fof(c_0_1244,plain,
! [X4,X5,X6] :
( X5 = X4
| ~ hBOOL(hAPP(hAPP(c_fequal(X6),X5),X4)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_790])])]) ).
fof(c_0_1245,plain,
! [X29,X30,X31] :
( ~ class_Orderings_Olinorder(X31)
| c_lessequals(X30,c_Orderings_Oord__class_Omax(X30,X29,X31),X31) ),
inference(variable_rename,[status(thm)],[c_0_791]) ).
fof(c_0_1246,plain,
! [X29,X30,X31] :
( ~ class_Orderings_Olinorder(X31)
| c_lessequals(X29,c_Orderings_Oord__class_Omax(X30,X29,X31),X31) ),
inference(variable_rename,[status(thm)],[c_0_792]) ).
fof(c_0_1247,plain,
! [X45,X46,X47] :
( ~ class_OrderedGroup_Ogroup__add(X47)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X47),X46),X45),X45,X47) = X46 ),
inference(variable_rename,[status(thm)],[c_0_793]) ).
fof(c_0_1248,plain,
! [X25,X26] :
( c_HOL_Oord__class_Oless(X25,X25,tc_nat)
| hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X25)),X26),X25) = X26 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_794])])]) ).
fof(c_0_1249,plain,
! [X35,X36] :
( hBOOL(hAPP(X36,X35))
| ~ hBOOL(hAPP(X36,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X36)))
| ~ hBOOL(hAPP(X36,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(variable_rename,[status(thm)],[c_0_795]) ).
fof(c_0_1250,plain,
! [X45,X46,X47] :
( ~ class_Orderings_Oorder(X47)
| c_HOL_Oord__class_Oless(X45,X46,X47)
| X46 = X45
| ~ c_lessequals(X45,X46,X47) ),
inference(variable_rename,[status(thm)],[c_0_796]) ).
fof(c_0_1251,plain,
! [X45,X46,X47] :
( ~ class_Orderings_Oorder(X47)
| c_HOL_Oord__class_Oless(X45,X46,X47)
| ~ c_lessequals(X45,X46,X47)
| X46 = X45 ),
inference(variable_rename,[status(thm)],[c_0_797]) ).
fof(c_0_1252,plain,
! [X29,X30,X31] :
( ~ class_Orderings_Oorder(X31)
| X30 = X29
| c_HOL_Oord__class_Oless(X30,X29,X31)
| ~ c_lessequals(X30,X29,X31) ),
inference(variable_rename,[status(thm)],[c_0_798]) ).
fof(c_0_1253,plain,
! [X29,X30,X31] :
( ~ class_Orderings_Oorder(X31)
| c_HOL_Oord__class_Oless(X30,X29,X31)
| X30 = X29
| ~ c_lessequals(X30,X29,X31) ),
inference(variable_rename,[status(thm)],[c_0_799]) ).
fof(c_0_1254,plain,
! [X45,X46,X47] :
( ~ class_Orderings_Oorder(X47)
| c_HOL_Oord__class_Oless(X46,X45,X47)
| X46 = X45
| ~ c_lessequals(X46,X45,X47) ),
inference(variable_rename,[status(thm)],[c_0_800]) ).
fof(c_0_1255,plain,
! [X45,X46,X47] :
( ~ class_Orderings_Oorder(X47)
| c_HOL_Oord__class_Oless(X46,X45,X47)
| ~ c_lessequals(X46,X45,X47)
| X46 = X45 ),
inference(variable_rename,[status(thm)],[c_0_801]) ).
fof(c_0_1256,plain,
! [X29,X30,X31] :
( ~ class_Orderings_Olinorder(X31)
| X30 = X29
| ~ c_lessequals(X30,X29,X31)
| c_HOL_Oord__class_Oless(X30,X29,X31) ),
inference(variable_rename,[status(thm)],[c_0_802]) ).
fof(c_0_1257,plain,
! [X29,X30,X31] :
( ~ class_Orderings_Olinorder(X31)
| X30 = X29
| c_HOL_Oord__class_Oless(X30,X29,X31)
| ~ c_lessequals(X30,X29,X31) ),
inference(variable_rename,[status(thm)],[c_0_803]) ).
fof(c_0_1258,plain,
! [X35,X36] :
( hBOOL(hAPP(X36,X35))
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X36),tc_nat)
| ~ hBOOL(hAPP(X36,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(variable_rename,[status(thm)],[c_0_804]) ).
fof(c_0_1259,plain,
! [X29,X30,X31] :
( ~ class_Orderings_Olinorder(X31)
| c_Orderings_Oord__class_Omax(X30,X29,X31) != X29
| c_lessequals(X30,X29,X31) ),
inference(variable_rename,[status(thm)],[c_0_805]) ).
fof(c_0_1260,plain,
! [X29,X30,X31] :
( ~ class_Orderings_Olinorder(X31)
| c_Orderings_Oord__class_Omax(X30,X29,X31) = X30
| ~ c_lessequals(X29,X30,X31) ),
inference(variable_rename,[status(thm)],[c_0_806]) ).
fof(c_0_1261,plain,
! [X29,X30,X31] :
( ~ class_Orderings_Olinorder(X31)
| c_Orderings_Oord__class_Omax(X30,X29,X31) = X29
| ~ c_lessequals(X30,X29,X31) ),
inference(variable_rename,[status(thm)],[c_0_807]) ).
fof(c_0_1262,plain,
! [X60,X61,X62] :
( c_Lambda_Oliftn(X60,c_Lambda_OdB_OVar(X62),X61) = c_Lambda_OdB_OVar(X62)
| ~ c_HOL_Oord__class_Oless(X62,X61,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_808]) ).
fof(c_0_1263,plain,
! [X29,X30,X31] :
( ~ class_Orderings_Oorder(X31)
| c_lessequals(X30,X29,X31)
| ~ c_HOL_Oord__class_Oless(X30,X29,X31) ),
inference(variable_rename,[status(thm)],[c_0_809]) ).
fof(c_0_1264,plain,
! [X29,X30,X31] :
( ~ class_Orderings_Opreorder(X31)
| c_lessequals(X30,X29,X31)
| ~ c_HOL_Oord__class_Oless(X30,X29,X31) ),
inference(variable_rename,[status(thm)],[c_0_810]) ).
fof(c_0_1265,plain,
! [X59,X60,X61] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X61),X60) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X61),X59)
| X60 = X59 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_811])])]) ).
fof(c_0_1266,plain,
! [X60,X61,X62] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X61),X62) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X60),X62)
| X61 = X60 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_812])])]) ).
fof(c_0_1267,plain,
! [X60,X61,X62] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X62),X61) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X62),X60)
| X61 = X60 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_813])])]) ).
fof(c_0_1268,plain,
! [X21,X22] :
( ~ class_Ring__and__Field_Oordered__semidom(X22)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X21,X22),c_HOL_Ozero__class_Ozero(X22),X22) ),
inference(variable_rename,[status(thm)],[c_0_814]) ).
fof(c_0_1269,plain,
! [X23,X24] :
( c_HOL_Ominus__class_Ominus(X24,X23,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_lessequals(X24,X23,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_815]) ).
fof(c_0_1270,plain,
! [X23,X24] :
( c_HOL_Ominus__class_Ominus(X24,X23,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(X24,X23,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_816]) ).
fof(c_0_1271,plain,
! [X23,X24] :
( c_HOL_Oord__class_Oless(X24,X23,tc_nat)
| X24 = X23
| ~ c_lessequals(X24,X23,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_817]) ).
fof(c_0_1272,plain,
! [X23,X24] :
( X24 = X23
| c_HOL_Oord__class_Oless(X24,X23,tc_nat)
| ~ c_lessequals(X24,X23,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_818]) ).
fof(c_0_1273,plain,
! [X23,X24] :
( c_HOL_Oord__class_Oless(X24,X23,tc_nat)
| X24 = X23
| ~ c_lessequals(X24,X23,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_819]) ).
fof(c_0_1274,plain,
! [X29,X30] :
( c_lessequals(X30,X29,tc_nat)
| ~ c_HOL_Oord__class_Oless(X30,X29,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_820]) ).
fof(c_0_1275,plain,
! [X23,X24] :
( c_lessequals(X24,X23,tc_nat)
| ~ c_HOL_Oord__class_Oless(X24,X23,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_821]) ).
fof(c_0_1276,plain,
! [X60,X61] :
( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X61)),X60) = c_Lambda_OdB_OVar(X61)
| ~ c_HOL_Oord__class_Oless(X61,X60,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_822]) ).
fof(c_0_1277,plain,
! [X44,X45] :
( hBOOL(hAPP(X45,X44))
| hBOOL(hAPP(X45,v_sko__Nat__Xnat__Xinducts__1(X45)))
| ~ hBOOL(hAPP(X45,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(variable_rename,[status(thm)],[c_0_823]) ).
fof(c_0_1278,plain,
! [X44,X45] :
( hBOOL(hAPP(X45,X44))
| hBOOL(hAPP(X45,v_sko__Nat__Xnat__Xinduct__1(X45)))
| ~ hBOOL(hAPP(X45,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(variable_rename,[status(thm)],[c_0_824]) ).
fof(c_0_1279,plain,
! [X44,X45] :
( hBOOL(hAPP(X45,X44))
| hBOOL(hAPP(X45,v_sko__List__Xupt__Xinduct__1(X45)))
| ~ hBOOL(hAPP(X45,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(variable_rename,[status(thm)],[c_0_825]) ).
fof(c_0_1280,plain,
! [X28,X29,X30,X31] :
( hAPP(hAPP(X29,X30),X28) = X30
| ~ c_OrderedGroup_Omonoid__add(X28,X29,X31) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_826])])]) ).
fof(c_0_1281,plain,
! [X28,X29,X30,X31] :
( hAPP(hAPP(X29,X28),X30) = X30
| ~ c_OrderedGroup_Omonoid__add(X28,X29,X31) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_827])])]) ).
fof(c_0_1282,plain,
! [X26,X27,X28] :
( ~ class_Ring__and__Field_Ozero__neq__one(X28)
| ~ class_Ring__and__Field_Ono__zero__divisors(X28)
| ~ class_Ring__and__Field_Omult__zero(X28)
| ~ class_Power_Opower(X28)
| c_Power_Opower__class_Opower(X27,X26,X28) != c_HOL_Ozero__class_Ozero(X28)
| X27 = c_HOL_Ozero__class_Ozero(X28) ),
inference(variable_rename,[status(thm)],[c_0_828]) ).
fof(c_0_1283,plain,
! [X26,X27] :
( ~ class_Ring__and__Field_Ozero__neq__one(X27)
| ~ class_Ring__and__Field_Ono__zero__divisors(X27)
| ~ class_Ring__and__Field_Omult__zero(X27)
| ~ class_Power_Opower(X27)
| c_Power_Opower__class_Opower(X26,c_HOL_Ozero__class_Ozero(tc_nat),X27) != c_HOL_Ozero__class_Ozero(X27) ),
inference(variable_rename,[status(thm)],[c_0_829]) ).
fof(c_0_1284,plain,
! [X60,X61,X62] :
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X62),X60,X61) = c_Lambda_OdB_OVar(X62)
| X62 = X61
| c_HOL_Oord__class_Oless(X61,X62,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_830]) ).
fof(c_0_1285,plain,
! [X29,X30,X31] :
( ~ class_Ring__and__Field_Oordered__idom(X31)
| c_HOL_Oord__class_Oless(X29,X30,X31)
| c_HOL_Oord__class_Oless(X30,X29,X31)
| X30 = X29 ),
inference(variable_rename,[status(thm)],[c_0_831]) ).
fof(c_0_1286,plain,
! [X29,X30,X31] :
( ~ class_Orderings_Olinorder(X31)
| X30 = X29
| c_HOL_Oord__class_Oless(X29,X30,X31)
| c_HOL_Oord__class_Oless(X30,X29,X31) ),
inference(variable_rename,[status(thm)],[c_0_832]) ).
fof(c_0_1287,plain,
! [X29,X30,X31] :
( ~ class_Orderings_Olinorder(X31)
| c_HOL_Oord__class_Oless(X29,X30,X31)
| c_HOL_Oord__class_Oless(X30,X29,X31)
| X30 = X29 ),
inference(variable_rename,[status(thm)],[c_0_833]) ).
fof(c_0_1288,plain,
! [X29,X30,X31] :
( ~ class_Orderings_Olinorder(X31)
| c_HOL_Oord__class_Oless(X29,X30,X31)
| X30 = X29
| c_HOL_Oord__class_Oless(X30,X29,X31) ),
inference(variable_rename,[status(thm)],[c_0_834]) ).
fof(c_0_1289,plain,
! [X29,X30,X31] :
( ~ class_Orderings_Olinorder(X31)
| X30 = X29
| c_HOL_Oord__class_Oless(X30,X29,X31)
| c_HOL_Oord__class_Oless(X29,X30,X31) ),
inference(variable_rename,[status(thm)],[c_0_835]) ).
fof(c_0_1290,plain,
! [X13,X14,X15,X16] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X16),X14) != hAPP(hAPP(c_Lambda_OdB_OApp,X15),X13)
| X16 = X15 ),
inference(variable_rename,[status(thm)],[c_0_836]) ).
fof(c_0_1291,plain,
! [X13,X14,X15,X16] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X16),X14) != hAPP(hAPP(c_Lambda_OdB_OApp,X15),X13)
| X14 = X13 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_837])])]) ).
fof(c_0_1292,plain,
! [X29,X30,X31] :
( ~ class_Orderings_Olinorder(X31)
| c_HOL_Oord__class_Oless(X30,X29,X31)
| c_lessequals(X29,X30,X31) ),
inference(variable_rename,[status(thm)],[c_0_838]) ).
fof(c_0_1293,plain,
! [X25,X26] :
( ~ class_Orderings_Olinorder(X26)
| c_HOL_Oord__class_Oless(X25,X25,X26)
| c_lessequals(X25,X25,X26) ),
inference(variable_rename,[status(thm)],[c_0_839]) ).
fof(c_0_1294,plain,
! [X29,X30,X31] :
( ~ class_Orderings_Olinorder(X31)
| c_lessequals(X29,X30,X31)
| c_HOL_Oord__class_Oless(X30,X29,X31) ),
inference(variable_rename,[status(thm)],[c_0_840]) ).
fof(c_0_1295,plain,
! [X29,X30,X31] :
( ~ class_Orderings_Olinorder(X31)
| c_HOL_Oord__class_Oless(X29,X30,X31)
| c_lessequals(X30,X29,X31) ),
inference(variable_rename,[status(thm)],[c_0_841]) ).
fof(c_0_1296,plain,
! [X29,X30,X31] :
( ~ class_Orderings_Olinorder(X31)
| c_lessequals(X29,X30,X31)
| c_lessequals(X30,X29,X31) ),
inference(variable_rename,[status(thm)],[c_0_842]) ).
fof(c_0_1297,plain,
! [X29,X30,X31] :
( ~ class_Orderings_Olinorder(X31)
| c_Orderings_Oord__class_Omax(X30,X29,X31) = c_Orderings_Oord__class_Omax(X29,X30,X31) ),
inference(variable_rename,[status(thm)],[c_0_843]) ).
fof(c_0_1298,plain,
! [X46,X47,X48] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X48)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X48),X47),X46) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X48),X46),X47) ),
inference(variable_rename,[status(thm)],[c_0_844]) ).
fof(c_0_1299,plain,
! [X45,X46,X47] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X47)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X47),X46),X45) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X47),X45),X46) ),
inference(variable_rename,[status(thm)],[c_0_845]) ).
fof(c_0_1300,plain,
! [X29,X30,X31] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X31)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X31),X30),X29) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X31),X29),X30) ),
inference(variable_rename,[status(thm)],[c_0_846]) ).
fof(c_0_1301,plain,
! [X31,X32,X33] :
( hAPP(X32,X31) = X33
| ~ c_Type_Otyping(X32,c_Lambda_OdB_OVar(X31),X33) ),
inference(variable_rename,[status(thm)],[c_0_847]) ).
fof(c_0_1302,plain,
! [X23,X24] :
( c_HOL_Oord__class_Oless(X23,X24,tc_nat)
| c_HOL_Oord__class_Oless(X24,X23,tc_nat)
| X24 = X23 ),
inference(variable_rename,[status(thm)],[c_0_848]) ).
fof(c_0_1303,plain,
! [X29,X30] :
( c_HOL_Oord__class_Oless(X29,X30,tc_nat)
| c_HOL_Oord__class_Oless(X30,X29,tc_nat)
| X30 = X29 ),
inference(variable_rename,[status(thm)],[c_0_849]) ).
fof(c_0_1304,plain,
! [X29,X30,X31] :
( ~ class_Ring__and__Field_Oidom(X31)
| ~ class_Int_Onumber__ring(X31)
| c_HOL_Ominus__class_Ominus(X30,X29,X31) != c_HOL_Ozero__class_Ozero(X31)
| X30 = X29 ),
inference(variable_rename,[status(thm)],[c_0_850]) ).
fof(c_0_1305,plain,
! [X23,X24] :
( c_lessequals(X23,X24,tc_nat)
| c_lessequals(X24,X23,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_851]) ).
fof(c_0_1306,plain,
! [X26,X27,X28] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X28)
| c_Power_Opower__class_Opower(X27,X26,X28) != c_HOL_Ozero__class_Ozero(X28)
| X27 = c_HOL_Ozero__class_Ozero(X28) ),
inference(variable_rename,[status(thm)],[c_0_852]) ).
fof(c_0_1307,plain,
! [X26,X27,X28] :
( ~ class_Ring__and__Field_Oidom(X28)
| ~ class_Int_Onumber__ring(X28)
| X26 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X26),X27)
| X27 = c_HOL_Ozero__class_Ozero(X28) ),
inference(variable_rename,[status(thm)],[c_0_853]) ).
fof(c_0_1308,plain,
! [X45,X46,X47] :
( ~ class_OrderedGroup_Ogroup__add(X47)
| c_HOL_Ominus__class_Ominus(X46,X45,X47) != c_HOL_Ozero__class_Ozero(X47)
| X46 = X45 ),
inference(variable_rename,[status(thm)],[c_0_854]) ).
fof(c_0_1309,plain,
! [X45,X46,X47] :
( ~ class_OrderedGroup_Oab__group__add(X47)
| c_HOL_Ominus__class_Ominus(X46,X45,X47) != c_HOL_Ozero__class_Ozero(X47)
| X46 = X45 ),
inference(variable_rename,[status(thm)],[c_0_855]) ).
fof(c_0_1310,plain,
! [X26,X27] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X27)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X26) != c_HOL_Ozero__class_Ozero(X27)
| X26 = c_HOL_Ozero__class_Ozero(X27) ),
inference(variable_rename,[status(thm)],[c_0_856]) ).
fof(c_0_1311,plain,
! [X47,X48,X49] :
( c_List_Olist_ONil(X49) != c_List_Oappend(X48,X47,X49)
| X48 = c_List_Olist_ONil(X49) ),
inference(variable_rename,[status(thm)],[c_0_857]) ).
fof(c_0_1312,plain,
! [X47,X48,X49] :
( c_List_Olist_ONil(X49) != c_List_Oappend(X48,X47,X49)
| X47 = c_List_Olist_ONil(X49) ),
inference(variable_rename,[status(thm)],[c_0_858]) ).
fof(c_0_1313,plain,
! [X47,X48,X49] :
( c_List_Oappend(X48,X47,X49) != c_List_Olist_ONil(X49)
| X48 = c_List_Olist_ONil(X49) ),
inference(variable_rename,[status(thm)],[c_0_859]) ).
fof(c_0_1314,plain,
! [X47,X48,X49] :
( c_List_Oappend(X48,X47,X49) != c_List_Olist_ONil(X49)
| X47 = c_List_Olist_ONil(X49) ),
inference(variable_rename,[status(thm)],[c_0_860]) ).
fof(c_0_1315,plain,
! [X23,X24] :
( ~ class_Ring__and__Field_Ozero__neq__one(X24)
| ~ class_Ring__and__Field_Ono__zero__divisors(X24)
| ~ class_Ring__and__Field_Omult__zero(X24)
| ~ class_Power_Opower(X24)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X24),X23,X24) = c_HOL_Ozero__class_Ozero(X24)
| X23 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_861]) ).
fof(c_0_1316,plain,
! [X25,X26,X27] :
( c_List_Oreplicate(X26,X25,X27) != c_List_Olist_ONil(X27)
| X26 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_862])])]) ).
fof(c_0_1317,plain,
! [X25,X26,X27] :
( c_List_Olist_ONil(X27) != c_List_Oreplicate(X26,X25,X27)
| X26 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_863])])]) ).
fof(c_0_1318,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_864]) ).
fof(c_0_1319,plain,
! [X21,X22] :
( ~ class_Ring__and__Field_Oordered__semidom(X22)
| c_lessequals(c_HOL_Ozero__class_Ozero(X22),c_Nat_Osemiring__1__class_Oof__nat(X21,X22),X22) ),
inference(variable_rename,[status(thm)],[c_0_865]) ).
fof(c_0_1320,plain,
! [X25,X26] :
( ~ class_Orderings_Oorder(X26)
| ~ c_HOL_Oord__class_Oless(X25,X25,X26) ),
inference(variable_rename,[status(thm)],[c_0_866]) ).
fof(c_0_1321,plain,
! [X25,X26] :
( ~ class_Orderings_Olinorder(X26)
| ~ c_HOL_Oord__class_Oless(X25,X25,X26) ),
inference(variable_rename,[status(thm)],[c_0_867]) ).
fof(c_0_1322,plain,
! [X25,X26] :
( ~ class_Orderings_Opreorder(X26)
| ~ c_HOL_Oord__class_Oless(X25,X25,X26) ),
inference(variable_rename,[status(thm)],[c_0_868]) ).
fof(c_0_1323,plain,
! [X47,X48,X49] :
( c_List_Oappend(X48,X47,X49) != X48
| X47 = c_List_Olist_ONil(X49) ),
inference(variable_rename,[status(thm)],[c_0_869]) ).
fof(c_0_1324,plain,
! [X47,X48,X49] :
( X48 != c_List_Oappend(X48,X47,X49)
| X47 = c_List_Olist_ONil(X49) ),
inference(variable_rename,[status(thm)],[c_0_870]) ).
fof(c_0_1325,plain,
! [X47,X48,X49] :
( c_List_Oappend(X48,X47,X49) != X47
| X48 = c_List_Olist_ONil(X49) ),
inference(variable_rename,[status(thm)],[c_0_871]) ).
fof(c_0_1326,plain,
! [X47,X48,X49] :
( X47 != c_List_Oappend(X48,X47,X49)
| X48 = c_List_Olist_ONil(X49) ),
inference(variable_rename,[status(thm)],[c_0_872]) ).
fof(c_0_1327,plain,
! [X23] :
( X23 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(X23,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_873]) ).
fof(c_0_1328,plain,
! [X23,X24] :
( ~ class_Ring__and__Field_Osemiring__0(X24)
| ~ class_Power_Opower(X24)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X24),X23,X24) = c_HOL_Ozero__class_Ozero(X24)
| X23 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_874]) ).
fof(c_0_1329,plain,
! [X9] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X9)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X9)) ),
inference(variable_rename,[status(thm)],[c_0_875]) ).
fof(c_0_1330,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_876]) ).
fof(c_0_1331,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_877])])]) ).
fof(c_0_1332,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_878]) ).
fof(c_0_1333,plain,
! [X26,X27] :
( X26 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X26),X27)
| X27 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_879]) ).
fof(c_0_1334,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_880])])]) ).
fof(c_0_1335,plain,
! [X25,X26] :
( ~ class_Ring__and__Field_Oidom(X26)
| ~ class_Int_Onumber__ring(X26)
| X25 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X26),X25),c_HOL_Ozero__class_Ozero(X26)) ),
inference(variable_rename,[status(thm)],[c_0_881]) ).
fof(c_0_1336,plain,
! [X25,X26] :
( ~ class_Ring__and__Field_Oidom(X26)
| ~ class_Int_Onumber__ring(X26)
| c_HOL_Ominus__class_Ominus(X25,X25,X26) = c_HOL_Ozero__class_Ozero(X26) ),
inference(variable_rename,[status(thm)],[c_0_882]) ).
fof(c_0_1337,plain,
! [X25,X26] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X26)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X26),c_HOL_Ozero__class_Ozero(X26)),X25) = X25 ),
inference(variable_rename,[status(thm)],[c_0_883]) ).
fof(c_0_1338,plain,
! [X26,X27] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X27)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),c_HOL_Ozero__class_Ozero(X27)),X26) = X26 ),
inference(variable_rename,[status(thm)],[c_0_884]) ).
fof(c_0_1339,plain,
! [X26,X27] :
( ~ class_OrderedGroup_Omonoid__add(X27)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),c_HOL_Ozero__class_Ozero(X27)),X26) = X26 ),
inference(variable_rename,[status(thm)],[c_0_885]) ).
fof(c_0_1340,plain,
! [X26,X27] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X27)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),c_HOL_Ozero__class_Ozero(X27)),X26) = X26 ),
inference(variable_rename,[status(thm)],[c_0_886]) ).
fof(c_0_1341,plain,
! [X26,X27] :
( ~ class_OrderedGroup_Ogroup__add(X27)
| c_HOL_Ominus__class_Ominus(X26,c_HOL_Ozero__class_Ozero(X27),X27) = X26 ),
inference(variable_rename,[status(thm)],[c_0_887]) ).
fof(c_0_1342,plain,
! [X25,X26] :
( ~ class_Orderings_Obot(X26)
| c_lessequals(c_Orderings_Obot__class_Obot(X26),X25,X26) ),
inference(variable_rename,[status(thm)],[c_0_888]) ).
fof(c_0_1343,plain,
! [X26,X27] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X27)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),c_HOL_Ozero__class_Ozero(X27)) = X26 ),
inference(variable_rename,[status(thm)],[c_0_889]) ).
fof(c_0_1344,plain,
! [X26,X27] :
( ~ class_OrderedGroup_Omonoid__add(X27)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),c_HOL_Ozero__class_Ozero(X27)) = X26 ),
inference(variable_rename,[status(thm)],[c_0_890]) ).
fof(c_0_1345,plain,
! [X26,X27] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X27)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),c_HOL_Ozero__class_Ozero(X27)) = X26 ),
inference(variable_rename,[status(thm)],[c_0_891]) ).
fof(c_0_1346,plain,
! [X26,X27] :
( ~ class_OrderedGroup_Ogroup__add(X27)
| c_HOL_Ominus__class_Ominus(X26,X26,X27) = c_HOL_Ozero__class_Ozero(X27) ),
inference(variable_rename,[status(thm)],[c_0_892]) ).
fof(c_0_1347,plain,
! [X25,X26] :
( ~ class_OrderedGroup_Ogroup__add(X26)
| c_HOL_Ominus__class_Ominus(X25,X25,X26) = c_HOL_Ozero__class_Ozero(X26) ),
inference(variable_rename,[status(thm)],[c_0_893]) ).
fof(c_0_1348,plain,
! [X25,X26] :
( ~ class_OrderedGroup_Oab__group__add(X26)
| c_HOL_Ominus__class_Ominus(X25,X25,X26) = c_HOL_Ozero__class_Ozero(X26) ),
inference(variable_rename,[status(thm)],[c_0_894]) ).
fof(c_0_1349,plain,
! [X25,X26] :
( ~ class_Orderings_Olinorder(X26)
| c_Orderings_Oord__class_Omax(X25,X25,X26) = X25 ),
inference(variable_rename,[status(thm)],[c_0_895]) ).
fof(c_0_1350,plain,
! [X25,X26] :
( ~ class_Orderings_Oorder(X26)
| c_lessequals(X25,X25,X26) ),
inference(variable_rename,[status(thm)],[c_0_896]) ).
fof(c_0_1351,plain,
! [X25,X26] :
( ~ class_Orderings_Opreorder(X26)
| c_lessequals(X25,X25,X26) ),
inference(variable_rename,[status(thm)],[c_0_897]) ).
fof(c_0_1352,plain,
! [X23] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X23,tc_nat)
| X23 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_898]) ).
fof(c_0_1353,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_899]) ).
fof(c_0_1354,plain,
! [X6,X7] :
( class_Orderings_Opreorder(tc_fun(X6,X7))
| ~ class_Orderings_Opreorder(X7) ),
inference(variable_rename,[status(thm)],[c_0_900]) ).
fof(c_0_1355,plain,
! [X6,X7] :
( class_Orderings_Oorder(tc_fun(X6,X7))
| ~ class_Orderings_Oorder(X7) ),
inference(variable_rename,[status(thm)],[c_0_901]) ).
fof(c_0_1356,plain,
! [X6,X7] :
( class_Orderings_Obot(tc_fun(X6,X7))
| ~ class_Orderings_Obot(X7) ),
inference(variable_rename,[status(thm)],[c_0_902]) ).
fof(c_0_1357,plain,
! [X4] :
( ~ class_OrderedGroup_Omonoid__add(X4)
| c_List_Olistsum(c_List_Olist_ONil(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(variable_rename,[status(thm)],[c_0_903]) ).
fof(c_0_1358,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_904]) ).
fof(c_0_1359,plain,
! [X4] :
( ~ class_OrderedGroup_Osemigroup__add(X4)
| c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(X4),X4) ),
inference(variable_rename,[status(thm)],[c_0_905]) ).
fof(c_0_1360,plain,
! [X71,X72] :
( c_Lambda_OdB_OAbs(X72) != c_Lambda_OdB_OAbs(X71)
| X72 = X71 ),
inference(variable_rename,[status(thm)],[c_0_906]) ).
fof(c_0_1361,plain,
! [X52,X53] :
( c_Lambda_OdB_OVar(X53) != c_Lambda_OdB_OVar(X52)
| X53 = X52 ),
inference(variable_rename,[status(thm)],[c_0_907]) ).
cnf(c_0_1362,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),X4),X2)))
| ~ c_Type_Otyping(c_Type_Oshift(X1,X2,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X3)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
| ~ c_Type_Otyping(X1,X4,v_T____) ),
inference(split_conjunct,[status(thm)],[c_0_908]) ).
cnf(c_0_1363,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X1,X2,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_909]) ).
cnf(c_0_1364,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_910]) ).
cnf(c_0_1365,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_911]) ).
cnf(c_0_1366,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_912]) ).
cnf(c_0_1367,plain,
( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X10)) = hAPP(hAPP(X2,X9),hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X10))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_913]) ).
cnf(c_0_1368,plain,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),hAPP(hAPP(X1,X9),X10)) = hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X9)),hAPP(hAPP(X1,X8),X10))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_914]) ).
cnf(c_0_1369,plain,
( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X10)) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),hAPP(hAPP(X2,X9),X10)))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_915]) ).
cnf(c_0_1370,plain,
( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X10)) = hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X9)),hAPP(hAPP(X2,X8),X10))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_916]) ).
cnf(c_0_1371,plain,
( hAPP(hAPP(X3,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,hAPP(hAPP(X3,X7),X9)),hAPP(hAPP(X3,X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_917]) ).
cnf(c_0_1372,plain,
( hAPP(hAPP(X2,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X9)),hAPP(hAPP(X2,X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_918]) ).
cnf(c_0_1373,plain,
( hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X8)) = hAPP(hAPP(X2,hAPP(hAPP(X1,X7),X9)),X8)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_919]) ).
cnf(c_0_1374,plain,
( hAPP(hAPP(X2,hAPP(hAPP(X3,X7),X8)),hAPP(hAPP(X3,X7),X9)) = hAPP(hAPP(X3,X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_920]) ).
cnf(c_0_1375,plain,
( hAPP(hAPP(X2,X7),hAPP(hAPP(X1,X8),X9)) = hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X7),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_921]) ).
cnf(c_0_1376,plain,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X9)),X8)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_922]) ).
cnf(c_0_1377,plain,
( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X9)),X8)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_923]) ).
cnf(c_0_1378,plain,
( hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X8)),X8) = hAPP(hAPP(X2,hAPP(hAPP(X1,X7),X5)),X8)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_924]) ).
cnf(c_0_1379,plain,
( hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9)) = hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_925]) ).
cnf(c_0_1380,plain,
( hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9)) = hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_926]) ).
cnf(c_0_1381,plain,
( hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9)) = hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_927]) ).
cnf(c_0_1382,plain,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_928]) ).
cnf(c_0_1383,plain,
( hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9)) = hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_929]) ).
cnf(c_0_1384,plain,
( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_930]) ).
cnf(c_0_1385,plain,
( hAPP(hAPP(X1,X7),hAPP(hAPP(X2,X8),X7)) = hAPP(hAPP(X2,hAPP(hAPP(X1,X8),X5)),X7)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_931]) ).
cnf(c_0_1386,plain,
( hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9)) = hAPP(hAPP(X1,X8),hAPP(hAPP(X1,X7),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_932]) ).
cnf(c_0_1387,plain,
( hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9)) = hAPP(hAPP(X2,X8),hAPP(hAPP(X2,X7),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_933]) ).
cnf(c_0_1388,plain,
( hAPP(hAPP(X1,X7),X7) = hAPP(hAPP(X2,hAPP(hAPP(X1,X5),X5)),X7)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_934]) ).
cnf(c_0_1389,plain,
( hAPP(hAPP(X2,X7),X8) = hAPP(hAPP(X2,X8),X7)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_935]) ).
cnf(c_0_1390,plain,
( hAPP(hAPP(X1,X7),X8) = hAPP(hAPP(X1,X8),X7)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_936]) ).
cnf(c_0_1391,plain,
( hAPP(hAPP(X1,X7),X8) = hAPP(hAPP(X1,X8),X7)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_937]) ).
cnf(c_0_1392,plain,
( hAPP(hAPP(X2,X7),X8) = hAPP(hAPP(X2,X8),X7)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_938]) ).
cnf(c_0_1393,plain,
( hAPP(hAPP(X3,X7),c_HOL_Ozero__class_Ozero(tc_nat)) = X5
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_939]) ).
cnf(c_0_1394,plain,
( hAPP(hAPP(X2,X5),X7) = X7
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_940]) ).
cnf(c_0_1395,plain,
( hAPP(hAPP(X2,X4),X7) = X4
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_941]) ).
cnf(c_0_1396,plain,
( hAPP(hAPP(X1,X4),X7) = X7
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_942]) ).
cnf(c_0_1397,plain,
( hAPP(hAPP(X2,X7),X5) = X7
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_943]) ).
cnf(c_0_1398,plain,
( hAPP(hAPP(X2,X5),X7) = X7
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_944]) ).
cnf(c_0_1399,plain,
( hAPP(hAPP(X2,X7),X4) = X4
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_945]) ).
cnf(c_0_1400,plain,
( hAPP(hAPP(X2,X4),X7) = X4
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_946]) ).
cnf(c_0_1401,plain,
( hAPP(hAPP(X1,X7),X4) = X7
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_947]) ).
cnf(c_0_1402,plain,
( hAPP(hAPP(X1,X4),X7) = X7
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_948]) ).
cnf(c_0_1403,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X5,X2,X6,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4),t_a))) ),
inference(split_conjunct,[status(thm)],[c_0_949]) ).
cnf(c_0_1404,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X5,X2,X6,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4),t_a))) ),
inference(split_conjunct,[status(thm)],[c_0_950]) ).
cnf(c_0_1405,plain,
( X4 = X5
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X5) ),
inference(split_conjunct,[status(thm)],[c_0_951]) ).
cnf(c_0_1406,plain,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X4,X5,X2,c_Lambda_OdB_OAbs(X3),t_a))) ),
inference(split_conjunct,[status(thm)],[c_0_952]) ).
cnf(c_0_1407,plain,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X4,X5,X2,c_Lambda_OdB_OAbs(X3),t_a))) ),
inference(split_conjunct,[status(thm)],[c_0_953]) ).
cnf(c_0_1408,plain,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X4,X5,c_Lambda_OdB_OVar(X3),t_a))) ),
inference(split_conjunct,[status(thm)],[c_0_954]) ).
cnf(c_0_1409,plain,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X4,X5,c_Lambda_OdB_OVar(X3),t_a))) ),
inference(split_conjunct,[status(thm)],[c_0_955]) ).
cnf(c_0_1410,plain,
( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X2,tc_Lambda_OdB)
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_956]) ).
cnf(c_0_1411,plain,
( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_957]) ).
cnf(c_0_1412,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X1,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_958]) ).
cnf(c_0_1413,plain,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_959]) ).
cnf(c_0_1414,plain,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_960]) ).
cnf(c_0_1415,plain,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_961]) ).
cnf(c_0_1416,plain,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_962]) ).
cnf(c_0_1417,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_963]) ).
cnf(c_0_1418,plain,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_964]) ).
cnf(c_0_1419,plain,
( c_List_Ofoldl(X1,hAPP(hAPP(X1,X3),X4),X5,X2,X2) = hAPP(hAPP(X1,X3),c_List_Ofoldl(X1,X4,X5,X2,X2))
| ~ c_OrderedGroup_Osemigroup__add(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_965]) ).
cnf(c_0_1420,plain,
( hAPP(hAPP(X2,X4),c_List_Ofoldl(X2,X1,X5,X3,X3)) = c_List_Ofoldl(X2,X4,X5,X3,X3)
| ~ c_OrderedGroup_Omonoid__add(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_966]) ).
cnf(c_0_1421,plain,
( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X3,c_HOL_Ozero__class_Ozero(X1),X1,X1))
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_967]) ).
cnf(c_0_1422,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_968]) ).
cnf(c_0_1423,plain,
( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| X2 = c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X2,X4,X3,X1),tc_Lambda_OdB,tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_969]) ).
cnf(c_0_1424,plain,
( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X2,X1,X1) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),X1,X1)
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_970]) ).
cnf(c_0_1425,plain,
( c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X3,X2,X1,X1)
| ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_971]) ).
cnf(c_0_1426,plain,
( hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) = X3
| hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_972]) ).
cnf(c_0_1427,plain,
( X1 = c_Lambda_OdB_OAbs(X2)
| c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X2) ),
inference(split_conjunct,[status(thm)],[c_0_973]) ).
cnf(c_0_1428,plain,
( c_Lambda_OdB_OVar(X1) = X2
| c_Lambda_OdB_OVar(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_974]) ).
cnf(c_0_1429,plain,
( c_Lambda_OdB_OAbs(X1) = X2
| c_Lambda_OdB_OAbs(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_975]) ).
cnf(c_0_1430,plain,
( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_976]) ).
cnf(c_0_1431,plain,
( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X3) ),
inference(split_conjunct,[status(thm)],[c_0_977]) ).
cnf(c_0_1432,plain,
( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| c_Lambda_OdB_OVar(X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_978]) ).
cnf(c_0_1433,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X1,X2,X2),X2),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_979]) ).
cnf(c_0_1434,plain,
( c_ListOrder_Ostep1(X1,X2,X5,X4)
| hBOOL(hAPP(hAPP(X1,X3),X6))
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_980]) ).
cnf(c_0_1435,plain,
( c_ListOrder_Ostep1(X1,X2,X5,X4)
| X2 = X5
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_981]) ).
cnf(c_0_1436,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_Nat_Onat_Onat__case(X2,X3,c_HOL_Ozero__class_Ozero(tc_nat),t_a))) ),
inference(split_conjunct,[status(thm)],[c_0_982]) ).
cnf(c_0_1437,plain,
( X3 = X6
| hBOOL(hAPP(hAPP(X1,X3),X6))
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_983]) ).
cnf(c_0_1438,plain,
( X3 = X6
| X2 = X5
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_984]) ).
cnf(c_0_1439,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_985]) ).
cnf(c_0_1440,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X1),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_986]) ).
cnf(c_0_1441,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X1,X2,X2),X2),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_987]) ).
cnf(c_0_1442,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),X4),X2)))
| ~ c_Type_Otyping(c_Type_Oshift(X1,X2,v_T____,tc_Type_Otype),v_a____,X3)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
| ~ c_Type_Otyping(X1,X4,v_T____) ),
inference(split_conjunct,[status(thm)],[c_0_988]) ).
cnf(c_0_1443,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X1),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_989]) ).
cnf(c_0_1444,plain,
( c_List_Olistsum(X1,X2) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X2),X1,c_HOL_Ozero__class_Ozero(X2),X2,X2)
| ~ class_OrderedGroup_Omonoid__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_990]) ).
cnf(c_0_1445,plain,
( c_List_Olistsum(X1,X2) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X2),c_HOL_Ozero__class_Ozero(X2),X1,X2,X2)
| ~ class_OrderedGroup_Omonoid__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_991]) ).
cnf(c_0_1446,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_992]) ).
cnf(c_0_1447,plain,
( c_Type_Otyping(X1,hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4),X5)
| ~ c_Type_Otyping(c_Type_Oshift(X1,X4,X6,tc_Type_Otype),X2,X5)
| ~ c_Type_Otyping(X1,X3,X6) ),
inference(split_conjunct,[status(thm)],[c_0_993]) ).
cnf(c_0_1448,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_994]) ).
cnf(c_0_1449,plain,
( hBOOL(hAPP(hAPP(X1,X2),X5))
| c_ListOrder_Ostep1(X1,X3,X6,X4)
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_995]) ).
cnf(c_0_1450,plain,
( X6 = X3
| c_ListOrder_Ostep1(X1,X3,X6,X4)
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_996]) ).
cnf(c_0_1451,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),X3,tc_nat))) ),
inference(split_conjunct,[status(thm)],[c_0_997]) ).
cnf(c_0_1452,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),X3,tc_nat))) ),
inference(split_conjunct,[status(thm)],[c_0_998]) ).
cnf(c_0_1453,plain,
( hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_999]) ).
cnf(c_0_1454,plain,
( hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_1000]) ).
cnf(c_0_1455,plain,
( c_ListOrder_Ostep1(X1,c_List_Oappend(X2,X3,X4),c_List_Oappend(X5,X3,X4),X4)
| ~ c_ListOrder_Ostep1(X1,X2,X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1001]) ).
cnf(c_0_1456,plain,
( c_ListOrder_Ostep1(X1,c_List_Oappend(X5,X2,X4),c_List_Oappend(X5,X3,X4),X4)
| ~ c_ListOrder_Ostep1(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1002]) ).
cnf(c_0_1457,plain,
( c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X5,X2,X4),c_List_Olist_OCons(X5,X3,X4),X4)
| ~ c_ListOrder_Ostep1(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1003]) ).
cnf(c_0_1458,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1004]) ).
cnf(c_0_1459,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1005]) ).
cnf(c_0_1460,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,X1),X3)),hAPP(hAPP(c_Lambda_Olift,X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1006]) ).
cnf(c_0_1461,plain,
( hBOOL(hAPP(hAPP(X1,X2),X5))
| X5 = X2
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_1007]) ).
cnf(c_0_1462,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_1008]) ).
cnf(c_0_1463,plain,
( X6 = X3
| X5 = X2
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_1009]) ).
cnf(c_0_1464,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_1010]) ).
cnf(c_0_1465,plain,
( c_Type_Otyping(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X2),X4),X3)
| ~ c_Type_Otyping(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1011]) ).
cnf(c_0_1466,plain,
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1012]) ).
cnf(c_0_1467,plain,
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1013]) ).
cnf(c_0_1468,plain,
( c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1014]) ).
cnf(c_0_1469,plain,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1015]) ).
cnf(c_0_1470,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,X1),X3)),hAPP(hAPP(c_Lambda_Olift,X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1016]) ).
cnf(c_0_1471,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1017]) ).
cnf(c_0_1472,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1018]) ).
cnf(c_0_1473,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X2),X5))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X3),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_1019]) ).
cnf(c_0_1474,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(X1,X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_1020]) ).
cnf(c_0_1475,plain,
( hAPP(c_Type_Oshift(X3,X2,X4,X5),X1) = hAPP(X3,X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1021]) ).
cnf(c_0_1476,plain,
( c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X3,X4),X4)
| ~ hBOOL(hAPP(hAPP(X1,X2),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_1022]) ).
cnf(c_0_1477,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1023]) ).
cnf(c_0_1478,plain,
( X1 = X2
| c_List_Oappend(X1,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4) != c_List_Oappend(X2,c_List_Olist_OCons(X5,c_List_Olist_ONil(X4),X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_1024]) ).
cnf(c_0_1479,plain,
( X1 = X2
| c_List_Oappend(X3,c_List_Olist_OCons(X1,c_List_Olist_ONil(X4),X4),X4) != c_List_Oappend(X5,c_List_Olist_OCons(X2,c_List_Olist_ONil(X4),X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_1025]) ).
cnf(c_0_1480,plain,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1026]) ).
cnf(c_0_1481,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Orderings_Oord__class_Omax(X2,X3,X1)),X4) = c_Orderings_Oord__class_Omax(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1027]) ).
cnf(c_0_1482,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_1028]) ).
cnf(c_0_1483,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1029]) ).
cnf(c_0_1484,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1030]) ).
cnf(c_0_1485,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_1031]) ).
cnf(c_0_1486,plain,
( hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)))
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1032]) ).
cnf(c_0_1487,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1033]) ).
cnf(c_0_1488,plain,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X1,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)),X3)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1034]) ).
cnf(c_0_1489,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)),X3) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X1,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1035]) ).
cnf(c_0_1490,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),X2,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1036]) ).
cnf(c_0_1491,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_1037]) ).
cnf(c_0_1492,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_1038]) ).
cnf(c_0_1493,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_1039]) ).
cnf(c_0_1494,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_1040]) ).
cnf(c_0_1495,plain,
( c_lessequals(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1041]) ).
cnf(c_0_1496,plain,
( X2 = X3
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| c_Power_Opower__class_Opower(X2,X4,X1) != c_Power_Opower__class_Opower(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1042]) ).
cnf(c_0_1497,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),c_Lambda_OdB_OVar(X2)),X3)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1043]) ).
cnf(c_0_1498,plain,
( c_lessequals(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),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_1044]) ).
cnf(c_0_1499,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X1)),c_Lambda_OdB_OAbs(X2)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1045]) ).
cnf(c_0_1500,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_1046]) ).
cnf(c_0_1501,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_1047]) ).
cnf(c_0_1502,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_1048]) ).
cnf(c_0_1503,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_1049]) ).
cnf(c_0_1504,plain,
( c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3) = c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(X1,X4,X3),c_HOL_Ominus__class_Ominus(X2,X4,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1050]) ).
cnf(c_0_1505,plain,
( c_Wellfounded_Oaccp(X1,X4,X3)
| ~ c_Wellfounded_Oaccp(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X3),X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1051]) ).
cnf(c_0_1506,plain,
( c_Wellfounded_Oaccp(X1,X3,X2)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| ~ c_Wellfounded_Oaccp(X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1052]) ).
cnf(c_0_1507,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1053]) ).
cnf(c_0_1508,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(X3,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1054]) ).
cnf(c_0_1509,plain,
( c_lessequals(X3,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1055]) ).
cnf(c_0_1510,plain,
( c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1056]) ).
cnf(c_0_1511,plain,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1057]) ).
cnf(c_0_1512,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_1058]) ).
cnf(c_0_1513,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_1059]) ).
cnf(c_0_1514,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_1060]) ).
cnf(c_0_1515,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_1061]) ).
cnf(c_0_1516,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_1062]) ).
cnf(c_0_1517,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X4),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X3,X4,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1063]) ).
cnf(c_0_1518,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1064]) ).
cnf(c_0_1519,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Olist_ONil(X3) != c_List_Omap(X4,X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1065]) ).
cnf(c_0_1520,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Omap(X3,X1,X2,X4) != c_List_Olist_ONil(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1066]) ).
cnf(c_0_1521,plain,
( c_Type_Otyping(X3,X2,X4)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| ~ c_Type_Otyping(X3,X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1067]) ).
cnf(c_0_1522,plain,
( c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1068]) ).
cnf(c_0_1523,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1069]) ).
cnf(c_0_1524,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_1070]) ).
cnf(c_0_1525,plain,
( c_HOL_Ominus__class_Ominus(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),X2,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1071]) ).
cnf(c_0_1526,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat)
| ~ c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1072]) ).
cnf(c_0_1527,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1073]) ).
cnf(c_0_1528,plain,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),X1,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat))
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1074]) ).
cnf(c_0_1529,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),X1,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1075]) ).
cnf(c_0_1530,plain,
( c_lessequals(X1,X2,X4)
| c_lessequals(X1,X3,X4)
| ~ c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
| ~ class_Orderings_Olinorder(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1076]) ).
cnf(c_0_1531,plain,
( c_HOL_Oord__class_Oless(X1,X2,X4)
| c_HOL_Oord__class_Oless(X1,X3,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
| ~ class_Orderings_Olinorder(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1077]) ).
cnf(c_0_1532,plain,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X2,tc_nat) = X1
| ~ c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1078]) ).
cnf(c_0_1533,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_1079]) ).
cnf(c_0_1534,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_1080]) ).
cnf(c_0_1535,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_1081]) ).
cnf(c_0_1536,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_1082]) ).
cnf(c_0_1537,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_1083]) ).
cnf(c_0_1538,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_1084]) ).
cnf(c_0_1539,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_1085]) ).
cnf(c_0_1540,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_1086]) ).
cnf(c_0_1541,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_1087]) ).
cnf(c_0_1542,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_1088]) ).
cnf(c_0_1543,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_1089]) ).
cnf(c_0_1544,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_1090]) ).
cnf(c_0_1545,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_1091]) ).
cnf(c_0_1546,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_1092]) ).
cnf(c_0_1547,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_1093]) ).
cnf(c_0_1548,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_1094]) ).
cnf(c_0_1549,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_1095]) ).
cnf(c_0_1550,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_1096]) ).
cnf(c_0_1551,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_1097]) ).
cnf(c_0_1552,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_1098]) ).
cnf(c_0_1553,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_1099]) ).
cnf(c_0_1554,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1100]) ).
cnf(c_0_1555,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1101]) ).
cnf(c_0_1556,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1102]) ).
cnf(c_0_1557,plain,
( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1103]) ).
cnf(c_0_1558,plain,
( c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1104]) ).
cnf(c_0_1559,plain,
( c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1105]) ).
cnf(c_0_1560,plain,
( c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1106]) ).
cnf(c_0_1561,plain,
( X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)),X2)
| ~ c_lessequals(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1107]) ).
cnf(c_0_1562,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)),X1) = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1108]) ).
cnf(c_0_1563,plain,
( X1 = X2
| ~ c_lessequals(X3,X1,tc_nat)
| ~ c_lessequals(X3,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(X1,X3,tc_nat) != c_HOL_Ominus__class_Ominus(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1109]) ).
cnf(c_0_1564,plain,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X3),X4)),X5) = hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5))
| ~ c_OrderedGroup_Osemigroup__add(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1110]) ).
cnf(c_0_1565,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1111]) ).
cnf(c_0_1566,plain,
( c_List_Olistsp(X1,c_List_Oappend(X2,X4,X3),X3)
| ~ c_List_Olistsp(X1,X2,X3)
| ~ c_List_Olistsp(X1,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1112]) ).
cnf(c_0_1567,plain,
( c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3) = c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1113]) ).
cnf(c_0_1568,plain,
( c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4) = c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omax(X1,X3,X4),X4)
| ~ class_Orderings_Olinorder(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1114]) ).
cnf(c_0_1569,plain,
( c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1115]) ).
cnf(c_0_1570,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1116]) ).
cnf(c_0_1571,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_1117]) ).
cnf(c_0_1572,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_1118]) ).
cnf(c_0_1573,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_1119]) ).
cnf(c_0_1574,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_1120]) ).
cnf(c_0_1575,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_1121]) ).
cnf(c_0_1576,plain,
( c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X5,X4,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1122]) ).
cnf(c_0_1577,plain,
( c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X5,X4,X3) != c_HOL_Ominus__class_Ominus(X2,X1,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1123]) ).
cnf(c_0_1578,plain,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1124]) ).
cnf(c_0_1579,plain,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1125]) ).
cnf(c_0_1580,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1126]) ).
cnf(c_0_1581,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1127]) ).
cnf(c_0_1582,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1128]) ).
cnf(c_0_1583,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1129]) ).
cnf(c_0_1584,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1130]) ).
cnf(c_0_1585,plain,
( c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1131]) ).
cnf(c_0_1586,plain,
( c_lessequals(X2,X4,X3)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1132]) ).
cnf(c_0_1587,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1133]) ).
cnf(c_0_1588,plain,
( c_lessequals(X2,X4,X3)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1134]) ).
cnf(c_0_1589,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1135]) ).
cnf(c_0_1590,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_1136]) ).
cnf(c_0_1591,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_1137]) ).
cnf(c_0_1592,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_1138]) ).
cnf(c_0_1593,plain,
( c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1139]) ).
cnf(c_0_1594,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1140]) ).
cnf(c_0_1595,plain,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3) = c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(X2,X3),c_Nat_Osemiring__1__class_Oof__nat(X1,X3),X3)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ class_Ring__and__Field_Oring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1141]) ).
cnf(c_0_1596,plain,
( c_List_Olistsp(X1,X2,X4)
| ~ c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_1142]) ).
cnf(c_0_1597,plain,
( c_List_Olistsp(X1,X3,X4)
| ~ c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_1143]) ).
cnf(c_0_1598,plain,
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1144]) ).
cnf(c_0_1599,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_1145]) ).
cnf(c_0_1600,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_1146]) ).
cnf(c_0_1601,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_1147]) ).
cnf(c_0_1602,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1148]) ).
cnf(c_0_1603,plain,
( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1149]) ).
cnf(c_0_1604,plain,
( c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1150]) ).
cnf(c_0_1605,plain,
( c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1151]) ).
cnf(c_0_1606,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),X3) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1152]) ).
cnf(c_0_1607,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),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_1153]) ).
cnf(c_0_1608,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),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_1154]) ).
cnf(c_0_1609,plain,
( c_Wellfounded_Oaccp(X1,X4,X3)
| ~ c_Wellfounded_Oaccp(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1155]) ).
cnf(c_0_1610,plain,
( c_Wellfounded_Oaccp(X1,X4,X3)
| ~ c_Wellfounded_Oaccp(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1156]) ).
cnf(c_0_1611,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_1157]) ).
cnf(c_0_1612,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_1158]) ).
cnf(c_0_1613,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_1159]) ).
cnf(c_0_1614,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_1160]) ).
cnf(c_0_1615,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_1161]) ).
cnf(c_0_1616,plain,
( hBOOL(hAPP(c_InductTermi_OIT,X1))
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_1162]) ).
cnf(c_0_1617,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1163]) ).
cnf(c_0_1618,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1164]) ).
cnf(c_0_1619,plain,
( c_Type_Otyping(X1,X4,X3)
| ~ c_Type_Otyping(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1165]) ).
cnf(c_0_1620,plain,
( c_List_Olistsum(c_List_Oappend(X1,X2,X3),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_List_Olistsum(X1,X3)),c_List_Olistsum(X2,X3))
| ~ class_OrderedGroup_Omonoid__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1166]) ).
cnf(c_0_1621,plain,
( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1167]) ).
cnf(c_0_1622,plain,
( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1168]) ).
cnf(c_0_1623,plain,
( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1169]) ).
cnf(c_0_1624,plain,
( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1170]) ).
cnf(c_0_1625,plain,
( c_lessequals(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1171]) ).
cnf(c_0_1626,plain,
( c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1172]) ).
cnf(c_0_1627,plain,
( c_lessequals(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1173]) ).
cnf(c_0_1628,plain,
( c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1174]) ).
cnf(c_0_1629,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1175]) ).
cnf(c_0_1630,plain,
( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = X1
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1176]) ).
cnf(c_0_1631,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_1177]) ).
cnf(c_0_1632,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1178]) ).
cnf(c_0_1633,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X1),c_Lambda_OdB_OVar(X2))))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1179]) ).
cnf(c_0_1634,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1180]) ).
cnf(c_0_1635,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1181]) ).
cnf(c_0_1636,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)) = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1182]) ).
cnf(c_0_1637,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_1183]) ).
cnf(c_0_1638,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_1184]) ).
cnf(c_0_1639,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_1185]) ).
cnf(c_0_1640,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_1186]) ).
cnf(c_0_1641,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_1187]) ).
cnf(c_0_1642,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_1188]) ).
cnf(c_0_1643,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_1189]) ).
cnf(c_0_1644,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_1190]) ).
cnf(c_0_1645,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X1)),c_Lambda_OdB_OAbs(X2)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1191]) ).
cnf(c_0_1646,plain,
( c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1192]) ).
cnf(c_0_1647,plain,
( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1193]) ).
cnf(c_0_1648,plain,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1194]) ).
cnf(c_0_1649,plain,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1195]) ).
cnf(c_0_1650,plain,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1196]) ).
cnf(c_0_1651,plain,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1197]) ).
cnf(c_0_1652,plain,
( c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1198]) ).
cnf(c_0_1653,plain,
( c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1199]) ).
cnf(c_0_1654,plain,
( c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1200]) ).
cnf(c_0_1655,plain,
( c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1201]) ).
cnf(c_0_1656,plain,
( c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X1,X2,X3),X3) = c_Orderings_Oord__class_Omax(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1202]) ).
cnf(c_0_1657,plain,
( c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1203]) ).
cnf(c_0_1658,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X1),X2)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1204]) ).
cnf(c_0_1659,plain,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X2,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X1),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1205]) ).
cnf(c_0_1660,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Lambda_Oliftn(X3,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1206]) ).
cnf(c_0_1661,plain,
( c_List_Olistsum(c_List_Olist_OCons(X1,X2,X3),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),c_List_Olistsum(X2,X3))
| ~ class_OrderedGroup_Omonoid__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1207]) ).
cnf(c_0_1662,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_1208]) ).
cnf(c_0_1663,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_1209]) ).
cnf(c_0_1664,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(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_1210]) ).
cnf(c_0_1665,plain,
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X3),X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1211]) ).
cnf(c_0_1666,plain,
( c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1212]) ).
cnf(c_0_1667,plain,
( c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1213]) ).
cnf(c_0_1668,plain,
( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1214]) ).
cnf(c_0_1669,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| hBOOL(hAPP(hAPP(X3,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1215]) ).
cnf(c_0_1670,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1216]) ).
cnf(c_0_1671,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1217]) ).
cnf(c_0_1672,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1218]) ).
cnf(c_0_1673,plain,
( X2 = X1
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1219]) ).
cnf(c_0_1674,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1220]) ).
cnf(c_0_1675,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
| ~ class_OrderedGroup_Oab__group__add(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1221]) ).
cnf(c_0_1676,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_1222]) ).
cnf(c_0_1677,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_1223]) ).
cnf(c_0_1678,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_1224]) ).
cnf(c_0_1679,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_1225]) ).
cnf(c_0_1680,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_1226]) ).
cnf(c_0_1681,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_1227]) ).
cnf(c_0_1682,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_1228]) ).
cnf(c_0_1683,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_1229]) ).
cnf(c_0_1684,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_1230]) ).
cnf(c_0_1685,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = X3
| c_List_Oreplicate(X1,X2,X4) != c_List_Oreplicate(X5,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1231]) ).
cnf(c_0_1686,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1232]) ).
cnf(c_0_1687,plain,
( X1 = X2
| c_List_Oreplicate(X1,X3,X4) != c_List_Oreplicate(X2,X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1233]) ).
cnf(c_0_1688,plain,
( X1 = X2
| c_List_Oappend(X1,X3,X4) != c_List_Oappend(X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1234]) ).
cnf(c_0_1689,plain,
( X1 = X2
| c_List_Oappend(X3,X1,X4) != c_List_Oappend(X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1235]) ).
cnf(c_0_1690,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_1236]) ).
cnf(c_0_1691,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_1237]) ).
cnf(c_0_1692,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_1238]) ).
cnf(c_0_1693,plain,
( X1 = X2
| c_List_Olist_OCons(X1,X3,X4) != c_List_Olist_OCons(X2,X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1239]) ).
cnf(c_0_1694,plain,
( X1 = X2
| c_List_Olist_OCons(X3,X1,X4) != c_List_Olist_OCons(X5,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1240]) ).
cnf(c_0_1695,plain,
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X1),X2,X1) = c_Lambda_Oliftn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1241]) ).
cnf(c_0_1696,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X2)),X3),X1) = c_Lambda_OdB_OVar(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1242]) ).
cnf(c_0_1697,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1243]) ).
cnf(c_0_1698,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1244]) ).
cnf(c_0_1699,plain,
( c_lessequals(X1,c_Orderings_Oord__class_Omax(X1,X2,X3),X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1245]) ).
cnf(c_0_1700,plain,
( c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X1,X3),X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1246]) ).
cnf(c_0_1701,plain,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X3,X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1247]) ).
cnf(c_0_1702,plain,
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1) = X2
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1248]) ).
cnf(c_0_1703,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1249]) ).
cnf(c_0_1704,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_1250]) ).
cnf(c_0_1705,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_1251]) ).
cnf(c_0_1706,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_1252]) ).
cnf(c_0_1707,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_1253]) ).
cnf(c_0_1708,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_1254]) ).
cnf(c_0_1709,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_1255]) ).
cnf(c_0_1710,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_1256]) ).
cnf(c_0_1711,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_1257]) ).
cnf(c_0_1712,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X1),tc_nat)
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(split_conjunct,[status(thm)],[c_0_1258]) ).
cnf(c_0_1713,plain,
( c_lessequals(X1,X2,X3)
| c_Orderings_Oord__class_Omax(X1,X2,X3) != X2
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1259]) ).
cnf(c_0_1714,plain,
( c_Orderings_Oord__class_Omax(X2,X1,X3) = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1260]) ).
cnf(c_0_1715,plain,
( c_Orderings_Oord__class_Omax(X1,X2,X3) = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1261]) ).
cnf(c_0_1716,plain,
( c_Lambda_Oliftn(X3,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1262]) ).
cnf(c_0_1717,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_1263]) ).
cnf(c_0_1718,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_1264]) ).
cnf(c_0_1719,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_1265]) ).
cnf(c_0_1720,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_1266]) ).
cnf(c_0_1721,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_1267]) ).
cnf(c_0_1722,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_1268]) ).
cnf(c_0_1723,plain,
( c_lessequals(X1,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1269]) ).
cnf(c_0_1724,plain,
( c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1270]) ).
cnf(c_0_1725,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1271]) ).
cnf(c_0_1726,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1272]) ).
cnf(c_0_1727,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1273]) ).
cnf(c_0_1728,plain,
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1274]) ).
cnf(c_0_1729,plain,
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1275]) ).
cnf(c_0_1730,plain,
( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X1)),X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1276]) ).
cnf(c_0_1731,plain,
( hBOOL(hAPP(X1,v_sko__Nat__Xnat__Xinducts__1(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(split_conjunct,[status(thm)],[c_0_1277]) ).
cnf(c_0_1732,plain,
( hBOOL(hAPP(X1,v_sko__Nat__Xnat__Xinduct__1(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(split_conjunct,[status(thm)],[c_0_1278]) ).
cnf(c_0_1733,plain,
( hBOOL(hAPP(X1,v_sko__List__Xupt__Xinduct__1(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(split_conjunct,[status(thm)],[c_0_1279]) ).
cnf(c_0_1734,plain,
( hAPP(hAPP(X2,X4),X1) = X4
| ~ c_OrderedGroup_Omonoid__add(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1280]) ).
cnf(c_0_1735,plain,
( hAPP(hAPP(X2,X1),X4) = X4
| ~ c_OrderedGroup_Omonoid__add(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1281]) ).
cnf(c_0_1736,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != 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_1282]) ).
cnf(c_0_1737,plain,
( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) != 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_1283]) ).
cnf(c_0_1738,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| c_Lambda_Osubstn(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1284]) ).
cnf(c_0_1739,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_1285]) ).
cnf(c_0_1740,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_1286]) ).
cnf(c_0_1741,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_1287]) ).
cnf(c_0_1742,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_1288]) ).
cnf(c_0_1743,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_1289]) ).
cnf(c_0_1744,plain,
( X1 = X2
| hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4) ),
inference(split_conjunct,[status(thm)],[c_0_1290]) ).
cnf(c_0_1745,plain,
( X1 = X2
| hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X4),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1291]) ).
cnf(c_0_1746,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_1292]) ).
cnf(c_0_1747,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_1293]) ).
cnf(c_0_1748,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_1294]) ).
cnf(c_0_1749,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_1295]) ).
cnf(c_0_1750,plain,
( c_lessequals(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1296]) ).
cnf(c_0_1751,plain,
( c_Orderings_Oord__class_Omax(X1,X2,X3) = c_Orderings_Oord__class_Omax(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1297]) ).
cnf(c_0_1752,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_1298]) ).
cnf(c_0_1753,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_1299]) ).
cnf(c_0_1754,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_1300]) ).
cnf(c_0_1755,plain,
( hAPP(X1,X2) = X3
| ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1301]) ).
cnf(c_0_1756,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1302]) ).
cnf(c_0_1757,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1303]) ).
cnf(c_0_1758,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1304]) ).
cnf(c_0_1759,plain,
( c_lessequals(X1,X2,tc_nat)
| c_lessequals(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1305]) ).
cnf(c_0_1760,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1306]) ).
cnf(c_0_1761,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_1307]) ).
cnf(c_0_1762,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1308]) ).
cnf(c_0_1763,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1309]) ).
cnf(c_0_1764,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_1310]) ).
cnf(c_0_1765,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Olist_ONil(X2) != c_List_Oappend(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1311]) ).
cnf(c_0_1766,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Olist_ONil(X2) != c_List_Oappend(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1312]) ).
cnf(c_0_1767,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X1,X3,X2) != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1313]) ).
cnf(c_0_1768,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X3,X1,X2) != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1314]) ).
cnf(c_0_1769,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = 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_1315]) ).
cnf(c_0_1770,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_List_Oreplicate(X1,X2,X3) != c_List_Olist_ONil(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1316]) ).
cnf(c_0_1771,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_List_Olist_ONil(X2) != c_List_Oreplicate(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1317]) ).
cnf(c_0_1772,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_1318]) ).
cnf(c_0_1773,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_1319]) ).
cnf(c_0_1774,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1320]) ).
cnf(c_0_1775,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1321]) ).
cnf(c_0_1776,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1322]) ).
cnf(c_0_1777,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X3,X1,X2) != X3 ),
inference(split_conjunct,[status(thm)],[c_0_1323]) ).
cnf(c_0_1778,plain,
( X1 = c_List_Olist_ONil(X2)
| X3 != c_List_Oappend(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1324]) ).
cnf(c_0_1779,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X1,X3,X2) != X3 ),
inference(split_conjunct,[status(thm)],[c_0_1325]) ).
cnf(c_0_1780,plain,
( X1 = c_List_Olist_ONil(X2)
| X3 != c_List_Oappend(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1326]) ).
cnf(c_0_1781,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1327]) ).
cnf(c_0_1782,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Osemiring__0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1328]) ).
cnf(c_0_1783,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1329]) ).
cnf(c_0_1784,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_1330]) ).
cnf(c_0_1785,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_1331]) ).
cnf(c_0_1786,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_1332]) ).
cnf(c_0_1787,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_1333]) ).
cnf(c_0_1788,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_1334]) ).
cnf(c_0_1789,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_1335]) ).
cnf(c_0_1790,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1336]) ).
cnf(c_0_1791,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_1337]) ).
cnf(c_0_1792,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_1338]) ).
cnf(c_0_1793,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_1339]) ).
cnf(c_0_1794,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_1340]) ).
cnf(c_0_1795,plain,
( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1341]) ).
cnf(c_0_1796,plain,
( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
| ~ class_Orderings_Obot(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1342]) ).
cnf(c_0_1797,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_1343]) ).
cnf(c_0_1798,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_1344]) ).
cnf(c_0_1799,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_1345]) ).
cnf(c_0_1800,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1346]) ).
cnf(c_0_1801,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1347]) ).
cnf(c_0_1802,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1348]) ).
cnf(c_0_1803,plain,
( c_Orderings_Oord__class_Omax(X1,X1,X2) = X1
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1349]) ).
cnf(c_0_1804,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1350]) ).
cnf(c_0_1805,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1351]) ).
cnf(c_0_1806,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1352]) ).
cnf(c_0_1807,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_1353]) ).
cnf(c_0_1808,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1354]) ).
cnf(c_0_1809,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1355]) ).
cnf(c_0_1810,plain,
( class_Orderings_Obot(tc_fun(X2,X1))
| ~ class_Orderings_Obot(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1356]) ).
cnf(c_0_1811,plain,
( c_List_Olistsum(c_List_Olist_ONil(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1357]) ).
cnf(c_0_1812,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_1358]) ).
cnf(c_0_1813,plain,
( c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(X1),X1)
| ~ class_OrderedGroup_Osemigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1359]) ).
cnf(c_0_1814,plain,
( X1 = X2
| c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1360]) ).
cnf(c_0_1815,plain,
( X1 = X2
| c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1361]) ).
cnf(c_0_1816,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),X4),X2)))
| ~ c_Type_Otyping(c_Type_Oshift(X1,X2,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X3)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
| ~ c_Type_Otyping(X1,X4,v_T____) ),
c_0_1362,
[final] ).
cnf(c_0_1817,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X1,X2,tc_Lambda_OdB) ),
c_0_1363,
[final] ).
cnf(c_0_1818,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
c_0_1364,
[final] ).
cnf(c_0_1819,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
c_0_1365,
[final] ).
cnf(c_0_1820,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X2)) ),
c_0_1366,
[final] ).
cnf(c_0_1821,plain,
( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X10)) = hAPP(hAPP(X2,X9),hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X10))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1367,
[final] ).
cnf(c_0_1822,plain,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),hAPP(hAPP(X1,X9),X10)) = hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X9)),hAPP(hAPP(X1,X8),X10))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1368,
[final] ).
cnf(c_0_1823,plain,
( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X10)) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),hAPP(hAPP(X2,X9),X10)))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1369,
[final] ).
cnf(c_0_1824,plain,
( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X10)) = hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X9)),hAPP(hAPP(X2,X8),X10))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1370,
[final] ).
cnf(c_0_1825,plain,
( hAPP(hAPP(X2,hAPP(hAPP(X3,X7),X9)),hAPP(hAPP(X3,X8),X9)) = hAPP(hAPP(X3,hAPP(hAPP(X2,X7),X8)),X9)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1371,
[final] ).
cnf(c_0_1826,plain,
( hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X9)),hAPP(hAPP(X2,X8),X9)) = hAPP(hAPP(X2,hAPP(hAPP(X1,X7),X8)),X9)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1372,
[final] ).
cnf(c_0_1827,plain,
( hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X8)) = hAPP(hAPP(X2,hAPP(hAPP(X1,X7),X9)),X8)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1373,
[final] ).
cnf(c_0_1828,plain,
( hAPP(hAPP(X2,hAPP(hAPP(X3,X7),X8)),hAPP(hAPP(X3,X7),X9)) = hAPP(hAPP(X3,X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1374,
[final] ).
cnf(c_0_1829,plain,
( hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X7),X9)) = hAPP(hAPP(X2,X7),hAPP(hAPP(X1,X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1375,
[final] ).
cnf(c_0_1830,plain,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X9)),X8)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1376,
[final] ).
cnf(c_0_1831,plain,
( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X9)),X8)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1377,
[final] ).
cnf(c_0_1832,plain,
( hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X8)),X8) = hAPP(hAPP(X2,hAPP(hAPP(X1,X7),X5)),X8)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1378,
[final] ).
cnf(c_0_1833,plain,
( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1379,
[final] ).
cnf(c_0_1834,plain,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1380,
[final] ).
cnf(c_0_1835,plain,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1381,
[final] ).
cnf(c_0_1836,plain,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1382,
[final] ).
cnf(c_0_1837,plain,
( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1383,
[final] ).
cnf(c_0_1838,plain,
( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1384,
[final] ).
cnf(c_0_1839,plain,
( hAPP(hAPP(X1,X7),hAPP(hAPP(X2,X8),X7)) = hAPP(hAPP(X2,hAPP(hAPP(X1,X8),X5)),X7)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1385,
[final] ).
cnf(c_0_1840,plain,
( hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9)) = hAPP(hAPP(X1,X8),hAPP(hAPP(X1,X7),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1386,
[final] ).
cnf(c_0_1841,plain,
( hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9)) = hAPP(hAPP(X2,X8),hAPP(hAPP(X2,X7),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1387,
[final] ).
cnf(c_0_1842,plain,
( hAPP(hAPP(X1,X7),X7) = hAPP(hAPP(X2,hAPP(hAPP(X1,X5),X5)),X7)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1388,
[final] ).
cnf(c_0_1843,plain,
( hAPP(hAPP(X2,X7),X8) = hAPP(hAPP(X2,X8),X7)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1389,
[final] ).
cnf(c_0_1844,plain,
( hAPP(hAPP(X1,X7),X8) = hAPP(hAPP(X1,X8),X7)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1390,
[final] ).
cnf(c_0_1845,plain,
( hAPP(hAPP(X1,X7),X8) = hAPP(hAPP(X1,X8),X7)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1391,
[final] ).
cnf(c_0_1846,plain,
( hAPP(hAPP(X2,X7),X8) = hAPP(hAPP(X2,X8),X7)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1392,
[final] ).
cnf(c_0_1847,plain,
( hAPP(hAPP(X3,X7),c_HOL_Ozero__class_Ozero(tc_nat)) = X5
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1393,
[final] ).
cnf(c_0_1848,plain,
( hAPP(hAPP(X2,X5),X7) = X7
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1394,
[final] ).
cnf(c_0_1849,plain,
( hAPP(hAPP(X2,X4),X7) = X4
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1395,
[final] ).
cnf(c_0_1850,plain,
( hAPP(hAPP(X1,X4),X7) = X7
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1396,
[final] ).
cnf(c_0_1851,plain,
( hAPP(hAPP(X2,X7),X5) = X7
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1397,
[final] ).
cnf(c_0_1852,plain,
( hAPP(hAPP(X2,X5),X7) = X7
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1398,
[final] ).
cnf(c_0_1853,plain,
( hAPP(hAPP(X2,X7),X4) = X4
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1399,
[final] ).
cnf(c_0_1854,plain,
( hAPP(hAPP(X2,X4),X7) = X4
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1400,
[final] ).
cnf(c_0_1855,plain,
( hAPP(hAPP(X1,X7),X4) = X7
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1401,
[final] ).
cnf(c_0_1856,plain,
( hAPP(hAPP(X1,X4),X7) = X7
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1402,
[final] ).
cnf(c_0_1857,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X5,X2,X6,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4),t_a))) ),
c_0_1403,
[final] ).
cnf(c_0_1858,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X5,X2,X6,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4),t_a))) ),
c_0_1404,
[final] ).
cnf(c_0_1859,plain,
( X4 = X5
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X5) ),
c_0_1405,
[final] ).
cnf(c_0_1860,plain,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X4,X5,X2,c_Lambda_OdB_OAbs(X3),t_a))) ),
c_0_1406,
[final] ).
cnf(c_0_1861,plain,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X4,X5,X2,c_Lambda_OdB_OAbs(X3),t_a))) ),
c_0_1407,
[final] ).
cnf(c_0_1862,plain,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X4,X5,c_Lambda_OdB_OVar(X3),t_a))) ),
c_0_1408,
[final] ).
cnf(c_0_1863,plain,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X4,X5,c_Lambda_OdB_OVar(X3),t_a))) ),
c_0_1409,
[final] ).
cnf(c_0_1864,plain,
( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X2,tc_Lambda_OdB)
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
c_0_1410,
[final] ).
cnf(c_0_1865,plain,
( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB) ),
c_0_1411,
[final] ).
cnf(c_0_1866,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X1,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB) ),
c_0_1412,
[final] ).
cnf(c_0_1867,plain,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
c_0_1413,
[final] ).
cnf(c_0_1868,plain,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
c_0_1414,
[final] ).
cnf(c_0_1869,plain,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
c_0_1415,
[final] ).
cnf(c_0_1870,plain,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
c_0_1416,
[final] ).
cnf(c_0_1871,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_1417,
[final] ).
cnf(c_0_1872,plain,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
c_0_1418,
[final] ).
cnf(c_0_1873,plain,
( c_List_Ofoldl(X1,hAPP(hAPP(X1,X3),X4),X5,X2,X2) = hAPP(hAPP(X1,X3),c_List_Ofoldl(X1,X4,X5,X2,X2))
| ~ c_OrderedGroup_Osemigroup__add(X1,X2) ),
c_0_1419,
[final] ).
cnf(c_0_1874,plain,
( hAPP(hAPP(X2,X4),c_List_Ofoldl(X2,X1,X5,X3,X3)) = c_List_Ofoldl(X2,X4,X5,X3,X3)
| ~ c_OrderedGroup_Omonoid__add(X1,X2,X3) ),
c_0_1420,
[final] ).
cnf(c_0_1875,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X3,c_HOL_Ozero__class_Ozero(X1),X1,X1)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1)
| ~ class_OrderedGroup_Omonoid__add(X1) ),
c_0_1421,
[final] ).
cnf(c_0_1876,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_1422,
[final] ).
cnf(c_0_1877,plain,
( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X2,X4,X3,X1),tc_Lambda_OdB,tc_Lambda_OdB) = X2
| hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
c_0_1423,
[final] ).
cnf(c_0_1878,plain,
( c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),X1,X1) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X2,X1,X1)
| ~ class_OrderedGroup_Omonoid__add(X1) ),
c_0_1424,
[final] ).
cnf(c_0_1879,plain,
( c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X3,X2,X1,X1)
| ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
c_0_1425,
[final] ).
cnf(c_0_1880,plain,
( hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) = X3
| hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
c_0_1426,
[final] ).
cnf(c_0_1881,plain,
( X1 = c_Lambda_OdB_OAbs(X2)
| c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X2) ),
c_0_1427,
[final] ).
cnf(c_0_1882,plain,
( c_Lambda_OdB_OVar(X1) = X2
| c_Lambda_OdB_OVar(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
c_0_1428,
[final] ).
cnf(c_0_1883,plain,
( c_Lambda_OdB_OAbs(X1) = X2
| c_Lambda_OdB_OAbs(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
c_0_1429,
[final] ).
cnf(c_0_1884,plain,
( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
c_0_1430,
[final] ).
cnf(c_0_1885,plain,
( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X3) ),
c_0_1431,
[final] ).
cnf(c_0_1886,plain,
( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| c_Lambda_OdB_OVar(X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
c_0_1432,
[final] ).
cnf(c_0_1887,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X1,X2,X2),X2),X3),X4)) ),
c_0_1433,
[final] ).
cnf(c_0_1888,plain,
( c_ListOrder_Ostep1(X1,X2,X5,X4)
| hBOOL(hAPP(hAPP(X1,X3),X6))
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
c_0_1434,
[final] ).
cnf(c_0_1889,plain,
( c_ListOrder_Ostep1(X1,X2,X5,X4)
| X2 = X5
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
c_0_1435,
[final] ).
cnf(c_0_1890,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_Nat_Onat_Onat__case(X2,X3,c_HOL_Ozero__class_Ozero(tc_nat),t_a))) ),
c_0_1436,
[final] ).
cnf(c_0_1891,plain,
( X3 = X6
| hBOOL(hAPP(hAPP(X1,X3),X6))
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
c_0_1437,
[final] ).
cnf(c_0_1892,plain,
( X3 = X6
| X2 = X5
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
c_0_1438,
[final] ).
cnf(c_0_1893,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
c_0_1439,
[final] ).
cnf(c_0_1894,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X1),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
c_0_1440,
[final] ).
cnf(c_0_1895,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X1,X2,X2),X2),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4)) ),
c_0_1441,
[final] ).
cnf(c_0_1896,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),X4),X2)))
| ~ c_Type_Otyping(c_Type_Oshift(X1,X2,v_T____,tc_Type_Otype),v_a____,X3)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
| ~ c_Type_Otyping(X1,X4,v_T____) ),
c_0_1442,
[final] ).
cnf(c_0_1897,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X1),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
c_0_1443,
[final] ).
cnf(c_0_1898,plain,
( c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X2),X1,c_HOL_Ozero__class_Ozero(X2),X2,X2) = c_List_Olistsum(X1,X2)
| ~ class_OrderedGroup_Omonoid__add(X2) ),
c_0_1444,
[final] ).
cnf(c_0_1899,plain,
( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X2),c_HOL_Ozero__class_Ozero(X2),X1,X2,X2) = c_List_Olistsum(X1,X2)
| ~ class_OrderedGroup_Omonoid__add(X2) ),
c_0_1445,
[final] ).
cnf(c_0_1900,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
c_0_1446,
[final] ).
cnf(c_0_1901,plain,
( c_Type_Otyping(X1,hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4),X5)
| ~ c_Type_Otyping(c_Type_Oshift(X1,X4,X6,tc_Type_Otype),X2,X5)
| ~ c_Type_Otyping(X1,X3,X6) ),
c_0_1447,
[final] ).
cnf(c_0_1902,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X3),X4)) ),
c_0_1448,
[final] ).
cnf(c_0_1903,plain,
( hBOOL(hAPP(hAPP(X1,X2),X5))
| c_ListOrder_Ostep1(X1,X3,X6,X4)
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
c_0_1449,
[final] ).
cnf(c_0_1904,plain,
( X6 = X3
| c_ListOrder_Ostep1(X1,X3,X6,X4)
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
c_0_1450,
[final] ).
cnf(c_0_1905,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),X3,tc_nat))) ),
c_0_1451,
[final] ).
cnf(c_0_1906,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),X3,tc_nat))) ),
c_0_1452,
[final] ).
cnf(c_0_1907,plain,
( hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5)) ),
c_0_1453,
[final] ).
cnf(c_0_1908,plain,
( hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5)) ),
c_0_1454,
[final] ).
cnf(c_0_1909,plain,
( c_ListOrder_Ostep1(X1,c_List_Oappend(X2,X3,X4),c_List_Oappend(X5,X3,X4),X4)
| ~ c_ListOrder_Ostep1(X1,X2,X5,X4) ),
c_0_1455,
[final] ).
cnf(c_0_1910,plain,
( c_ListOrder_Ostep1(X1,c_List_Oappend(X5,X2,X4),c_List_Oappend(X5,X3,X4),X4)
| ~ c_ListOrder_Ostep1(X1,X2,X3,X4) ),
c_0_1456,
[final] ).
cnf(c_0_1911,plain,
( c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X5,X2,X4),c_List_Olist_OCons(X5,X3,X4),X4)
| ~ c_ListOrder_Ostep1(X1,X2,X3,X4) ),
c_0_1457,
[final] ).
cnf(c_0_1912,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
c_0_1458,
[final] ).
cnf(c_0_1913,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
c_0_1459,
[final] ).
cnf(c_0_1914,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,X1),X3)),hAPP(hAPP(c_Lambda_Olift,X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
c_0_1460,
[final] ).
cnf(c_0_1915,plain,
( hBOOL(hAPP(hAPP(X1,X2),X5))
| X5 = X2
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
c_0_1461,
[final] ).
cnf(c_0_1916,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X4),X5)) ),
c_0_1462,
[final] ).
cnf(c_0_1917,plain,
( X6 = X3
| X5 = X2
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
c_0_1463,
[final] ).
cnf(c_0_1918,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_1464,
[final] ).
cnf(c_0_1919,plain,
( c_Type_Otyping(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X2),X4),X3)
| ~ c_Type_Otyping(X1,X2,X3) ),
c_0_1465,
[final] ).
cnf(c_0_1920,plain,
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
c_0_1466,
[final] ).
cnf(c_0_1921,plain,
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
c_0_1467,
[final] ).
cnf(c_0_1922,plain,
( c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
c_0_1468,
[final] ).
cnf(c_0_1923,plain,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
c_0_1469,
[final] ).
cnf(c_0_1924,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,X1),X3)),hAPP(hAPP(c_Lambda_Olift,X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
c_0_1470,
[final] ).
cnf(c_0_1925,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
c_0_1471,
[final] ).
cnf(c_0_1926,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
c_0_1472,
[final] ).
cnf(c_0_1927,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X2),X5))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X3),X5)) ),
c_0_1473,
[final] ).
cnf(c_0_1928,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(X1,X4),X5)) ),
c_0_1474,
[final] ).
cnf(c_0_1929,plain,
( hAPP(c_Type_Oshift(X3,X2,X4,X5),X1) = hAPP(X3,X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1475,
[final] ).
cnf(c_0_1930,plain,
( c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X3,X4),X4)
| ~ hBOOL(hAPP(hAPP(X1,X2),X5)) ),
c_0_1476,
[final] ).
cnf(c_0_1931,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
c_0_1477,
[final] ).
cnf(c_0_1932,plain,
( X1 = X2
| c_List_Oappend(X1,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4) != c_List_Oappend(X2,c_List_Olist_OCons(X5,c_List_Olist_ONil(X4),X4),X4) ),
c_0_1478,
[final] ).
cnf(c_0_1933,plain,
( X1 = X2
| c_List_Oappend(X3,c_List_Olist_OCons(X1,c_List_Olist_ONil(X4),X4),X4) != c_List_Oappend(X5,c_List_Olist_OCons(X2,c_List_Olist_ONil(X4),X4),X4) ),
c_0_1479,
[final] ).
cnf(c_0_1934,plain,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
c_0_1480,
[final] ).
cnf(c_0_1935,plain,
( c_Orderings_Oord__class_Omax(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Orderings_Oord__class_Omax(X2,X3,X1)),X4)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
c_0_1481,
[final] ).
cnf(c_0_1936,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_1482,
[final] ).
cnf(c_0_1937,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) ),
c_0_1483,
[final] ).
cnf(c_0_1938,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
c_0_1484,
[final] ).
cnf(c_0_1939,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_1485,
[final] ).
cnf(c_0_1940,plain,
( hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)))
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
c_0_1486,
[final] ).
cnf(c_0_1941,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat) ),
c_0_1487,
[final] ).
cnf(c_0_1942,plain,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X1,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)),X3)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_1488,
[final] ).
cnf(c_0_1943,plain,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X1,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)),X3)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_1489,
[final] ).
cnf(c_0_1944,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),X2,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ),
c_0_1490,
[final] ).
cnf(c_0_1945,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_1491,
[final] ).
cnf(c_0_1946,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_1492,
[final] ).
cnf(c_0_1947,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_1493,
[final] ).
cnf(c_0_1948,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_1494,
[final] ).
cnf(c_0_1949,plain,
( c_lessequals(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),X2,tc_nat) ),
c_0_1495,
[final] ).
cnf(c_0_1950,plain,
( X2 = X3
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| c_Power_Opower__class_Opower(X2,X4,X1) != c_Power_Opower__class_Opower(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_1496,
[final] ).
cnf(c_0_1951,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),c_Lambda_OdB_OVar(X2)),X3)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
c_0_1497,
[final] ).
cnf(c_0_1952,plain,
( c_lessequals(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),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_1498,
[final] ).
cnf(c_0_1953,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X1)),c_Lambda_OdB_OAbs(X2)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
c_0_1499,
[final] ).
cnf(c_0_1954,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_1500,
[final] ).
cnf(c_0_1955,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_1501,
[final] ).
cnf(c_0_1956,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_1502,
[final] ).
cnf(c_0_1957,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_1503,
[final] ).
cnf(c_0_1958,plain,
( c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(X1,X4,X3),c_HOL_Ominus__class_Ominus(X2,X4,X3),X3) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_1504,
[final] ).
cnf(c_0_1959,plain,
( c_Wellfounded_Oaccp(X1,X4,X3)
| ~ c_Wellfounded_Oaccp(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X3),X4),X2)) ),
c_0_1505,
[final] ).
cnf(c_0_1960,plain,
( c_Wellfounded_Oaccp(X1,X3,X2)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| ~ c_Wellfounded_Oaccp(X1,X4,X2) ),
c_0_1506,
[final] ).
cnf(c_0_1961,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
c_0_1507,
[final] ).
cnf(c_0_1962,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(X3,X1,tc_nat) ),
c_0_1508,
[final] ).
cnf(c_0_1963,plain,
( c_lessequals(X3,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_1509,
[final] ).
cnf(c_0_1964,plain,
( c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),tc_nat) ),
c_0_1510,
[final] ).
cnf(c_0_1965,plain,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),tc_nat) ),
c_0_1511,
[final] ).
cnf(c_0_1966,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_1512,
[final] ).
cnf(c_0_1967,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_1513,
[final] ).
cnf(c_0_1968,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_1514,
[final] ).
cnf(c_0_1969,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_1515,
[final] ).
cnf(c_0_1970,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_1516,
[final] ).
cnf(c_0_1971,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X4),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X3,X4,tc_nat) ),
c_0_1517,
[final] ).
cnf(c_0_1972,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
c_0_1518,
[final] ).
cnf(c_0_1973,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Omap(X4,X1,X2,X3) != c_List_Olist_ONil(X3) ),
c_0_1519,
[final] ).
cnf(c_0_1974,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Omap(X3,X1,X2,X4) != c_List_Olist_ONil(X4) ),
c_0_1520,
[final] ).
cnf(c_0_1975,plain,
( c_Type_Otyping(X3,X2,X4)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| ~ c_Type_Otyping(X3,X1,X4) ),
c_0_1521,
[final] ).
cnf(c_0_1976,plain,
( c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) ),
c_0_1522,
[final] ).
cnf(c_0_1977,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) ),
c_0_1523,
[final] ).
cnf(c_0_1978,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_1524,
[final] ).
cnf(c_0_1979,plain,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),X2,tc_nat) = c_HOL_Ominus__class_Ominus(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_1525,
[final] ).
cnf(c_0_1980,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat)
| ~ c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat) ),
c_0_1526,
[final] ).
cnf(c_0_1981,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat) ),
c_0_1527,
[final] ).
cnf(c_0_1982,plain,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),X1,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat))
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_1528,
[final] ).
cnf(c_0_1983,plain,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),X1,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat))
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_1529,
[final] ).
cnf(c_0_1984,plain,
( c_lessequals(X1,X2,X4)
| c_lessequals(X1,X3,X4)
| ~ c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
| ~ class_Orderings_Olinorder(X4) ),
c_0_1530,
[final] ).
cnf(c_0_1985,plain,
( c_HOL_Oord__class_Oless(X1,X2,X4)
| c_HOL_Oord__class_Oless(X1,X3,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
| ~ class_Orderings_Olinorder(X4) ),
c_0_1531,
[final] ).
cnf(c_0_1986,plain,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X2,tc_nat) = X1
| ~ c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) ),
c_0_1532,
[final] ).
cnf(c_0_1987,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_1533,
[final] ).
cnf(c_0_1988,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_1534,
[final] ).
cnf(c_0_1989,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_1535,
[final] ).
cnf(c_0_1990,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_1536,
[final] ).
cnf(c_0_1991,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_1537,
[final] ).
cnf(c_0_1992,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_1538,
[final] ).
cnf(c_0_1993,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_1539,
[final] ).
cnf(c_0_1994,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_1540,
[final] ).
cnf(c_0_1995,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_1541,
[final] ).
cnf(c_0_1996,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_1542,
[final] ).
cnf(c_0_1997,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_1543,
[final] ).
cnf(c_0_1998,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_1544,
[final] ).
cnf(c_0_1999,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_1545,
[final] ).
cnf(c_0_2000,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_1546,
[final] ).
cnf(c_0_2001,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_1547,
[final] ).
cnf(c_0_2002,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_1548,
[final] ).
cnf(c_0_2003,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_1549,
[final] ).
cnf(c_0_2004,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_1550,
[final] ).
cnf(c_0_2005,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_1551,
[final] ).
cnf(c_0_2006,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_1552,
[final] ).
cnf(c_0_2007,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_1553,
[final] ).
cnf(c_0_2008,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_1554,
[final] ).
cnf(c_0_2009,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_1555,
[final] ).
cnf(c_0_2010,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) ),
c_0_1556,
[final] ).
cnf(c_0_2011,plain,
( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1557,
[final] ).
cnf(c_0_2012,plain,
( c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1558,
[final] ).
cnf(c_0_2013,plain,
( c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1559,
[final] ).
cnf(c_0_2014,plain,
( c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1560,
[final] ).
cnf(c_0_2015,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)),X2) = X1
| ~ c_lessequals(X2,X1,tc_nat) ),
c_0_1561,
[final] ).
cnf(c_0_2016,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)),X1) = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_1562,
[final] ).
cnf(c_0_2017,plain,
( X1 = X2
| ~ c_lessequals(X3,X1,tc_nat)
| ~ c_lessequals(X3,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(X1,X3,tc_nat) != c_HOL_Ominus__class_Ominus(X2,X3,tc_nat) ),
c_0_1563,
[final] ).
cnf(c_0_2018,plain,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X3),X4)),X5) = hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5))
| ~ c_OrderedGroup_Osemigroup__add(X1,X2) ),
c_0_1564,
[final] ).
cnf(c_0_2019,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
c_0_1565,
[final] ).
cnf(c_0_2020,plain,
( c_List_Olistsp(X1,c_List_Oappend(X2,X4,X3),X3)
| ~ c_List_Olistsp(X1,X2,X3)
| ~ c_List_Olistsp(X1,X4,X3) ),
c_0_1566,
[final] ).
cnf(c_0_2021,plain,
( c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3) = c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1567,
[final] ).
cnf(c_0_2022,plain,
( c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4) = c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omax(X1,X3,X4),X4)
| ~ class_Orderings_Olinorder(X4) ),
c_0_1568,
[final] ).
cnf(c_0_2023,plain,
( c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_1569,
[final] ).
cnf(c_0_2024,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_1570,
[final] ).
cnf(c_0_2025,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_1571,
[final] ).
cnf(c_0_2026,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_1572,
[final] ).
cnf(c_0_2027,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_1573,
[final] ).
cnf(c_0_2028,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_1574,
[final] ).
cnf(c_0_2029,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_1575,
[final] ).
cnf(c_0_2030,plain,
( c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X5,X4,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_1576,
[final] ).
cnf(c_0_2031,plain,
( c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X5,X4,X3) != c_HOL_Ominus__class_Ominus(X2,X1,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_1577,
[final] ).
cnf(c_0_2032,plain,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_1578,
[final] ).
cnf(c_0_2033,plain,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_1579,
[final] ).
cnf(c_0_2034,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_1580,
[final] ).
cnf(c_0_2035,plain,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_1581,
[final] ).
cnf(c_0_2036,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1582,
[final] ).
cnf(c_0_2037,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1583,
[final] ).
cnf(c_0_2038,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1584,
[final] ).
cnf(c_0_2039,plain,
( c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1585,
[final] ).
cnf(c_0_2040,plain,
( c_lessequals(X2,X4,X3)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1586,
[final] ).
cnf(c_0_2041,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1587,
[final] ).
cnf(c_0_2042,plain,
( c_lessequals(X2,X4,X3)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1588,
[final] ).
cnf(c_0_2043,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1589,
[final] ).
cnf(c_0_2044,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_1590,
[final] ).
cnf(c_0_2045,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_1591,
[final] ).
cnf(c_0_2046,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_1592,
[final] ).
cnf(c_0_2047,plain,
( c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) ),
c_0_1593,
[final] ).
cnf(c_0_2048,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
c_0_1594,
[final] ).
cnf(c_0_2049,plain,
( c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(X2,X3),c_Nat_Osemiring__1__class_Oof__nat(X1,X3),X3) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ class_Ring__and__Field_Oring__1(X3) ),
c_0_1595,
[final] ).
cnf(c_0_2050,plain,
( c_List_Olistsp(X1,X2,X4)
| ~ c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4) ),
c_0_1596,
[final] ).
cnf(c_0_2051,plain,
( c_List_Olistsp(X1,X3,X4)
| ~ c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4) ),
c_0_1597,
[final] ).
cnf(c_0_2052,plain,
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ),
c_0_1598,
[final] ).
cnf(c_0_2053,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_1599,
[final] ).
cnf(c_0_2054,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_1600,
[final] ).
cnf(c_0_2055,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_1601,
[final] ).
cnf(c_0_2056,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
c_0_1602,
[final] ).
cnf(c_0_2057,plain,
( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat) ),
c_0_1603,
[final] ).
cnf(c_0_2058,plain,
( c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat) ),
c_0_1604,
[final] ).
cnf(c_0_2059,plain,
( c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat) ),
c_0_1605,
[final] ).
cnf(c_0_2060,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),X3) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
c_0_1606,
[final] ).
cnf(c_0_2061,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_1607,
[final] ).
cnf(c_0_2062,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_1608,
[final] ).
cnf(c_0_2063,plain,
( c_Wellfounded_Oaccp(X1,X4,X3)
| ~ c_Wellfounded_Oaccp(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X2)) ),
c_0_1609,
[final] ).
cnf(c_0_2064,plain,
( c_Wellfounded_Oaccp(X1,X4,X3)
| ~ c_Wellfounded_Oaccp(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X2)) ),
c_0_1610,
[final] ).
cnf(c_0_2065,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_1611,
[final] ).
cnf(c_0_2066,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_1612,
[final] ).
cnf(c_0_2067,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_1613,
[final] ).
cnf(c_0_2068,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_1614,
[final] ).
cnf(c_0_2069,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_1615,
[final] ).
cnf(c_0_2070,plain,
( hBOOL(hAPP(c_InductTermi_OIT,X1))
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB) ),
c_0_1616,
[final] ).
cnf(c_0_2071,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_1617,
[final] ).
cnf(c_0_2072,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_1618,
[final] ).
cnf(c_0_2073,plain,
( c_Type_Otyping(X1,X4,X3)
| ~ c_Type_Otyping(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X2),X4)) ),
c_0_1619,
[final] ).
cnf(c_0_2074,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_List_Olistsum(X1,X3)),c_List_Olistsum(X2,X3)) = c_List_Olistsum(c_List_Oappend(X1,X2,X3),X3)
| ~ class_OrderedGroup_Omonoid__add(X3) ),
c_0_1620,
[final] ).
cnf(c_0_2075,plain,
( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1621,
[final] ).
cnf(c_0_2076,plain,
( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1622,
[final] ).
cnf(c_0_2077,plain,
( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1623,
[final] ).
cnf(c_0_2078,plain,
( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1624,
[final] ).
cnf(c_0_2079,plain,
( c_lessequals(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1625,
[final] ).
cnf(c_0_2080,plain,
( c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1626,
[final] ).
cnf(c_0_2081,plain,
( c_lessequals(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1627,
[final] ).
cnf(c_0_2082,plain,
( c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1628,
[final] ).
cnf(c_0_2083,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1629,
[final] ).
cnf(c_0_2084,plain,
( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = X1
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_1630,
[final] ).
cnf(c_0_2085,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_1631,
[final] ).
cnf(c_0_2086,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1632,
[final] ).
cnf(c_0_2087,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X1),c_Lambda_OdB_OVar(X2))))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
c_0_1633,
[final] ).
cnf(c_0_2088,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
c_0_1634,
[final] ).
cnf(c_0_2089,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
c_0_1635,
[final] ).
cnf(c_0_2090,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)) = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_1636,
[final] ).
cnf(c_0_2091,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_1637,
[final] ).
cnf(c_0_2092,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_1638,
[final] ).
cnf(c_0_2093,plain,
( c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1639,
[final] ).
cnf(c_0_2094,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_1640,
[final] ).
cnf(c_0_2095,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_1641,
[final] ).
cnf(c_0_2096,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_1642,
[final] ).
cnf(c_0_2097,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_1643,
[final] ).
cnf(c_0_2098,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_1644,
[final] ).
cnf(c_0_2099,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X1)),c_Lambda_OdB_OAbs(X2)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
c_0_1645,
[final] ).
cnf(c_0_2100,plain,
( c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
c_0_1646,
[final] ).
cnf(c_0_2101,plain,
( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
c_0_1647,
[final] ).
cnf(c_0_2102,plain,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1648,
[final] ).
cnf(c_0_2103,plain,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1649,
[final] ).
cnf(c_0_2104,plain,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1650,
[final] ).
cnf(c_0_2105,plain,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1651,
[final] ).
cnf(c_0_2106,plain,
( c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_1652,
[final] ).
cnf(c_0_2107,plain,
( c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_1653,
[final] ).
cnf(c_0_2108,plain,
( c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_1654,
[final] ).
cnf(c_0_2109,plain,
( c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_1655,
[final] ).
cnf(c_0_2110,plain,
( c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X1,X2,X3),X3) = c_Orderings_Oord__class_Omax(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1656,
[final] ).
cnf(c_0_2111,plain,
( c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) ),
c_0_1657,
[final] ).
cnf(c_0_2112,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X1),X2)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
c_0_1658,
[final] ).
cnf(c_0_2113,plain,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X2,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X1),tc_nat) ),
c_0_1659,
[final] ).
cnf(c_0_2114,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Lambda_Oliftn(X3,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3)) ),
c_0_1660,
[final] ).
cnf(c_0_2115,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),c_List_Olistsum(X2,X3)) = c_List_Olistsum(c_List_Olist_OCons(X1,X2,X3),X3)
| ~ class_OrderedGroup_Omonoid__add(X3) ),
c_0_1661,
[final] ).
cnf(c_0_2116,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)) = X1 ),
c_0_1662,
[final] ).
cnf(c_0_2117,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_1663,
[final] ).
cnf(c_0_2118,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(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_1664,
[final] ).
cnf(c_0_2119,plain,
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X3),X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1665,
[final] ).
cnf(c_0_2120,plain,
( c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
c_0_1666,
[final] ).
cnf(c_0_2121,plain,
( c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
c_0_1667,
[final] ).
cnf(c_0_2122,plain,
( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
c_0_1668,
[final] ).
cnf(c_0_2123,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| hBOOL(hAPP(hAPP(X3,X2),X1)) ),
c_0_1669,
[final] ).
cnf(c_0_2124,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
c_0_1670,
[final] ).
cnf(c_0_2125,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1671,
[final] ).
cnf(c_0_2126,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1672,
[final] ).
cnf(c_0_2127,plain,
( X2 = X1
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1673,
[final] ).
cnf(c_0_2128,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
c_0_1674,
[final] ).
cnf(c_0_2129,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
| ~ class_OrderedGroup_Oab__group__add(X4) ),
c_0_1675,
[final] ).
cnf(c_0_2130,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_1676,
[final] ).
cnf(c_0_2131,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ c_lessequals(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_1677,
[final] ).
cnf(c_0_2132,plain,
( ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1678,
[final] ).
cnf(c_0_2133,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1679,
[final] ).
cnf(c_0_2134,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_1680,
[final] ).
cnf(c_0_2135,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1681,
[final] ).
cnf(c_0_2136,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1682,
[final] ).
cnf(c_0_2137,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_1683,
[final] ).
cnf(c_0_2138,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_1684,
[final] ).
cnf(c_0_2139,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = X3
| c_List_Oreplicate(X1,X2,X4) != c_List_Oreplicate(X5,X3,X4) ),
c_0_1685,
[final] ).
cnf(c_0_2140,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_1686,
[final] ).
cnf(c_0_2141,plain,
( X1 = X2
| c_List_Oreplicate(X1,X3,X4) != c_List_Oreplicate(X2,X5,X4) ),
c_0_1687,
[final] ).
cnf(c_0_2142,plain,
( X1 = X2
| c_List_Oappend(X1,X3,X4) != c_List_Oappend(X2,X3,X4) ),
c_0_1688,
[final] ).
cnf(c_0_2143,plain,
( X1 = X2
| c_List_Oappend(X3,X1,X4) != c_List_Oappend(X3,X2,X4) ),
c_0_1689,
[final] ).
cnf(c_0_2144,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_1690,
[final] ).
cnf(c_0_2145,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_1691,
[final] ).
cnf(c_0_2146,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_1692,
[final] ).
cnf(c_0_2147,plain,
( X1 = X2
| c_List_Olist_OCons(X1,X3,X4) != c_List_Olist_OCons(X2,X5,X4) ),
c_0_1693,
[final] ).
cnf(c_0_2148,plain,
( X1 = X2
| c_List_Olist_OCons(X3,X1,X4) != c_List_Olist_OCons(X5,X2,X4) ),
c_0_1694,
[final] ).
cnf(c_0_2149,plain,
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X1),X2,X1) = c_Lambda_Oliftn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
c_0_1695,
[final] ).
cnf(c_0_2150,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X2)),X3),X1) = c_Lambda_OdB_OVar(X2) ),
c_0_1696,
[final] ).
cnf(c_0_2151,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X2,X1,tc_nat) ),
c_0_1697,
[final] ).
cnf(c_0_2152,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3)) ),
c_0_1698,
[final] ).
cnf(c_0_2153,plain,
( c_lessequals(X1,c_Orderings_Oord__class_Omax(X1,X2,X3),X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1699,
[final] ).
cnf(c_0_2154,plain,
( c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X1,X3),X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1700,
[final] ).
cnf(c_0_2155,plain,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X3,X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
c_0_1701,
[final] ).
cnf(c_0_2156,plain,
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1) = X2
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
c_0_1702,
[final] ).
cnf(c_0_2157,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X1))) ),
c_0_1703,
[final] ).
cnf(c_0_2158,plain,
( X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1704,
[final] ).
cnf(c_0_2159,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1705,
[final] ).
cnf(c_0_2160,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1706,
[final] ).
cnf(c_0_2161,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1707,
[final] ).
cnf(c_0_2162,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1708,
[final] ).
cnf(c_0_2163,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1709,
[final] ).
cnf(c_0_2164,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1710,
[final] ).
cnf(c_0_2165,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1711,
[final] ).
cnf(c_0_2166,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X1),tc_nat)
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
c_0_1712,
[final] ).
cnf(c_0_2167,plain,
( c_lessequals(X1,X2,X3)
| c_Orderings_Oord__class_Omax(X1,X2,X3) != X2
| ~ class_Orderings_Olinorder(X3) ),
c_0_1713,
[final] ).
cnf(c_0_2168,plain,
( c_Orderings_Oord__class_Omax(X2,X1,X3) = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1714,
[final] ).
cnf(c_0_2169,plain,
( c_Orderings_Oord__class_Omax(X1,X2,X3) = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1715,
[final] ).
cnf(c_0_2170,plain,
( c_Lambda_Oliftn(X3,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1716,
[final] ).
cnf(c_0_2171,plain,
( c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1717,
[final] ).
cnf(c_0_2172,plain,
( c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_1718,
[final] ).
cnf(c_0_2173,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_1719,
[final] ).
cnf(c_0_2174,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_1720,
[final] ).
cnf(c_0_2175,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_1721,
[final] ).
cnf(c_0_2176,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_1722,
[final] ).
cnf(c_0_2177,plain,
( c_lessequals(X1,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_1723,
[final] ).
cnf(c_0_2178,plain,
( c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_1724,
[final] ).
cnf(c_0_2179,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_1725,
[final] ).
cnf(c_0_2180,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_1726,
[final] ).
cnf(c_0_2181,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_1727,
[final] ).
cnf(c_0_2182,plain,
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1728,
[final] ).
cnf(c_0_2183,plain,
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1729,
[final] ).
cnf(c_0_2184,plain,
( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X1)),X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1730,
[final] ).
cnf(c_0_2185,plain,
( hBOOL(hAPP(X1,v_sko__Nat__Xnat__Xinducts__1(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
c_0_1731,
[final] ).
cnf(c_0_2186,plain,
( hBOOL(hAPP(X1,v_sko__Nat__Xnat__Xinduct__1(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
c_0_1732,
[final] ).
cnf(c_0_2187,plain,
( hBOOL(hAPP(X1,v_sko__List__Xupt__Xinduct__1(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
c_0_1733,
[final] ).
cnf(c_0_2188,plain,
( hAPP(hAPP(X2,X4),X1) = X4
| ~ c_OrderedGroup_Omonoid__add(X1,X2,X3) ),
c_0_1734,
[final] ).
cnf(c_0_2189,plain,
( hAPP(hAPP(X2,X1),X4) = X4
| ~ c_OrderedGroup_Omonoid__add(X1,X2,X3) ),
c_0_1735,
[final] ).
cnf(c_0_2190,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != 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_1736,
[final] ).
cnf(c_0_2191,plain,
( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) != 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_1737,
[final] ).
cnf(c_0_2192,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| c_Lambda_Osubstn(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
c_0_1738,
[final] ).
cnf(c_0_2193,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_1739,
[final] ).
cnf(c_0_2194,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_1740,
[final] ).
cnf(c_0_2195,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_1741,
[final] ).
cnf(c_0_2196,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_1742,
[final] ).
cnf(c_0_2197,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_1743,
[final] ).
cnf(c_0_2198,plain,
( X1 = X2
| hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4) ),
c_0_1744,
[final] ).
cnf(c_0_2199,plain,
( X1 = X2
| hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X4),X2) ),
c_0_1745,
[final] ).
cnf(c_0_2200,plain,
( c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1746,
[final] ).
cnf(c_0_2201,plain,
( c_lessequals(X1,X1,X2)
| c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_1747,
[final] ).
cnf(c_0_2202,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1748,
[final] ).
cnf(c_0_2203,plain,
( c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1749,
[final] ).
cnf(c_0_2204,plain,
( c_lessequals(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1750,
[final] ).
cnf(c_0_2205,plain,
( c_Orderings_Oord__class_Omax(X1,X2,X3) = c_Orderings_Oord__class_Omax(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1751,
[final] ).
cnf(c_0_2206,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_1752,
[final] ).
cnf(c_0_2207,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_1753,
[final] ).
cnf(c_0_2208,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_1754,
[final] ).
cnf(c_0_2209,plain,
( hAPP(X1,X2) = X3
| ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3) ),
c_0_1755,
[final] ).
cnf(c_0_2210,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
c_0_1756,
[final] ).
cnf(c_0_2211,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
c_0_1757,
[final] ).
cnf(c_0_2212,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
c_0_1758,
[final] ).
cnf(c_0_2213,plain,
( c_lessequals(X1,X2,tc_nat)
| c_lessequals(X2,X1,tc_nat) ),
c_0_1759,
[final] ).
cnf(c_0_2214,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X2) ),
c_0_1760,
[final] ).
cnf(c_0_2215,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_1761,
[final] ).
cnf(c_0_2216,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
c_0_1762,
[final] ).
cnf(c_0_2217,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
c_0_1763,
[final] ).
cnf(c_0_2218,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_1764,
[final] ).
cnf(c_0_2219,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X1,X3,X2) != c_List_Olist_ONil(X2) ),
c_0_1765,
[final] ).
cnf(c_0_2220,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X3,X1,X2) != c_List_Olist_ONil(X2) ),
c_0_1766,
[final] ).
cnf(c_0_2221,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X1,X3,X2) != c_List_Olist_ONil(X2) ),
c_0_1767,
[final] ).
cnf(c_0_2222,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X3,X1,X2) != c_List_Olist_ONil(X2) ),
c_0_1768,
[final] ).
cnf(c_0_2223,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = 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_1769,
[final] ).
cnf(c_0_2224,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_List_Oreplicate(X1,X2,X3) != c_List_Olist_ONil(X3) ),
c_0_1770,
[final] ).
cnf(c_0_2225,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_List_Oreplicate(X1,X3,X2) != c_List_Olist_ONil(X2) ),
c_0_1771,
[final] ).
cnf(c_0_2226,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_1772,
[final] ).
cnf(c_0_2227,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_1773,
[final] ).
cnf(c_0_2228,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
c_0_1774,
[final] ).
cnf(c_0_2229,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_1775,
[final] ).
cnf(c_0_2230,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
c_0_1776,
[final] ).
cnf(c_0_2231,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X3,X1,X2) != X3 ),
c_0_1777,
[final] ).
cnf(c_0_2232,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X3,X1,X2) != X3 ),
c_0_1778,
[final] ).
cnf(c_0_2233,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X1,X3,X2) != X3 ),
c_0_1779,
[final] ).
cnf(c_0_2234,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X1,X3,X2) != X3 ),
c_0_1780,
[final] ).
cnf(c_0_2235,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
c_0_1781,
[final] ).
cnf(c_0_2236,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Osemiring__0(X2) ),
c_0_1782,
[final] ).
cnf(c_0_2237,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
c_0_1783,
[final] ).
cnf(c_0_2238,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_1784,
[final] ).
cnf(c_0_2239,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_1785,
[final] ).
cnf(c_0_2240,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_1786,
[final] ).
cnf(c_0_2241,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != X2 ),
c_0_1787,
[final] ).
cnf(c_0_2242,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != X2 ),
c_0_1788,
[final] ).
cnf(c_0_2243,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_1789,
[final] ).
cnf(c_0_2244,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_1790,
[final] ).
cnf(c_0_2245,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_1791,
[final] ).
cnf(c_0_2246,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_1792,
[final] ).
cnf(c_0_2247,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
c_0_1793,
[final] ).
cnf(c_0_2248,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_1794,
[final] ).
cnf(c_0_2249,plain,
( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_1795,
[final] ).
cnf(c_0_2250,plain,
( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
| ~ class_Orderings_Obot(X1) ),
c_0_1796,
[final] ).
cnf(c_0_2251,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_1797,
[final] ).
cnf(c_0_2252,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
c_0_1798,
[final] ).
cnf(c_0_2253,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_1799,
[final] ).
cnf(c_0_2254,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_1800,
[final] ).
cnf(c_0_2255,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_1801,
[final] ).
cnf(c_0_2256,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
c_0_1802,
[final] ).
cnf(c_0_2257,plain,
( c_Orderings_Oord__class_Omax(X1,X1,X2) = X1
| ~ class_Orderings_Olinorder(X2) ),
c_0_1803,
[final] ).
cnf(c_0_2258,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
c_0_1804,
[final] ).
cnf(c_0_2259,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
c_0_1805,
[final] ).
cnf(c_0_2260,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
c_0_1806,
[final] ).
cnf(c_0_2261,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_1807,
[final] ).
cnf(c_0_2262,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
c_0_1808,
[final] ).
cnf(c_0_2263,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
c_0_1809,
[final] ).
cnf(c_0_2264,plain,
( class_Orderings_Obot(tc_fun(X2,X1))
| ~ class_Orderings_Obot(X1) ),
c_0_1810,
[final] ).
cnf(c_0_2265,plain,
( c_List_Olistsum(c_List_Olist_ONil(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Omonoid__add(X1) ),
c_0_1811,
[final] ).
cnf(c_0_2266,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_1812,
[final] ).
cnf(c_0_2267,plain,
( c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(X1),X1)
| ~ class_OrderedGroup_Osemigroup__add(X1) ),
c_0_1813,
[final] ).
cnf(c_0_2268,plain,
( X1 = X2
| c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
c_0_1814,
[final] ).
cnf(c_0_2269,plain,
( X1 = X2
| c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
c_0_1815,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_1816_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),X4),X2)))
| ~ c_Type_Otyping(c_Type_Oshift(X1,X2,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X3)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
| ~ c_Type_Otyping(X1,X4,v_T____) ),
inference(literals_permutation,[status(thm)],[c_0_1816]) ).
cnf(c_0_1816_1,axiom,
( ~ c_Type_Otyping(c_Type_Oshift(X1,X2,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X3)
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),X4),X2)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
| ~ c_Type_Otyping(X1,X4,v_T____) ),
inference(literals_permutation,[status(thm)],[c_0_1816]) ).
cnf(c_0_1816_2,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
| ~ c_Type_Otyping(c_Type_Oshift(X1,X2,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X3)
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),X4),X2)))
| ~ c_Type_Otyping(X1,X4,v_T____) ),
inference(literals_permutation,[status(thm)],[c_0_1816]) ).
cnf(c_0_1816_3,axiom,
( ~ c_Type_Otyping(X1,X4,v_T____)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
| ~ c_Type_Otyping(c_Type_Oshift(X1,X2,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X3)
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),X4),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1816]) ).
cnf(c_0_1817_0,axiom,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X1,X2,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1817]) ).
cnf(c_0_1817_1,axiom,
( ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X1,X2,tc_Lambda_OdB)
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(literals_permutation,[status(thm)],[c_0_1817]) ).
cnf(c_0_1818_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1818]) ).
cnf(c_0_1818_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(literals_permutation,[status(thm)],[c_0_1818]) ).
cnf(c_0_1819_0,axiom,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1819]) ).
cnf(c_0_1819_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(literals_permutation,[status(thm)],[c_0_1819]) ).
cnf(c_0_1820_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1820]) ).
cnf(c_0_1820_1,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1820]) ).
cnf(c_0_1820_2,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X2))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(literals_permutation,[status(thm)],[c_0_1820]) ).
cnf(c_0_1821_0,axiom,
( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X10)) = hAPP(hAPP(X2,X9),hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X10))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1821]) ).
cnf(c_0_1821_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X10)) = hAPP(hAPP(X2,X9),hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X10)) ),
inference(literals_permutation,[status(thm)],[c_0_1821]) ).
cnf(c_0_1822_0,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),hAPP(hAPP(X1,X9),X10)) = hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X9)),hAPP(hAPP(X1,X8),X10))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1822]) ).
cnf(c_0_1822_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),hAPP(hAPP(X1,X9),X10)) = hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X9)),hAPP(hAPP(X1,X8),X10)) ),
inference(literals_permutation,[status(thm)],[c_0_1822]) ).
cnf(c_0_1823_0,axiom,
( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X10)) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),hAPP(hAPP(X2,X9),X10)))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1823]) ).
cnf(c_0_1823_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X10)) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),hAPP(hAPP(X2,X9),X10))) ),
inference(literals_permutation,[status(thm)],[c_0_1823]) ).
cnf(c_0_1824_0,axiom,
( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X10)) = hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X9)),hAPP(hAPP(X2,X8),X10))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1824]) ).
cnf(c_0_1824_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X10)) = hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X9)),hAPP(hAPP(X2,X8),X10)) ),
inference(literals_permutation,[status(thm)],[c_0_1824]) ).
cnf(c_0_1825_0,axiom,
( hAPP(hAPP(X2,hAPP(hAPP(X3,X7),X9)),hAPP(hAPP(X3,X8),X9)) = hAPP(hAPP(X3,hAPP(hAPP(X2,X7),X8)),X9)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1825]) ).
cnf(c_0_1825_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X2,hAPP(hAPP(X3,X7),X9)),hAPP(hAPP(X3,X8),X9)) = hAPP(hAPP(X3,hAPP(hAPP(X2,X7),X8)),X9) ),
inference(literals_permutation,[status(thm)],[c_0_1825]) ).
cnf(c_0_1826_0,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X9)),hAPP(hAPP(X2,X8),X9)) = hAPP(hAPP(X2,hAPP(hAPP(X1,X7),X8)),X9)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1826]) ).
cnf(c_0_1826_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X9)),hAPP(hAPP(X2,X8),X9)) = hAPP(hAPP(X2,hAPP(hAPP(X1,X7),X8)),X9) ),
inference(literals_permutation,[status(thm)],[c_0_1826]) ).
cnf(c_0_1827_0,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X8)) = hAPP(hAPP(X2,hAPP(hAPP(X1,X7),X9)),X8)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1827]) ).
cnf(c_0_1827_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X8)) = hAPP(hAPP(X2,hAPP(hAPP(X1,X7),X9)),X8) ),
inference(literals_permutation,[status(thm)],[c_0_1827]) ).
cnf(c_0_1828_0,axiom,
( hAPP(hAPP(X2,hAPP(hAPP(X3,X7),X8)),hAPP(hAPP(X3,X7),X9)) = hAPP(hAPP(X3,X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1828]) ).
cnf(c_0_1828_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X2,hAPP(hAPP(X3,X7),X8)),hAPP(hAPP(X3,X7),X9)) = hAPP(hAPP(X3,X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X9)) ),
inference(literals_permutation,[status(thm)],[c_0_1828]) ).
cnf(c_0_1829_0,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X7),X9)) = hAPP(hAPP(X2,X7),hAPP(hAPP(X1,X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1829]) ).
cnf(c_0_1829_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X7),X9)) = hAPP(hAPP(X2,X7),hAPP(hAPP(X1,X8),X9)) ),
inference(literals_permutation,[status(thm)],[c_0_1829]) ).
cnf(c_0_1830_0,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X9)),X8)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1830]) ).
cnf(c_0_1830_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X9)),X8) ),
inference(literals_permutation,[status(thm)],[c_0_1830]) ).
cnf(c_0_1831_0,axiom,
( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X9)),X8)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1831]) ).
cnf(c_0_1831_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X9)),X8) ),
inference(literals_permutation,[status(thm)],[c_0_1831]) ).
cnf(c_0_1832_0,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X8)),X8) = hAPP(hAPP(X2,hAPP(hAPP(X1,X7),X5)),X8)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1832]) ).
cnf(c_0_1832_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X8)),X8) = hAPP(hAPP(X2,hAPP(hAPP(X1,X7),X5)),X8) ),
inference(literals_permutation,[status(thm)],[c_0_1832]) ).
cnf(c_0_1833_0,axiom,
( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1833]) ).
cnf(c_0_1833_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9)) ),
inference(literals_permutation,[status(thm)],[c_0_1833]) ).
cnf(c_0_1834_0,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1834]) ).
cnf(c_0_1834_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9)) ),
inference(literals_permutation,[status(thm)],[c_0_1834]) ).
cnf(c_0_1835_0,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1835]) ).
cnf(c_0_1835_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9)) ),
inference(literals_permutation,[status(thm)],[c_0_1835]) ).
cnf(c_0_1836_0,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1836]) ).
cnf(c_0_1836_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9)) ),
inference(literals_permutation,[status(thm)],[c_0_1836]) ).
cnf(c_0_1837_0,axiom,
( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1837]) ).
cnf(c_0_1837_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9)) ),
inference(literals_permutation,[status(thm)],[c_0_1837]) ).
cnf(c_0_1838_0,axiom,
( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1838]) ).
cnf(c_0_1838_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9)) ),
inference(literals_permutation,[status(thm)],[c_0_1838]) ).
cnf(c_0_1839_0,axiom,
( hAPP(hAPP(X1,X7),hAPP(hAPP(X2,X8),X7)) = hAPP(hAPP(X2,hAPP(hAPP(X1,X8),X5)),X7)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1839]) ).
cnf(c_0_1839_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X1,X7),hAPP(hAPP(X2,X8),X7)) = hAPP(hAPP(X2,hAPP(hAPP(X1,X8),X5)),X7) ),
inference(literals_permutation,[status(thm)],[c_0_1839]) ).
cnf(c_0_1840_0,axiom,
( hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9)) = hAPP(hAPP(X1,X8),hAPP(hAPP(X1,X7),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1840]) ).
cnf(c_0_1840_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9)) = hAPP(hAPP(X1,X8),hAPP(hAPP(X1,X7),X9)) ),
inference(literals_permutation,[status(thm)],[c_0_1840]) ).
cnf(c_0_1841_0,axiom,
( hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9)) = hAPP(hAPP(X2,X8),hAPP(hAPP(X2,X7),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1841]) ).
cnf(c_0_1841_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9)) = hAPP(hAPP(X2,X8),hAPP(hAPP(X2,X7),X9)) ),
inference(literals_permutation,[status(thm)],[c_0_1841]) ).
cnf(c_0_1842_0,axiom,
( hAPP(hAPP(X1,X7),X7) = hAPP(hAPP(X2,hAPP(hAPP(X1,X5),X5)),X7)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1842]) ).
cnf(c_0_1842_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X1,X7),X7) = hAPP(hAPP(X2,hAPP(hAPP(X1,X5),X5)),X7) ),
inference(literals_permutation,[status(thm)],[c_0_1842]) ).
cnf(c_0_1843_0,axiom,
( hAPP(hAPP(X2,X7),X8) = hAPP(hAPP(X2,X8),X7)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1843]) ).
cnf(c_0_1843_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X2,X7),X8) = hAPP(hAPP(X2,X8),X7) ),
inference(literals_permutation,[status(thm)],[c_0_1843]) ).
cnf(c_0_1844_0,axiom,
( hAPP(hAPP(X1,X7),X8) = hAPP(hAPP(X1,X8),X7)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1844]) ).
cnf(c_0_1844_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X1,X7),X8) = hAPP(hAPP(X1,X8),X7) ),
inference(literals_permutation,[status(thm)],[c_0_1844]) ).
cnf(c_0_1845_0,axiom,
( hAPP(hAPP(X1,X7),X8) = hAPP(hAPP(X1,X8),X7)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1845]) ).
cnf(c_0_1845_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X1,X7),X8) = hAPP(hAPP(X1,X8),X7) ),
inference(literals_permutation,[status(thm)],[c_0_1845]) ).
cnf(c_0_1846_0,axiom,
( hAPP(hAPP(X2,X7),X8) = hAPP(hAPP(X2,X8),X7)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1846]) ).
cnf(c_0_1846_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X2,X7),X8) = hAPP(hAPP(X2,X8),X7) ),
inference(literals_permutation,[status(thm)],[c_0_1846]) ).
cnf(c_0_1847_0,axiom,
( hAPP(hAPP(X3,X7),c_HOL_Ozero__class_Ozero(tc_nat)) = X5
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1847]) ).
cnf(c_0_1847_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X3,X7),c_HOL_Ozero__class_Ozero(tc_nat)) = X5 ),
inference(literals_permutation,[status(thm)],[c_0_1847]) ).
cnf(c_0_1848_0,axiom,
( hAPP(hAPP(X2,X5),X7) = X7
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1848]) ).
cnf(c_0_1848_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X2,X5),X7) = X7 ),
inference(literals_permutation,[status(thm)],[c_0_1848]) ).
cnf(c_0_1849_0,axiom,
( hAPP(hAPP(X2,X4),X7) = X4
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1849]) ).
cnf(c_0_1849_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X2,X4),X7) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_1849]) ).
cnf(c_0_1850_0,axiom,
( hAPP(hAPP(X1,X4),X7) = X7
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1850]) ).
cnf(c_0_1850_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X1,X4),X7) = X7 ),
inference(literals_permutation,[status(thm)],[c_0_1850]) ).
cnf(c_0_1851_0,axiom,
( hAPP(hAPP(X2,X7),X5) = X7
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1851]) ).
cnf(c_0_1851_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X2,X7),X5) = X7 ),
inference(literals_permutation,[status(thm)],[c_0_1851]) ).
cnf(c_0_1852_0,axiom,
( hAPP(hAPP(X2,X5),X7) = X7
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1852]) ).
cnf(c_0_1852_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X2,X5),X7) = X7 ),
inference(literals_permutation,[status(thm)],[c_0_1852]) ).
cnf(c_0_1853_0,axiom,
( hAPP(hAPP(X2,X7),X4) = X4
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1853]) ).
cnf(c_0_1853_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X2,X7),X4) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_1853]) ).
cnf(c_0_1854_0,axiom,
( hAPP(hAPP(X2,X4),X7) = X4
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1854]) ).
cnf(c_0_1854_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X2,X4),X7) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_1854]) ).
cnf(c_0_1855_0,axiom,
( hAPP(hAPP(X1,X7),X4) = X7
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1855]) ).
cnf(c_0_1855_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X1,X7),X4) = X7 ),
inference(literals_permutation,[status(thm)],[c_0_1855]) ).
cnf(c_0_1856_0,axiom,
( hAPP(hAPP(X1,X4),X7) = X7
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1856]) ).
cnf(c_0_1856_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X1,X4),X7) = X7 ),
inference(literals_permutation,[status(thm)],[c_0_1856]) ).
cnf(c_0_1857_0,axiom,
( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X5,X2,X6,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4),t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_1857]) ).
cnf(c_0_1857_1,axiom,
( ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X5,X2,X6,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4),t_a)))
| hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_1857]) ).
cnf(c_0_1858_0,axiom,
( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X5,X2,X6,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4),t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_1858]) ).
cnf(c_0_1858_1,axiom,
( ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X5,X2,X6,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4),t_a)))
| hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_1858]) ).
cnf(c_0_1859_0,axiom,
( X4 = X5
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1859]) ).
cnf(c_0_1859_1,axiom,
( ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
| X4 = X5
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1859]) ).
cnf(c_0_1859_2,axiom,
( ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X5)
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
| X4 = X5 ),
inference(literals_permutation,[status(thm)],[c_0_1859]) ).
cnf(c_0_1860_0,axiom,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X4,X5,X2,c_Lambda_OdB_OAbs(X3),t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_1860]) ).
cnf(c_0_1860_1,axiom,
( ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X4,X5,X2,c_Lambda_OdB_OAbs(X3),t_a)))
| hBOOL(hAPP(X1,hAPP(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1860]) ).
cnf(c_0_1861_0,axiom,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X4,X5,X2,c_Lambda_OdB_OAbs(X3),t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_1861]) ).
cnf(c_0_1861_1,axiom,
( ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X4,X5,X2,c_Lambda_OdB_OAbs(X3),t_a)))
| hBOOL(hAPP(X1,hAPP(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1861]) ).
cnf(c_0_1862_0,axiom,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X4,X5,c_Lambda_OdB_OVar(X3),t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_1862]) ).
cnf(c_0_1862_1,axiom,
( ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X4,X5,c_Lambda_OdB_OVar(X3),t_a)))
| hBOOL(hAPP(X1,hAPP(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1862]) ).
cnf(c_0_1863_0,axiom,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X4,X5,c_Lambda_OdB_OVar(X3),t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_1863]) ).
cnf(c_0_1863_1,axiom,
( ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X4,X5,c_Lambda_OdB_OVar(X3),t_a)))
| hBOOL(hAPP(X1,hAPP(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1863]) ).
cnf(c_0_1864_0,axiom,
( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X2,tc_Lambda_OdB)
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1864]) ).
cnf(c_0_1864_1,axiom,
( ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X2,tc_Lambda_OdB)
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1864]) ).
cnf(c_0_1864_2,axiom,
( ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X2,tc_Lambda_OdB)
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1864]) ).
cnf(c_0_1865_0,axiom,
( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1865]) ).
cnf(c_0_1865_1,axiom,
( ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB)
| c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1865]) ).
cnf(c_0_1866_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X1,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1866]) ).
cnf(c_0_1866_1,axiom,
( ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X1,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(literals_permutation,[status(thm)],[c_0_1866]) ).
cnf(c_0_1867_0,axiom,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1867]) ).
cnf(c_0_1867_1,axiom,
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1867]) ).
cnf(c_0_1868_0,axiom,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1868]) ).
cnf(c_0_1868_1,axiom,
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1868]) ).
cnf(c_0_1869_0,axiom,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1869]) ).
cnf(c_0_1869_1,axiom,
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1869]) ).
cnf(c_0_1870_0,axiom,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1870]) ).
cnf(c_0_1870_1,axiom,
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1870]) ).
cnf(c_0_1871_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_1871]) ).
cnf(c_0_1871_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_1871]) ).
cnf(c_0_1872_0,axiom,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1872]) ).
cnf(c_0_1872_1,axiom,
( c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1872]) ).
cnf(c_0_1873_0,axiom,
( c_List_Ofoldl(X1,hAPP(hAPP(X1,X3),X4),X5,X2,X2) = hAPP(hAPP(X1,X3),c_List_Ofoldl(X1,X4,X5,X2,X2))
| ~ c_OrderedGroup_Osemigroup__add(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1873]) ).
cnf(c_0_1873_1,axiom,
( ~ c_OrderedGroup_Osemigroup__add(X1,X2)
| c_List_Ofoldl(X1,hAPP(hAPP(X1,X3),X4),X5,X2,X2) = hAPP(hAPP(X1,X3),c_List_Ofoldl(X1,X4,X5,X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1873]) ).
cnf(c_0_1874_0,axiom,
( hAPP(hAPP(X2,X4),c_List_Ofoldl(X2,X1,X5,X3,X3)) = c_List_Ofoldl(X2,X4,X5,X3,X3)
| ~ c_OrderedGroup_Omonoid__add(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1874]) ).
cnf(c_0_1874_1,axiom,
( ~ c_OrderedGroup_Omonoid__add(X1,X2,X3)
| hAPP(hAPP(X2,X4),c_List_Ofoldl(X2,X1,X5,X3,X3)) = c_List_Ofoldl(X2,X4,X5,X3,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1874]) ).
cnf(c_0_1875_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X3,c_HOL_Ozero__class_Ozero(X1),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_1875]) ).
cnf(c_0_1875_1,axiom,
( ~ class_OrderedGroup_Omonoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X3,c_HOL_Ozero__class_Ozero(X1),X1,X1)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1875]) ).
cnf(c_0_1876_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_1876]) ).
cnf(c_0_1876_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_1876]) ).
cnf(c_0_1877_0,axiom,
( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X2,X4,X3,X1),tc_Lambda_OdB,tc_Lambda_OdB) = X2
| hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1877]) ).
cnf(c_0_1877_1,axiom,
( c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X2,X4,X3,X1),tc_Lambda_OdB,tc_Lambda_OdB) = X2
| X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1877]) ).
cnf(c_0_1877_2,axiom,
( hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB)
| c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X2,X4,X3,X1),tc_Lambda_OdB,tc_Lambda_OdB) = X2
| X1 = c_List_Olist_ONil(tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1877]) ).
cnf(c_0_1878_0,axiom,
( c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),X1,X1) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X2,X1,X1)
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1878]) ).
cnf(c_0_1878_1,axiom,
( ~ class_OrderedGroup_Omonoid__add(X1)
| c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),X1,X1) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X2,X1,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1878]) ).
cnf(c_0_1879_0,axiom,
( c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X3,X2,X1,X1)
| ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1879]) ).
cnf(c_0_1879_1,axiom,
( ~ class_OrderedGroup_Oab__semigroup__add(X1)
| c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X3,X2,X1,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1879]) ).
cnf(c_0_1880_0,axiom,
( hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) = X3
| hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1880]) ).
cnf(c_0_1880_1,axiom,
( hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_1880]) ).
cnf(c_0_1881_0,axiom,
( X1 = c_Lambda_OdB_OAbs(X2)
| c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1881]) ).
cnf(c_0_1881_1,axiom,
( c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X2)
| X1 = c_Lambda_OdB_OAbs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1881]) ).
cnf(c_0_1882_0,axiom,
( c_Lambda_OdB_OVar(X1) = X2
| c_Lambda_OdB_OVar(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1882]) ).
cnf(c_0_1882_1,axiom,
( c_Lambda_OdB_OVar(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OVar(X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1882]) ).
cnf(c_0_1883_0,axiom,
( c_Lambda_OdB_OAbs(X1) = X2
| c_Lambda_OdB_OAbs(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1883]) ).
cnf(c_0_1883_1,axiom,
( c_Lambda_OdB_OAbs(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1883]) ).
cnf(c_0_1884_0,axiom,
( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1884]) ).
cnf(c_0_1884_1,axiom,
( c_Lambda_OdB_OAbs(X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB)
| X1 = c_List_Olist_ONil(tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1884]) ).
cnf(c_0_1885_0,axiom,
( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1885]) ).
cnf(c_0_1885_1,axiom,
( c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X3)
| X1 = c_List_Olist_ONil(tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1885]) ).
cnf(c_0_1886_0,axiom,
( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| c_Lambda_OdB_OVar(X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1886]) ).
cnf(c_0_1886_1,axiom,
( c_Lambda_OdB_OVar(X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB)
| X1 = c_List_Olist_ONil(tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1886]) ).
cnf(c_0_1887_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X1,X2,X2),X2),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1887]) ).
cnf(c_0_1887_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X1,X2,X2),X2),X3),X4))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1887]) ).
cnf(c_0_1888_0,axiom,
( c_ListOrder_Ostep1(X1,X2,X5,X4)
| hBOOL(hAPP(hAPP(X1,X3),X6))
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1888]) ).
cnf(c_0_1888_1,axiom,
( hBOOL(hAPP(hAPP(X1,X3),X6))
| c_ListOrder_Ostep1(X1,X2,X5,X4)
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1888]) ).
cnf(c_0_1888_2,axiom,
( ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4)
| hBOOL(hAPP(hAPP(X1,X3),X6))
| c_ListOrder_Ostep1(X1,X2,X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1888]) ).
cnf(c_0_1889_0,axiom,
( c_ListOrder_Ostep1(X1,X2,X5,X4)
| X2 = X5
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1889]) ).
cnf(c_0_1889_1,axiom,
( X2 = X5
| c_ListOrder_Ostep1(X1,X2,X5,X4)
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1889]) ).
cnf(c_0_1889_2,axiom,
( ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4)
| X2 = X5
| c_ListOrder_Ostep1(X1,X2,X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1889]) ).
cnf(c_0_1890_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_Nat_Onat_Onat__case(X2,X3,c_HOL_Ozero__class_Ozero(tc_nat),t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_1890]) ).
cnf(c_0_1890_1,axiom,
( ~ hBOOL(hAPP(X1,c_Nat_Onat_Onat__case(X2,X3,c_HOL_Ozero__class_Ozero(tc_nat),t_a)))
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1890]) ).
cnf(c_0_1891_0,axiom,
( X3 = X6
| hBOOL(hAPP(hAPP(X1,X3),X6))
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1891]) ).
cnf(c_0_1891_1,axiom,
( hBOOL(hAPP(hAPP(X1,X3),X6))
| X3 = X6
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1891]) ).
cnf(c_0_1891_2,axiom,
( ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4)
| hBOOL(hAPP(hAPP(X1,X3),X6))
| X3 = X6 ),
inference(literals_permutation,[status(thm)],[c_0_1891]) ).
cnf(c_0_1892_0,axiom,
( X3 = X6
| X2 = X5
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1892]) ).
cnf(c_0_1892_1,axiom,
( X2 = X5
| X3 = X6
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1892]) ).
cnf(c_0_1892_2,axiom,
( ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4)
| X2 = X5
| X3 = X6 ),
inference(literals_permutation,[status(thm)],[c_0_1892]) ).
cnf(c_0_1893_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1893]) ).
cnf(c_0_1893_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_1893]) ).
cnf(c_0_1894_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X1),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1894]) ).
cnf(c_0_1894_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X1),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_1894]) ).
cnf(c_0_1895_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X1,X2,X2),X2),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1895]) ).
cnf(c_0_1895_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X1,X2,X2),X2),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1895]) ).
cnf(c_0_1896_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),X4),X2)))
| ~ c_Type_Otyping(c_Type_Oshift(X1,X2,v_T____,tc_Type_Otype),v_a____,X3)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
| ~ c_Type_Otyping(X1,X4,v_T____) ),
inference(literals_permutation,[status(thm)],[c_0_1896]) ).
cnf(c_0_1896_1,axiom,
( ~ c_Type_Otyping(c_Type_Oshift(X1,X2,v_T____,tc_Type_Otype),v_a____,X3)
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),X4),X2)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
| ~ c_Type_Otyping(X1,X4,v_T____) ),
inference(literals_permutation,[status(thm)],[c_0_1896]) ).
cnf(c_0_1896_2,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
| ~ c_Type_Otyping(c_Type_Oshift(X1,X2,v_T____,tc_Type_Otype),v_a____,X3)
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),X4),X2)))
| ~ c_Type_Otyping(X1,X4,v_T____) ),
inference(literals_permutation,[status(thm)],[c_0_1896]) ).
cnf(c_0_1896_3,axiom,
( ~ c_Type_Otyping(X1,X4,v_T____)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
| ~ c_Type_Otyping(c_Type_Oshift(X1,X2,v_T____,tc_Type_Otype),v_a____,X3)
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),X4),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1896]) ).
cnf(c_0_1897_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X1),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1897]) ).
cnf(c_0_1897_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X1),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_1897]) ).
cnf(c_0_1898_0,axiom,
( c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X2),X1,c_HOL_Ozero__class_Ozero(X2),X2,X2) = c_List_Olistsum(X1,X2)
| ~ class_OrderedGroup_Omonoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1898]) ).
cnf(c_0_1898_1,axiom,
( ~ class_OrderedGroup_Omonoid__add(X2)
| c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X2),X1,c_HOL_Ozero__class_Ozero(X2),X2,X2) = c_List_Olistsum(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1898]) ).
cnf(c_0_1899_0,axiom,
( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X2),c_HOL_Ozero__class_Ozero(X2),X1,X2,X2) = c_List_Olistsum(X1,X2)
| ~ class_OrderedGroup_Omonoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1899]) ).
cnf(c_0_1899_1,axiom,
( ~ class_OrderedGroup_Omonoid__add(X2)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X2),c_HOL_Ozero__class_Ozero(X2),X1,X2,X2) = c_List_Olistsum(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1899]) ).
cnf(c_0_1900_0,axiom,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1900]) ).
cnf(c_0_1900_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_1900]) ).
cnf(c_0_1901_0,axiom,
( c_Type_Otyping(X1,hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4),X5)
| ~ c_Type_Otyping(c_Type_Oshift(X1,X4,X6,tc_Type_Otype),X2,X5)
| ~ c_Type_Otyping(X1,X3,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1901]) ).
cnf(c_0_1901_1,axiom,
( ~ c_Type_Otyping(c_Type_Oshift(X1,X4,X6,tc_Type_Otype),X2,X5)
| c_Type_Otyping(X1,hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4),X5)
| ~ c_Type_Otyping(X1,X3,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1901]) ).
cnf(c_0_1901_2,axiom,
( ~ c_Type_Otyping(X1,X3,X6)
| ~ c_Type_Otyping(c_Type_Oshift(X1,X4,X6,tc_Type_Otype),X2,X5)
| c_Type_Otyping(X1,hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1901]) ).
cnf(c_0_1902_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1902]) ).
cnf(c_0_1902_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1902]) ).
cnf(c_0_1902_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_1902]) ).
cnf(c_0_1903_0,axiom,
( hBOOL(hAPP(hAPP(X1,X2),X5))
| c_ListOrder_Ostep1(X1,X3,X6,X4)
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1903]) ).
cnf(c_0_1903_1,axiom,
( c_ListOrder_Ostep1(X1,X3,X6,X4)
| hBOOL(hAPP(hAPP(X1,X2),X5))
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1903]) ).
cnf(c_0_1903_2,axiom,
( ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4)
| c_ListOrder_Ostep1(X1,X3,X6,X4)
| hBOOL(hAPP(hAPP(X1,X2),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1903]) ).
cnf(c_0_1904_0,axiom,
( X6 = X3
| c_ListOrder_Ostep1(X1,X3,X6,X4)
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1904]) ).
cnf(c_0_1904_1,axiom,
( c_ListOrder_Ostep1(X1,X3,X6,X4)
| X6 = X3
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1904]) ).
cnf(c_0_1904_2,axiom,
( ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4)
| c_ListOrder_Ostep1(X1,X3,X6,X4)
| X6 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_1904]) ).
cnf(c_0_1905_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),X3,tc_nat))) ),
inference(literals_permutation,[status(thm)],[c_0_1905]) ).
cnf(c_0_1905_1,axiom,
( ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),X3,tc_nat)))
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1905]) ).
cnf(c_0_1906_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),X3,tc_nat))) ),
inference(literals_permutation,[status(thm)],[c_0_1906]) ).
cnf(c_0_1906_1,axiom,
( ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),X3,tc_nat)))
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1906]) ).
cnf(c_0_1907_0,axiom,
( hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1907]) ).
cnf(c_0_1907_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5))
| hBOOL(hAPP(hAPP(X1,X5),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1907]) ).
cnf(c_0_1908_0,axiom,
( hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1908]) ).
cnf(c_0_1908_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5))
| hBOOL(hAPP(hAPP(X1,X5),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1908]) ).
cnf(c_0_1909_0,axiom,
( c_ListOrder_Ostep1(X1,c_List_Oappend(X2,X3,X4),c_List_Oappend(X5,X3,X4),X4)
| ~ c_ListOrder_Ostep1(X1,X2,X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1909]) ).
cnf(c_0_1909_1,axiom,
( ~ c_ListOrder_Ostep1(X1,X2,X5,X4)
| c_ListOrder_Ostep1(X1,c_List_Oappend(X2,X3,X4),c_List_Oappend(X5,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1909]) ).
cnf(c_0_1910_0,axiom,
( c_ListOrder_Ostep1(X1,c_List_Oappend(X5,X2,X4),c_List_Oappend(X5,X3,X4),X4)
| ~ c_ListOrder_Ostep1(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1910]) ).
cnf(c_0_1910_1,axiom,
( ~ c_ListOrder_Ostep1(X1,X2,X3,X4)
| c_ListOrder_Ostep1(X1,c_List_Oappend(X5,X2,X4),c_List_Oappend(X5,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1910]) ).
cnf(c_0_1911_0,axiom,
( c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X5,X2,X4),c_List_Olist_OCons(X5,X3,X4),X4)
| ~ c_ListOrder_Ostep1(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1911]) ).
cnf(c_0_1911_1,axiom,
( ~ c_ListOrder_Ostep1(X1,X2,X3,X4)
| c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X5,X2,X4),c_List_Olist_OCons(X5,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1911]) ).
cnf(c_0_1912_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1912]) ).
cnf(c_0_1912_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1912]) ).
cnf(c_0_1913_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1913]) ).
cnf(c_0_1913_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1913]) ).
cnf(c_0_1914_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,X1),X3)),hAPP(hAPP(c_Lambda_Olift,X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1914]) ).
cnf(c_0_1914_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,X1),X3)),hAPP(hAPP(c_Lambda_Olift,X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1914]) ).
cnf(c_0_1915_0,axiom,
( hBOOL(hAPP(hAPP(X1,X2),X5))
| X5 = X2
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1915]) ).
cnf(c_0_1915_1,axiom,
( X5 = X2
| hBOOL(hAPP(hAPP(X1,X2),X5))
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1915]) ).
cnf(c_0_1915_2,axiom,
( ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4)
| X5 = X2
| hBOOL(hAPP(hAPP(X1,X2),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1915]) ).
cnf(c_0_1916_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1916]) ).
cnf(c_0_1916_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1916]) ).
cnf(c_0_1916_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1916]) ).
cnf(c_0_1917_0,axiom,
( X6 = X3
| X5 = X2
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1917]) ).
cnf(c_0_1917_1,axiom,
( X5 = X2
| X6 = X3
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1917]) ).
cnf(c_0_1917_2,axiom,
( ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4)
| X5 = X2
| X6 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_1917]) ).
cnf(c_0_1918_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_1918]) ).
cnf(c_0_1918_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_1918]) ).
cnf(c_0_1919_0,axiom,
( c_Type_Otyping(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X2),X4),X3)
| ~ c_Type_Otyping(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1919]) ).
cnf(c_0_1919_1,axiom,
( ~ c_Type_Otyping(X1,X2,X3)
| c_Type_Otyping(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X2),X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1919]) ).
cnf(c_0_1920_0,axiom,
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1920]) ).
cnf(c_0_1920_1,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1920]) ).
cnf(c_0_1921_0,axiom,
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1921]) ).
cnf(c_0_1921_1,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1921]) ).
cnf(c_0_1922_0,axiom,
( c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1922]) ).
cnf(c_0_1922_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1922]) ).
cnf(c_0_1922_2,axiom,
( ~ c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1922]) ).
cnf(c_0_1922_3,axiom,
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1922]) ).
cnf(c_0_1923_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1923]) ).
cnf(c_0_1923_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1923]) ).
cnf(c_0_1923_2,axiom,
( ~ c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1923]) ).
cnf(c_0_1923_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1923]) ).
cnf(c_0_1924_0,axiom,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,X1),X3)),hAPP(hAPP(c_Lambda_Olift,X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1924]) ).
cnf(c_0_1924_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,X1),X3)),hAPP(hAPP(c_Lambda_Olift,X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1924]) ).
cnf(c_0_1925_0,axiom,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1925]) ).
cnf(c_0_1925_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1925]) ).
cnf(c_0_1926_0,axiom,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1926]) ).
cnf(c_0_1926_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1926]) ).
cnf(c_0_1927_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X2),X5))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1927]) ).
cnf(c_0_1927_1,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X2),X5))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1927]) ).
cnf(c_0_1927_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X3),X5))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X2),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1927]) ).
cnf(c_0_1928_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(X1,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1928]) ).
cnf(c_0_1928_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5))
| ~ hBOOL(hAPP(hAPP(X1,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1928]) ).
cnf(c_0_1928_2,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X4),X5))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1928]) ).
cnf(c_0_1929_0,axiom,
( hAPP(c_Type_Oshift(X3,X2,X4,X5),X1) = hAPP(X3,X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1929]) ).
cnf(c_0_1929_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| hAPP(c_Type_Oshift(X3,X2,X4,X5),X1) = hAPP(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1929]) ).
cnf(c_0_1930_0,axiom,
( c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X3,X4),X4)
| ~ hBOOL(hAPP(hAPP(X1,X2),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1930]) ).
cnf(c_0_1930_1,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X2),X5))
| c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1930]) ).
cnf(c_0_1931_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1931]) ).
cnf(c_0_1931_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1931]) ).
cnf(c_0_1931_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1931]) ).
cnf(c_0_1931_3,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1931]) ).
cnf(c_0_1932_0,axiom,
( X1 = X2
| c_List_Oappend(X1,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4) != c_List_Oappend(X2,c_List_Olist_OCons(X5,c_List_Olist_ONil(X4),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1932]) ).
cnf(c_0_1932_1,axiom,
( c_List_Oappend(X1,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4) != c_List_Oappend(X2,c_List_Olist_OCons(X5,c_List_Olist_ONil(X4),X4),X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1932]) ).
cnf(c_0_1933_0,axiom,
( X1 = X2
| c_List_Oappend(X3,c_List_Olist_OCons(X1,c_List_Olist_ONil(X4),X4),X4) != c_List_Oappend(X5,c_List_Olist_OCons(X2,c_List_Olist_ONil(X4),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1933]) ).
cnf(c_0_1933_1,axiom,
( c_List_Oappend(X3,c_List_Olist_OCons(X1,c_List_Olist_ONil(X4),X4),X4) != c_List_Oappend(X5,c_List_Olist_OCons(X2,c_List_Olist_ONil(X4),X4),X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1933]) ).
cnf(c_0_1934_0,axiom,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1934]) ).
cnf(c_0_1934_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1934]) ).
cnf(c_0_1934_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1934]) ).
cnf(c_0_1934_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1934]) ).
cnf(c_0_1934_4,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1934]) ).
cnf(c_0_1935_0,axiom,
( c_Orderings_Oord__class_Omax(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Orderings_Oord__class_Omax(X2,X3,X1)),X4)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1935]) ).
cnf(c_0_1935_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_Orderings_Oord__class_Omax(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Orderings_Oord__class_Omax(X2,X3,X1)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1935]) ).
cnf(c_0_1936_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_1936]) ).
cnf(c_0_1936_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_1936]) ).
cnf(c_0_1937_0,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1937]) ).
cnf(c_0_1937_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1937]) ).
cnf(c_0_1937_2,axiom,
( ~ c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1937]) ).
cnf(c_0_1937_3,axiom,
( ~ c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1937]) ).
cnf(c_0_1938_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1938]) ).
cnf(c_0_1938_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1938]) ).
cnf(c_0_1938_2,axiom,
( ~ c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1938]) ).
cnf(c_0_1938_3,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1938]) ).
cnf(c_0_1939_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_1939]) ).
cnf(c_0_1939_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_1939]) ).
cnf(c_0_1939_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_1939]) ).
cnf(c_0_1939_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_1939]) ).
cnf(c_0_1940_0,axiom,
( hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)))
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1940]) ).
cnf(c_0_1940_1,axiom,
( ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)))
| hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1940]) ).
cnf(c_0_1940_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)))
| hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(literals_permutation,[status(thm)],[c_0_1940]) ).
cnf(c_0_1941_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1941]) ).
cnf(c_0_1941_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1941]) ).
cnf(c_0_1941_2,axiom,
( ~ c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1941]) ).
cnf(c_0_1942_0,axiom,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X1,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)),X3)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1942]) ).
cnf(c_0_1942_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X1,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1942]) ).
cnf(c_0_1943_0,axiom,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X1,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)),X3)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1943]) ).
cnf(c_0_1943_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X1,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1943]) ).
cnf(c_0_1944_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),X2,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1944]) ).
cnf(c_0_1944_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),X2,tc_nat)
| ~ c_lessequals(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1944]) ).
cnf(c_0_1944_2,axiom,
( ~ c_lessequals(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1944]) ).
cnf(c_0_1945_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_1945]) ).
cnf(c_0_1945_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_1945]) ).
cnf(c_0_1945_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_1945]) ).
cnf(c_0_1946_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_1946]) ).
cnf(c_0_1946_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_1946]) ).
cnf(c_0_1946_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_1946]) ).
cnf(c_0_1947_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_1947]) ).
cnf(c_0_1947_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_1947]) ).
cnf(c_0_1947_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_1947]) ).
cnf(c_0_1948_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_1948]) ).
cnf(c_0_1948_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_1948]) ).
cnf(c_0_1948_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_1948]) ).
cnf(c_0_1949_0,axiom,
( c_lessequals(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1949]) ).
cnf(c_0_1949_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1949]) ).
cnf(c_0_1949_2,axiom,
( ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),X2,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1949]) ).
cnf(c_0_1950_0,axiom,
( X2 = X3
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| c_Power_Opower__class_Opower(X2,X4,X1) != c_Power_Opower__class_Opower(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1950]) ).
cnf(c_0_1950_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| X2 = X3
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| c_Power_Opower__class_Opower(X2,X4,X1) != c_Power_Opower__class_Opower(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1950]) ).
cnf(c_0_1950_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| X2 = X3
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| c_Power_Opower__class_Opower(X2,X4,X1) != c_Power_Opower__class_Opower(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1950]) ).
cnf(c_0_1950_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| X2 = X3
| c_Power_Opower__class_Opower(X2,X4,X1) != c_Power_Opower__class_Opower(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1950]) ).
cnf(c_0_1950_4,axiom,
( c_Power_Opower__class_Opower(X2,X4,X1) != c_Power_Opower__class_Opower(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| ~ 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_1950]) ).
cnf(c_0_1950_5,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_Power_Opower__class_Opower(X2,X4,X1) != c_Power_Opower__class_Opower(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| ~ 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_1950]) ).
cnf(c_0_1951_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),c_Lambda_OdB_OVar(X2)),X3)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1951]) ).
cnf(c_0_1951_1,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),c_Lambda_OdB_OVar(X2)),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1951]) ).
cnf(c_0_1952_0,axiom,
( c_lessequals(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),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_1952]) ).
cnf(c_0_1952_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),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_1952]) ).
cnf(c_0_1952_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1952]) ).
cnf(c_0_1952_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(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1952]) ).
cnf(c_0_1953_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X1)),c_Lambda_OdB_OAbs(X2)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1953]) ).
cnf(c_0_1953_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X1)),c_Lambda_OdB_OAbs(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1953]) ).
cnf(c_0_1954_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_1954]) ).
cnf(c_0_1954_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_1954]) ).
cnf(c_0_1954_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_1954]) ).
cnf(c_0_1954_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_1954]) ).
cnf(c_0_1955_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_1955]) ).
cnf(c_0_1955_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_1955]) ).
cnf(c_0_1955_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_1955]) ).
cnf(c_0_1955_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_1955]) ).
cnf(c_0_1956_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_1956]) ).
cnf(c_0_1956_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_1956]) ).
cnf(c_0_1956_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_1956]) ).
cnf(c_0_1956_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_1956]) ).
cnf(c_0_1957_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_1957]) ).
cnf(c_0_1957_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_1957]) ).
cnf(c_0_1957_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_1957]) ).
cnf(c_0_1957_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_1957]) ).
cnf(c_0_1958_0,axiom,
( c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(X1,X4,X3),c_HOL_Ominus__class_Ominus(X2,X4,X3),X3) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1958]) ).
cnf(c_0_1958_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(X1,X4,X3),c_HOL_Ominus__class_Ominus(X2,X4,X3),X3) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1958]) ).
cnf(c_0_1959_0,axiom,
( c_Wellfounded_Oaccp(X1,X4,X3)
| ~ c_Wellfounded_Oaccp(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X3),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1959]) ).
cnf(c_0_1959_1,axiom,
( ~ c_Wellfounded_Oaccp(X1,X2,X3)
| c_Wellfounded_Oaccp(X1,X4,X3)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X3),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1959]) ).
cnf(c_0_1959_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X3),X4),X2))
| ~ c_Wellfounded_Oaccp(X1,X2,X3)
| c_Wellfounded_Oaccp(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1959]) ).
cnf(c_0_1960_0,axiom,
( c_Wellfounded_Oaccp(X1,X3,X2)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| ~ c_Wellfounded_Oaccp(X1,X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1960]) ).
cnf(c_0_1960_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| c_Wellfounded_Oaccp(X1,X3,X2)
| ~ c_Wellfounded_Oaccp(X1,X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1960]) ).
cnf(c_0_1960_2,axiom,
( ~ c_Wellfounded_Oaccp(X1,X4,X2)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| c_Wellfounded_Oaccp(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1960]) ).
cnf(c_0_1961_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1961]) ).
cnf(c_0_1961_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1961]) ).
cnf(c_0_1961_2,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1961]) ).
cnf(c_0_1962_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(X3,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1962]) ).
cnf(c_0_1962_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X3,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1962]) ).
cnf(c_0_1962_2,axiom,
( ~ c_lessequals(X3,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1962]) ).
cnf(c_0_1963_0,axiom,
( c_lessequals(X3,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1963]) ).
cnf(c_0_1963_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(X3,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1963]) ).
cnf(c_0_1964_0,axiom,
( c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1964]) ).
cnf(c_0_1964_1,axiom,
( ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),tc_nat)
| c_lessequals(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1964]) ).
cnf(c_0_1965_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1965]) ).
cnf(c_0_1965_1,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),tc_nat)
| c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1965]) ).
cnf(c_0_1966_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_1966]) ).
cnf(c_0_1966_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_1966]) ).
cnf(c_0_1967_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_1967]) ).
cnf(c_0_1967_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_1967]) ).
cnf(c_0_1968_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_1968]) ).
cnf(c_0_1968_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_1968]) ).
cnf(c_0_1969_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_1969]) ).
cnf(c_0_1969_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_1969]) ).
cnf(c_0_1970_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_1970]) ).
cnf(c_0_1970_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_1970]) ).
cnf(c_0_1971_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X4),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X3,X4,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1971]) ).
cnf(c_0_1971_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X4),tc_nat)
| ~ c_lessequals(X3,X4,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1971]) ).
cnf(c_0_1971_2,axiom,
( ~ c_lessequals(X3,X4,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X4),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1971]) ).
cnf(c_0_1972_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1972]) ).
cnf(c_0_1972_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1972]) ).
cnf(c_0_1972_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X4),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1972]) ).
cnf(c_0_1973_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Omap(X4,X1,X2,X3) != c_List_Olist_ONil(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1973]) ).
cnf(c_0_1973_1,axiom,
( c_List_Omap(X4,X1,X2,X3) != c_List_Olist_ONil(X3)
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1973]) ).
cnf(c_0_1974_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Omap(X3,X1,X2,X4) != c_List_Olist_ONil(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1974]) ).
cnf(c_0_1974_1,axiom,
( c_List_Omap(X3,X1,X2,X4) != c_List_Olist_ONil(X4)
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1974]) ).
cnf(c_0_1975_0,axiom,
( c_Type_Otyping(X3,X2,X4)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| ~ c_Type_Otyping(X3,X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1975]) ).
cnf(c_0_1975_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| c_Type_Otyping(X3,X2,X4)
| ~ c_Type_Otyping(X3,X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1975]) ).
cnf(c_0_1975_2,axiom,
( ~ c_Type_Otyping(X3,X1,X4)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| c_Type_Otyping(X3,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1975]) ).
cnf(c_0_1976_0,axiom,
( c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1976]) ).
cnf(c_0_1976_1,axiom,
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat)
| c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1976]) ).
cnf(c_0_1977_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1977]) ).
cnf(c_0_1977_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1977]) ).
cnf(c_0_1978_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_1978]) ).
cnf(c_0_1978_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_1978]) ).
cnf(c_0_1978_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_1978]) ).
cnf(c_0_1979_0,axiom,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),X2,tc_nat) = c_HOL_Ominus__class_Ominus(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1979]) ).
cnf(c_0_1979_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),X2,tc_nat) = c_HOL_Ominus__class_Ominus(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1979]) ).
cnf(c_0_1980_0,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat)
| ~ c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1980]) ).
cnf(c_0_1980_1,axiom,
( ~ c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1980]) ).
cnf(c_0_1981_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1981]) ).
cnf(c_0_1981_1,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1981]) ).
cnf(c_0_1982_0,axiom,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),X1,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat))
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1982]) ).
cnf(c_0_1982_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),X1,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1982]) ).
cnf(c_0_1983_0,axiom,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),X1,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat))
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1983]) ).
cnf(c_0_1983_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),X1,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1983]) ).
cnf(c_0_1984_0,axiom,
( c_lessequals(X1,X2,X4)
| c_lessequals(X1,X3,X4)
| ~ c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
| ~ class_Orderings_Olinorder(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1984]) ).
cnf(c_0_1984_1,axiom,
( c_lessequals(X1,X3,X4)
| c_lessequals(X1,X2,X4)
| ~ c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
| ~ class_Orderings_Olinorder(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1984]) ).
cnf(c_0_1984_2,axiom,
( ~ c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
| c_lessequals(X1,X3,X4)
| c_lessequals(X1,X2,X4)
| ~ class_Orderings_Olinorder(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1984]) ).
cnf(c_0_1984_3,axiom,
( ~ class_Orderings_Olinorder(X4)
| ~ c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
| c_lessequals(X1,X3,X4)
| c_lessequals(X1,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1984]) ).
cnf(c_0_1985_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X4)
| c_HOL_Oord__class_Oless(X1,X3,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
| ~ class_Orderings_Olinorder(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1985]) ).
cnf(c_0_1985_1,axiom,
( c_HOL_Oord__class_Oless(X1,X3,X4)
| c_HOL_Oord__class_Oless(X1,X2,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
| ~ class_Orderings_Olinorder(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1985]) ).
cnf(c_0_1985_2,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
| c_HOL_Oord__class_Oless(X1,X3,X4)
| c_HOL_Oord__class_Oless(X1,X2,X4)
| ~ class_Orderings_Olinorder(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1985]) ).
cnf(c_0_1985_3,axiom,
( ~ class_Orderings_Olinorder(X4)
| ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
| c_HOL_Oord__class_Oless(X1,X3,X4)
| c_HOL_Oord__class_Oless(X1,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1985]) ).
cnf(c_0_1986_0,axiom,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X2,tc_nat) = X1
| ~ c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1986]) ).
cnf(c_0_1986_1,axiom,
( ~ c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X2,tc_nat) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1986]) ).
cnf(c_0_1987_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_1987]) ).
cnf(c_0_1987_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_1987]) ).
cnf(c_0_1987_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_1987]) ).
cnf(c_0_1987_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_1987]) ).
cnf(c_0_1988_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_1988]) ).
cnf(c_0_1988_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_1988]) ).
cnf(c_0_1988_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_1988]) ).
cnf(c_0_1988_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_1988]) ).
cnf(c_0_1989_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_1989]) ).
cnf(c_0_1989_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_1989]) ).
cnf(c_0_1989_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_1989]) ).
cnf(c_0_1989_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_1989]) ).
cnf(c_0_1990_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_1990]) ).
cnf(c_0_1990_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_1990]) ).
cnf(c_0_1990_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_1990]) ).
cnf(c_0_1990_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_1990]) ).
cnf(c_0_1991_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_1991]) ).
cnf(c_0_1991_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_1991]) ).
cnf(c_0_1991_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_1991]) ).
cnf(c_0_1991_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_1991]) ).
cnf(c_0_1992_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_1992]) ).
cnf(c_0_1992_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_1992]) ).
cnf(c_0_1992_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_1992]) ).
cnf(c_0_1992_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_1992]) ).
cnf(c_0_1993_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_1993]) ).
cnf(c_0_1993_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_1993]) ).
cnf(c_0_1993_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_1993]) ).
cnf(c_0_1993_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_1993]) ).
cnf(c_0_1994_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_1994]) ).
cnf(c_0_1994_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_1994]) ).
cnf(c_0_1994_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_1994]) ).
cnf(c_0_1994_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_1994]) ).
cnf(c_0_1995_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_1995]) ).
cnf(c_0_1995_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_1995]) ).
cnf(c_0_1995_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_1995]) ).
cnf(c_0_1995_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_1995]) ).
cnf(c_0_1995_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_1995]) ).
cnf(c_0_1996_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_1996]) ).
cnf(c_0_1996_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_1996]) ).
cnf(c_0_1996_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_1996]) ).
cnf(c_0_1996_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_1996]) ).
cnf(c_0_1996_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_1996]) ).
cnf(c_0_1997_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_1997]) ).
cnf(c_0_1997_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_1997]) ).
cnf(c_0_1997_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_1997]) ).
cnf(c_0_1997_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_1997]) ).
cnf(c_0_1997_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_1997]) ).
cnf(c_0_1998_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_1998]) ).
cnf(c_0_1998_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_1998]) ).
cnf(c_0_1998_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_1998]) ).
cnf(c_0_1998_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_1998]) ).
cnf(c_0_1998_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_1998]) ).
cnf(c_0_1999_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_1999]) ).
cnf(c_0_1999_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_1999]) ).
cnf(c_0_1999_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_1999]) ).
cnf(c_0_2000_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_2000]) ).
cnf(c_0_2000_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_2000]) ).
cnf(c_0_2000_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_2000]) ).
cnf(c_0_2001_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_2001]) ).
cnf(c_0_2001_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_2001]) ).
cnf(c_0_2001_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_2001]) ).
cnf(c_0_2002_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_2002]) ).
cnf(c_0_2002_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_2002]) ).
cnf(c_0_2002_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_2002]) ).
cnf(c_0_2003_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_2003]) ).
cnf(c_0_2003_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_2003]) ).
cnf(c_0_2003_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_2003]) ).
cnf(c_0_2004_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_2004]) ).
cnf(c_0_2004_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_2004]) ).
cnf(c_0_2004_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_2004]) ).
cnf(c_0_2005_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_2005]) ).
cnf(c_0_2005_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_2005]) ).
cnf(c_0_2005_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_2005]) ).
cnf(c_0_2006_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_2006]) ).
cnf(c_0_2006_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_2006]) ).
cnf(c_0_2006_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_2006]) ).
cnf(c_0_2007_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_2007]) ).
cnf(c_0_2007_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_2007]) ).
cnf(c_0_2007_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_2007]) ).
cnf(c_0_2007_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_2007]) ).
cnf(c_0_2008_0,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2008]) ).
cnf(c_0_2008_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2008]) ).
cnf(c_0_2009_0,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2009]) ).
cnf(c_0_2009_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2009]) ).
cnf(c_0_2010_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2010]) ).
cnf(c_0_2010_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2010]) ).
cnf(c_0_2010_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2010]) ).
cnf(c_0_2011_0,axiom,
( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2011]) ).
cnf(c_0_2011_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2011]) ).
cnf(c_0_2011_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2011]) ).
cnf(c_0_2011_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2011]) ).
cnf(c_0_2012_0,axiom,
( c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2012]) ).
cnf(c_0_2012_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2012]) ).
cnf(c_0_2012_2,axiom,
( ~ c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2012]) ).
cnf(c_0_2012_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2012]) ).
cnf(c_0_2013_0,axiom,
( c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2013]) ).
cnf(c_0_2013_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2013]) ).
cnf(c_0_2013_2,axiom,
( ~ c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2013]) ).
cnf(c_0_2013_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2013]) ).
cnf(c_0_2014_0,axiom,
( c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2014]) ).
cnf(c_0_2014_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2014]) ).
cnf(c_0_2014_2,axiom,
( ~ c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2014]) ).
cnf(c_0_2014_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2014]) ).
cnf(c_0_2015_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)),X2) = X1
| ~ c_lessequals(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2015]) ).
cnf(c_0_2015_1,axiom,
( ~ c_lessequals(X2,X1,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2015]) ).
cnf(c_0_2016_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)),X1) = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2016]) ).
cnf(c_0_2016_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)),X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2016]) ).
cnf(c_0_2017_0,axiom,
( X1 = X2
| ~ c_lessequals(X3,X1,tc_nat)
| ~ c_lessequals(X3,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(X1,X3,tc_nat) != c_HOL_Ominus__class_Ominus(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2017]) ).
cnf(c_0_2017_1,axiom,
( ~ c_lessequals(X3,X1,tc_nat)
| X1 = X2
| ~ c_lessequals(X3,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(X1,X3,tc_nat) != c_HOL_Ominus__class_Ominus(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2017]) ).
cnf(c_0_2017_2,axiom,
( ~ c_lessequals(X3,X2,tc_nat)
| ~ c_lessequals(X3,X1,tc_nat)
| X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X3,tc_nat) != c_HOL_Ominus__class_Ominus(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2017]) ).
cnf(c_0_2017_3,axiom,
( c_HOL_Ominus__class_Ominus(X1,X3,tc_nat) != c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)
| ~ c_lessequals(X3,X2,tc_nat)
| ~ c_lessequals(X3,X1,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2017]) ).
cnf(c_0_2018_0,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X3),X4)),X5) = hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5))
| ~ c_OrderedGroup_Osemigroup__add(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2018]) ).
cnf(c_0_2018_1,axiom,
( ~ c_OrderedGroup_Osemigroup__add(X1,X2)
| hAPP(hAPP(X1,hAPP(hAPP(X1,X3),X4)),X5) = hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2018]) ).
cnf(c_0_2019_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2019]) ).
cnf(c_0_2019_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2019]) ).
cnf(c_0_2019_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2019]) ).
cnf(c_0_2020_0,axiom,
( c_List_Olistsp(X1,c_List_Oappend(X2,X4,X3),X3)
| ~ c_List_Olistsp(X1,X2,X3)
| ~ c_List_Olistsp(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2020]) ).
cnf(c_0_2020_1,axiom,
( ~ c_List_Olistsp(X1,X2,X3)
| c_List_Olistsp(X1,c_List_Oappend(X2,X4,X3),X3)
| ~ c_List_Olistsp(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2020]) ).
cnf(c_0_2020_2,axiom,
( ~ c_List_Olistsp(X1,X4,X3)
| ~ c_List_Olistsp(X1,X2,X3)
| c_List_Olistsp(X1,c_List_Oappend(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2020]) ).
cnf(c_0_2021_0,axiom,
( c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3) = c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2021]) ).
cnf(c_0_2021_1,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3) = c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2021]) ).
cnf(c_0_2022_0,axiom,
( c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4) = c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omax(X1,X3,X4),X4)
| ~ class_Orderings_Olinorder(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2022]) ).
cnf(c_0_2022_1,axiom,
( ~ class_Orderings_Olinorder(X4)
| c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4) = c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omax(X1,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2022]) ).
cnf(c_0_2023_0,axiom,
( c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2023]) ).
cnf(c_0_2023_1,axiom,
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2023]) ).
cnf(c_0_2023_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2023]) ).
cnf(c_0_2024_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2024]) ).
cnf(c_0_2024_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2024]) ).
cnf(c_0_2024_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2024]) ).
cnf(c_0_2025_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_2025]) ).
cnf(c_0_2025_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_2025]) ).
cnf(c_0_2025_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_2025]) ).
cnf(c_0_2026_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_2026]) ).
cnf(c_0_2026_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_2026]) ).
cnf(c_0_2026_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_2026]) ).
cnf(c_0_2027_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_2027]) ).
cnf(c_0_2027_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_2027]) ).
cnf(c_0_2027_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_2027]) ).
cnf(c_0_2028_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_2028]) ).
cnf(c_0_2028_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_2028]) ).
cnf(c_0_2028_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_2028]) ).
cnf(c_0_2029_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_2029]) ).
cnf(c_0_2029_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_2029]) ).
cnf(c_0_2029_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_2029]) ).
cnf(c_0_2030_0,axiom,
( c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X5,X4,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2030]) ).
cnf(c_0_2030_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X5,X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X5,X4,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2030]) ).
cnf(c_0_2030_2,axiom,
( c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X5,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2030]) ).
cnf(c_0_2030_3,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X5,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2030]) ).
cnf(c_0_2031_0,axiom,
( c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X5,X4,X3) != c_HOL_Ominus__class_Ominus(X2,X1,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2031]) ).
cnf(c_0_2031_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X5,X3)
| c_HOL_Ominus__class_Ominus(X5,X4,X3) != c_HOL_Ominus__class_Ominus(X2,X1,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2031]) ).
cnf(c_0_2031_2,axiom,
( c_HOL_Ominus__class_Ominus(X5,X4,X3) != c_HOL_Ominus__class_Ominus(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2031]) ).
cnf(c_0_2031_3,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X5,X4,X3) != c_HOL_Ominus__class_Ominus(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2031]) ).
cnf(c_0_2032_0,axiom,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2032]) ).
cnf(c_0_2032_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2032]) ).
cnf(c_0_2032_2,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2032]) ).
cnf(c_0_2032_3,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2032]) ).
cnf(c_0_2033_0,axiom,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2033]) ).
cnf(c_0_2033_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3)
| c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2033]) ).
cnf(c_0_2033_2,axiom,
( c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2033]) ).
cnf(c_0_2033_3,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2033]) ).
cnf(c_0_2034_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2034]) ).
cnf(c_0_2034_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2034]) ).
cnf(c_0_2035_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2035]) ).
cnf(c_0_2035_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2035]) ).
cnf(c_0_2036_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2036]) ).
cnf(c_0_2036_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2036]) ).
cnf(c_0_2037_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2037]) ).
cnf(c_0_2037_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2037]) ).
cnf(c_0_2038_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2038]) ).
cnf(c_0_2038_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2038]) ).
cnf(c_0_2038_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2038]) ).
cnf(c_0_2039_0,axiom,
( c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2039]) ).
cnf(c_0_2039_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2039]) ).
cnf(c_0_2039_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| c_HOL_Oord__class_Oless(X2,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2039]) ).
cnf(c_0_2040_0,axiom,
( c_lessequals(X2,X4,X3)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2040]) ).
cnf(c_0_2040_1,axiom,
( ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| c_lessequals(X2,X4,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2040]) ).
cnf(c_0_2040_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| c_lessequals(X2,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2040]) ).
cnf(c_0_2041_0,axiom,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2041]) ).
cnf(c_0_2041_1,axiom,
( ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| c_lessequals(X1,X4,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2041]) ).
cnf(c_0_2041_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| c_lessequals(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2041]) ).
cnf(c_0_2042_0,axiom,
( c_lessequals(X2,X4,X3)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2042]) ).
cnf(c_0_2042_1,axiom,
( ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| c_lessequals(X2,X4,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2042]) ).
cnf(c_0_2042_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| c_lessequals(X2,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2042]) ).
cnf(c_0_2043_0,axiom,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2043]) ).
cnf(c_0_2043_1,axiom,
( ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| c_lessequals(X1,X4,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2043]) ).
cnf(c_0_2043_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| c_lessequals(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2043]) ).
cnf(c_0_2044_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_2044]) ).
cnf(c_0_2044_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_2044]) ).
cnf(c_0_2045_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_2045]) ).
cnf(c_0_2045_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_2045]) ).
cnf(c_0_2046_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_2046]) ).
cnf(c_0_2046_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_2046]) ).
cnf(c_0_2047_0,axiom,
( c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2047]) ).
cnf(c_0_2047_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2047]) ).
cnf(c_0_2047_2,axiom,
( ~ c_lessequals(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2047]) ).
cnf(c_0_2048_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2048]) ).
cnf(c_0_2048_1,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2048]) ).
cnf(c_0_2049_0,axiom,
( c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(X2,X3),c_Nat_Osemiring__1__class_Oof__nat(X1,X3),X3) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ class_Ring__and__Field_Oring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2049]) ).
cnf(c_0_2049_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(X2,X3),c_Nat_Osemiring__1__class_Oof__nat(X1,X3),X3) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3)
| ~ class_Ring__and__Field_Oring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2049]) ).
cnf(c_0_2049_2,axiom,
( ~ class_Ring__and__Field_Oring__1(X3)
| ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(X2,X3),c_Nat_Osemiring__1__class_Oof__nat(X1,X3),X3) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2049]) ).
cnf(c_0_2050_0,axiom,
( c_List_Olistsp(X1,X2,X4)
| ~ c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2050]) ).
cnf(c_0_2050_1,axiom,
( ~ c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4)
| c_List_Olistsp(X1,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2050]) ).
cnf(c_0_2051_0,axiom,
( c_List_Olistsp(X1,X3,X4)
| ~ c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2051]) ).
cnf(c_0_2051_1,axiom,
( ~ c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4)
| c_List_Olistsp(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2051]) ).
cnf(c_0_2052_0,axiom,
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2052]) ).
cnf(c_0_2052_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2052]) ).
cnf(c_0_2053_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_2053]) ).
cnf(c_0_2053_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_2053]) ).
cnf(c_0_2053_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_2053]) ).
cnf(c_0_2053_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_2053]) ).
cnf(c_0_2053_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_2053]) ).
cnf(c_0_2054_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_2054]) ).
cnf(c_0_2054_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_2054]) ).
cnf(c_0_2054_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_2054]) ).
cnf(c_0_2054_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_2054]) ).
cnf(c_0_2054_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_2054]) ).
cnf(c_0_2055_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_2055]) ).
cnf(c_0_2055_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_2055]) ).
cnf(c_0_2055_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_2055]) ).
cnf(c_0_2055_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_2055]) ).
cnf(c_0_2056_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2056]) ).
cnf(c_0_2056_1,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2056]) ).
cnf(c_0_2056_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2056]) ).
cnf(c_0_2057_0,axiom,
( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2057]) ).
cnf(c_0_2057_1,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat)
| c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2057]) ).
cnf(c_0_2058_0,axiom,
( c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2058]) ).
cnf(c_0_2058_1,axiom,
( ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat)
| c_lessequals(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2058]) ).
cnf(c_0_2059_0,axiom,
( c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2059]) ).
cnf(c_0_2059_1,axiom,
( ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat)
| c_lessequals(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2059]) ).
cnf(c_0_2060_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),X3) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2060]) ).
cnf(c_0_2060_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),X3) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2060]) ).
cnf(c_0_2061_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),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_2061]) ).
cnf(c_0_2061_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2061]) ).
cnf(c_0_2061_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),c_Power_Opower__class_Opower(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2061]) ).
cnf(c_0_2062_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),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_2062]) ).
cnf(c_0_2062_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),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2062]) ).
cnf(c_0_2062_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),c_Power_Opower__class_Opower(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2062]) ).
cnf(c_0_2063_0,axiom,
( c_Wellfounded_Oaccp(X1,X4,X3)
| ~ c_Wellfounded_Oaccp(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2063]) ).
cnf(c_0_2063_1,axiom,
( ~ c_Wellfounded_Oaccp(X1,X2,X3)
| c_Wellfounded_Oaccp(X1,X4,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2063]) ).
cnf(c_0_2063_2,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X4),X2))
| ~ c_Wellfounded_Oaccp(X1,X2,X3)
| c_Wellfounded_Oaccp(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2063]) ).
cnf(c_0_2064_0,axiom,
( c_Wellfounded_Oaccp(X1,X4,X3)
| ~ c_Wellfounded_Oaccp(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2064]) ).
cnf(c_0_2064_1,axiom,
( ~ c_Wellfounded_Oaccp(X1,X2,X3)
| c_Wellfounded_Oaccp(X1,X4,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2064]) ).
cnf(c_0_2064_2,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X4),X2))
| ~ c_Wellfounded_Oaccp(X1,X2,X3)
| c_Wellfounded_Oaccp(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2064]) ).
cnf(c_0_2065_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_2065]) ).
cnf(c_0_2065_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_2065]) ).
cnf(c_0_2065_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_2065]) ).
cnf(c_0_2066_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_2066]) ).
cnf(c_0_2066_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_2066]) ).
cnf(c_0_2066_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_2066]) ).
cnf(c_0_2067_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_2067]) ).
cnf(c_0_2067_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_2067]) ).
cnf(c_0_2067_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_2067]) ).
cnf(c_0_2068_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_2068]) ).
cnf(c_0_2068_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_2068]) ).
cnf(c_0_2068_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_2068]) ).
cnf(c_0_2069_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_2069]) ).
cnf(c_0_2069_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_2069]) ).
cnf(c_0_2069_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_2069]) ).
cnf(c_0_2070_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,X1))
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_2070]) ).
cnf(c_0_2070_1,axiom,
( ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2070]) ).
cnf(c_0_2071_0,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2071]) ).
cnf(c_0_2071_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2071]) ).
cnf(c_0_2071_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2071]) ).
cnf(c_0_2072_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2072]) ).
cnf(c_0_2072_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2072]) ).
cnf(c_0_2072_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2072]) ).
cnf(c_0_2073_0,axiom,
( c_Type_Otyping(X1,X4,X3)
| ~ c_Type_Otyping(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2073]) ).
cnf(c_0_2073_1,axiom,
( ~ c_Type_Otyping(X1,X2,X3)
| c_Type_Otyping(X1,X4,X3)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2073]) ).
cnf(c_0_2073_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X2),X4))
| ~ c_Type_Otyping(X1,X2,X3)
| c_Type_Otyping(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2073]) ).
cnf(c_0_2074_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_List_Olistsum(X1,X3)),c_List_Olistsum(X2,X3)) = c_List_Olistsum(c_List_Oappend(X1,X2,X3),X3)
| ~ class_OrderedGroup_Omonoid__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2074]) ).
cnf(c_0_2074_1,axiom,
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_List_Olistsum(X1,X3)),c_List_Olistsum(X2,X3)) = c_List_Olistsum(c_List_Oappend(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2074]) ).
cnf(c_0_2075_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2075]) ).
cnf(c_0_2075_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2075]) ).
cnf(c_0_2075_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2075]) ).
cnf(c_0_2076_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2076]) ).
cnf(c_0_2076_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2076]) ).
cnf(c_0_2076_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2076]) ).
cnf(c_0_2077_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2077]) ).
cnf(c_0_2077_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2077]) ).
cnf(c_0_2077_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2077]) ).
cnf(c_0_2078_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2078]) ).
cnf(c_0_2078_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2078]) ).
cnf(c_0_2078_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2078]) ).
cnf(c_0_2079_0,axiom,
( c_lessequals(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2079]) ).
cnf(c_0_2079_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2079]) ).
cnf(c_0_2079_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2079]) ).
cnf(c_0_2080_0,axiom,
( c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2080]) ).
cnf(c_0_2080_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2080]) ).
cnf(c_0_2080_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2080]) ).
cnf(c_0_2081_0,axiom,
( c_lessequals(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2081]) ).
cnf(c_0_2081_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2081]) ).
cnf(c_0_2081_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2081]) ).
cnf(c_0_2082_0,axiom,
( c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2082]) ).
cnf(c_0_2082_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2082]) ).
cnf(c_0_2082_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2082]) ).
cnf(c_0_2083_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2083]) ).
cnf(c_0_2083_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2083]) ).
cnf(c_0_2084_0,axiom,
( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = X1
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2084]) ).
cnf(c_0_2084_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2084]) ).
cnf(c_0_2085_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_2085]) ).
cnf(c_0_2085_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_2085]) ).
cnf(c_0_2086_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2086]) ).
cnf(c_0_2086_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2086]) ).
cnf(c_0_2087_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X1),c_Lambda_OdB_OVar(X2))))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2087]) ).
cnf(c_0_2087_1,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X1),c_Lambda_OdB_OVar(X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_2087]) ).
cnf(c_0_2088_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2088]) ).
cnf(c_0_2088_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2088]) ).
cnf(c_0_2089_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2089]) ).
cnf(c_0_2089_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2089]) ).
cnf(c_0_2090_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)) = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2090]) ).
cnf(c_0_2090_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2090]) ).
cnf(c_0_2091_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_2091]) ).
cnf(c_0_2091_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_2091]) ).
cnf(c_0_2091_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_2091]) ).
cnf(c_0_2091_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_2091]) ).
cnf(c_0_2092_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_2092]) ).
cnf(c_0_2092_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_2092]) ).
cnf(c_0_2092_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_2092]) ).
cnf(c_0_2092_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_2092]) ).
cnf(c_0_2093_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_2093]) ).
cnf(c_0_2093_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_2093]) ).
cnf(c_0_2093_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_2093]) ).
cnf(c_0_2093_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_2093]) ).
cnf(c_0_2094_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_2094]) ).
cnf(c_0_2094_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_2094]) ).
cnf(c_0_2094_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_2094]) ).
cnf(c_0_2094_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_2094]) ).
cnf(c_0_2095_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_2095]) ).
cnf(c_0_2095_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_2095]) ).
cnf(c_0_2095_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_2095]) ).
cnf(c_0_2095_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_2095]) ).
cnf(c_0_2096_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_2096]) ).
cnf(c_0_2096_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_2096]) ).
cnf(c_0_2096_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_2096]) ).
cnf(c_0_2096_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_2096]) ).
cnf(c_0_2097_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_2097]) ).
cnf(c_0_2097_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_2097]) ).
cnf(c_0_2097_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_2097]) ).
cnf(c_0_2097_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_2097]) ).
cnf(c_0_2098_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_2098]) ).
cnf(c_0_2098_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_2098]) ).
cnf(c_0_2098_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_2098]) ).
cnf(c_0_2098_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_2098]) ).
cnf(c_0_2099_0,axiom,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X1)),c_Lambda_OdB_OAbs(X2)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2099]) ).
cnf(c_0_2099_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X1)),c_Lambda_OdB_OAbs(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2099]) ).
cnf(c_0_2100_0,axiom,
( c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2100]) ).
cnf(c_0_2100_1,axiom,
( ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
| c_lessequals(X1,X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2100]) ).
cnf(c_0_2100_2,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
| c_lessequals(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2100]) ).
cnf(c_0_2101_0,axiom,
( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2101]) ).
cnf(c_0_2101_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
| c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2101]) ).
cnf(c_0_2101_2,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
| c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2101]) ).
cnf(c_0_2102_0,axiom,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2102]) ).
cnf(c_0_2102_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2102]) ).
cnf(c_0_2103_0,axiom,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2103]) ).
cnf(c_0_2103_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2103]) ).
cnf(c_0_2104_0,axiom,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2104]) ).
cnf(c_0_2104_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2104]) ).
cnf(c_0_2105_0,axiom,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2105]) ).
cnf(c_0_2105_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2105]) ).
cnf(c_0_2106_0,axiom,
( c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2106]) ).
cnf(c_0_2106_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2106]) ).
cnf(c_0_2107_0,axiom,
( c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2107]) ).
cnf(c_0_2107_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2107]) ).
cnf(c_0_2108_0,axiom,
( c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2108]) ).
cnf(c_0_2108_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2108]) ).
cnf(c_0_2109_0,axiom,
( c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2109]) ).
cnf(c_0_2109_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2109]) ).
cnf(c_0_2110_0,axiom,
( c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X1,X2,X3),X3) = c_Orderings_Oord__class_Omax(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2110]) ).
cnf(c_0_2110_1,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X1,X2,X3),X3) = c_Orderings_Oord__class_Omax(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2110]) ).
cnf(c_0_2111_0,axiom,
( c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2111]) ).
cnf(c_0_2111_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2111]) ).
cnf(c_0_2111_2,axiom,
( ~ c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2111]) ).
cnf(c_0_2112_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X1),X2)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2112]) ).
cnf(c_0_2112_1,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2112]) ).
cnf(c_0_2113_0,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X2,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X1),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2113]) ).
cnf(c_0_2113_1,axiom,
( hBOOL(hAPP(X1,X3))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X2,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X1),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2113]) ).
cnf(c_0_2113_2,axiom,
( ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X1,X3))
| hBOOL(hAPP(X1,X2))
| ~ c_HOL_Oord__class_Oless(X2,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X1),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2113]) ).
cnf(c_0_2113_3,axiom,
( ~ c_HOL_Oord__class_Oless(X2,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X1),tc_nat)
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X1,X3))
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2113]) ).
cnf(c_0_2114_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Lambda_Oliftn(X3,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2114]) ).
cnf(c_0_2114_1,axiom,
( c_Lambda_Oliftn(X3,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3))
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2114]) ).
cnf(c_0_2115_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),c_List_Olistsum(X2,X3)) = c_List_Olistsum(c_List_Olist_OCons(X1,X2,X3),X3)
| ~ class_OrderedGroup_Omonoid__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2115]) ).
cnf(c_0_2115_1,axiom,
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),c_List_Olistsum(X2,X3)) = c_List_Olistsum(c_List_Olist_OCons(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2115]) ).
cnf(c_0_2116_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2116]) ).
cnf(c_0_2116_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)) = X1
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2116]) ).
cnf(c_0_2117_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_2117]) ).
cnf(c_0_2117_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_2117]) ).
cnf(c_0_2117_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_2117]) ).
cnf(c_0_2117_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_2117]) ).
cnf(c_0_2118_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(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_2118]) ).
cnf(c_0_2118_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2118]) ).
cnf(c_0_2118_2,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2118]) ).
cnf(c_0_2119_0,axiom,
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X3),X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2119]) ).
cnf(c_0_2119_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X3),X2) = c_Lambda_OdB_OVar(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2119]) ).
cnf(c_0_2120_0,axiom,
( c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2120]) ).
cnf(c_0_2120_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2120]) ).
cnf(c_0_2120_2,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2120]) ).
cnf(c_0_2121_0,axiom,
( c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2121]) ).
cnf(c_0_2121_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2121]) ).
cnf(c_0_2121_2,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2121]) ).
cnf(c_0_2122_0,axiom,
( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2122]) ).
cnf(c_0_2122_1,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_2122]) ).
cnf(c_0_2123_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| hBOOL(hAPP(hAPP(X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2123]) ).
cnf(c_0_2123_1,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| hBOOL(hAPP(hAPP(X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2123]) ).
cnf(c_0_2123_2,axiom,
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| hBOOL(hAPP(hAPP(X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2123]) ).
cnf(c_0_2123_3,axiom,
( hBOOL(hAPP(hAPP(X3,X2),X1))
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2123]) ).
cnf(c_0_2124_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2124]) ).
cnf(c_0_2124_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2124]) ).
cnf(c_0_2124_2,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2124]) ).
cnf(c_0_2125_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_2125]) ).
cnf(c_0_2125_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_2125]) ).
cnf(c_0_2125_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_2125]) ).
cnf(c_0_2125_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_2125]) ).
cnf(c_0_2126_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_2126]) ).
cnf(c_0_2126_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_2126]) ).
cnf(c_0_2126_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_2126]) ).
cnf(c_0_2126_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_2126]) ).
cnf(c_0_2127_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_2127]) ).
cnf(c_0_2127_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_2127]) ).
cnf(c_0_2127_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_2127]) ).
cnf(c_0_2127_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_2127]) ).
cnf(c_0_2128_0,axiom,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2128]) ).
cnf(c_0_2128_1,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
| X1 = X2
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2128]) ).
cnf(c_0_2128_2,axiom,
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2128]) ).
cnf(c_0_2129_0,axiom,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
| ~ class_OrderedGroup_Oab__group__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2129]) ).
cnf(c_0_2129_1,axiom,
( c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
| X1 = X2
| ~ class_OrderedGroup_Oab__group__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2129]) ).
cnf(c_0_2129_2,axiom,
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2129]) ).
cnf(c_0_2130_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_2130]) ).
cnf(c_0_2130_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_2130]) ).
cnf(c_0_2130_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_2130]) ).
cnf(c_0_2130_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_2130]) ).
cnf(c_0_2131_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_2131]) ).
cnf(c_0_2131_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_2131]) ).
cnf(c_0_2131_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_2131]) ).
cnf(c_0_2132_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_2132]) ).
cnf(c_0_2132_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_2132]) ).
cnf(c_0_2132_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_2132]) ).
cnf(c_0_2133_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_2133]) ).
cnf(c_0_2133_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_2133]) ).
cnf(c_0_2133_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_2133]) ).
cnf(c_0_2134_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_2134]) ).
cnf(c_0_2134_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_2134]) ).
cnf(c_0_2134_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_2134]) ).
cnf(c_0_2135_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_2135]) ).
cnf(c_0_2135_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_2135]) ).
cnf(c_0_2135_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_2135]) ).
cnf(c_0_2136_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_2136]) ).
cnf(c_0_2136_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_2136]) ).
cnf(c_0_2136_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_2136]) ).
cnf(c_0_2137_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_2137]) ).
cnf(c_0_2137_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_2137]) ).
cnf(c_0_2137_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_2137]) ).
cnf(c_0_2138_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_2138]) ).
cnf(c_0_2138_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_2138]) ).
cnf(c_0_2138_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_2138]) ).
cnf(c_0_2139_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = X3
| c_List_Oreplicate(X1,X2,X4) != c_List_Oreplicate(X5,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2139]) ).
cnf(c_0_2139_1,axiom,
( X2 = X3
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_List_Oreplicate(X1,X2,X4) != c_List_Oreplicate(X5,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2139]) ).
cnf(c_0_2139_2,axiom,
( c_List_Oreplicate(X1,X2,X4) != c_List_Oreplicate(X5,X3,X4)
| X2 = X3
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2139]) ).
cnf(c_0_2140_0,axiom,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2140]) ).
cnf(c_0_2140_1,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = X2
| c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2140]) ).
cnf(c_0_2140_2,axiom,
( c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2140]) ).
cnf(c_0_2141_0,axiom,
( X1 = X2
| c_List_Oreplicate(X1,X3,X4) != c_List_Oreplicate(X2,X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2141]) ).
cnf(c_0_2141_1,axiom,
( c_List_Oreplicate(X1,X3,X4) != c_List_Oreplicate(X2,X5,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2141]) ).
cnf(c_0_2142_0,axiom,
( X1 = X2
| c_List_Oappend(X1,X3,X4) != c_List_Oappend(X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2142]) ).
cnf(c_0_2142_1,axiom,
( c_List_Oappend(X1,X3,X4) != c_List_Oappend(X2,X3,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2142]) ).
cnf(c_0_2143_0,axiom,
( X1 = X2
| c_List_Oappend(X3,X1,X4) != c_List_Oappend(X3,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2143]) ).
cnf(c_0_2143_1,axiom,
( c_List_Oappend(X3,X1,X4) != c_List_Oappend(X3,X2,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2143]) ).
cnf(c_0_2144_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_2144]) ).
cnf(c_0_2144_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_2144]) ).
cnf(c_0_2144_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_2144]) ).
cnf(c_0_2145_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_2145]) ).
cnf(c_0_2145_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_2145]) ).
cnf(c_0_2145_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_2145]) ).
cnf(c_0_2146_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_2146]) ).
cnf(c_0_2146_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_2146]) ).
cnf(c_0_2146_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_2146]) ).
cnf(c_0_2147_0,axiom,
( X1 = X2
| c_List_Olist_OCons(X1,X3,X4) != c_List_Olist_OCons(X2,X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2147]) ).
cnf(c_0_2147_1,axiom,
( c_List_Olist_OCons(X1,X3,X4) != c_List_Olist_OCons(X2,X5,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2147]) ).
cnf(c_0_2148_0,axiom,
( X1 = X2
| c_List_Olist_OCons(X3,X1,X4) != c_List_Olist_OCons(X5,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2148]) ).
cnf(c_0_2148_1,axiom,
( c_List_Olist_OCons(X3,X1,X4) != c_List_Olist_OCons(X5,X2,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2148]) ).
cnf(c_0_2149_0,axiom,
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X1),X2,X1) = c_Lambda_Oliftn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2149]) ).
cnf(c_0_2149_1,axiom,
( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
| c_Lambda_Osubstn(c_Lambda_OdB_OVar(X1),X2,X1) = c_Lambda_Oliftn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_2149]) ).
cnf(c_0_2150_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X2)),X3),X1) = c_Lambda_OdB_OVar(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2150]) ).
cnf(c_0_2150_1,axiom,
( X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X2)),X3),X1) = c_Lambda_OdB_OVar(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2150]) ).
cnf(c_0_2150_2,axiom,
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X2)),X3),X1) = c_Lambda_OdB_OVar(X2)
| X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2150]) ).
cnf(c_0_2151_0,axiom,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2151]) ).
cnf(c_0_2151_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| X1 = X2
| ~ c_lessequals(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2151]) ).
cnf(c_0_2151_2,axiom,
( ~ c_lessequals(X2,X1,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2151]) ).
cnf(c_0_2152_0,axiom,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2152]) ).
cnf(c_0_2152_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3))
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2152]) ).
cnf(c_0_2153_0,axiom,
( c_lessequals(X1,c_Orderings_Oord__class_Omax(X1,X2,X3),X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2153]) ).
cnf(c_0_2153_1,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X1,c_Orderings_Oord__class_Omax(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2153]) ).
cnf(c_0_2154_0,axiom,
( c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X1,X3),X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2154]) ).
cnf(c_0_2154_1,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2154]) ).
cnf(c_0_2155_0,axiom,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X3,X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2155]) ).
cnf(c_0_2155_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X3,X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2155]) ).
cnf(c_0_2156_0,axiom,
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1) = X2
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2156]) ).
cnf(c_0_2156_1,axiom,
( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
| hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2156]) ).
cnf(c_0_2157_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2157]) ).
cnf(c_0_2157_1,axiom,
( ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2157]) ).
cnf(c_0_2157_2,axiom,
( ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X1)))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2157]) ).
cnf(c_0_2158_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_2158]) ).
cnf(c_0_2158_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_2158]) ).
cnf(c_0_2158_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_2158]) ).
cnf(c_0_2158_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_2158]) ).
cnf(c_0_2159_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_2159]) ).
cnf(c_0_2159_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_2159]) ).
cnf(c_0_2159_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_2159]) ).
cnf(c_0_2159_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_2159]) ).
cnf(c_0_2160_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_2160]) ).
cnf(c_0_2160_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_2160]) ).
cnf(c_0_2160_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_2160]) ).
cnf(c_0_2160_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_2160]) ).
cnf(c_0_2161_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_2161]) ).
cnf(c_0_2161_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_2161]) ).
cnf(c_0_2161_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_2161]) ).
cnf(c_0_2161_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_2161]) ).
cnf(c_0_2162_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_2162]) ).
cnf(c_0_2162_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_2162]) ).
cnf(c_0_2162_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_2162]) ).
cnf(c_0_2162_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_2162]) ).
cnf(c_0_2163_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_2163]) ).
cnf(c_0_2163_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_2163]) ).
cnf(c_0_2163_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_2163]) ).
cnf(c_0_2163_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_2163]) ).
cnf(c_0_2164_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_2164]) ).
cnf(c_0_2164_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_2164]) ).
cnf(c_0_2164_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_2164]) ).
cnf(c_0_2164_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_2164]) ).
cnf(c_0_2165_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_2165]) ).
cnf(c_0_2165_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_2165]) ).
cnf(c_0_2165_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_2165]) ).
cnf(c_0_2165_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_2165]) ).
cnf(c_0_2166_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X1),tc_nat)
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(literals_permutation,[status(thm)],[c_0_2166]) ).
cnf(c_0_2166_1,axiom,
( hBOOL(hAPP(X1,X2))
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X1),tc_nat)
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(literals_permutation,[status(thm)],[c_0_2166]) ).
cnf(c_0_2166_2,axiom,
( ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X1,X2))
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X1),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2166]) ).
cnf(c_0_2167_0,axiom,
( c_lessequals(X1,X2,X3)
| c_Orderings_Oord__class_Omax(X1,X2,X3) != X2
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2167]) ).
cnf(c_0_2167_1,axiom,
( c_Orderings_Oord__class_Omax(X1,X2,X3) != X2
| c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2167]) ).
cnf(c_0_2167_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_Orderings_Oord__class_Omax(X1,X2,X3) != X2
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2167]) ).
cnf(c_0_2168_0,axiom,
( c_Orderings_Oord__class_Omax(X2,X1,X3) = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2168]) ).
cnf(c_0_2168_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_Orderings_Oord__class_Omax(X2,X1,X3) = X2
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2168]) ).
cnf(c_0_2168_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X1,X2,X3)
| c_Orderings_Oord__class_Omax(X2,X1,X3) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2168]) ).
cnf(c_0_2169_0,axiom,
( c_Orderings_Oord__class_Omax(X1,X2,X3) = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2169]) ).
cnf(c_0_2169_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_Orderings_Oord__class_Omax(X1,X2,X3) = X2
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2169]) ).
cnf(c_0_2169_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X1,X2,X3)
| c_Orderings_Oord__class_Omax(X1,X2,X3) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2169]) ).
cnf(c_0_2170_0,axiom,
( c_Lambda_Oliftn(X3,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2170]) ).
cnf(c_0_2170_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Lambda_Oliftn(X3,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2170]) ).
cnf(c_0_2171_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_2171]) ).
cnf(c_0_2171_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_2171]) ).
cnf(c_0_2171_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_2171]) ).
cnf(c_0_2172_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_2172]) ).
cnf(c_0_2172_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_2172]) ).
cnf(c_0_2172_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_2172]) ).
cnf(c_0_2173_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_2173]) ).
cnf(c_0_2173_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_2173]) ).
cnf(c_0_2174_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_2174]) ).
cnf(c_0_2174_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_2174]) ).
cnf(c_0_2175_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_2175]) ).
cnf(c_0_2175_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_2175]) ).
cnf(c_0_2176_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_2176]) ).
cnf(c_0_2176_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_2176]) ).
cnf(c_0_2177_0,axiom,
( c_lessequals(X1,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2177]) ).
cnf(c_0_2177_1,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2177]) ).
cnf(c_0_2178_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2178]) ).
cnf(c_0_2178_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2178]) ).
cnf(c_0_2179_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2179]) ).
cnf(c_0_2179_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2179]) ).
cnf(c_0_2179_2,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2179]) ).
cnf(c_0_2180_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2180]) ).
cnf(c_0_2180_1,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2180]) ).
cnf(c_0_2180_2,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2180]) ).
cnf(c_0_2181_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2181]) ).
cnf(c_0_2181_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2181]) ).
cnf(c_0_2181_2,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2181]) ).
cnf(c_0_2182_0,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2182]) ).
cnf(c_0_2182_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2182]) ).
cnf(c_0_2183_0,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2183]) ).
cnf(c_0_2183_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2183]) ).
cnf(c_0_2184_0,axiom,
( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X1)),X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2184]) ).
cnf(c_0_2184_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X1)),X2) = c_Lambda_OdB_OVar(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2184]) ).
cnf(c_0_2185_0,axiom,
( hBOOL(hAPP(X1,v_sko__Nat__Xnat__Xinducts__1(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(literals_permutation,[status(thm)],[c_0_2185]) ).
cnf(c_0_2185_1,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,v_sko__Nat__Xnat__Xinducts__1(X1)))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(literals_permutation,[status(thm)],[c_0_2185]) ).
cnf(c_0_2185_2,axiom,
( ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,v_sko__Nat__Xnat__Xinducts__1(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2185]) ).
cnf(c_0_2186_0,axiom,
( hBOOL(hAPP(X1,v_sko__Nat__Xnat__Xinduct__1(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(literals_permutation,[status(thm)],[c_0_2186]) ).
cnf(c_0_2186_1,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,v_sko__Nat__Xnat__Xinduct__1(X1)))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(literals_permutation,[status(thm)],[c_0_2186]) ).
cnf(c_0_2186_2,axiom,
( ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,v_sko__Nat__Xnat__Xinduct__1(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2186]) ).
cnf(c_0_2187_0,axiom,
( hBOOL(hAPP(X1,v_sko__List__Xupt__Xinduct__1(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(literals_permutation,[status(thm)],[c_0_2187]) ).
cnf(c_0_2187_1,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,v_sko__List__Xupt__Xinduct__1(X1)))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(literals_permutation,[status(thm)],[c_0_2187]) ).
cnf(c_0_2187_2,axiom,
( ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,v_sko__List__Xupt__Xinduct__1(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2187]) ).
cnf(c_0_2188_0,axiom,
( hAPP(hAPP(X2,X4),X1) = X4
| ~ c_OrderedGroup_Omonoid__add(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2188]) ).
cnf(c_0_2188_1,axiom,
( ~ c_OrderedGroup_Omonoid__add(X1,X2,X3)
| hAPP(hAPP(X2,X4),X1) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_2188]) ).
cnf(c_0_2189_0,axiom,
( hAPP(hAPP(X2,X1),X4) = X4
| ~ c_OrderedGroup_Omonoid__add(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2189]) ).
cnf(c_0_2189_1,axiom,
( ~ c_OrderedGroup_Omonoid__add(X1,X2,X3)
| hAPP(hAPP(X2,X1),X4) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_2189]) ).
cnf(c_0_2190_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != 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_2190]) ).
cnf(c_0_2190_1,axiom,
( c_Power_Opower__class_Opower(X1,X3,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_2190]) ).
cnf(c_0_2190_2,axiom,
( ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != 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_2190]) ).
cnf(c_0_2190_3,axiom,
( ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != 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_2190]) ).
cnf(c_0_2190_4,axiom,
( ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != 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_2190]) ).
cnf(c_0_2190_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)
| c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2190]) ).
cnf(c_0_2191_0,axiom,
( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) != 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_2191]) ).
cnf(c_0_2191_1,axiom,
( ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) != 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_2191]) ).
cnf(c_0_2191_2,axiom,
( ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) != 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_2191]) ).
cnf(c_0_2191_3,axiom,
( ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2191]) ).
cnf(c_0_2191_4,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)
| c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) != c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2191]) ).
cnf(c_0_2192_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| c_Lambda_Osubstn(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2192]) ).
cnf(c_0_2192_1,axiom,
( X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Lambda_Osubstn(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2192]) ).
cnf(c_0_2192_2,axiom,
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2)
| X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2192]) ).
cnf(c_0_2193_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_2193]) ).
cnf(c_0_2193_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_2193]) ).
cnf(c_0_2193_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_2193]) ).
cnf(c_0_2193_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_2193]) ).
cnf(c_0_2194_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_2194]) ).
cnf(c_0_2194_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_2194]) ).
cnf(c_0_2194_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_2194]) ).
cnf(c_0_2194_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_2194]) ).
cnf(c_0_2195_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_2195]) ).
cnf(c_0_2195_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_2195]) ).
cnf(c_0_2195_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_2195]) ).
cnf(c_0_2195_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_2195]) ).
cnf(c_0_2196_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_2196]) ).
cnf(c_0_2196_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_2196]) ).
cnf(c_0_2196_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_2196]) ).
cnf(c_0_2196_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_2196]) ).
cnf(c_0_2197_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_2197]) ).
cnf(c_0_2197_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_2197]) ).
cnf(c_0_2197_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_2197]) ).
cnf(c_0_2197_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_2197]) ).
cnf(c_0_2198_0,axiom,
( X1 = X2
| hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2198]) ).
cnf(c_0_2198_1,axiom,
( hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2198]) ).
cnf(c_0_2199_0,axiom,
( X1 = X2
| hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2199]) ).
cnf(c_0_2199_1,axiom,
( hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X4),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2199]) ).
cnf(c_0_2200_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_2200]) ).
cnf(c_0_2200_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_2200]) ).
cnf(c_0_2200_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_2200]) ).
cnf(c_0_2201_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_2201]) ).
cnf(c_0_2201_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_2201]) ).
cnf(c_0_2201_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_2201]) ).
cnf(c_0_2202_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_2202]) ).
cnf(c_0_2202_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_2202]) ).
cnf(c_0_2202_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_2202]) ).
cnf(c_0_2203_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_2203]) ).
cnf(c_0_2203_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_2203]) ).
cnf(c_0_2203_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_2203]) ).
cnf(c_0_2204_0,axiom,
( c_lessequals(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2204]) ).
cnf(c_0_2204_1,axiom,
( c_lessequals(X2,X1,X3)
| c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2204]) ).
cnf(c_0_2204_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X2,X1,X3)
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2204]) ).
cnf(c_0_2205_0,axiom,
( c_Orderings_Oord__class_Omax(X1,X2,X3) = c_Orderings_Oord__class_Omax(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2205]) ).
cnf(c_0_2205_1,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_Orderings_Oord__class_Omax(X1,X2,X3) = c_Orderings_Oord__class_Omax(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2205]) ).
cnf(c_0_2206_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_2206]) ).
cnf(c_0_2206_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_2206]) ).
cnf(c_0_2207_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_2207]) ).
cnf(c_0_2207_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_2207]) ).
cnf(c_0_2208_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_2208]) ).
cnf(c_0_2208_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_2208]) ).
cnf(c_0_2209_0,axiom,
( hAPP(X1,X2) = X3
| ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2209]) ).
cnf(c_0_2209_1,axiom,
( ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3)
| hAPP(X1,X2) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2209]) ).
cnf(c_0_2210_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2210]) ).
cnf(c_0_2210_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2210]) ).
cnf(c_0_2210_2,axiom,
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2210]) ).
cnf(c_0_2211_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2211]) ).
cnf(c_0_2211_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2211]) ).
cnf(c_0_2211_2,axiom,
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2211]) ).
cnf(c_0_2212_0,axiom,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2212]) ).
cnf(c_0_2212_1,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2212]) ).
cnf(c_0_2212_2,axiom,
( ~ class_Int_Onumber__ring(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2212]) ).
cnf(c_0_2212_3,axiom,
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2212]) ).
cnf(c_0_2213_0,axiom,
( c_lessequals(X1,X2,tc_nat)
| c_lessequals(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2213]) ).
cnf(c_0_2213_1,axiom,
( c_lessequals(X2,X1,tc_nat)
| c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2213]) ).
cnf(c_0_2214_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2214]) ).
cnf(c_0_2214_1,axiom,
( c_Power_Opower__class_Opower(X1,X3,X2) != 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_2214]) ).
cnf(c_0_2214_2,axiom,
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2214]) ).
cnf(c_0_2215_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_2215]) ).
cnf(c_0_2215_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_2215]) ).
cnf(c_0_2215_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_2215]) ).
cnf(c_0_2215_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_2215]) ).
cnf(c_0_2216_0,axiom,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2216]) ).
cnf(c_0_2216_1,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2216]) ).
cnf(c_0_2216_2,axiom,
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2216]) ).
cnf(c_0_2217_0,axiom,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2217]) ).
cnf(c_0_2217_1,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2217]) ).
cnf(c_0_2217_2,axiom,
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2217]) ).
cnf(c_0_2218_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_2218]) ).
cnf(c_0_2218_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_2218]) ).
cnf(c_0_2218_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_2218]) ).
cnf(c_0_2219_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X1,X3,X2) != c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2219]) ).
cnf(c_0_2219_1,axiom,
( c_List_Oappend(X1,X3,X2) != c_List_Olist_ONil(X2)
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2219]) ).
cnf(c_0_2220_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X3,X1,X2) != c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2220]) ).
cnf(c_0_2220_1,axiom,
( c_List_Oappend(X3,X1,X2) != c_List_Olist_ONil(X2)
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2220]) ).
cnf(c_0_2221_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X1,X3,X2) != c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2221]) ).
cnf(c_0_2221_1,axiom,
( c_List_Oappend(X1,X3,X2) != c_List_Olist_ONil(X2)
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2221]) ).
cnf(c_0_2222_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X3,X1,X2) != c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2222]) ).
cnf(c_0_2222_1,axiom,
( c_List_Oappend(X3,X1,X2) != c_List_Olist_ONil(X2)
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2222]) ).
cnf(c_0_2223_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = 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_2223]) ).
cnf(c_0_2223_1,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = 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_2223]) ).
cnf(c_0_2223_2,axiom,
( ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = 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_2223]) ).
cnf(c_0_2223_3,axiom,
( ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = 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_2223]) ).
cnf(c_0_2223_4,axiom,
( ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = 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_2223]) ).
cnf(c_0_2223_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)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2223]) ).
cnf(c_0_2224_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_List_Oreplicate(X1,X2,X3) != c_List_Olist_ONil(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2224]) ).
cnf(c_0_2224_1,axiom,
( c_List_Oreplicate(X1,X2,X3) != c_List_Olist_ONil(X3)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2224]) ).
cnf(c_0_2225_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_List_Oreplicate(X1,X3,X2) != c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2225]) ).
cnf(c_0_2225_1,axiom,
( c_List_Oreplicate(X1,X3,X2) != c_List_Olist_ONil(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2225]) ).
cnf(c_0_2226_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_2226]) ).
cnf(c_0_2226_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_2226]) ).
cnf(c_0_2227_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_2227]) ).
cnf(c_0_2227_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_2227]) ).
cnf(c_0_2228_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2228]) ).
cnf(c_0_2228_1,axiom,
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2228]) ).
cnf(c_0_2229_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2229]) ).
cnf(c_0_2229_1,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2229]) ).
cnf(c_0_2230_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2230]) ).
cnf(c_0_2230_1,axiom,
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2230]) ).
cnf(c_0_2231_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X3,X1,X2) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_2231]) ).
cnf(c_0_2231_1,axiom,
( c_List_Oappend(X3,X1,X2) != X3
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2231]) ).
cnf(c_0_2232_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X3,X1,X2) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_2232]) ).
cnf(c_0_2232_1,axiom,
( c_List_Oappend(X3,X1,X2) != X3
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2232]) ).
cnf(c_0_2233_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X1,X3,X2) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_2233]) ).
cnf(c_0_2233_1,axiom,
( c_List_Oappend(X1,X3,X2) != X3
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2233]) ).
cnf(c_0_2234_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X1,X3,X2) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_2234]) ).
cnf(c_0_2234_1,axiom,
( c_List_Oappend(X1,X3,X2) != X3
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2234]) ).
cnf(c_0_2235_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2235]) ).
cnf(c_0_2235_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2235]) ).
cnf(c_0_2236_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Osemiring__0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2236]) ).
cnf(c_0_2236_1,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = 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_2236]) ).
cnf(c_0_2236_2,axiom,
( ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = 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_2236]) ).
cnf(c_0_2236_3,axiom,
( ~ class_Ring__and__Field_Osemiring__0(X2)
| ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2236]) ).
cnf(c_0_2237_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2237]) ).
cnf(c_0_2237_1,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2237]) ).
cnf(c_0_2238_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_2238]) ).
cnf(c_0_2238_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_2238]) ).
cnf(c_0_2239_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_2239]) ).
cnf(c_0_2239_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_2239]) ).
cnf(c_0_2240_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_2240]) ).
cnf(c_0_2240_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_2240]) ).
cnf(c_0_2241_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_2241]) ).
cnf(c_0_2241_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_2241]) ).
cnf(c_0_2242_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_2242]) ).
cnf(c_0_2242_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_2242]) ).
cnf(c_0_2243_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_2243]) ).
cnf(c_0_2243_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_2243]) ).
cnf(c_0_2243_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_2243]) ).
cnf(c_0_2244_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2244]) ).
cnf(c_0_2244_1,axiom,
( ~ class_Int_Onumber__ring(X2)
| c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2244]) ).
cnf(c_0_2244_2,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2244]) ).
cnf(c_0_2245_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_2245]) ).
cnf(c_0_2245_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_2245]) ).
cnf(c_0_2246_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_2246]) ).
cnf(c_0_2246_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_2246]) ).
cnf(c_0_2247_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_2247]) ).
cnf(c_0_2247_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_2247]) ).
cnf(c_0_2248_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_2248]) ).
cnf(c_0_2248_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_2248]) ).
cnf(c_0_2249_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2249]) ).
cnf(c_0_2249_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2249]) ).
cnf(c_0_2250_0,axiom,
( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
| ~ class_Orderings_Obot(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2250]) ).
cnf(c_0_2250_1,axiom,
( ~ class_Orderings_Obot(X1)
| c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2250]) ).
cnf(c_0_2251_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_2251]) ).
cnf(c_0_2251_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_2251]) ).
cnf(c_0_2252_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_2252]) ).
cnf(c_0_2252_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_2252]) ).
cnf(c_0_2253_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_2253]) ).
cnf(c_0_2253_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_2253]) ).
cnf(c_0_2254_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2254]) ).
cnf(c_0_2254_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2254]) ).
cnf(c_0_2255_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2255]) ).
cnf(c_0_2255_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2255]) ).
cnf(c_0_2256_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2256]) ).
cnf(c_0_2256_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X2)
| c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2256]) ).
cnf(c_0_2257_0,axiom,
( c_Orderings_Oord__class_Omax(X1,X1,X2) = X1
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2257]) ).
cnf(c_0_2257_1,axiom,
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omax(X1,X1,X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2257]) ).
cnf(c_0_2258_0,axiom,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2258]) ).
cnf(c_0_2258_1,axiom,
( ~ class_Orderings_Oorder(X2)
| c_lessequals(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2258]) ).
cnf(c_0_2259_0,axiom,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2259]) ).
cnf(c_0_2259_1,axiom,
( ~ class_Orderings_Opreorder(X2)
| c_lessequals(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2259]) ).
cnf(c_0_2260_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2260]) ).
cnf(c_0_2260_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2260]) ).
cnf(c_0_2261_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_2261]) ).
cnf(c_0_2261_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_2261]) ).
cnf(c_0_2261_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_2261]) ).
cnf(c_0_2262_0,axiom,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2262]) ).
cnf(c_0_2262_1,axiom,
( ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2262]) ).
cnf(c_0_2263_0,axiom,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2263]) ).
cnf(c_0_2263_1,axiom,
( ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2263]) ).
cnf(c_0_2264_0,axiom,
( class_Orderings_Obot(tc_fun(X2,X1))
| ~ class_Orderings_Obot(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2264]) ).
cnf(c_0_2264_1,axiom,
( ~ class_Orderings_Obot(X1)
| class_Orderings_Obot(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2264]) ).
cnf(c_0_2265_0,axiom,
( c_List_Olistsum(c_List_Olist_ONil(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2265]) ).
cnf(c_0_2265_1,axiom,
( ~ class_OrderedGroup_Omonoid__add(X1)
| c_List_Olistsum(c_List_Olist_ONil(X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2265]) ).
cnf(c_0_2266_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_2266]) ).
cnf(c_0_2266_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_2266]) ).
cnf(c_0_2267_0,axiom,
( c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(X1),X1)
| ~ class_OrderedGroup_Osemigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2267]) ).
cnf(c_0_2267_1,axiom,
( ~ class_OrderedGroup_Osemigroup__add(X1)
| c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2267]) ).
cnf(c_0_2268_0,axiom,
( X1 = X2
| c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2268]) ).
cnf(c_0_2268_1,axiom,
( c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2268]) ).
cnf(c_0_2269_0,axiom,
( X1 = X2
| c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2269]) ).
cnf(c_0_2269_1,axiom,
( c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2269]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_851,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))),
file('<stdin>',cls_conjecture_0) ).
fof(c_0_1_852,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_2_853,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))),
c_0_1 ).
cnf(c_0_3_854,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4_855,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))),
c_0_3,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_0,plain,
( ~ c_Type_Otyping(X0,X1,v_T____)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| ~ c_Type_Otyping(c_Type_Oshift(X0,X2,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X3)
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),X1),X2))) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_52d6a3.p',c_0_1816_0) ).
cnf(c_1688,plain,
( ~ c_Type_Otyping(X0,X1,v_T____)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| ~ c_Type_Otyping(c_Type_Oshift(X0,X2,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X3)
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),X1),X2))) ),
inference(copy,[status(esa)],[c_0]) ).
cnf(c_34466,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),X0)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,v_u____))
| ~ c_Type_Otyping(c_Type_Oshift(X1,X0,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X2)
| ~ c_Type_Otyping(X1,v_u____,v_T____) ),
inference(instantiation,[status(thm)],[c_1688]) ).
cnf(c_56282,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),X0)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,v_u____))
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,X0,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X1)
| ~ c_Type_Otyping(v_e____,v_u____,v_T____) ),
inference(instantiation,[status(thm)],[c_34466]) ).
cnf(c_86578,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,v_u____))
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____)
| ~ c_Type_Otyping(v_e____,v_u____,v_T____) ),
inference(instantiation,[status(thm)],[c_56282]) ).
cnf(c_1217,plain,
c_Type_Otyping(v_e____,v_u____,v_T____),
file('/export/starexec/sandbox2/tmp/iprover_modulo_52d6a3.p',c_0_838_0) ).
cnf(c_1218,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
file('/export/starexec/sandbox2/tmp/iprover_modulo_52d6a3.p',c_0_837_0) ).
cnf(c_1219,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
file('/export/starexec/sandbox2/tmp/iprover_modulo_52d6a3.p',c_0_836_0) ).
cnf(c_1376,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))),
file('/export/starexec/sandbox2/tmp/iprover_modulo_52d6a3.p',c_0_4) ).
cnf(contradiction,plain,
$false,
inference(minisat,[status(thm)],[c_86578,c_1217,c_1218,c_1219,c_1376]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL836-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : iprover_modulo %s %d
% 0.08/0.36 % Computer : n017.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 5 17:12:37 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.13/0.36 % Running in mono-core mode
% 0.19/0.54 % Orienting using strategy Equiv(ClausalAll)
% 0.19/0.54 % Orientation found
% 0.19/0.54 % 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/sandbox2/tmp/iprover_proof_2c6c01.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_52d6a3.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_4343e8 | grep -v "SZS"
% 0.31/0.57
% 0.31/0.57 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.31/0.57
% 0.31/0.57 %
% 0.31/0.57 % ------ iProver source info
% 0.31/0.57
% 0.31/0.57 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.31/0.57 % git: non_committed_changes: true
% 0.31/0.57 % git: last_make_outside_of_git: true
% 0.31/0.57
% 0.31/0.57 %
% 0.31/0.57 % ------ Input Options
% 0.31/0.57
% 0.31/0.57 % --out_options all
% 0.31/0.57 % --tptp_safe_out true
% 0.31/0.57 % --problem_path ""
% 0.31/0.57 % --include_path ""
% 0.31/0.57 % --clausifier .//eprover
% 0.31/0.57 % --clausifier_options --tstp-format
% 0.31/0.57 % --stdin false
% 0.31/0.57 % --dbg_backtrace false
% 0.31/0.57 % --dbg_dump_prop_clauses false
% 0.31/0.57 % --dbg_dump_prop_clauses_file -
% 0.31/0.57 % --dbg_out_stat false
% 0.31/0.57
% 0.31/0.57 % ------ General Options
% 0.31/0.57
% 0.31/0.57 % --fof false
% 0.31/0.57 % --time_out_real 150.
% 0.31/0.57 % --time_out_prep_mult 0.2
% 0.31/0.57 % --time_out_virtual -1.
% 0.31/0.57 % --schedule none
% 0.31/0.57 % --ground_splitting input
% 0.31/0.57 % --splitting_nvd 16
% 0.31/0.57 % --non_eq_to_eq false
% 0.31/0.57 % --prep_gs_sim true
% 0.31/0.57 % --prep_unflatten false
% 0.31/0.57 % --prep_res_sim true
% 0.31/0.57 % --prep_upred true
% 0.31/0.57 % --res_sim_input true
% 0.31/0.57 % --clause_weak_htbl true
% 0.31/0.57 % --gc_record_bc_elim false
% 0.31/0.57 % --symbol_type_check false
% 0.31/0.57 % --clausify_out false
% 0.31/0.57 % --large_theory_mode false
% 0.31/0.57 % --prep_sem_filter none
% 0.31/0.57 % --prep_sem_filter_out false
% 0.31/0.57 % --preprocessed_out false
% 0.31/0.57 % --sub_typing false
% 0.31/0.57 % --brand_transform false
% 0.31/0.57 % --pure_diseq_elim true
% 0.31/0.57 % --min_unsat_core false
% 0.31/0.57 % --pred_elim true
% 0.31/0.57 % --add_important_lit false
% 0.31/0.57 % --soft_assumptions false
% 0.31/0.57 % --reset_solvers false
% 0.31/0.57 % --bc_imp_inh []
% 0.31/0.57 % --conj_cone_tolerance 1.5
% 0.31/0.57 % --prolific_symb_bound 500
% 0.31/0.57 % --lt_threshold 2000
% 0.31/0.57
% 0.31/0.57 % ------ SAT Options
% 0.31/0.57
% 0.31/0.57 % --sat_mode false
% 0.31/0.57 % --sat_fm_restart_options ""
% 0.31/0.57 % --sat_gr_def false
% 0.31/0.57 % --sat_epr_types true
% 0.31/0.57 % --sat_non_cyclic_types false
% 0.31/0.57 % --sat_finite_models false
% 0.31/0.57 % --sat_fm_lemmas false
% 0.31/0.57 % --sat_fm_prep false
% 0.31/0.57 % --sat_fm_uc_incr true
% 0.31/0.57 % --sat_out_model small
% 0.31/0.57 % --sat_out_clauses false
% 0.31/0.57
% 0.31/0.57 % ------ QBF Options
% 0.31/0.57
% 0.31/0.57 % --qbf_mode false
% 0.31/0.57 % --qbf_elim_univ true
% 0.31/0.57 % --qbf_sk_in true
% 0.31/0.57 % --qbf_pred_elim true
% 0.31/0.57 % --qbf_split 32
% 0.31/0.57
% 0.31/0.57 % ------ BMC1 Options
% 0.31/0.57
% 0.31/0.57 % --bmc1_incremental false
% 0.31/0.57 % --bmc1_axioms reachable_all
% 0.31/0.57 % --bmc1_min_bound 0
% 0.31/0.57 % --bmc1_max_bound -1
% 0.31/0.57 % --bmc1_max_bound_default -1
% 0.31/0.57 % --bmc1_symbol_reachability true
% 0.31/0.57 % --bmc1_property_lemmas false
% 0.31/0.57 % --bmc1_k_induction false
% 0.31/0.57 % --bmc1_non_equiv_states false
% 0.31/0.57 % --bmc1_deadlock false
% 0.31/0.57 % --bmc1_ucm false
% 0.31/0.57 % --bmc1_add_unsat_core none
% 0.31/0.57 % --bmc1_unsat_core_children false
% 0.31/0.57 % --bmc1_unsat_core_extrapolate_axioms false
% 0.31/0.57 % --bmc1_out_stat full
% 0.31/0.57 % --bmc1_ground_init false
% 0.31/0.57 % --bmc1_pre_inst_next_state false
% 0.31/0.57 % --bmc1_pre_inst_state false
% 0.31/0.57 % --bmc1_pre_inst_reach_state false
% 0.31/0.57 % --bmc1_out_unsat_core false
% 0.31/0.57 % --bmc1_aig_witness_out false
% 0.31/0.57 % --bmc1_verbose false
% 0.31/0.57 % --bmc1_dump_clauses_tptp false
% 3.89/4.23 % --bmc1_dump_unsat_core_tptp false
% 3.89/4.23 % --bmc1_dump_file -
% 3.89/4.23 % --bmc1_ucm_expand_uc_limit 128
% 3.89/4.23 % --bmc1_ucm_n_expand_iterations 6
% 3.89/4.23 % --bmc1_ucm_extend_mode 1
% 3.89/4.23 % --bmc1_ucm_init_mode 2
% 3.89/4.23 % --bmc1_ucm_cone_mode none
% 3.89/4.23 % --bmc1_ucm_reduced_relation_type 0
% 3.89/4.23 % --bmc1_ucm_relax_model 4
% 3.89/4.23 % --bmc1_ucm_full_tr_after_sat true
% 3.89/4.23 % --bmc1_ucm_expand_neg_assumptions false
% 3.89/4.23 % --bmc1_ucm_layered_model none
% 3.89/4.23 % --bmc1_ucm_max_lemma_size 10
% 3.89/4.23
% 3.89/4.23 % ------ AIG Options
% 3.89/4.23
% 3.89/4.23 % --aig_mode false
% 3.89/4.23
% 3.89/4.23 % ------ Instantiation Options
% 3.89/4.23
% 3.89/4.23 % --instantiation_flag true
% 3.89/4.23 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 3.89/4.23 % --inst_solver_per_active 750
% 3.89/4.23 % --inst_solver_calls_frac 0.5
% 3.89/4.23 % --inst_passive_queue_type priority_queues
% 3.89/4.23 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 3.89/4.23 % --inst_passive_queues_freq [25;2]
% 3.89/4.23 % --inst_dismatching true
% 3.89/4.23 % --inst_eager_unprocessed_to_passive true
% 3.89/4.23 % --inst_prop_sim_given true
% 3.89/4.23 % --inst_prop_sim_new false
% 3.89/4.23 % --inst_orphan_elimination true
% 3.89/4.23 % --inst_learning_loop_flag true
% 3.89/4.23 % --inst_learning_start 3000
% 3.89/4.23 % --inst_learning_factor 2
% 3.89/4.23 % --inst_start_prop_sim_after_learn 3
% 3.89/4.23 % --inst_sel_renew solver
% 3.89/4.23 % --inst_lit_activity_flag true
% 3.89/4.23 % --inst_out_proof true
% 3.89/4.23
% 3.89/4.23 % ------ Resolution Options
% 3.89/4.23
% 3.89/4.23 % --resolution_flag true
% 3.89/4.23 % --res_lit_sel kbo_max
% 3.89/4.23 % --res_to_prop_solver none
% 3.89/4.23 % --res_prop_simpl_new false
% 3.89/4.23 % --res_prop_simpl_given false
% 3.89/4.23 % --res_passive_queue_type priority_queues
% 3.89/4.23 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 3.89/4.23 % --res_passive_queues_freq [15;5]
% 3.89/4.23 % --res_forward_subs full
% 3.89/4.23 % --res_backward_subs full
% 3.89/4.23 % --res_forward_subs_resolution true
% 3.89/4.23 % --res_backward_subs_resolution true
% 3.89/4.23 % --res_orphan_elimination false
% 3.89/4.23 % --res_time_limit 1000.
% 3.89/4.23 % --res_out_proof true
% 3.89/4.23 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_2c6c01.s
% 3.89/4.23 % --modulo true
% 3.89/4.23
% 3.89/4.23 % ------ Combination Options
% 3.89/4.23
% 3.89/4.23 % --comb_res_mult 1000
% 3.89/4.23 % --comb_inst_mult 300
% 3.89/4.23 % ------
% 3.89/4.23
% 3.89/4.23 % ------ Parsing...% successful
% 3.89/4.23
% 3.89/4.23 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e pe_s pe_e snvd_s sp: 0 0s snvd_e %
% 3.89/4.23
% 3.89/4.23 % ------ Proving...
% 3.89/4.23 % ------ Problem Properties
% 3.89/4.23
% 3.89/4.23 %
% 3.89/4.23 % EPR false
% 3.89/4.23 % Horn false
% 3.89/4.23 % Has equality true
% 3.89/4.23
% 3.89/4.23 % % ------ Input Options Time Limit: Unbounded
% 3.89/4.23
% 3.89/4.23
% 3.89/4.23 Compiling...
% 3.89/4.23 Loading plugin: done.
% 3.89/4.23 Compiling...
% 3.89/4.23 Loading plugin: done.
% 3.89/4.23 Compiling...
% 3.89/4.23 Loading plugin: done.
% 3.89/4.23 Compiling...
% 3.89/4.23 Loading plugin: done.
% 3.89/4.23 Compiling...
% 3.89/4.23 Loading plugin: done.
% 3.89/4.23 Compiling...
% 3.89/4.23 Loading plugin: done.
% 3.89/4.23 Compiling...
% 3.89/4.23 Loading plugin: done.
% 3.89/4.23 Compiling...
% 3.89/4.23 Loading plugin: done.
% 3.89/4.23 Compiling...
% 3.89/4.23 Loading plugin: done.
% 3.89/4.23 Compiling...
% 3.89/4.23 Loading plugin: done.
% 3.89/4.23 Compiling...
% 3.89/4.23 Loading plugin: done.
% 3.89/4.23 Compiling...
% 3.89/4.23 Loading plugin: done.
% 3.89/4.23 Compiling...
% 3.89/4.23 Loading plugin: done.
% 3.89/4.23 Compiling...
% 3.89/4.23 Loading plugin: done.
% 3.89/4.23 Compiling...
% 3.89/4.23 Loading plugin: done.
% 3.89/4.23 Compiling...
% 3.89/4.23 Loading plugin: done.
% 3.89/4.23 Compiling...
% 3.89/4.23 Loading plugin: done.
% 3.89/4.23 Compiling...
% 3.89/4.23 Loading plugin: done.
% 3.89/4.23 Compiling...
% 3.89/4.23 Loading plugin: done.
% 3.89/4.23 Compiling...
% 3.89/4.23 Loading plugin: done.
% 3.89/4.23 Compiling...
% 3.89/4.23 Loading plugin: done.
% 3.89/4.23 % % ------ Current options:
% 3.89/4.23
% 3.89/4.23 % ------ Input Options
% 3.89/4.23
% 3.89/4.23 % --out_options all
% 3.89/4.23 % --tptp_safe_out true
% 3.89/4.23 % --problem_path ""
% 3.89/4.23 % --include_path ""
% 3.89/4.23 % --clausifier .//eprover
% 3.89/4.23 % --clausifier_options --tstp-format
% 3.89/4.23 % --stdin false
% 3.89/4.23 % --dbg_backtrace false
% 3.89/4.23 % --dbg_dump_prop_clauses false
% 3.89/4.23 % --dbg_dump_prop_clauses_file -
% 3.89/4.23 % --dbg_out_stat false
% 3.89/4.23
% 3.89/4.23 % ------ General Options
% 3.89/4.23
% 3.89/4.23 % --fof false
% 3.89/4.23 % --time_out_real 150.
% 3.89/4.23 % --time_out_prep_mult 0.2
% 3.89/4.23 % --time_out_virtual -1.
% 3.89/4.23 % --schedule none
% 3.89/4.23 % --ground_splitting input
% 3.89/4.23 % --splitting_nvd 16
% 3.89/4.23 % --non_eq_to_eq false
% 3.89/4.23 % --prep_gs_sim true
% 3.89/4.23 % --prep_unflatten false
% 3.89/4.23 % --prep_res_sim true
% 3.89/4.23 % --prep_upred true
% 3.89/4.23 % --res_sim_input true
% 3.89/4.23 % --clause_weak_htbl true
% 3.89/4.23 % --gc_record_bc_elim false
% 3.89/4.23 % --symbol_type_check false
% 3.89/4.23 % --clausify_out false
% 3.89/4.23 % --large_theory_mode false
% 3.89/4.23 % --prep_sem_filter none
% 3.89/4.23 % --prep_sem_filter_out false
% 3.89/4.23 % --preprocessed_out false
% 3.89/4.23 % --sub_typing false
% 3.89/4.23 % --brand_transform false
% 3.89/4.23 % --pure_diseq_elim true
% 3.89/4.23 % --min_unsat_core false
% 3.89/4.23 % --pred_elim true
% 3.89/4.23 % --add_important_lit false
% 3.89/4.23 % --soft_assumptions false
% 3.89/4.23 % --reset_solvers false
% 3.89/4.23 % --bc_imp_inh []
% 3.89/4.23 % --conj_cone_tolerance 1.5
% 3.89/4.23 % --prolific_symb_bound 500
% 3.89/4.23 % --lt_threshold 2000
% 3.89/4.23
% 3.89/4.23 % ------ SAT Options
% 3.89/4.23
% 3.89/4.23 % --sat_mode false
% 3.89/4.23 % --sat_fm_restart_options ""
% 3.89/4.23 % --sat_gr_def false
% 3.89/4.23 % --sat_epr_types true
% 3.89/4.23 % --sat_non_cyclic_types false
% 3.89/4.23 % --sat_finite_models false
% 3.89/4.23 % --sat_fm_lemmas false
% 3.89/4.23 % --sat_fm_prep false
% 3.89/4.23 % --sat_fm_uc_incr true
% 3.89/4.23 % --sat_out_model small
% 3.89/4.23 % --sat_out_clauses false
% 3.89/4.23
% 3.89/4.23 % ------ QBF Options
% 3.89/4.23
% 3.89/4.23 % --qbf_mode false
% 3.89/4.23 % --qbf_elim_univ true
% 3.89/4.23 % --qbf_sk_in true
% 3.89/4.23 % --qbf_pred_elim true
% 3.89/4.23 % --qbf_split 32
% 3.89/4.23
% 3.89/4.23 % ------ BMC1 Options
% 3.89/4.23
% 3.89/4.23 % --bmc1_incremental false
% 3.89/4.23 % --bmc1_axioms reachable_all
% 3.89/4.23 % --bmc1_min_bound 0
% 3.89/4.23 % --bmc1_max_bound -1
% 3.89/4.23 % --bmc1_max_bound_default -1
% 3.89/4.23 % --bmc1_symbol_reachability true
% 3.89/4.23 % --bmc1_property_lemmas false
% 3.89/4.23 % --bmc1_k_induction false
% 3.89/4.23 % --bmc1_non_equiv_states false
% 3.89/4.23 % --bmc1_deadlock false
% 3.89/4.23 % --bmc1_ucm false
% 3.89/4.23 % --bmc1_add_unsat_core none
% 3.89/4.23 % --bmc1_unsat_core_children false
% 3.89/4.23 % --bmc1_unsat_core_extrapolate_axioms false
% 3.89/4.23 % --bmc1_out_stat full
% 3.89/4.23 % --bmc1_ground_init false
% 3.89/4.23 % --bmc1_pre_inst_next_state false
% 3.89/4.23 % --bmc1_pre_inst_state false
% 3.89/4.23 % --bmc1_pre_inst_reach_state false
% 3.89/4.23 % --bmc1_out_unsat_core false
% 3.89/4.23 % --bmc1_aig_witness_out false
% 3.89/4.23 % --bmc1_verbose false
% 3.89/4.23 % --bmc1_dump_clauses_tptp false
% 3.89/4.23 % --bmc1_dump_unsat_core_tptp false
% 3.89/4.23 % --bmc1_dump_file -
% 3.89/4.23 % --bmc1_ucm_expand_uc_limit 128
% 3.89/4.23 % --bmc1_ucm_n_expand_iterations 6
% 3.89/4.23 % --bmc1_ucm_extend_mode 1
% 3.89/4.23 % --bmc1_ucm_init_mode 2
% 3.89/4.23 % --bmc1_ucm_cone_mode none
% 3.89/4.23 % --bmc1_ucm_reduced_relation_type 0
% 3.89/4.23 % --bmc1_ucm_relax_model 4
% 3.89/4.23 % --bmc1_ucm_full_tr_after_sat true
% 3.89/4.23 % --bmc1_ucm_expand_neg_assumptions false
% 30.01/30.34 % --bmc1_ucm_layered_model none
% 30.01/30.34 % --bmc1_ucm_max_lemma_size 10
% 30.01/30.34
% 30.01/30.34 % ------ AIG Options
% 30.01/30.34
% 30.01/30.34 % --aig_mode false
% 30.01/30.34
% 30.01/30.34 % ------ Instantiation Options
% 30.01/30.34
% 30.01/30.34 % --instantiation_flag true
% 30.01/30.34 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 30.01/30.34 % --inst_solver_per_active 750
% 30.01/30.34 % --inst_solver_calls_frac 0.5
% 30.01/30.34 % --inst_passive_queue_type priority_queues
% 30.01/30.34 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 30.01/30.34 % --inst_passive_queues_freq [25;2]
% 30.01/30.34 % --inst_dismatching true
% 30.01/30.34 % --inst_eager_unprocessed_to_passive true
% 30.01/30.34 % --inst_prop_sim_given true
% 30.01/30.34 % --inst_prop_sim_new false
% 30.01/30.34 % --inst_orphan_elimination true
% 30.01/30.34 % --inst_learning_loop_flag true
% 30.01/30.34 % --inst_learning_start 3000
% 30.01/30.34 % --inst_learning_factor 2
% 30.01/30.34 % --inst_start_prop_sim_after_learn 3
% 30.01/30.34 % --inst_sel_renew solver
% 30.01/30.34 % --inst_lit_activity_flag true
% 30.01/30.34 % --inst_out_proof true
% 30.01/30.34
% 30.01/30.34 % ------ Resolution Options
% 30.01/30.34
% 30.01/30.34 % --resolution_flag true
% 30.01/30.34 % --res_lit_sel kbo_max
% 30.01/30.34 % --res_to_prop_solver none
% 30.01/30.34 % --res_prop_simpl_new false
% 30.01/30.34 % --res_prop_simpl_given false
% 30.01/30.34 % --res_passive_queue_type priority_queues
% 30.01/30.34 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 30.01/30.34 % --res_passive_queues_freq [15;5]
% 30.01/30.34 % --res_forward_subs full
% 30.01/30.34 % --res_backward_subs full
% 30.01/30.34 % --res_forward_subs_resolution true
% 30.01/30.34 % --res_backward_subs_resolution true
% 30.01/30.34 % --res_orphan_elimination false
% 30.01/30.34 % --res_time_limit 1000.
% 30.01/30.34 % --res_out_proof true
% 30.01/30.34 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_2c6c01.s
% 30.01/30.34 % --modulo true
% 30.01/30.34
% 30.01/30.34 % ------ Combination Options
% 30.01/30.34
% 30.01/30.34 % --comb_res_mult 1000
% 30.01/30.34 % --comb_inst_mult 300
% 30.01/30.34 % ------
% 30.01/30.34
% 30.01/30.34
% 30.01/30.34
% 30.01/30.34 % ------ Proving...
% 30.01/30.34 %
% 30.01/30.34
% 30.01/30.34
% 30.01/30.34 % ------ Statistics
% 30.01/30.34
% 30.01/30.34 % ------ General
% 30.01/30.34
% 30.01/30.34 % num_of_input_clauses: 1377
% 30.01/30.34 % num_of_input_neg_conjectures: 1
% 30.01/30.34 % num_of_splits: 0
% 30.01/30.34 % num_of_split_atoms: 0
% 30.01/30.34 % num_of_sem_filtered_clauses: 0
% 30.01/30.34 % num_of_subtypes: 0
% 30.01/30.34 % monotx_restored_types: 0
% 30.01/30.34 % sat_num_of_epr_types: 0
% 30.01/30.34 % sat_num_of_non_cyclic_types: 0
% 30.01/30.34 % sat_guarded_non_collapsed_types: 0
% 30.01/30.34 % is_epr: 0
% 30.01/30.34 % is_horn: 0
% 30.01/30.34 % has_eq: 1
% 30.01/30.34 % num_pure_diseq_elim: 0
% 30.01/30.34 % simp_replaced_by: 0
% 30.01/30.34 % res_preprocessed: 2
% 30.01/30.34 % prep_upred: 0
% 30.01/30.34 % prep_unflattend: 0
% 30.01/30.34 % pred_elim_cands: 0
% 30.01/30.34 % pred_elim: 0
% 30.01/30.34 % pred_elim_cl: 0
% 30.01/30.34 % pred_elim_cycles: 0
% 30.01/30.34 % forced_gc_time: 0
% 30.01/30.34 % gc_basic_clause_elim: 0
% 30.01/30.34 % parsing_time: 0.098
% 30.01/30.34 % sem_filter_time: 0.
% 30.01/30.34 % pred_elim_time: 0.
% 30.01/30.34 % out_proof_time: 0.002
% 30.01/30.34 % monotx_time: 0.
% 30.01/30.34 % subtype_inf_time: 0.
% 30.01/30.34 % unif_index_cands_time: 0.035
% 30.01/30.34 % unif_index_add_time: 0.024
% 30.01/30.34 % total_time: 29.794
% 30.01/30.34 % num_of_symbols: 128
% 30.01/30.34 % num_of_terms: 73047
% 30.01/30.34
% 30.01/30.34 % ------ Propositional Solver
% 30.01/30.34
% 30.01/30.34 % prop_solver_calls: 6
% 30.01/30.34 % prop_fast_solver_calls: 3
% 30.01/30.34 % prop_num_of_clauses: 5317
% 30.01/30.34 % prop_preprocess_simplified: 10226
% 30.01/30.34 % prop_fo_subsumed: 0
% 30.01/30.34 % prop_solver_time: 0.002
% 30.01/30.36 % prop_fast_solver_time: 0.
% 30.01/30.36 % prop_unsat_core_time: 0.001
% 30.01/30.36
% 30.01/30.36 % ------ QBF
% 30.01/30.36
% 30.01/30.36 % qbf_q_res: 0
% 30.01/30.36 % qbf_num_tautologies: 0
% 30.01/30.36 % qbf_prep_cycles: 0
% 30.01/30.36
% 30.01/30.36 % ------ BMC1
% 30.01/30.36
% 30.01/30.36 % bmc1_current_bound: -1
% 30.01/30.36 % bmc1_last_solved_bound: -1
% 30.01/30.36 % bmc1_unsat_core_size: -1
% 30.01/30.36 % bmc1_unsat_core_parents_size: -1
% 30.01/30.36 % bmc1_merge_next_fun: 0
% 30.01/30.36 % bmc1_unsat_core_clauses_time: 0.
% 30.01/30.36
% 30.01/30.36 % ------ Instantiation
% 30.01/30.36
% 30.01/30.36 % inst_num_of_clauses: 3413
% 30.01/30.36 % inst_num_in_passive: 1851
% 30.01/30.36 % inst_num_in_active: 874
% 30.01/30.36 % inst_num_in_unprocessed: 686
% 30.01/30.36 % inst_num_of_loops: 922
% 30.01/30.36 % inst_num_of_learning_restarts: 0
% 30.01/30.36 % inst_num_moves_active_passive: 46
% 30.01/30.36 % inst_lit_activity: 744
% 30.01/30.36 % inst_lit_activity_moves: 1
% 30.01/30.36 % inst_num_tautologies: 0
% 30.01/30.36 % inst_num_prop_implied: 0
% 30.01/30.36 % inst_num_existing_simplified: 0
% 30.01/30.36 % inst_num_eq_res_simplified: 0
% 30.01/30.36 % inst_num_child_elim: 0
% 30.01/30.36 % inst_num_of_dismatching_blockings: 811
% 30.01/30.36 % inst_num_of_non_proper_insts: 1661
% 30.01/30.36 % inst_num_of_duplicates: 4257
% 30.01/30.36 % inst_inst_num_from_inst_to_res: 0
% 30.01/30.36 % inst_dismatching_checking_time: 0.017
% 30.01/30.36
% 30.01/30.36 % ------ Resolution
% 30.01/30.36
% 30.01/30.36 % res_num_of_clauses: 20747
% 30.01/30.36 % res_num_in_passive: 17792
% 30.01/30.36 % res_num_in_active: 2148
% 30.01/30.36 % res_num_of_loops: 4000
% 30.01/30.36 % res_forward_subset_subsumed: 6763
% 30.01/30.36 % res_backward_subset_subsumed: 24
% 30.01/30.36 % res_forward_subsumed: 2348
% 30.01/30.36 % res_backward_subsumed: 14
% 30.01/30.36 % res_forward_subsumption_resolution: 28
% 30.01/30.36 % res_backward_subsumption_resolution: 0
% 30.01/30.36 % res_clause_to_clause_subsumption: 73504
% 30.01/30.36 % res_orphan_elimination: 0
% 30.01/30.36 % res_tautology_del: 778
% 30.01/30.36 % res_num_eq_res_simplified: 0
% 30.01/30.36 % res_num_sel_changes: 0
% 30.01/30.36 % res_moves_from_active_to_pass: 0
% 30.01/30.36
% 30.01/30.36 % Status Unsatisfiable
% 30.01/30.36 % SZS status Unsatisfiable
% 30.01/30.36 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------