TSTP Solution File: LCL806-1 by iProverMo---2.5-0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : LCL806-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 11:40:01 EDT 2022
% Result : Unsatisfiable 174.89s 175.09s
% Output : CNFRefutation 174.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 416
% Syntax : Number of formulae : 2851 ( 913 unt; 0 def)
% Number of atoms : 5825 (2026 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 5826 (2852 ~;2974 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 27 ( 2 avg)
% Number of predicates : 32 ( 30 usr; 1 prp; 0-4 aty)
% Number of functors : 78 ( 78 usr; 35 con; 0-5 aty)
% Number of variables : 7589 ( 570 sgn3171 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0,axiom,
c_List_Olistsp(hAPP(hAPP(c_COMBS(tc_Lambda_OdB,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_and),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_bool),tc_bool,tc_Lambda_OdB),c_All(tc_fun(tc_nat,tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_bool),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_fun(tc_nat,tc_Type_Otype)),c_All(tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_bool)),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_Type_Otype,tc_bool),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_bool),tc_bool,tc_Type_Otype),c_All(tc_Lambda_OdB)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_bool),tc_Type_Otype),hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_bool,tc_Lambda_OdB),c_All(tc_nat))))),hAPP(hAPP(c_COMBS(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_fun(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),c_COMBS(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Type_Otype),c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool),tc_Lambda_OdB)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Type_Otype),c_COMBS(tc_nat,tc_bool,tc_bool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_Type_Otype),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_nat),c_implies)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Type_Otype,tc_bool))),hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Lambda_OdB,tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype)),tc_fun(tc_nat,tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool)),tc_nat),c_Type_Otyping)),hAPP(hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_Type_Otype))),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Type_Otype,tc_fun(tc_nat,tc_Type_Otype))),c_Type_Oshift(tc_Type_Otype))),v_T____))))))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBS(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),c_COMBB(tc_bool,tc_bool,tc_nat)),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_implies),c_InductTermi_OIT))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBS(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_bool,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),c_COMBB(tc_bool,tc_bool,tc_nat))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_bool),tc_fun(tc_Lambda_OdB,tc_fun(tc_bool,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_implies)),hAPP(hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_Lambda_OdB,tc_Type_Otype,tc_bool)),c_Type_Otyping)),v_T____)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_nat,tc_Lambda_OdB),tc_fun(tc_nat,tc_bool),tc_Lambda_OdB),hAPP(c_COMBB(tc_Lambda_OdB,tc_bool,tc_nat),c_InductTermi_OIT))),c_Lambda_Osubst)))))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),c_Ex(tc_Type_Otype)),hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)))),v_bs____,tc_Lambda_OdB),
file('<stdin>',cls_CHAINED_0_01) ).
fof(c_0_1,axiom,
! [X35,X28,X16,X22,X36,X37,X23] :
( X36 = c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X23,X36,X22,X35),X23,tc_Type_Otype,tc_Type_Otype)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X16),X28,tc_Lambda_OdB,tc_Lambda_OdB)),X36))
| ~ c_Type_Otypings(X22,X28,X37)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X16),X28,tc_Lambda_OdB,tc_Lambda_OdB),X35,tc_Lambda_OdB,tc_Lambda_OdB)),X23)) ),
file('<stdin>',cls_var__app__types_0) ).
fof(c_0_2,axiom,
! [X35,X28,X16,X22,X36,X37,X23] :
( c_Type_Otypings(X22,X35,c_Type_Osko__Type__Xvar__app__types__1__1(X23,X36,X22,X35))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X16),X28,tc_Lambda_OdB,tc_Lambda_OdB)),X36))
| ~ c_Type_Otypings(X22,X28,X37)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X16),X28,tc_Lambda_OdB,tc_Lambda_OdB),X35,tc_Lambda_OdB,tc_Lambda_OdB)),X23)) ),
file('<stdin>',cls_var__app__types_1) ).
fof(c_0_3,axiom,
! [X28,X16,X22,X36,X23] :
( X23 = X36
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X16),X28,tc_Lambda_OdB,tc_Lambda_OdB)),X36))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X16),X28,tc_Lambda_OdB,tc_Lambda_OdB)),X23)) ),
file('<stdin>',cls_var__app__type__eq_0) ).
fof(c_0_4,axiom,
! [X28,X16,X22,X23] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),c_Lambda_OdB_OVar(X16)),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X23,X22,X16,X28),X23,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X16),X28,tc_Lambda_OdB,tc_Lambda_OdB)),X23)) ),
file('<stdin>',cls_var__app__typesE_0) ).
fof(c_0_5,axiom,
! [X28,X29,X22,X23] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),X29),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X23,X22,X29,X28),X23,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),c_List_Ofoldl(c_Lambda_OdB_OApp,X29,X28,tc_Lambda_OdB,tc_Lambda_OdB)),X23)) ),
file('<stdin>',cls_list__app__typeE_0) ).
fof(c_0_6,axiom,
! [X28,X29,X22,X23] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),X29),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X23,X22,X29,X28),X23,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),c_List_Ofoldl(c_Lambda_OdB_OApp,X29,X28,tc_Lambda_OdB,tc_Lambda_OdB)),X23)) ),
file('<stdin>',cls_list__app__typeD_0) ).
fof(c_0_7,axiom,
! [X28,X29,X22,X37,X23] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),c_List_Ofoldl(c_Lambda_OdB_OApp,X29,X28,tc_Lambda_OdB,tc_Lambda_OdB)),X23))
| ~ c_Type_Otypings(X22,X28,X37)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),X29),c_List_Ofoldr(c_Type_Otype_OFun,X37,X23,tc_Type_Otype,tc_Type_Otype))) ),
file('<stdin>',cls_list__app__typeI_0) ).
fof(c_0_8,axiom,
! [X26,X28,X29,X16] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,X29,X28,tc_Lambda_OdB,tc_Lambda_OdB)),X26),X16) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),X26),X16),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),X26)),X16),X28,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
file('<stdin>',cls_subst__map_0) ).
fof(c_0_9,axiom,
! [X21,X2,X4] :
( X21 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X4,X2,X21),tc_Lambda_OdB,tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X21)) ),
file('<stdin>',cls_head__Var__reduction_1) ).
fof(c_0_10,axiom,
! [X28,X16,X22,X23] :
( c_Type_Otypings(X22,X28,c_Type_Osko__Type__Xvar__app__typesE__1__1(X23,X22,X16,X28))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X16),X28,tc_Lambda_OdB,tc_Lambda_OdB)),X23)) ),
file('<stdin>',cls_var__app__typesE_1) ).
fof(c_0_11,axiom,
! [X28,X29,X22,X23] :
( c_Type_Otypings(X22,X28,c_Type_Osko__Type__Xlist__app__typeD__1__1(X23,X22,X29,X28))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),c_List_Ofoldl(c_Lambda_OdB_OApp,X29,X28,tc_Lambda_OdB,tc_Lambda_OdB)),X23)) ),
file('<stdin>',cls_list__app__typeD_1) ).
fof(c_0_12,axiom,
! [X28,X29,X22,X23] :
( c_Type_Otypings(X22,X28,c_Type_Osko__Type__Xlist__app__typeE__1__1(X23,X22,X29,X28))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),c_List_Ofoldl(c_Lambda_OdB_OApp,X29,X28,tc_Lambda_OdB,tc_Lambda_OdB)),X23)) ),
file('<stdin>',cls_list__app__typeE_1) ).
fof(c_0_13,axiom,
! [X21,X2,X4] :
( c_ListOrder_Ostep1(c_Lambda_Obeta,X2,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X4,X2,X21),tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X21)) ),
file('<stdin>',cls_head__Var__reduction_0) ).
fof(c_0_14,axiom,
! [X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X2,X1,tc_Lambda_OdB) ),
file('<stdin>',cls_apps__preserves__betas_0) ).
fof(c_0_15,axiom,
! [X1,X27,X3] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X27,X1,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X3),X27)) ),
file('<stdin>',cls_apps__preserves__beta2_0) ).
fof(c_0_16,axiom,
! [X1,X27,X3] :
( 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,X27,X1,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X3),X27)) ),
file('<stdin>',cls_apps__preserves__beta_0) ).
fof(c_0_17,axiom,
c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),v_u____)),v_i____),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
file('<stdin>',cls_CHAINED_0) ).
fof(c_0_18,axiom,
c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),v_u____)),v_i____),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
file('<stdin>',cls_Cons_I3_J_0) ).
fof(c_0_19,axiom,
! [X1,X27,X3] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3)),X27),X1,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X27))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X27),c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('<stdin>',cls_Beta_0) ).
fof(c_0_20,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),c_Lambda_OdB_OVar(v_n____)),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)))),
file('<stdin>',cls_varT_0) ).
fof(c_0_21,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_H____)),
file('<stdin>',cls_nT_0) ).
fof(c_0_22,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_ea______),v_ia______),v_T____)),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_Ha______)),
file('<stdin>',cls_Var_I2_J_0) ).
fof(c_0_23,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_e____),v_u____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)))),
file('<stdin>',cls_uT_H_0) ).
fof(c_0_24,axiom,
! [X28,X29,X16] : hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,X29,X28,tc_Lambda_OdB,tc_Lambda_OdB)),X16) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X29),X16),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),X16),X28,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
file('<stdin>',cls_lift__map_0) ).
fof(c_0_25,axiom,
! [X26,X28,X16,X22,X37,X23] :
( c_Type_Otypings(X22,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),X26)),X16),X28,tc_Lambda_OdB,tc_Lambda_OdB),X37)
| ~ c_Type_Otypings(hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X22),X16),X23),X28,X37)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),X26),X23)) ),
file('<stdin>',cls_substs__lemma_0) ).
fof(c_0_26,axiom,
! [X54,X47,X30,X55,X44,X43,X9] : c_Fun_Ofcomp(c_Fun_Ofcomp(X30,X47,X9,X55,X44),X54,X9,X44,X43) = c_Fun_Ofcomp(X30,c_Fun_Ofcomp(X47,X54,X55,X44,X43),X9,X55,X43),
file('<stdin>',cls_fcomp__assoc_0) ).
fof(c_0_27,axiom,
! [X54,X47,X30,X55,X44,X43,X9] : c_Fun_Ocomp(X30,c_Fun_Ocomp(X47,X54,X55,X44,X9),X44,X43,X9) = c_Fun_Ocomp(c_Fun_Ocomp(X30,X47,X44,X43,X55),X54,X55,X43,X9),
file('<stdin>',cls_o__assoc_0) ).
fof(c_0_28,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
file('<stdin>',cls_headT_0) ).
fof(c_0_29,axiom,
! [X26,X29,X22,X23] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),X29),hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X23,X22,X29,X26)),X23)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),hAPP(hAPP(c_Lambda_OdB_OApp,X29),X26)),X23)) ),
file('<stdin>',cls_typing__elims_I2_J_0) ).
fof(c_0_30,axiom,
! [X12,X13,X58,X47,X59,X30,X60,X55,X44,X43,X9] :
( hAPP(X30,hAPP(X47,X13)) != hAPP(X59,hAPP(X58,X12))
| hAPP(c_Fun_Ocomp(X30,X47,X43,X9,X44),X13) = hAPP(c_Fun_Ocomp(X59,X58,X55,X9,X60),X12) ),
file('<stdin>',cls_comp__cong_0) ).
fof(c_0_31,axiom,
! [X2,X4] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_List_Olistsp(c_InductTermi_OIT,X2,tc_Lambda_OdB) ),
file('<stdin>',cls_IT_OVar_0) ).
fof(c_0_32,axiom,
! [X29,X22,X23] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X22),c_HOL_Ozero__class_Ozero(tc_nat)),c_Type_Osko__Type__Xtyping__elims__3__1(X23,X22,X29))),X29),c_Type_Osko__Type__Xtyping__elims__3__2(X23,X22,X29)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),c_Lambda_OdB_OAbs(X29)),X23)) ),
file('<stdin>',cls_typing__elims_I3_J_1) ).
fof(c_0_33,axiom,
! [X26,X29,X16,X67,X36,X23] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X67),X26),X36))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X67),X16),X36)),X29),X23))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X67),hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),X26),X16)),X23)) ),
file('<stdin>',cls_subst__lemma_0) ).
fof(c_0_34,axiom,
! [X21,X19,X32,X6,X7,X55,X44,X43,X9] :
( c_Fun_Ocomp(X7,X6,X44,X43,X9) != c_Fun_Ocomp(X32,X19,X55,X43,X9)
| hAPP(X7,hAPP(X6,X21)) = hAPP(X32,hAPP(X19,X21)) ),
file('<stdin>',cls_o__eq__dest_0) ).
fof(c_0_35,axiom,
! [X21,X32,X6,X7,X44,X43,X9] :
( c_Fun_Ocomp(X7,X6,X44,X43,X9) != c_Fun_Ocomp(c_Fun_Oid(X43),X32,X43,X43,X9)
| hAPP(X7,hAPP(X6,X21)) = hAPP(X32,X21) ),
file('<stdin>',cls_o__eq__id__dest_0) ).
fof(c_0_36,axiom,
! [X1,X2,X4,X5] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X1,tc_Lambda_OdB,tc_Lambda_OdB)
| X5 = X4 ),
file('<stdin>',cls_Var__apps__eq__Var__apps__conv_0) ).
fof(c_0_37,axiom,
! [X1,X2,X4,X5] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X1,tc_Lambda_OdB,tc_Lambda_OdB)
| X2 = X1 ),
file('<stdin>',cls_Var__apps__eq__Var__apps__conv_1) ).
fof(c_0_38,axiom,
! [X1,X27,X2,X3] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X27),X1,tc_Lambda_OdB,tc_Lambda_OdB)
| X3 = X27 ),
file('<stdin>',cls_Abs__apps__eq__Abs__apps__conv_0) ).
fof(c_0_39,axiom,
! [X1,X27,X2,X3] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X27),X1,tc_Lambda_OdB,tc_Lambda_OdB)
| X2 = X1 ),
file('<stdin>',cls_Abs__apps__eq__Abs__apps__conv_1) ).
fof(c_0_40,axiom,
! [X31,X11,X13,X9] :
( ~ class_OrderedGroup_Osemigroup__add(X9)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X13),X11),X31,X9,X9) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X13),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X9),X11,X31,X9,X9)) ),
file('<stdin>',cls_foldl__assoc_0) ).
fof(c_0_41,axiom,
! [X28,X1,X3,X4] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X28,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X1,tc_Lambda_OdB,tc_Lambda_OdB),
file('<stdin>',cls_Var__apps__neq__Abs__apps_0) ).
fof(c_0_42,axiom,
! [X28,X27,X3] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X28,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X27,X28,tc_Lambda_OdB,tc_Lambda_OdB)
| X3 = X27 ),
file('<stdin>',cls_apps__eq__tail__conv_0) ).
fof(c_0_43,axiom,
! [X34,X7,X9] :
( ~ class_OrderedGroup_Omonoid__add(X9)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X9),X7,X34,X9,X9) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X9),X34,c_HOL_Ozero__class_Ozero(X9),X9,X9)) ),
file('<stdin>',cls_foldl__foldr1__lemma_0) ).
fof(c_0_44,axiom,
! [X31,X13,X9] :
( ~ class_OrderedGroup_Omonoid__add(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X13),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X9),c_HOL_Ozero__class_Ozero(X9),X31,X9,X9)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X9),X13,X31,X9,X9) ),
file('<stdin>',cls_foldl__absorb0_0) ).
fof(c_0_45,axiom,
! [X26,X29,X16,X22,X64,X65,X66] :
( v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X66),X65)
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),X26),X16)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),X26),X66))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X26))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X22),X16),X66)),X29),X64))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X29)) ),
file('<stdin>',cls_MI1_0) ).
fof(c_0_46,axiom,
! [X26,X29,X16,X22,X64,X65,X66] :
( v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X66),X65)
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),X26),X16)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),X26),X65))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X26))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X22),X16),X65)),X29),X64))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X29)) ),
file('<stdin>',cls_MI2_0) ).
fof(c_0_47,axiom,
! [X26,X61,X62,X63] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),X26),X61)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X62),X26),v_T____))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X26))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X62),X61),v_T____)),v_b____),X63)) ),
file('<stdin>',cls_CHAINED_0_02) ).
fof(c_0_48,axiom,
! [X26,X61,X62,X63] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),X26),X61)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X62),X26),v_T____))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X26))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X62),X61),v_T____)),v_b____),X63)) ),
file('<stdin>',cls_Cons_I1_J_0) ).
fof(c_0_49,axiom,
! [X34,X47,X30,X44,X43,X9] : c_List_Omap(X30,c_List_Omap(X47,X34,X44,X43),X43,X9) = c_List_Omap(c_Fun_Ocomp(X30,X47,X43,X9,X44),X34,X44,X9),
file('<stdin>',cls_map__map_0) ).
fof(c_0_50,axiom,
! [X29,X53,X36,X23] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X53),c_Lambda_OdB_OAbs(X29)),hAPP(hAPP(c_Type_Otype_OFun,X23),X36)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X53),c_HOL_Ozero__class_Ozero(tc_nat)),X23)),X29),X36)) ),
file('<stdin>',cls_Abs_0) ).
fof(c_0_51,axiom,
! [X21,X26,X29,X15,X16] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),hAPP(hAPP(c_Lambda_Olift,X21),X16)),c_Suc(X15))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X26),X21),X15)),X16) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),X26),X16)),X21),X15)
| ~ c_HOL_Oord__class_Oless(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
file('<stdin>',cls_subst__subst_0) ).
fof(c_0_52,axiom,
! [X29,X22,X23] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X22),c_HOL_Ozero__class_Ozero(tc_nat)),c_Type_Osko__Type__Xabs__typeE__1__1(X22,X29))),X29),c_Type_Osko__Type__Xabs__typeE__1__2(X22,X29)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),c_Lambda_OdB_OAbs(X29)),X23)) ),
file('<stdin>',cls_abs__typeE_0) ).
fof(c_0_53,axiom,
! [X30,X32,X44,X43] : hAPP(c_Fun_Ocomp(c_COMBK(X32,X43,X44),X30,X44,X43,t_a),v_x) = X32,
file('<stdin>',cls_K__record__comp_0) ).
fof(c_0_54,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_b____),v_sko__CHAINED__1(v_T____,v_b____,v_e____,v_i____))),
file('<stdin>',cls_CHAINED_1) ).
fof(c_0_55,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_b____),v_sko__local__XCons__1__1(v_T____,v_b____,v_e____,v_i____))),
file('<stdin>',cls_Cons_I1_J_1) ).
fof(c_0_56,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_b____),v_sko__local__XCons__Xhyps__1__1(v_T____,v_b____,v_e____,v_i____))),
file('<stdin>',cls_Cons_Ohyps_I1_J_1) ).
fof(c_0_57,axiom,
! [X4,X5,X30,X9] : c_Nat_Ocompow(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4),X30,X9,X9) = c_Fun_Ocomp(c_Nat_Ocompow(X5,X30,X9,X9),c_Nat_Ocompow(X4,X30,X9,X9),X9,X9,X9),
file('<stdin>',cls_funpow__add_0) ).
fof(c_0_58,axiom,
! [X13,X47,X30,X44,X43,X9] : hAPP(c_Fun_Ofcomp(X30,X47,X43,X44,X9),X13) = hAPP(X47,hAPP(X30,X13)),
file('<stdin>',cls_fcomp__apply_0) ).
fof(c_0_59,axiom,
! [X21,X6,X7,X44,X43,X9] : hAPP(X7,hAPP(X6,X21)) = hAPP(c_Fun_Ocomp(X7,X6,X44,X43,X9),X21),
file('<stdin>',cls_o__eq__dest__lhs_0) ).
fof(c_0_60,axiom,
! [X13,X47,X30,X44,X43,X9] : hAPP(c_Fun_Ocomp(X30,X47,X43,X9,X44),X13) = hAPP(X30,hAPP(X47,X13)),
file('<stdin>',cls_o__apply_0) ).
fof(c_0_61,axiom,
! [X47,X30,X44,X43] : hAPP(c_Fun_Ofcomp(X30,X47,t_a,X44,X43),v_x) = hAPP(X47,hAPP(X30,v_x)),
file('<stdin>',cls_fcomp__def_0) ).
fof(c_0_62,axiom,
! [X47,X30,X44,X43] : hAPP(c_Fun_Ocomp(X30,X47,X44,X43,t_a),v_x) = hAPP(X30,hAPP(X47,v_x)),
file('<stdin>',cls_o__def_0) ).
fof(c_0_63,axiom,
! [X34,X9] :
( ~ class_OrderedGroup_Omonoid__add(X9)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X9),c_HOL_Ozero__class_Ozero(X9),X34,X9,X9) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X9),X34,c_HOL_Ozero__class_Ozero(X9),X9,X9) ),
file('<stdin>',cls_foldl__foldr1_0) ).
fof(c_0_64,axiom,
! [X34,X7,X9] :
( ~ class_OrderedGroup_Oab__semigroup__add(X9)
| c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X9),X34,X7,X9,X9) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X9),X7,X34,X9,X9) ),
file('<stdin>',cls_foldr__conv__foldl_0) ).
fof(c_0_65,axiom,
v_T____ = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
file('<stdin>',cls_T_0) ).
fof(c_0_66,axiom,
! [X29,X16,X22,X36,X23] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X22),X16),X36)),hAPP(hAPP(c_Lambda_Olift,X29),X16)),X23))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),X29),X23)) ),
file('<stdin>',cls_lift__type_0) ).
fof(c_0_67,axiom,
! [X16,X22,X36,X23,X9] : hAPP(hAPP(hAPP(c_Type_Oshift(X9),hAPP(hAPP(hAPP(c_Type_Oshift(X9),X22),X16),X36)),c_HOL_Ozero__class_Ozero(tc_nat)),X23) = hAPP(hAPP(hAPP(c_Type_Oshift(X9),hAPP(hAPP(hAPP(c_Type_Oshift(X9),X22),c_HOL_Ozero__class_Ozero(tc_nat)),X23)),c_Suc(X16)),X36),
file('<stdin>',cls_shift__commute_0) ).
fof(c_0_68,axiom,
! [X29,X1,X27,X4] : hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X27)),X29) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X1,tc_Lambda_OdB,tc_Lambda_OdB),
file('<stdin>',cls_Abs__App__neq__Var__apps_0) ).
fof(c_0_69,axiom,
! [X4,X30,X9] : c_Nat_Ocompow(c_Suc(X4),X30,X9,X9) = c_Fun_Ocomp(X30,c_Nat_Ocompow(X4,X30,X9,X9),X9,X9,X9),
file('<stdin>',cls_funpow_Osimps_I2_J_0) ).
fof(c_0_70,axiom,
! [X1,X27,X5] :
( c_Lambda_OdB_OVar(X5) != c_List_Ofoldl(c_Lambda_OdB_OApp,X27,X1,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OVar(X5) = X27 ),
file('<stdin>',cls_Var__eq__apps__conv_0) ).
fof(c_0_71,axiom,
! [X1,X27,X3] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X27,X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X3)
| X27 = c_Lambda_OdB_OAbs(X3) ),
file('<stdin>',cls_apps__eq__Abs__conv_0) ).
fof(c_0_72,axiom,
! [X1,X27,X3] :
( c_Lambda_OdB_OAbs(X3) != c_List_Ofoldl(c_Lambda_OdB_OApp,X27,X1,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(X3) = X27 ),
file('<stdin>',cls_Abs__eq__apps__conv_0) ).
fof(c_0_73,axiom,
! [X29,X27,X15,X16] :
( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),X27),X15)),X16) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X29),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,X27),X16)),X15)
| ~ c_HOL_Oord__class_Oless(X15,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
file('<stdin>',cls_lift__subst_0) ).
fof(c_0_74,axiom,
! [X26,X29,X22,X23] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),X26),c_Type_Osko__Type__Xtyping__elims__2__1(X23,X22,X29,X26)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),hAPP(hAPP(c_Lambda_OdB_OApp,X29),X26)),X23)) ),
file('<stdin>',cls_typing__elims_I2_J_1) ).
fof(c_0_75,axiom,
! [X28,X16,X22,X36,X37] :
( c_Type_Otypings(hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X22),X16),X36),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),X16),X28,tc_Lambda_OdB,tc_Lambda_OdB),X37)
| ~ c_Type_Otypings(X22,X28,X37) ),
file('<stdin>',cls_lift__types_0) ).
fof(c_0_76,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_a____),v_T_H_H____)),
file('<stdin>',cls_argT_0) ).
fof(c_0_77,axiom,
! [X13,X4,X30,X9] : hAPP(X30,hAPP(c_Nat_Ocompow(X4,X30,X9,X9),X13)) = hAPP(c_Nat_Ocompow(X4,X30,X9,X9),hAPP(X30,X13)),
file('<stdin>',cls_funpow__swap1_0) ).
fof(c_0_78,axiom,
! [X28] :
( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),c_HOL_Ozero__class_Ozero(tc_nat)),X28,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_List_Olistsp(c_InductTermi_OIT,X28,tc_Lambda_OdB) ),
file('<stdin>',cls_lifts__IT_0) ).
fof(c_0_79,axiom,
! [X29,X27,X3,X16] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),X3),X16)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),X27),X16)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X3),X27)) ),
file('<stdin>',cls_subst__preserves__beta2_H_0) ).
fof(c_0_80,axiom,
! [X29,X27,X3,X16] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X29),X16)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X27),X29),X16)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X3),X27)) ),
file('<stdin>',cls_subst__preserves__beta_H_0) ).
fof(c_0_81,axiom,
! [X29,X27,X3,X16] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),X3),X16)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),X27),X16)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X3),X27)) ),
file('<stdin>',cls_subst__preserves__beta2_0) ).
fof(c_0_82,axiom,
! [X29,X27,X53,X36,X23] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X53),hAPP(hAPP(c_Lambda_OdB_OApp,X27),X29)),X36))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X53),X29),X23))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X53),X27),hAPP(hAPP(c_Type_Otype_OFun,X23),X36))) ),
file('<stdin>',cls_App_0) ).
fof(c_0_83,axiom,
! [X29,X27,X15,X16] :
( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),X27),X15)),X16) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X29),X16)),hAPP(hAPP(c_Lambda_Olift,X27),X16)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
file('<stdin>',cls_lift__subst__lt_0) ).
fof(c_0_84,axiom,
! [X29,X27,X3,X16] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X29),X16)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X27),X29),X16)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X3),X27)) ),
file('<stdin>',cls_subst__preserves__beta_0) ).
fof(c_0_85,axiom,
! [X47,X43,X9] : c_Fun_Ofcomp(c_Fun_Oid(X9),X47,X9,X9,X43) = X47,
file('<stdin>',cls_id__fcomp_0) ).
fof(c_0_86,axiom,
! [X30,X43,X9] : c_Fun_Ofcomp(X30,c_Fun_Oid(X43),X9,X43,X43) = X30,
file('<stdin>',cls_fcomp__id_0) ).
fof(c_0_87,axiom,
! [X30,X43,X9] : c_Fun_Ocomp(X30,c_Fun_Oid(X9),X9,X43,X9) = X30,
file('<stdin>',cls_o__id_0) ).
fof(c_0_88,axiom,
! [X47,X43,X9] : c_Fun_Ocomp(c_Fun_Oid(X43),X47,X43,X43,X9) = X47,
file('<stdin>',cls_id__o_0) ).
fof(c_0_89,axiom,
! [X38,X29,X39,X27] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X27),X29)),hAPP(hAPP(c_Lambda_OdB_OApp,X39),X38)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X29),X38))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X27),X39)) ),
file('<stdin>',cls_rtrancl__beta__App_0) ).
fof(c_0_90,axiom,
! [X19,X6,X8] :
( ~ hBOOL(hAPP(X8,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X19),X6,tc_nat)))
| hBOOL(hAPP(X8,X19)) ),
file('<stdin>',cls_nat__diff__split_1) ).
fof(c_0_91,axiom,
! [X13,X6,X8] :
( ~ hBOOL(hAPP(X8,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X13),X6,tc_nat)))
| hBOOL(hAPP(X8,X13)) ),
file('<stdin>',cls_nat__diff__split__asm_1) ).
fof(c_0_92,axiom,
! [X26,X29,X27,X14] : hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,X29),X26)),X27),X14) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),X27),X14)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X26),X27),X14)),
file('<stdin>',cls_subst__App_0) ).
fof(c_0_93,axiom,
! [X27,X3,X16] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,X3),X16)),hAPP(hAPP(c_Lambda_Olift,X27),X16)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X3),X27)) ),
file('<stdin>',cls_lift__preserves__beta_H_0) ).
fof(c_0_94,axiom,
! [X38,X29,X27] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X27),X29)),hAPP(hAPP(c_Lambda_OdB_OApp,X27),X38)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X29),X38)) ),
file('<stdin>',cls_rtrancl__beta__AppR_0) ).
fof(c_0_95,axiom,
! [X29,X39,X27] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X27),X29)),hAPP(hAPP(c_Lambda_OdB_OApp,X39),X29)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X27),X39)) ),
file('<stdin>',cls_rtrancl__beta__AppL_0) ).
fof(c_0_96,axiom,
! [X4,X9] :
( ~ class_Ring__and__Field_Osemiring__1(X9)
| c_Nat_Osemiring__1__class_Oof__nat(X4,X9) = c_Nat_Osemiring__1__class_Oof__nat__aux(hAPP(hAPP(c_COMBC(X9,X9,X9),c_HOL_Oplus__class_Oplus(X9)),c_HOL_Oone__class_Oone(X9)),X4,c_HOL_Ozero__class_Ozero(X9),X9) ),
file('<stdin>',cls_semiring__1__class_Oof__nat__code_0) ).
fof(c_0_97,axiom,
! [X29,X27] : hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X27)),X29)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X27),X29),c_HOL_Ozero__class_Ozero(tc_nat)))),
file('<stdin>',cls_beta_0) ).
fof(c_0_98,axiom,
! [X29,X27,X14] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(X29)),X27),X14) = c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),hAPP(hAPP(c_Lambda_Olift,X27),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)))),
file('<stdin>',cls_subst__Abs_0) ).
fof(c_0_99,axiom,
! [X41,X11,X13,X3,X9] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X3,X9),X13),X41))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X3,X9),X11),X41))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X3,X9),X13),X11)) ),
file('<stdin>',cls_rtranclp__trans_0) ).
fof(c_0_100,axiom,
! [X19,X32,X6,X7,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X6)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X32),X19)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X32)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X6),X19)) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I20_J_0) ).
fof(c_0_101,axiom,
! [X38,X29,X22,X23] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),X38),X23))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),X29),X23))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X29),X38)) ),
file('<stdin>',cls_subject__reduction_H_0) ).
fof(c_0_102,axiom,
! [X29,X22,X23] :
( X23 = hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(X23,X22,X29)),c_Type_Osko__Type__Xtyping__elims__3__2(X23,X22,X29))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),c_Lambda_OdB_OAbs(X29)),X23)) ),
file('<stdin>',cls_typing__elims_I3_J_0) ).
fof(c_0_103,axiom,
! [X26,X29,X27] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X26),X27)),hAPP(hAPP(c_Lambda_OdB_OApp,X26),X29)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X27),X29)) ),
file('<stdin>',cls_appR_0) ).
fof(c_0_104,axiom,
! [X26,X29,X27] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X27),X26)),hAPP(hAPP(c_Lambda_OdB_OApp,X29),X26)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X27),X29)) ),
file('<stdin>',cls_appL_0) ).
fof(c_0_105,axiom,
! [X27,X3,X16] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,X3),X16)),hAPP(hAPP(c_Lambda_Olift,X27),X16)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X3),X27)) ),
file('<stdin>',cls_lift__preserves__beta_0) ).
fof(c_0_106,axiom,
! [X3,X32,X6,X7,X9] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X3,X9),X7),X32))
| ~ hBOOL(hAPP(hAPP(X3,X6),X32))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X3,X9),X7),X6)) ),
file('<stdin>',cls_rtranclp_Ortrancl__into__rtrancl_0) ).
fof(c_0_107,axiom,
! [X3,X32,X6,X7,X9] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X3,X9),X7),X32))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X3,X9),X6),X32))
| ~ hBOOL(hAPP(hAPP(X3,X7),X6)) ),
file('<stdin>',cls_converse__rtranclp__into__rtranclp_0) ).
fof(c_0_108,axiom,
! [X29,X14,X16] :
( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X29),X16)),c_Suc(X14)) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X29),X14)),X16)
| ~ c_HOL_Oord__class_Oless(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
file('<stdin>',cls_lift__lift_0) ).
fof(c_0_109,axiom,
! [X24,X25] : c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,X25),X24),tc_Type_Otype) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X25,tc_Type_Otype)),c_Nat_Osize__class_Osize(X24,tc_Type_Otype))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
file('<stdin>',cls_type_Osize_I4_J_0) ).
fof(c_0_110,axiom,
! [X4,X5] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X5,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X4))
| X5 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_add__eq__if_1) ).
fof(c_0_111,axiom,
! [X38,X29,X22,X23] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),X38),X23))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X29),X38))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),X29),X23)) ),
file('<stdin>',cls_subject__reduction_0) ).
fof(c_0_112,axiom,
! [X48,X42,X8,X44,X43,X9] : hAPP(hAPP(hAPP(c_COMBC(X43,X44,X9),X8),X42),X48) = hAPP(hAPP(X8,X48),X42),
file('<stdin>',cls_COMBC__def_0) ).
fof(c_0_113,axiom,
! [X4,X17,X16,X9] :
( ~ class_Ring__and__Field_Osemiring__1(X9)
| c_Nat_Osemiring__1__class_Oof__nat__aux(X17,c_Suc(X4),X16,X9) = c_Nat_Osemiring__1__class_Oof__nat__aux(X17,X4,hAPP(X17,X16),X9) ),
file('<stdin>',cls_of__nat__aux_Osimps_I2_J_0) ).
fof(c_0_114,axiom,
! [X32,X6,X7,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X6)),X32) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X32)),X6) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I23_J_0) ).
fof(c_0_115,axiom,
! [X6,X7,X8] :
( hBOOL(hAPP(X8,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X7,X6,tc_nat)
| ~ hBOOL(hAPP(X8,c_HOL_Ominus__class_Ominus(X7,X6,tc_nat))) ),
file('<stdin>',cls_nat__diff__split_0) ).
fof(c_0_116,axiom,
! [X26,X29,X27,X14] : c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,X29),X26),X27,X14) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(X29,X27,X14)),c_Lambda_Osubstn(X26,X27,X14)),
file('<stdin>',cls_substn_Osimps_I2_J_0) ).
fof(c_0_117,axiom,
! [X29,X27,X4,X14] : c_Lambda_Oliftn(X4,hAPP(hAPP(c_Lambda_OdB_OApp,X27),X29),X14) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(X4,X27,X14)),c_Lambda_Oliftn(X4,X29,X14)),
file('<stdin>',cls_liftn_Osimps_I2_J_0) ).
fof(c_0_118,axiom,
! [X32,X6,X7,X9] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X9)
| c_HOL_Oord__class_Oless(X7,X6,X9)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X32),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X32),X6),X9) ),
file('<stdin>',cls_add__less__cancel__left_0) ).
fof(c_0_119,axiom,
! [X32,X6,X7,X9] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X9)
| c_HOL_Oord__class_Oless(X7,X6,X9)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X32),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X6),X32),X9) ),
file('<stdin>',cls_add__less__cancel__right_0) ).
fof(c_0_120,axiom,
! [X3,X15,X16] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),c_Lambda_OdB_OVar(X16)),X15)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X3)) ),
file('<stdin>',cls_subst__Var__IT_0) ).
fof(c_0_121,axiom,
! [X39,X27] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X27)),c_Lambda_OdB_OAbs(X39)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X27),X39)) ),
file('<stdin>',cls_rtrancl__beta__Abs_0) ).
fof(c_0_122,axiom,
! [X15,X16,X22,X23,X9] :
( hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(X9),X22),X16),X23),X15) = hAPP(X22,c_HOL_Ominus__class_Ominus(X15,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X16,X15,tc_nat) ),
file('<stdin>',cls_shift__lt_0) ).
fof(c_0_123,axiom,
! [X19,X32,X6,X7,X9] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X9)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X32),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X6),X19),X9)
| ~ c_HOL_Oord__class_Oless(X32,X19,X9)
| ~ c_HOL_Oord__class_Oless(X7,X6,X9) ),
file('<stdin>',cls_add__strict__mono_0) ).
fof(c_0_124,axiom,
! [X29,X27,X14] : hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,X27),X29)),X14) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X27),X14)),hAPP(hAPP(c_Lambda_Olift,X29),X14)),
file('<stdin>',cls_lift_Osimps_I2_J_0) ).
fof(c_0_125,axiom,
! [X4,X5,X18] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X18,X4,tc_nat),c_HOL_Ominus__class_Ominus(X18,X5,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X18,tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
file('<stdin>',cls_diff__less__mono2_0) ).
fof(c_0_126,axiom,
! [X4,X5,X14] :
( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X4),tc_nat) ),
file('<stdin>',cls_nat__add__left__cancel__less_0) ).
fof(c_0_127,axiom,
! [X32,X6,X7,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X6)),X32) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X6),X32)) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I21_J_0) ).
fof(c_0_128,axiom,
! [X19,X32,X7,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X32),X19)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X32)),X19) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I25_J_0) ).
fof(c_0_129,axiom,
! [X32,X6,X7,X9] :
( ~ class_OrderedGroup_Oab__semigroup__add(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X6)),X32) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X6),X32)) ),
file('<stdin>',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
fof(c_0_130,axiom,
! [X32,X6,X7,X9] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X6)),X32) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X6),X32)) ),
file('<stdin>',cls_comm__monoid__add_Omult__assoc_0) ).
fof(c_0_131,axiom,
! [X41,X11,X13,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X11),X41)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X13),X11)),X41) ),
file('<stdin>',cls_class__semiring_Oadd__a_0) ).
fof(c_0_132,axiom,
! [X18,X14,X15,X16] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X18),tc_nat)
| ~ c_HOL_Oord__class_Oless(X14,X18,tc_nat)
| ~ c_HOL_Oord__class_Oless(X16,X15,tc_nat) ),
file('<stdin>',cls_add__less__mono_0) ).
fof(c_0_133,axiom,
! [X14,X15,X16] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X14),X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X16,c_HOL_Ominus__class_Ominus(X15,X14,tc_nat),tc_nat) ),
file('<stdin>',cls_less__diff__conv_0) ).
fof(c_0_134,axiom,
! [X24,X25] : c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X25),X24)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(X25)),c_Type_Otype_Otype__size(X24))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
file('<stdin>',cls_type_Osize_I2_J_0) ).
fof(c_0_135,axiom,
! [X41,X11,X13,X26,X9] :
( ~ class_OrderedGroup_Oab__group__add(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X11),X41)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X11),X26)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X13),X41) = X26 ),
file('<stdin>',cls_add__cancel__21_0) ).
fof(c_0_136,axiom,
! [X14,X15,X16] :
( c_HOL_Oord__class_Oless(X16,c_HOL_Ominus__class_Ominus(X15,X14,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X14),X15,tc_nat) ),
file('<stdin>',cls_less__diff__conv_1) ).
fof(c_0_137,axiom,
! [X29,X27,X14] : hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X29),X14)),X27),X14) = X29,
file('<stdin>',cls_subst__lift_0) ).
fof(c_0_138,axiom,
! [X29,X27,X4] : c_Lambda_Osubstn(X29,X27,X4) = hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),c_Lambda_Oliftn(X4,X27,c_HOL_Ozero__class_Ozero(tc_nat))),X4),
file('<stdin>',cls_substn__subst__n_0) ).
fof(c_0_139,axiom,
! [X29,X27,X14] : c_Lambda_Osubstn(c_Lambda_OdB_OAbs(X29),X27,X14) = c_Lambda_OdB_OAbs(c_Lambda_Osubstn(X29,X27,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)))),
file('<stdin>',cls_substn_Osimps_I3_J_0) ).
fof(c_0_140,axiom,
! [X27,X4,X14] : c_Lambda_Oliftn(X4,c_Lambda_OdB_OAbs(X27),X14) = c_Lambda_OdB_OAbs(c_Lambda_Oliftn(X4,X27,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)))),
file('<stdin>',cls_liftn_Osimps_I3_J_0) ).
fof(c_0_141,axiom,
! [X4,X5,X14] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4)),X14) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X14)),
file('<stdin>',cls_nat__add__assoc_0) ).
fof(c_0_142,axiom,
! [X6,X7,X9] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X9)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X6),X9)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X9),X6,X9)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X9),X7,X9) ),
file('<stdin>',cls_add__pos__pos_0) ).
fof(c_0_143,axiom,
! [X6,X7,X9] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X9)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X6),c_HOL_Ozero__class_Ozero(X9),X9)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X9),X9)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(X9),X9) ),
file('<stdin>',cls_add__neg__neg_0) ).
fof(c_0_144,axiom,
! [X32,X6,X7,X9] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X9)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X32),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X32),X6),X9)
| ~ c_HOL_Oord__class_Oless(X7,X6,X9) ),
file('<stdin>',cls_add__less__cancel__left_1) ).
fof(c_0_145,axiom,
! [X32,X6,X7,X9] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X9)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X32),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X32),X6),X9)
| ~ c_HOL_Oord__class_Oless(X7,X6,X9) ),
file('<stdin>',cls_add__strict__left__mono_0) ).
fof(c_0_146,axiom,
! [X32,X6,X7,X9] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X9)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X32),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X6),X32),X9)
| ~ c_HOL_Oord__class_Oless(X7,X6,X9) ),
file('<stdin>',cls_add__less__cancel__right_1) ).
fof(c_0_147,axiom,
! [X32,X6,X7,X9] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X9)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X32),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X6),X32),X9)
| ~ c_HOL_Oord__class_Oless(X7,X6,X9) ),
file('<stdin>',cls_add__strict__right__mono_0) ).
fof(c_0_148,axiom,
! [X32,X6,X7,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X9)
| c_HOL_Oord__class_Oless(X6,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X32),X9)
| ~ c_HOL_Oord__class_Oless(X6,X32,X9)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X9),X7,X9) ),
file('<stdin>',cls_pos__add__strict_0) ).
fof(c_0_149,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4),tc_nat) ),
file('<stdin>',cls_add__gr__0_0) ).
fof(c_0_150,axiom,
! [X15,X16,X22,X23,X9] :
( hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(X9),X22),X16),X23),X15) = hAPP(X22,X15)
| ~ c_HOL_Oord__class_Oless(X15,X16,tc_nat) ),
file('<stdin>',cls_shift__gt_0) ).
fof(c_0_151,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
file('<stdin>',cls_diff__less_0) ).
fof(c_0_152,axiom,
! [X4,X5,X14] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X5),X4,tc_nat),c_Suc(X14),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),X14,tc_nat),
file('<stdin>',cls_Suc__diff__diff_0) ).
fof(c_0_153,axiom,
! [X16,X22,X23] :
( hAPP(X22,X16) = X23
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),c_Lambda_OdB_OVar(X16)),X23)) ),
file('<stdin>',cls_typing__elims_I1_J_0) ).
fof(c_0_154,axiom,
! [X6,X7,X9] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X9)
| c_HOL_Oord__class_Oless(X7,X6,X9)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X7,X6,X9),c_HOL_Ozero__class_Ozero(X9),X9) ),
file('<stdin>',cls_less__iff__diff__less__0_1) ).
fof(c_0_155,axiom,
! [X7,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X9)
| c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(X9),X9)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X7),c_HOL_Ozero__class_Ozero(X9),X9) ),
file('<stdin>',cls_even__less__0__iff_0) ).
fof(c_0_156,axiom,
! [X7,X9] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X9)
| c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(X9),X9)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X7),c_HOL_Ozero__class_Ozero(X9),X9) ),
file('<stdin>',cls_double__add__less__zero__iff__single__less__zero_0) ).
fof(c_0_157,axiom,
! [X7,X9] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X9)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X9),X7,X9)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X7),X9) ),
file('<stdin>',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
fof(c_0_158,axiom,
! [X10,X11,X12,X13,X9] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X9)
| c_HOL_Ominus__class_Ominus(X13,X11,X9) != c_HOL_Ominus__class_Ominus(X12,X10,X9)
| c_HOL_Oord__class_Oless(X12,X10,X9)
| ~ c_HOL_Oord__class_Oless(X13,X11,X9) ),
file('<stdin>',cls_less__eqI_0) ).
fof(c_0_159,axiom,
! [X10,X11,X12,X13,X9] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X9)
| c_HOL_Ominus__class_Ominus(X13,X11,X9) != c_HOL_Ominus__class_Ominus(X12,X10,X9)
| c_HOL_Oord__class_Oless(X13,X11,X9)
| ~ c_HOL_Oord__class_Oless(X12,X10,X9) ),
file('<stdin>',cls_less__eqI_1) ).
fof(c_0_160,axiom,
! [X27,X14] : hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(X27)),X14) = c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)))),
file('<stdin>',cls_lift_Osimps_I3_J_0) ).
fof(c_0_161,axiom,
! [X4,X5,X14] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
file('<stdin>',cls_nat__add__left__cancel__less_1) ).
fof(c_0_162,axiom,
! [X14,X15,X16] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X14),tc_nat)
| ~ c_HOL_Oord__class_Oless(X16,X15,tc_nat) ),
file('<stdin>',cls_add__less__mono1_0) ).
fof(c_0_163,axiom,
! [X19,X32,X7,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X32),X19)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X32),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X19)) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I22_J_0) ).
fof(c_0_164,axiom,
! [X32,X6,X7,X9] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X6),X32)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X32)) ),
file('<stdin>',cls_comm__monoid__add_Omult__left__commute_0) ).
fof(c_0_165,axiom,
! [X41,X11,X13,X9] :
( ~ class_OrderedGroup_Oab__group__add(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X11),X41)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X13),X41)) ),
file('<stdin>',cls_add__cancel__21_1) ).
fof(c_0_166,axiom,
! [X11,X13,X3,X9] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X3,X9),X13),X11))
| ~ hBOOL(hAPP(hAPP(X3,X13),X11)) ),
file('<stdin>',cls_r__into__rtranclp_0) ).
fof(c_0_167,axiom,
! [X14,X15,X16] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X16,X15,tc_nat),X14,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X16,X14,tc_nat),X15,tc_nat),
file('<stdin>',cls_diff__commute_0) ).
fof(c_0_168,axiom,
! [X29,X4,X14] : c_Lambda_Oliftn(c_Suc(X4),X29,X14) = hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(X4,X29,X14)),X14),
file('<stdin>',cls_liftn__lift_0) ).
fof(c_0_169,axiom,
! [X27,X14,X16] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X16)),X27),X14) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X16,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X14,X16,tc_nat) ),
file('<stdin>',cls_subst__Var_0) ).
fof(c_0_170,axiom,
! [X26,X15,X16] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X15)),X26),X16) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X15,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X16,X15,tc_nat) ),
file('<stdin>',cls_subst__gt_0) ).
fof(c_0_171,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X4,X5,tc_nat),tc_nat) ),
file('<stdin>',cls_zero__less__diff_0) ).
fof(c_0_172,axiom,
! [X14,X15,X16] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X16,X15,tc_nat),X14,tc_nat) = c_HOL_Ominus__class_Ominus(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X14),tc_nat),
file('<stdin>',cls_diff__diff__left_0) ).
fof(c_0_173,axiom,
! [X4,X5,X14] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X4),tc_nat) = c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),
file('<stdin>',cls_diff__cancel_0) ).
fof(c_0_174,axiom,
! [X4,X5,X14] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X14),tc_nat) = c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),
file('<stdin>',cls_diff__cancel2_0) ).
fof(c_0_175,axiom,
! [X4,X5,X18,X14] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X18) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X4)
| ~ c_HOL_Oord__class_Oless(X14,X18,tc_nat)
| c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
file('<stdin>',cls_less__add__eq__less_0) ).
fof(c_0_176,axiom,
! [X14,X15,X16] :
( c_HOL_Oord__class_Oless(X16,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X15),X14,tc_nat) ),
file('<stdin>',cls_add__lessD1_0) ).
fof(c_0_177,axiom,
! [X6,X7,X9] :
( ~ class_OrderedGroup_Ogroup__add(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),c_HOL_Ominus__class_Ominus(X7,X6,X9)),X6) = X7 ),
file('<stdin>',cls_diff__add__cancel_0) ).
fof(c_0_178,axiom,
! [X41,X11,X13] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X41)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X41)),
file('<stdin>',cls_nat__add__left__commute_0) ).
fof(c_0_179,axiom,
! [X7,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X9)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X7),c_HOL_Ozero__class_Ozero(X9),X9)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(X9),X9) ),
file('<stdin>',cls_even__less__0__iff_1) ).
fof(c_0_180,axiom,
! [X7,X9] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X9)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X7),c_HOL_Ozero__class_Ozero(X9),X9)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(X9),X9) ),
file('<stdin>',cls_double__add__less__zero__iff__single__less__zero_1) ).
fof(c_0_181,axiom,
! [X7,X9] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X9)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X7),X9)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X9),X7,X9) ),
file('<stdin>',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
fof(c_0_182,axiom,
! [X6,X7,X9] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X9)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X7,X6,X9),c_HOL_Ozero__class_Ozero(X9),X9)
| ~ c_HOL_Oord__class_Oless(X7,X6,X9) ),
file('<stdin>',cls_less__iff__diff__less__0_0) ).
fof(c_0_183,axiom,
! [X17,X16,X9] :
( ~ class_Ring__and__Field_Osemiring__1(X9)
| c_Nat_Osemiring__1__class_Oof__nat__aux(X17,c_HOL_Ozero__class_Ozero(tc_nat),X16,X9) = X16 ),
file('<stdin>',cls_of__nat__aux_Osimps_I1_J_0) ).
fof(c_0_184,axiom,
! [X27,X14,X16] :
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X16),X27,X14) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X16,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X14,X16,tc_nat) ),
file('<stdin>',cls_substn_Osimps_I1_J_0) ).
fof(c_0_185,axiom,
! [X4,X16] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Suc(X16),tc_nat),X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
file('<stdin>',cls_diff__Suc__less_0) ).
fof(c_0_186,axiom,
! [X30,X9] : c_Nat_Ocompow(c_HOL_Ozero__class_Ozero(tc_nat),X30,X9,X9) = c_Fun_Oid(X9),
file('<stdin>',cls_funpow_Osimps_I1_J_0) ).
fof(c_0_187,axiom,
! [X13,X53] : hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X53),c_Lambda_OdB_OVar(X13)),hAPP(X53,X13))),
file('<stdin>',cls_typing_OVar_0) ).
fof(c_0_188,axiom,
! [X13,X22,X23,X9] : hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(X9),X22),X13),X23),X13) = X23,
file('<stdin>',cls_shift__eq_0) ).
fof(c_0_189,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X4,X5,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
file('<stdin>',cls_zero__less__diff_1) ).
fof(c_0_190,axiom,
! [X4,X5,X9] :
( ~ class_Ring__and__Field_Osemiring__1(X9)
| c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4),X9) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),c_Nat_Osemiring__1__class_Oof__nat(X5,X9)),c_Nat_Osemiring__1__class_Oof__nat(X4,X9)) ),
file('<stdin>',cls_of__nat__add_0) ).
fof(c_0_191,axiom,
! [X4,X14,X15] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X15,X4,tc_nat),X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(X15,X14,tc_nat) ),
file('<stdin>',cls_less__imp__diff__less_0) ).
fof(c_0_192,axiom,
! [X5,X16] : c_HOL_Oord__class_Oless(X16,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X5)),tc_nat),
file('<stdin>',cls_less__add__Suc1_0) ).
fof(c_0_193,axiom,
! [X5,X16] : c_HOL_Oord__class_Oless(X16,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X16)),tc_nat),
file('<stdin>',cls_less__add__Suc2_0) ).
fof(c_0_194,axiom,
! [X13,X5] : c_HOL_Oord__class_Oless(X5,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X13)),tc_nat),
file('<stdin>',cls_less__iff__Suc__add_1) ).
fof(c_0_195,axiom,
! [X29,X16] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X29),c_Lambda_OdB_OVar(X16))))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X29)) ),
file('<stdin>',cls_app__Var__IT_0) ).
fof(c_0_196,axiom,
c_Type_Otypings(hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____),v_as____,v_Ts____),
file('<stdin>',cls_argsT_0) ).
fof(c_0_197,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
file('<stdin>',cls_add__gr__0_2) ).
fof(c_0_198,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
file('<stdin>',cls_add__gr__0_1) ).
fof(c_0_199,axiom,
! [X41,X11,X13,X9] :
( ~ class_Orderings_Opreorder(X9)
| c_HOL_Oord__class_Oless(X13,X41,X9)
| ~ c_HOL_Oord__class_Oless(X11,X41,X9)
| ~ c_HOL_Oord__class_Oless(X13,X11,X9) ),
file('<stdin>',cls_order__less__trans_0) ).
fof(c_0_200,axiom,
! [X41,X11,X13,X9] :
( ~ class_Orderings_Oorder(X9)
| c_HOL_Oord__class_Oless(X41,X13,X9)
| ~ c_HOL_Oord__class_Oless(X41,X11,X9)
| ~ c_HOL_Oord__class_Oless(X11,X13,X9) ),
file('<stdin>',cls_xt1_I10_J_0) ).
fof(c_0_201,axiom,
! [X29,X27] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X27)),c_Lambda_OdB_OAbs(X29)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X27),X29)) ),
file('<stdin>',cls_abs_0) ).
fof(c_0_202,axiom,
! [X4,X5,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X9)
| c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X5,X9),c_Nat_Osemiring__1__class_Oof__nat(X4,X9),X9) ),
file('<stdin>',cls_of__nat__less__iff_0) ).
fof(c_0_203,axiom,
! [X41,X11,X13] :
( c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X41),tc_nat)
| ~ c_HOL_Oord__class_Oless(X13,X11,tc_nat) ),
file('<stdin>',cls_termination__basic__simps_I1_J_0) ).
fof(c_0_204,axiom,
! [X41,X11,X13] :
( c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X41),tc_nat)
| ~ c_HOL_Oord__class_Oless(X13,X41,tc_nat) ),
file('<stdin>',cls_termination__basic__simps_I2_J_0) ).
fof(c_0_205,axiom,
! [X5,X15,X16] :
( c_HOL_Oord__class_Oless(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X5),tc_nat)
| ~ c_HOL_Oord__class_Oless(X16,X15,tc_nat) ),
file('<stdin>',cls_trans__less__add1_0) ).
fof(c_0_206,axiom,
! [X5,X15,X16] :
( c_HOL_Oord__class_Oless(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X15),tc_nat)
| ~ c_HOL_Oord__class_Oless(X16,X15,tc_nat) ),
file('<stdin>',cls_trans__less__add2_0) ).
fof(c_0_207,axiom,
! [X14,X15,X16] :
( c_HOL_Oord__class_Oless(c_Suc(X16),X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(X15,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(X16,X15,tc_nat) ),
file('<stdin>',cls_less__trans__Suc_0) ).
fof(c_0_208,axiom,
! [X15,X16] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X16),X16,tc_nat),
file('<stdin>',cls_not__add__less2_0) ).
fof(c_0_209,axiom,
! [X15,X16] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X15),X16,tc_nat),
file('<stdin>',cls_not__add__less1_0) ).
fof(c_0_210,axiom,
! [X4] :
( c_Suc(c_HOL_Ominus__class_Ominus(X4,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X4
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
file('<stdin>',cls_Suc__pred_0) ).
fof(c_0_211,axiom,
! [X4,X5] : c_HOL_Ominus__class_Ominus(X5,c_Suc(X4),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X5,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X4,tc_nat),
file('<stdin>',cls_diff__Suc__eq__diff__pred_0) ).
fof(c_0_212,axiom,
! [X29,X16] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X29),X16)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X29)) ),
file('<stdin>',cls_lift__IT_0) ).
fof(c_0_213,axiom,
! [X4,X14,X16] :
( c_Lambda_Oliftn(X4,c_Lambda_OdB_OVar(X16),X14) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X4))
| c_HOL_Oord__class_Oless(X16,X14,tc_nat) ),
file('<stdin>',cls_liftn_Osimps_I1_J_1) ).
fof(c_0_214,axiom,
! [X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X9)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),c_HOL_Oone__class_Oone(X9)),c_HOL_Oone__class_Oone(X9)),X9) ),
file('<stdin>',cls_zero__less__two_0) ).
fof(c_0_215,axiom,
! [X4,X5] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Ominus__class_Ominus(X5,X4,tc_nat)) = X5
| c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
file('<stdin>',cls_add__diff__inverse_0) ).
fof(c_0_216,axiom,
! [X4] :
( X4 = c_Suc(c_HOL_Ominus__class_Ominus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
file('<stdin>',cls_Suc__pred_H_0) ).
fof(c_0_217,axiom,
! [X4] :
( c_Suc(c_HOL_Ominus__class_Ominus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X4
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
file('<stdin>',cls_Suc__diff__1_0) ).
fof(c_0_218,axiom,
! [X14,X16] :
( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X16)),X14) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),c_HOL_Oone__class_Oone(tc_nat)))
| c_HOL_Oord__class_Oless(X16,X14,tc_nat) ),
file('<stdin>',cls_lift_Osimps_I1_J_1) ).
fof(c_0_219,axiom,
! [X4,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X9)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X9),c_Nat_Osemiring__1__class_Oof__nat(X4,X9),X9) ),
file('<stdin>',cls_of__nat__0__less__iff_0) ).
fof(c_0_220,axiom,
! [X26,X15,X16] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X15)),X26),X16) = c_Lambda_OdB_OVar(X15)
| ~ c_HOL_Oord__class_Oless(X15,X16,tc_nat) ),
file('<stdin>',cls_subst__lt_0) ).
fof(c_0_221,axiom,
! [X4,X5,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X9)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X5,X9),c_Nat_Osemiring__1__class_Oof__nat(X4,X9),X9)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
file('<stdin>',cls_of__nat__less__iff_1) ).
fof(c_0_222,axiom,
! [X4,X5,X8] :
( hBOOL(hAPP(hAPP(X8,X4),X5))
| c_HOL_Oord__class_Oless(X4,X5,tc_nat)
| X5 = X4
| c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
file('<stdin>',cls_nat__less__cases_0) ).
fof(c_0_223,axiom,
! [X3,X7,X9] : hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X3,X9),X7),X7)),
file('<stdin>',cls_rtranclp_Ortrancl__refl_0) ).
fof(c_0_224,axiom,
! [X13,X3,X9] : hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X3,X9),X13),X13)),
file('<stdin>',cls_Nitpick_Ortranclp__def_1) ).
fof(c_0_225,axiom,
! [X4,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X9)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X9),c_Nat_Osemiring__1__class_Oof__nat(X4,X9),X9)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
file('<stdin>',cls_of__nat__0__less__iff_1) ).
fof(c_0_226,axiom,
! [X41,X11,X13,X9] :
( ~ class_Ring__and__Field_Oidom(X9)
| ~ class_Int_Onumber__ring(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X13),X11) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X13),X41)
| X11 = X41 ),
file('<stdin>',cls_class__ringb_Oadd__cancel_0) ).
fof(c_0_227,axiom,
! [X10,X12,X13,X9] :
( ~ class_OrderedGroup_Oab__group__add(X9)
| c_HOL_Ominus__class_Ominus(X13,X13,X9) != c_HOL_Ominus__class_Ominus(X12,X10,X9)
| X12 = X10 ),
file('<stdin>',cls_eq__eqI_0) ).
fof(c_0_228,axiom,
! [X11,X20,X13,X9] :
( ~ class_OrderedGroup_Oab__group__add(X9)
| c_HOL_Ominus__class_Ominus(X20,X11,X9) != c_HOL_Ominus__class_Ominus(X13,X13,X9)
| X20 = X11 ),
file('<stdin>',cls_eq__eqI_1) ).
fof(c_0_229,axiom,
! [X6,X7,X9] :
( ~ class_Orderings_Opreorder(X9)
| ~ c_HOL_Oord__class_Oless(X6,X7,X9)
| ~ c_HOL_Oord__class_Oless(X7,X6,X9) ),
file('<stdin>',cls_order__less__asym_H_0) ).
fof(c_0_230,axiom,
! [X11,X13,X9] :
( ~ class_Orderings_Opreorder(X9)
| ~ c_HOL_Oord__class_Oless(X11,X13,X9)
| ~ c_HOL_Oord__class_Oless(X13,X11,X9) ),
file('<stdin>',cls_order__less__asym_0) ).
fof(c_0_231,axiom,
! [X11,X13,X9] :
( ~ class_Orderings_Olinorder(X9)
| ~ c_HOL_Oord__class_Oless(X13,X11,X9)
| ~ c_HOL_Oord__class_Oless(X11,X13,X9) ),
file('<stdin>',cls_not__less__iff__gr__or__eq_1) ).
fof(c_0_232,axiom,
! [X6,X7,X9] :
( ~ class_Orderings_Oorder(X9)
| ~ c_HOL_Oord__class_Oless(X7,X6,X9)
| ~ c_HOL_Oord__class_Oless(X6,X7,X9) ),
file('<stdin>',cls_xt1_I9_J_0) ).
fof(c_0_233,axiom,
! [X4,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,c_Suc(X5),tc_nat) ),
file('<stdin>',cls_not__less__eq_1) ).
fof(c_0_234,axiom,
! [X4,X5] :
( c_HOL_Ominus__class_Ominus(X4,X5,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X5,X4,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X5 = X4 ),
file('<stdin>',cls_diffs0__imp__equal_0) ).
fof(c_0_235,axiom,
! [X7,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X9)
| c_HOL_Oord__class_Oless(X7,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),c_HOL_Oone__class_Oone(X9)),X9) ),
file('<stdin>',cls_less__add__one_0) ).
fof(c_0_236,axiom,
! [X32,X6,X7,X9] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X6),X7) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X32),X7)
| X6 = X32 ),
file('<stdin>',cls_add__right__cancel_0) ).
fof(c_0_237,axiom,
! [X32,X6,X7,X9] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X6) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X32)
| X6 = X32 ),
file('<stdin>',cls_add__left__cancel_0) ).
fof(c_0_238,axiom,
! [X32,X6,X7,X9] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X6) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X32)
| X6 = X32 ),
file('<stdin>',cls_add__imp__eq_0) ).
fof(c_0_239,axiom,
! [X13,X27] :
( c_HOL_Oord__class_Oless(X13,X13,tc_nat)
| c_Lambda_Osubstn(c_Lambda_OdB_OVar(X13),X27,X13) = c_Lambda_Oliftn(X13,X27,c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('<stdin>',cls_substn_Osimps_I1_J_1) ).
fof(c_0_240,axiom,
! [X27,X14,X16] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X16)),X27),X14) = c_Lambda_OdB_OVar(X16)
| X16 = X14
| c_HOL_Oord__class_Oless(X14,X16,tc_nat) ),
file('<stdin>',cls_subst__Var_2) ).
fof(c_0_241,axiom,
! [X6,X7,X9] :
( ~ class_OrderedGroup_Ogroup__add(X9)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X6),X6,X9) = X7 ),
file('<stdin>',cls_add__diff__cancel_0) ).
fof(c_0_242,axiom,
! [X13,X27] :
( c_HOL_Oord__class_Oless(X13,X13,tc_nat)
| hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X13)),X27),X13) = X27 ),
file('<stdin>',cls_subst__Var_1) ).
fof(c_0_243,axiom,
! [X4,X5] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),c_Suc(X5),tc_nat),
file('<stdin>',cls_diff__less__Suc_0) ).
fof(c_0_244,axiom,
! [X29,X16] : ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X16)),X29)),
file('<stdin>',cls_beta__cases_I1_J_0) ).
fof(c_0_245,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X5),c_Suc(X4),tc_nat) ),
file('<stdin>',cls_Suc__less__eq_0) ).
fof(c_0_246,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_ea______),v_ua______),v_T____)),
file('<stdin>',cls_Var_I4_J_0) ).
fof(c_0_247,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_e____),v_u____),v_T____)),
file('<stdin>',cls_uT_0) ).
fof(c_0_248,axiom,
! [X4,X5] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X5)),X4) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4)),
file('<stdin>',cls_add__Suc_0) ).
fof(c_0_249,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_Suc(X5),c_Suc(X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
file('<stdin>',cls_Suc__mono_0) ).
fof(c_0_250,axiom,
! [X13,X4] :
( c_HOL_Oord__class_Oless(c_Suc(X13),c_Suc(X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(X13,X4,tc_nat) ),
file('<stdin>',cls_less__Suc__eq__0__disj_3) ).
fof(c_0_251,axiom,
! [X4,X5] :
( X4 = X5
| ~ c_HOL_Oord__class_Oless(X4,c_Suc(X5),tc_nat)
| c_HOL_Oord__class_Oless(X4,X5,tc_nat) ),
file('<stdin>',cls_not__less__less__Suc__eq_0) ).
fof(c_0_252,axiom,
! [X4,X5] :
( X5 = X4
| ~ c_HOL_Oord__class_Oless(X4,c_Suc(X5),tc_nat)
| c_HOL_Oord__class_Oless(X4,X5,tc_nat) ),
file('<stdin>',cls_less__antisym_0) ).
fof(c_0_253,axiom,
! [X4,X5] :
( X5 = X4
| c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,c_Suc(X4),tc_nat) ),
file('<stdin>',cls_less__SucE_0) ).
fof(c_0_254,axiom,
! [X4,X14,X16] :
( c_Lambda_Oliftn(X4,c_Lambda_OdB_OVar(X16),X14) = c_Lambda_OdB_OVar(X16)
| ~ c_HOL_Oord__class_Oless(X16,X14,tc_nat) ),
file('<stdin>',cls_liftn_Osimps_I1_J_0) ).
fof(c_0_255,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_Suc(X5),X4,tc_nat)
| c_Suc(X5) = X4
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
file('<stdin>',cls_Suc__lessI_0) ).
fof(c_0_256,axiom,
! [X4,X5,X14] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X5) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X4)
| X5 = X4 ),
file('<stdin>',cls_nat__add__left__cancel_0) ).
fof(c_0_257,axiom,
! [X4,X5,X14] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X14) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X14)
| X5 = X4 ),
file('<stdin>',cls_nat__add__right__cancel_0) ).
fof(c_0_258,axiom,
! [X41,X11,X13] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X11) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X41)
| X11 = X41 ),
file('<stdin>',cls_natgb_Oadd__cancel_0) ).
fof(c_0_259,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X5),X4,tc_nat) ),
file('<stdin>',cls_Suc__lessD_0) ).
fof(c_0_260,axiom,
! [X4,X5] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),c_Suc(X4)) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4)),
file('<stdin>',cls_add__Suc__right_0) ).
fof(c_0_261,axiom,
! [X29,X27] : c_Lambda_Osubstn(X29,X27,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),X27),c_HOL_Ozero__class_Ozero(tc_nat)),
file('<stdin>',cls_substn__subst__0_0) ).
fof(c_0_262,axiom,
! [X4,X5] : c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X5),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_diff__add__0_0) ).
fof(c_0_263,axiom,
! [X4,X5] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X5),X4,tc_nat) = X5,
file('<stdin>',cls_diff__add__inverse_0) ).
fof(c_0_264,axiom,
! [X4,X5] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4),X4,tc_nat) = X5,
file('<stdin>',cls_diff__add__inverse2_0) ).
fof(c_0_265,axiom,
! [X5,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X9)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X5,X9),c_HOL_Ozero__class_Ozero(X9),X9) ),
file('<stdin>',cls_of__nat__less__0__iff_0) ).
fof(c_0_266,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(X5,c_Suc(X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
file('<stdin>',cls_less__SucI_0) ).
fof(c_0_267,axiom,
! [X14,X16] :
( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X16)),X14) = c_Lambda_OdB_OVar(X16)
| ~ c_HOL_Oord__class_Oless(X16,X14,tc_nat) ),
file('<stdin>',cls_lift_Osimps_I1_J_0) ).
fof(c_0_268,axiom,
! [X42,X8,X43,X9] : hAPP(c_COMBK(X8,X9,X43),X42) = X8,
file('<stdin>',cls_COMBK__def_0) ).
fof(c_0_269,axiom,
! [X27,X14,X16] :
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X16),X27,X14) = c_Lambda_OdB_OVar(X16)
| X16 = X14
| c_HOL_Oord__class_Oless(X14,X16,tc_nat) ),
file('<stdin>',cls_substn_Osimps_I1_J_2) ).
fof(c_0_270,axiom,
! [X11,X13,X9] :
( ~ class_Orderings_Olinorder(X9)
| X13 = X11
| c_HOL_Oord__class_Oless(X13,X11,X9)
| c_HOL_Oord__class_Oless(X11,X13,X9) ),
file('<stdin>',cls_linorder__antisym__conv3_0) ).
fof(c_0_271,axiom,
! [X11,X13,X9] :
( ~ class_Orderings_Olinorder(X9)
| c_HOL_Oord__class_Oless(X11,X13,X9)
| X13 = X11
| c_HOL_Oord__class_Oless(X13,X11,X9) ),
file('<stdin>',cls_linorder__less__linear_0) ).
fof(c_0_272,axiom,
! [X11,X13,X9] :
( ~ class_Orderings_Olinorder(X9)
| c_HOL_Oord__class_Oless(X11,X13,X9)
| c_HOL_Oord__class_Oless(X13,X11,X9)
| X13 = X11 ),
file('<stdin>',cls_linorder__neqE_0) ).
fof(c_0_273,axiom,
! [X11,X13,X9] :
( ~ class_Orderings_Olinorder(X9)
| X13 = X11
| c_HOL_Oord__class_Oless(X11,X13,X9)
| c_HOL_Oord__class_Oless(X13,X11,X9) ),
file('<stdin>',cls_not__less__iff__gr__or__eq_0) ).
fof(c_0_274,axiom,
! [X11,X13,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X9)
| c_HOL_Oord__class_Oless(X11,X13,X9)
| c_HOL_Oord__class_Oless(X13,X11,X9)
| X13 = X11 ),
file('<stdin>',cls_linorder__neqE__ordered__idom_0) ).
fof(c_0_275,axiom,
! [X56,X24,X57,X25] :
( hAPP(hAPP(c_Type_Otype_OFun,X25),X24) != hAPP(hAPP(c_Type_Otype_OFun,X57),X56)
| X25 = X57 ),
file('<stdin>',cls_type_Osimps_I2_J_0) ).
fof(c_0_276,axiom,
! [X56,X24,X57,X25] :
( hAPP(hAPP(c_Type_Otype_OFun,X25),X24) != hAPP(hAPP(c_Type_Otype_OFun,X57),X56)
| X24 = X56 ),
file('<stdin>',cls_type_Osimps_I2_J_1) ).
fof(c_0_277,axiom,
! [X45,X51,X46,X52] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X52),X51) != hAPP(hAPP(c_Lambda_OdB_OApp,X46),X45)
| X52 = X46 ),
file('<stdin>',cls_dB_Osimps_I2_J_0) ).
fof(c_0_278,axiom,
! [X45,X51,X46,X52] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X52),X51) != hAPP(hAPP(c_Lambda_OdB_OApp,X46),X45)
| X51 = X45 ),
file('<stdin>',cls_dB_Osimps_I2_J_1) ).
fof(c_0_279,axiom,
! [X4,X5] : c_HOL_Ominus__class_Ominus(c_Suc(X5),c_Suc(X4),tc_nat) = c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),
file('<stdin>',cls_diff__Suc__Suc_0) ).
fof(c_0_280,axiom,
! [X5,X9] :
( ~ class_Ring__and__Field_Osemiring__1(X9)
| c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X5),X9) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),c_HOL_Oone__class_Oone(X9)),c_Nat_Osemiring__1__class_Oof__nat(X5,X9)) ),
file('<stdin>',cls_of__nat__Suc_0) ).
fof(c_0_281,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(X4,c_Suc(X5),tc_nat)
| c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
file('<stdin>',cls_not__less__eq_0) ).
fof(c_0_282,axiom,
! [X13] :
( c_HOL_Oord__class_Oless(X13,X13,tc_nat)
| c_HOL_Oord__class_Oless(X13,c_Suc(X13),tc_nat) ),
file('<stdin>',cls_not__less__less__Suc__eq_1) ).
fof(c_0_283,axiom,
! [X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X9)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X9),c_HOL_Ozero__class_Ozero(X9),X9) ),
file('<stdin>',cls_not__one__less__zero_0) ).
fof(c_0_284,axiom,
! [X32,X7,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X32) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X32),X7) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I24_J_0) ).
fof(c_0_285,axiom,
! [X6,X7,X9] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X6) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X6),X7) ),
file('<stdin>',cls_comm__monoid__add_Omult__commute_0) ).
fof(c_0_286,axiom,
! [X11,X13,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X13),X11) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X11),X13) ),
file('<stdin>',cls_class__semiring_Oadd__c_0) ).
fof(c_0_287,axiom,
! [X26,X14] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X14)),X26),X14) = X26,
file('<stdin>',cls_subst__eq_0) ).
fof(c_0_288,axiom,
! [X4,X5] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X5)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),c_Suc(X4)),
file('<stdin>',cls_add__Suc__shift_0) ).
fof(c_0_289,axiom,
! [X11,X13] :
( c_HOL_Oord__class_Oless(X11,X13,tc_nat)
| c_HOL_Oord__class_Oless(X13,X11,tc_nat)
| X13 = X11 ),
file('<stdin>',cls_linorder__neqE__nat_0) ).
fof(c_0_290,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(X4,X5,tc_nat)
| c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| X5 = X4 ),
file('<stdin>',cls_nat__neq__iff_0) ).
fof(c_0_291,axiom,
! [X11,X13,X9] :
( ~ class_Ring__and__Field_Oidom(X9)
| ~ class_Int_Onumber__ring(X9)
| c_HOL_Ominus__class_Ominus(X13,X11,X9) != c_HOL_Ozero__class_Ozero(X9)
| X13 = X11 ),
file('<stdin>',cls_class__ringb_Osubr0__iff_0) ).
fof(c_0_292,axiom,
! [X4] :
( X4 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
file('<stdin>',cls_less__Suc0_0) ).
fof(c_0_293,axiom,
! [X13,X7,X9] :
( ~ class_Ring__and__Field_Oidom(X9)
| ~ class_Int_Onumber__ring(X9)
| X13 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X13),X7)
| X7 = c_HOL_Ozero__class_Ozero(X9) ),
file('<stdin>',cls_class__ringb_Oadd__r0__iff_0) ).
fof(c_0_294,axiom,
! [X6,X7,X9] :
( ~ class_OrderedGroup_Oab__group__add(X9)
| c_HOL_Ominus__class_Ominus(X7,X6,X9) != c_HOL_Ozero__class_Ozero(X9)
| X7 = X6 ),
file('<stdin>',cls_eq__iff__diff__eq__0_1) ).
fof(c_0_295,axiom,
! [X6,X7,X9] :
( ~ class_OrderedGroup_Ogroup__add(X9)
| c_HOL_Ominus__class_Ominus(X7,X6,X9) != c_HOL_Ozero__class_Ozero(X9)
| X7 = X6 ),
file('<stdin>',cls_right__minus__eq_0) ).
fof(c_0_296,axiom,
! [X7,X9] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X7) != c_HOL_Ozero__class_Ozero(X9)
| X7 = c_HOL_Ozero__class_Ozero(X9) ),
file('<stdin>',cls_double__eq__0__iff_0) ).
fof(c_0_297,axiom,
! [X4,X5] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X5 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('<stdin>',cls_add__is__1_1) ).
fof(c_0_298,axiom,
! [X4,X5] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4)
| X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X5 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('<stdin>',cls_one__is__add_1) ).
fof(c_0_299,axiom,
! [X4,X5] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X5 = c_HOL_Ozero__class_Ozero(tc_nat)
| X5 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('<stdin>',cls_add__is__1_0) ).
fof(c_0_300,axiom,
! [X4,X5] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_add__is__1_3) ).
fof(c_0_301,axiom,
! [X4,X5] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4)
| X5 = c_HOL_Ozero__class_Ozero(tc_nat)
| X5 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('<stdin>',cls_one__is__add_0) ).
fof(c_0_302,axiom,
! [X4,X5] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4)
| X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_one__is__add_3) ).
fof(c_0_303,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('<stdin>',cls_neq0__conv_1) ).
fof(c_0_304,axiom,
! [X13,X9] :
( ~ class_Orderings_Opreorder(X9)
| ~ c_HOL_Oord__class_Oless(X13,X13,X9) ),
file('<stdin>',cls_order__less__irrefl_0) ).
fof(c_0_305,axiom,
! [X13,X9] :
( ~ class_Orderings_Olinorder(X9)
| ~ c_HOL_Oord__class_Oless(X13,X13,X9) ),
file('<stdin>',cls_linorder__neq__iff_1) ).
fof(c_0_306,axiom,
! [X13,X9] :
( ~ class_Orderings_Oorder(X9)
| ~ c_HOL_Oord__class_Oless(X13,X13,X9) ),
file('<stdin>',cls_order__less__le_1) ).
fof(c_0_307,axiom,
! [X4,X5] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X5),
file('<stdin>',cls_nat__add__commute_0) ).
fof(c_0_308,axiom,
! [X4,X5] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X5 = c_HOL_Ozero__class_Ozero(tc_nat)
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_add__is__1_2) ).
fof(c_0_309,axiom,
! [X4,X5] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4)
| X5 = c_HOL_Ozero__class_Ozero(tc_nat)
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_one__is__add_2) ).
fof(c_0_310,axiom,
! [X5] : ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('<stdin>',cls_gr__implies__not0_0) ).
fof(c_0_311,axiom,
! [X4] : ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('<stdin>',cls_not__less0_0) ).
fof(c_0_312,axiom,
! [X70,X71,X9] :
( X71 = X70
| ~ c_fequal(X71,X70,X9) ),
file('<stdin>',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(c_0_313,axiom,
! [X4] : ~ c_HOL_Oord__class_Oless(X4,X4,tc_nat),
file('<stdin>',cls_less__not__refl_0) ).
fof(c_0_314,axiom,
! [X13] : ~ c_HOL_Oord__class_Oless(X13,X13,tc_nat),
file('<stdin>',cls_nat__less__le_1) ).
fof(c_0_315,axiom,
! [X3] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X3)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X3)) ),
file('<stdin>',cls_Lambda_0) ).
fof(c_0_316,axiom,
! [X9] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),c_HOL_Ozero__class_Ozero(X9)),c_HOL_Ozero__class_Ozero(X9)) = c_HOL_Ozero__class_Ozero(X9) ),
file('<stdin>',cls_double__eq__0__iff_1) ).
fof(c_0_317,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
file('<stdin>',cls_add__is__1_4) ).
fof(c_0_318,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)),
file('<stdin>',cls_one__is__add_4) ).
fof(c_0_319,axiom,
! [X4,X5] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4) != c_HOL_Ozero__class_Ozero(tc_nat)
| X5 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_add__is__0_0) ).
fof(c_0_320,axiom,
! [X4,X5] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4) != c_HOL_Ozero__class_Ozero(tc_nat)
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_add__is__0_1) ).
fof(c_0_321,axiom,
! [X4,X5] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4) != X5
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_add__eq__self__zero_0) ).
fof(c_0_322,axiom,
! [X13,X7] :
( X13 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X7)
| X7 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_natgb_Oadd__r0__iff_0) ).
fof(c_0_323,axiom,
! [X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X9)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X9),c_HOL_Oone__class_Oone(X9),X9) ),
file('<stdin>',cls_zero__less__one_0) ).
fof(c_0_324,axiom,
! [X13,X9] :
( ~ class_Ring__and__Field_Oidom(X9)
| ~ class_Int_Onumber__ring(X9)
| X13 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X13),c_HOL_Ozero__class_Ozero(X9)) ),
file('<stdin>',cls_class__ringb_Oadd__r0__iff_1) ).
fof(c_0_325,axiom,
! [X13,X9] :
( ~ class_Ring__and__Field_Oidom(X9)
| ~ class_Int_Onumber__ring(X9)
| c_HOL_Ominus__class_Ominus(X13,X13,X9) = c_HOL_Ozero__class_Ozero(X9) ),
file('<stdin>',cls_class__ringb_Osubr0__iff_1) ).
fof(c_0_326,axiom,
! [X7,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),c_HOL_Ozero__class_Ozero(X9)),X7) = X7 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I5_J_0) ).
fof(c_0_327,axiom,
! [X7,X9] :
( ~ class_OrderedGroup_Omonoid__add(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),c_HOL_Ozero__class_Ozero(X9)),X7) = X7 ),
file('<stdin>',cls_add__0__left_0) ).
fof(c_0_328,axiom,
! [X7,X9] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),c_HOL_Ozero__class_Ozero(X9)),X7) = X7 ),
file('<stdin>',cls_comm__monoid__add_Omult__1_0) ).
fof(c_0_329,axiom,
! [X13,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),c_HOL_Ozero__class_Ozero(X9)),X13) = X13 ),
file('<stdin>',cls_class__semiring_Oadd__0_0) ).
fof(c_0_330,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
file('<stdin>',cls_one__is__add_5) ).
fof(c_0_331,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
file('<stdin>',cls_add__is__1_5) ).
fof(c_0_332,axiom,
! [X7,X9] :
( ~ class_OrderedGroup_Ogroup__add(X9)
| c_HOL_Ominus__class_Ominus(X7,c_HOL_Ozero__class_Ozero(X9),X9) = X7 ),
file('<stdin>',cls_diff__0__right_0) ).
fof(c_0_333,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
file('<stdin>',cls_less__Suc0_1) ).
fof(c_0_334,axiom,
! [X7,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),c_HOL_Ozero__class_Ozero(X9)) = X7 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(c_0_335,axiom,
! [X7,X9] :
( ~ class_OrderedGroup_Omonoid__add(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),c_HOL_Ozero__class_Ozero(X9)) = X7 ),
file('<stdin>',cls_monoid__add__class_Oadd__0__right_0) ).
fof(c_0_336,axiom,
! [X7,X9] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),c_HOL_Ozero__class_Ozero(X9)) = X7 ),
file('<stdin>',cls_comm__monoid__add_Omult__1__right_0) ).
fof(c_0_337,axiom,
! [X13,X9] :
( ~ class_OrderedGroup_Oab__group__add(X9)
| c_HOL_Ominus__class_Ominus(X13,X13,X9) = c_HOL_Ozero__class_Ozero(X9) ),
file('<stdin>',cls_eq__iff__diff__eq__0_0) ).
fof(c_0_338,axiom,
! [X13,X9] :
( ~ class_OrderedGroup_Ogroup__add(X9)
| c_HOL_Ominus__class_Ominus(X13,X13,X9) = c_HOL_Ozero__class_Ozero(X9) ),
file('<stdin>',cls_right__minus__eq_1) ).
fof(c_0_339,axiom,
! [X7,X9] :
( ~ class_OrderedGroup_Ogroup__add(X9)
| c_HOL_Ominus__class_Ominus(X7,X7,X9) = c_HOL_Ozero__class_Ozero(X9) ),
file('<stdin>',cls_diff__self_0) ).
fof(c_0_340,axiom,
! [X49,X51,X52] : hAPP(hAPP(c_Lambda_OdB_OApp,X52),X51) != c_Lambda_OdB_OAbs(X49),
file('<stdin>',cls_dB_Osimps_I8_J_0) ).
fof(c_0_341,axiom,
! [X49,X51,X52] : c_Lambda_OdB_OAbs(X49) != hAPP(hAPP(c_Lambda_OdB_OApp,X52),X51),
file('<stdin>',cls_dB_Osimps_I9_J_0) ).
fof(c_0_342,axiom,
! [X40,X45,X46] : c_Lambda_OdB_OVar(X40) != hAPP(hAPP(c_Lambda_OdB_OApp,X46),X45),
file('<stdin>',cls_dB_Osimps_I4_J_0) ).
fof(c_0_343,axiom,
! [X40,X45,X46] : hAPP(hAPP(c_Lambda_OdB_OApp,X46),X45) != c_Lambda_OdB_OVar(X40),
file('<stdin>',cls_dB_Osimps_I5_J_0) ).
fof(c_0_344,axiom,
! [X4] : c_HOL_Ominus__class_Ominus(c_Suc(X4),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X4,
file('<stdin>',cls_diff__Suc__1_0) ).
fof(c_0_345,axiom,
! [X4] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X4),tc_nat),
file('<stdin>',cls_zero__less__Suc_0) ).
fof(c_0_346,axiom,
! [X13] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X13),tc_nat),
file('<stdin>',cls_gr0__conv__Suc_1) ).
fof(c_0_347,axiom,
! [X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_gr0I_0) ).
fof(c_0_348,axiom,
! [X13] : c_HOL_Oord__class_Oless(X13,c_Suc(X13),tc_nat),
file('<stdin>',cls_less__Suc__eq_2) ).
fof(c_0_349,axiom,
! [X4] : c_HOL_Oord__class_Oless(X4,c_Suc(X4),tc_nat),
file('<stdin>',cls_lessI_0) ).
fof(c_0_350,axiom,
! [X29,X14] : c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X29,X14) = X29,
file('<stdin>',cls_liftn__0_0) ).
fof(c_0_351,axiom,
! [X4] : c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_diff__0__eq__0_0) ).
fof(c_0_352,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),
file('<stdin>',cls_add__is__0_2) ).
fof(c_0_353,axiom,
! [X5] : c_HOL_Ominus__class_Ominus(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X5,
file('<stdin>',cls_minus__nat_Odiff__0_0) ).
fof(c_0_354,axiom,
! [X4] : c_Suc(X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X4),
file('<stdin>',cls_Suc__eq__plus1__left_0) ).
fof(c_0_355,axiom,
! [X5] : c_HOL_Ominus__class_Ominus(X5,X5,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_diff__self__eq__0_0) ).
fof(c_0_356,axiom,
! [X13,X9] : c_fequal(X13,X13,X9),
file('<stdin>',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
fof(c_0_357,axiom,
! [X3,X9] : c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(X3,X9),X9) = c_Transitive__Closure_Ortranclp(X3,X9),
file('<stdin>',cls_rtranclp__idemp_0) ).
fof(c_0_358,axiom,
! [X4,X5,X9] :
( ~ class_Nat_Osemiring__char__0(X9)
| c_Nat_Osemiring__1__class_Oof__nat(X5,X9) != c_Nat_Osemiring__1__class_Oof__nat(X4,X9)
| X5 = X4 ),
file('<stdin>',cls_of__nat__eq__iff_0) ).
fof(c_0_359,axiom,
! [X4] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X4) = X4,
file('<stdin>',cls_plus__nat_Oadd__0_0) ).
fof(c_0_360,axiom,
! [X4] : c_Suc(X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),
file('<stdin>',cls_Suc__eq__plus1_0) ).
fof(c_0_361,axiom,
! [X5] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),c_HOL_Ozero__class_Ozero(tc_nat)) = X5,
file('<stdin>',cls_Nat_Oadd__0__right_0) ).
fof(c_0_362,axiom,
! [X13] : X13 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Ozero__class_Ozero(tc_nat)),
file('<stdin>',cls_natgb_Oadd__r0__iff_1) ).
fof(c_0_363,axiom,
! [X4] : hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X4))),
file('<stdin>',cls_Var__IT_0) ).
fof(c_0_364,axiom,
! [X68,X69] :
( class_Orderings_Oorder(tc_fun(X68,X69))
| ~ class_Orderings_Oorder(X69) ),
file('<stdin>',clsarity_fun__Orderings_Oorder) ).
fof(c_0_365,axiom,
! [X68,X69] :
( class_Orderings_Opreorder(tc_fun(X68,X69))
| ~ class_Orderings_Opreorder(X69) ),
file('<stdin>',clsarity_fun__Orderings_Opreorder) ).
fof(c_0_366,axiom,
! [X9] :
( ~ class_Ring__and__Field_Osemiring__1(X9)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X9) = c_HOL_Oone__class_Oone(X9) ),
file('<stdin>',cls_of__nat__1_0) ).
fof(c_0_367,axiom,
! [X9] :
( ~ class_Ring__and__Field_Osemiring__1(X9)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X9) = c_HOL_Ozero__class_Ozero(X9) ),
file('<stdin>',cls_of__nat__0_0) ).
fof(c_0_368,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
file('<stdin>',cls_uIT_0) ).
fof(c_0_369,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_ua______)),
file('<stdin>',cls_Var_I3_J_0) ).
fof(c_0_370,axiom,
! [X13,X9] : hAPP(c_Fun_Oid(X9),X13) = X13,
file('<stdin>',cls_id__apply_0) ).
fof(c_0_371,axiom,
! [X9] :
( ~ class_Ring__and__Field_Ozero__neq__one(X9)
| c_HOL_Ozero__class_Ozero(X9) != c_HOL_Oone__class_Oone(X9) ),
file('<stdin>',cls_zero__neq__one_0) ).
fof(c_0_372,axiom,
! [X9] :
( ~ class_Ring__and__Field_Ozero__neq__one(X9)
| c_HOL_Oone__class_Oone(X9) != c_HOL_Ozero__class_Ozero(X9) ),
file('<stdin>',cls_one__neq__zero_0) ).
fof(c_0_373,axiom,
hAPP(c_Fun_Oid(t_a),v_x) = v_x,
file('<stdin>',cls_id__def_0) ).
fof(c_0_374,axiom,
! [X33,X40] :
( c_Lambda_OdB_OVar(X40) != c_Lambda_OdB_OVar(X33)
| X40 = X33 ),
file('<stdin>',cls_dB_Osimps_I1_J_0) ).
fof(c_0_375,axiom,
! [X49,X50] :
( c_Lambda_OdB_OAbs(X50) != c_Lambda_OdB_OAbs(X49)
| X50 = X49 ),
file('<stdin>',cls_dB_Osimps_I3_J_0) ).
fof(c_0_376,axiom,
! [X11,X13] :
( c_Suc(X13) != c_Suc(X11)
| X13 = X11 ),
file('<stdin>',cls_Suc__inject_0) ).
fof(c_0_377,axiom,
! [X33,X40] :
( c_Suc(X40) != c_Suc(X33)
| X40 = X33 ),
file('<stdin>',cls_nat_Oinject_0) ).
fof(c_0_378,axiom,
! [X40,X49] : c_Lambda_OdB_OAbs(X49) != c_Lambda_OdB_OVar(X40),
file('<stdin>',cls_dB_Osimps_I7_J_0) ).
fof(c_0_379,axiom,
! [X40,X49] : c_Lambda_OdB_OVar(X40) != c_Lambda_OdB_OAbs(X49),
file('<stdin>',cls_dB_Osimps_I6_J_0) ).
fof(c_0_380,axiom,
! [X33] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X33),
file('<stdin>',cls_nat_Osimps_I2_J_0) ).
fof(c_0_381,axiom,
! [X5] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X5),
file('<stdin>',cls_Zero__neq__Suc_0) ).
fof(c_0_382,axiom,
! [X5] : c_Suc(X5) != c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_Suc__neq__Zero_0) ).
fof(c_0_383,axiom,
! [X33] : c_Suc(X33) != c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_nat_Osimps_I3_J_0) ).
fof(c_0_384,axiom,
c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
file('<stdin>',cls_One__nat__def_0) ).
fof(c_0_385,axiom,
! [X4] : X4 != c_Suc(X4),
file('<stdin>',cls_n__not__Suc__n_0) ).
fof(c_0_386,axiom,
! [X4] : c_Suc(X4) != X4,
file('<stdin>',cls_Suc__n__not__n_0) ).
fof(c_0_387,axiom,
class_Orderings_Oorder(tc_bool),
file('<stdin>',clsarity_bool__Orderings_Oorder) ).
fof(c_0_388,axiom,
class_Orderings_Opreorder(tc_bool),
file('<stdin>',clsarity_bool__Orderings_Opreorder) ).
fof(c_0_389,axiom,
class_Orderings_Oorder(tc_nat),
file('<stdin>',clsarity_nat__Orderings_Oorder) ).
fof(c_0_390,axiom,
class_Orderings_Olinorder(tc_nat),
file('<stdin>',clsarity_nat__Orderings_Olinorder) ).
fof(c_0_391,axiom,
class_Orderings_Opreorder(tc_nat),
file('<stdin>',clsarity_nat__Orderings_Opreorder) ).
fof(c_0_392,axiom,
class_Nat_Osemiring__char__0(tc_nat),
file('<stdin>',clsarity_nat__Nat_Osemiring__char__0) ).
fof(c_0_393,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Omonoid__add) ).
fof(c_0_394,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Osemiring__1) ).
fof(c_0_395,axiom,
class_OrderedGroup_Osemigroup__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Osemigroup__add) ).
fof(c_0_396,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
fof(c_0_397,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
fof(c_0_398,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
fof(c_0_399,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
fof(c_0_400,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(c_0_401,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(c_0_402,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(c_0_403,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
fof(c_0_404,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(c_0_405,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(c_0_406,axiom,
v_n____ = v_i____,
file('<stdin>',cls_True_0) ).
fof(c_0_407,axiom,
c_List_Olistsp(hAPP(hAPP(c_COMBS(tc_Lambda_OdB,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_and),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_bool),tc_bool,tc_Lambda_OdB),c_All(tc_fun(tc_nat,tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_bool),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_fun(tc_nat,tc_Type_Otype)),c_All(tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_bool)),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_Type_Otype,tc_bool),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_bool),tc_bool,tc_Type_Otype),c_All(tc_Lambda_OdB)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_bool),tc_Type_Otype),hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_bool,tc_Lambda_OdB),c_All(tc_nat))))),hAPP(hAPP(c_COMBS(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_fun(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),c_COMBS(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Type_Otype),c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool),tc_Lambda_OdB)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Type_Otype),c_COMBS(tc_nat,tc_bool,tc_bool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_Type_Otype),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_nat),c_implies)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Type_Otype,tc_bool))),hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Lambda_OdB,tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype)),tc_fun(tc_nat,tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool)),tc_nat),c_Type_Otyping)),hAPP(hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_Type_Otype))),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Type_Otype,tc_fun(tc_nat,tc_Type_Otype))),c_Type_Oshift(tc_Type_Otype))),v_T____))))))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBS(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),c_COMBB(tc_bool,tc_bool,tc_nat)),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_implies),c_InductTermi_OIT))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBS(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_bool,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),c_COMBB(tc_bool,tc_bool,tc_nat))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_bool),tc_fun(tc_Lambda_OdB,tc_fun(tc_bool,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_implies)),hAPP(hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_Lambda_OdB,tc_Type_Otype,tc_bool)),c_Type_Otyping)),v_T____)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_nat,tc_Lambda_OdB),tc_fun(tc_nat,tc_bool),tc_Lambda_OdB),hAPP(c_COMBB(tc_Lambda_OdB,tc_bool,tc_nat),c_InductTermi_OIT))),c_Lambda_Osubst)))))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),c_Ex(tc_Type_Otype)),hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)))),v_bs____,tc_Lambda_OdB),
c_0_0 ).
fof(c_0_408,plain,
! [X35,X28,X16,X22,X36,X37,X23] :
( X36 = c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X23,X36,X22,X35),X23,tc_Type_Otype,tc_Type_Otype)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X16),X28,tc_Lambda_OdB,tc_Lambda_OdB)),X36))
| ~ c_Type_Otypings(X22,X28,X37)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X16),X28,tc_Lambda_OdB,tc_Lambda_OdB),X35,tc_Lambda_OdB,tc_Lambda_OdB)),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_409,plain,
! [X35,X28,X16,X22,X36,X37,X23] :
( c_Type_Otypings(X22,X35,c_Type_Osko__Type__Xvar__app__types__1__1(X23,X36,X22,X35))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X16),X28,tc_Lambda_OdB,tc_Lambda_OdB)),X36))
| ~ c_Type_Otypings(X22,X28,X37)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X16),X28,tc_Lambda_OdB,tc_Lambda_OdB),X35,tc_Lambda_OdB,tc_Lambda_OdB)),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_410,plain,
! [X28,X16,X22,X36,X23] :
( X23 = X36
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X16),X28,tc_Lambda_OdB,tc_Lambda_OdB)),X36))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X16),X28,tc_Lambda_OdB,tc_Lambda_OdB)),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_411,plain,
! [X28,X16,X22,X23] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),c_Lambda_OdB_OVar(X16)),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X23,X22,X16,X28),X23,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X16),X28,tc_Lambda_OdB,tc_Lambda_OdB)),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_412,plain,
! [X28,X29,X22,X23] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),X29),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X23,X22,X29,X28),X23,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),c_List_Ofoldl(c_Lambda_OdB_OApp,X29,X28,tc_Lambda_OdB,tc_Lambda_OdB)),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_413,plain,
! [X28,X29,X22,X23] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),X29),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X23,X22,X29,X28),X23,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),c_List_Ofoldl(c_Lambda_OdB_OApp,X29,X28,tc_Lambda_OdB,tc_Lambda_OdB)),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_414,plain,
! [X28,X29,X22,X37,X23] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),c_List_Ofoldl(c_Lambda_OdB_OApp,X29,X28,tc_Lambda_OdB,tc_Lambda_OdB)),X23))
| ~ c_Type_Otypings(X22,X28,X37)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),X29),c_List_Ofoldr(c_Type_Otype_OFun,X37,X23,tc_Type_Otype,tc_Type_Otype))) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_415,axiom,
! [X26,X28,X29,X16] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,X29,X28,tc_Lambda_OdB,tc_Lambda_OdB)),X26),X16) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),X26),X16),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),X26)),X16),X28,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
c_0_8 ).
fof(c_0_416,plain,
! [X21,X2,X4] :
( X21 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X4,X2,X21),tc_Lambda_OdB,tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X21)) ),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_417,plain,
! [X28,X16,X22,X23] :
( c_Type_Otypings(X22,X28,c_Type_Osko__Type__Xvar__app__typesE__1__1(X23,X22,X16,X28))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X16),X28,tc_Lambda_OdB,tc_Lambda_OdB)),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_418,plain,
! [X28,X29,X22,X23] :
( c_Type_Otypings(X22,X28,c_Type_Osko__Type__Xlist__app__typeD__1__1(X23,X22,X29,X28))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),c_List_Ofoldl(c_Lambda_OdB_OApp,X29,X28,tc_Lambda_OdB,tc_Lambda_OdB)),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_419,plain,
! [X28,X29,X22,X23] :
( c_Type_Otypings(X22,X28,c_Type_Osko__Type__Xlist__app__typeE__1__1(X23,X22,X29,X28))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),c_List_Ofoldl(c_Lambda_OdB_OApp,X29,X28,tc_Lambda_OdB,tc_Lambda_OdB)),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_420,plain,
! [X21,X2,X4] :
( c_ListOrder_Ostep1(c_Lambda_Obeta,X2,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X4,X2,X21),tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X21)) ),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_421,plain,
! [X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X2,X1,tc_Lambda_OdB) ),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_422,plain,
! [X1,X27,X3] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X27,X1,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X3),X27)) ),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_423,plain,
! [X1,X27,X3] :
( 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,X27,X1,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X3),X27)) ),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_424,axiom,
c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),v_u____)),v_i____),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
c_0_17 ).
fof(c_0_425,axiom,
c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),v_u____)),v_i____),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
c_0_18 ).
fof(c_0_426,plain,
! [X1,X27,X3] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3)),X27),X1,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X27))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X27),c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_427,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),c_Lambda_OdB_OVar(v_n____)),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)))),
c_0_20 ).
fof(c_0_428,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_H____)),
c_0_21 ).
fof(c_0_429,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_ea______),v_ia______),v_T____)),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_Ha______)),
c_0_22 ).
fof(c_0_430,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_e____),v_u____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)))),
c_0_23 ).
fof(c_0_431,axiom,
! [X28,X29,X16] : hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,X29,X28,tc_Lambda_OdB,tc_Lambda_OdB)),X16) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X29),X16),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),X16),X28,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
c_0_24 ).
fof(c_0_432,plain,
! [X26,X28,X16,X22,X37,X23] :
( c_Type_Otypings(X22,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),X26)),X16),X28,tc_Lambda_OdB,tc_Lambda_OdB),X37)
| ~ c_Type_Otypings(hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X22),X16),X23),X28,X37)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),X26),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_433,axiom,
! [X54,X47,X30,X55,X44,X43,X9] : c_Fun_Ofcomp(c_Fun_Ofcomp(X30,X47,X9,X55,X44),X54,X9,X44,X43) = c_Fun_Ofcomp(X30,c_Fun_Ofcomp(X47,X54,X55,X44,X43),X9,X55,X43),
c_0_26 ).
fof(c_0_434,axiom,
! [X54,X47,X30,X55,X44,X43,X9] : c_Fun_Ocomp(X30,c_Fun_Ocomp(X47,X54,X55,X44,X9),X44,X43,X9) = c_Fun_Ocomp(c_Fun_Ocomp(X30,X47,X44,X43,X55),X54,X55,X43,X9),
c_0_27 ).
fof(c_0_435,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
c_0_28 ).
fof(c_0_436,plain,
! [X26,X29,X22,X23] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),X29),hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X23,X22,X29,X26)),X23)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),hAPP(hAPP(c_Lambda_OdB_OApp,X29),X26)),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_29]) ).
fof(c_0_437,axiom,
! [X12,X13,X58,X47,X59,X30,X60,X55,X44,X43,X9] :
( hAPP(X30,hAPP(X47,X13)) != hAPP(X59,hAPP(X58,X12))
| hAPP(c_Fun_Ocomp(X30,X47,X43,X9,X44),X13) = hAPP(c_Fun_Ocomp(X59,X58,X55,X9,X60),X12) ),
c_0_30 ).
fof(c_0_438,plain,
! [X2,X4] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_List_Olistsp(c_InductTermi_OIT,X2,tc_Lambda_OdB) ),
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_439,plain,
! [X29,X22,X23] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X22),c_HOL_Ozero__class_Ozero(tc_nat)),c_Type_Osko__Type__Xtyping__elims__3__1(X23,X22,X29))),X29),c_Type_Osko__Type__Xtyping__elims__3__2(X23,X22,X29)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),c_Lambda_OdB_OAbs(X29)),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_440,plain,
! [X26,X29,X16,X67,X36,X23] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X67),X26),X36))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X67),X16),X36)),X29),X23))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X67),hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),X26),X16)),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_441,axiom,
! [X21,X19,X32,X6,X7,X55,X44,X43,X9] :
( c_Fun_Ocomp(X7,X6,X44,X43,X9) != c_Fun_Ocomp(X32,X19,X55,X43,X9)
| hAPP(X7,hAPP(X6,X21)) = hAPP(X32,hAPP(X19,X21)) ),
c_0_34 ).
fof(c_0_442,axiom,
! [X21,X32,X6,X7,X44,X43,X9] :
( c_Fun_Ocomp(X7,X6,X44,X43,X9) != c_Fun_Ocomp(c_Fun_Oid(X43),X32,X43,X43,X9)
| hAPP(X7,hAPP(X6,X21)) = hAPP(X32,X21) ),
c_0_35 ).
fof(c_0_443,axiom,
! [X1,X2,X4,X5] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X1,tc_Lambda_OdB,tc_Lambda_OdB)
| X5 = X4 ),
c_0_36 ).
fof(c_0_444,axiom,
! [X1,X2,X4,X5] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X1,tc_Lambda_OdB,tc_Lambda_OdB)
| X2 = X1 ),
c_0_37 ).
fof(c_0_445,axiom,
! [X1,X27,X2,X3] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X27),X1,tc_Lambda_OdB,tc_Lambda_OdB)
| X3 = X27 ),
c_0_38 ).
fof(c_0_446,axiom,
! [X1,X27,X2,X3] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X27),X1,tc_Lambda_OdB,tc_Lambda_OdB)
| X2 = X1 ),
c_0_39 ).
fof(c_0_447,plain,
! [X31,X11,X13,X9] :
( ~ class_OrderedGroup_Osemigroup__add(X9)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X13),X11),X31,X9,X9) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X13),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X9),X11,X31,X9,X9)) ),
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_448,axiom,
! [X28,X1,X3,X4] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X28,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X1,tc_Lambda_OdB,tc_Lambda_OdB),
c_0_41 ).
fof(c_0_449,axiom,
! [X28,X27,X3] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X28,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X27,X28,tc_Lambda_OdB,tc_Lambda_OdB)
| X3 = X27 ),
c_0_42 ).
fof(c_0_450,plain,
! [X34,X7,X9] :
( ~ class_OrderedGroup_Omonoid__add(X9)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X9),X7,X34,X9,X9) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X9),X34,c_HOL_Ozero__class_Ozero(X9),X9,X9)) ),
inference(fof_simplification,[status(thm)],[c_0_43]) ).
fof(c_0_451,plain,
! [X31,X13,X9] :
( ~ class_OrderedGroup_Omonoid__add(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X13),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X9),c_HOL_Ozero__class_Ozero(X9),X31,X9,X9)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X9),X13,X31,X9,X9) ),
inference(fof_simplification,[status(thm)],[c_0_44]) ).
fof(c_0_452,plain,
! [X26,X29,X16,X22,X64,X65,X66] :
( v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X66),X65)
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),X26),X16)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),X26),X66))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X26))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X22),X16),X66)),X29),X64))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X29)) ),
inference(fof_simplification,[status(thm)],[c_0_45]) ).
fof(c_0_453,plain,
! [X26,X29,X16,X22,X64,X65,X66] :
( v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X66),X65)
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),X26),X16)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),X26),X65))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X26))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X22),X16),X65)),X29),X64))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X29)) ),
inference(fof_simplification,[status(thm)],[c_0_46]) ).
fof(c_0_454,plain,
! [X26,X61,X62,X63] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),X26),X61)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X62),X26),v_T____))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X26))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X62),X61),v_T____)),v_b____),X63)) ),
inference(fof_simplification,[status(thm)],[c_0_47]) ).
fof(c_0_455,plain,
! [X26,X61,X62,X63] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),X26),X61)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X62),X26),v_T____))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X26))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X62),X61),v_T____)),v_b____),X63)) ),
inference(fof_simplification,[status(thm)],[c_0_48]) ).
fof(c_0_456,axiom,
! [X34,X47,X30,X44,X43,X9] : c_List_Omap(X30,c_List_Omap(X47,X34,X44,X43),X43,X9) = c_List_Omap(c_Fun_Ocomp(X30,X47,X43,X9,X44),X34,X44,X9),
c_0_49 ).
fof(c_0_457,plain,
! [X29,X53,X36,X23] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X53),c_Lambda_OdB_OAbs(X29)),hAPP(hAPP(c_Type_Otype_OFun,X23),X36)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X53),c_HOL_Ozero__class_Ozero(tc_nat)),X23)),X29),X36)) ),
inference(fof_simplification,[status(thm)],[c_0_50]) ).
fof(c_0_458,plain,
! [X21,X26,X29,X15,X16] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),hAPP(hAPP(c_Lambda_Olift,X21),X16)),c_Suc(X15))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X26),X21),X15)),X16) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),X26),X16)),X21),X15)
| ~ c_HOL_Oord__class_Oless(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_51]) ).
fof(c_0_459,plain,
! [X29,X22,X23] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X22),c_HOL_Ozero__class_Ozero(tc_nat)),c_Type_Osko__Type__Xabs__typeE__1__1(X22,X29))),X29),c_Type_Osko__Type__Xabs__typeE__1__2(X22,X29)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),c_Lambda_OdB_OAbs(X29)),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_52]) ).
fof(c_0_460,axiom,
! [X30,X32,X44,X43] : hAPP(c_Fun_Ocomp(c_COMBK(X32,X43,X44),X30,X44,X43,t_a),v_x) = X32,
c_0_53 ).
fof(c_0_461,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_b____),v_sko__CHAINED__1(v_T____,v_b____,v_e____,v_i____))),
c_0_54 ).
fof(c_0_462,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_b____),v_sko__local__XCons__1__1(v_T____,v_b____,v_e____,v_i____))),
c_0_55 ).
fof(c_0_463,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_b____),v_sko__local__XCons__Xhyps__1__1(v_T____,v_b____,v_e____,v_i____))),
c_0_56 ).
fof(c_0_464,axiom,
! [X4,X5,X30,X9] : c_Nat_Ocompow(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4),X30,X9,X9) = c_Fun_Ocomp(c_Nat_Ocompow(X5,X30,X9,X9),c_Nat_Ocompow(X4,X30,X9,X9),X9,X9,X9),
c_0_57 ).
fof(c_0_465,axiom,
! [X13,X47,X30,X44,X43,X9] : hAPP(c_Fun_Ofcomp(X30,X47,X43,X44,X9),X13) = hAPP(X47,hAPP(X30,X13)),
c_0_58 ).
fof(c_0_466,axiom,
! [X21,X6,X7,X44,X43,X9] : hAPP(X7,hAPP(X6,X21)) = hAPP(c_Fun_Ocomp(X7,X6,X44,X43,X9),X21),
c_0_59 ).
fof(c_0_467,axiom,
! [X13,X47,X30,X44,X43,X9] : hAPP(c_Fun_Ocomp(X30,X47,X43,X9,X44),X13) = hAPP(X30,hAPP(X47,X13)),
c_0_60 ).
fof(c_0_468,axiom,
! [X47,X30,X44,X43] : hAPP(c_Fun_Ofcomp(X30,X47,t_a,X44,X43),v_x) = hAPP(X47,hAPP(X30,v_x)),
c_0_61 ).
fof(c_0_469,axiom,
! [X47,X30,X44,X43] : hAPP(c_Fun_Ocomp(X30,X47,X44,X43,t_a),v_x) = hAPP(X30,hAPP(X47,v_x)),
c_0_62 ).
fof(c_0_470,plain,
! [X34,X9] :
( ~ class_OrderedGroup_Omonoid__add(X9)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X9),c_HOL_Ozero__class_Ozero(X9),X34,X9,X9) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X9),X34,c_HOL_Ozero__class_Ozero(X9),X9,X9) ),
inference(fof_simplification,[status(thm)],[c_0_63]) ).
fof(c_0_471,plain,
! [X34,X7,X9] :
( ~ class_OrderedGroup_Oab__semigroup__add(X9)
| c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X9),X34,X7,X9,X9) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X9),X7,X34,X9,X9) ),
inference(fof_simplification,[status(thm)],[c_0_64]) ).
fof(c_0_472,axiom,
v_T____ = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
c_0_65 ).
fof(c_0_473,plain,
! [X29,X16,X22,X36,X23] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X22),X16),X36)),hAPP(hAPP(c_Lambda_Olift,X29),X16)),X23))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),X29),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_66]) ).
fof(c_0_474,axiom,
! [X16,X22,X36,X23,X9] : hAPP(hAPP(hAPP(c_Type_Oshift(X9),hAPP(hAPP(hAPP(c_Type_Oshift(X9),X22),X16),X36)),c_HOL_Ozero__class_Ozero(tc_nat)),X23) = hAPP(hAPP(hAPP(c_Type_Oshift(X9),hAPP(hAPP(hAPP(c_Type_Oshift(X9),X22),c_HOL_Ozero__class_Ozero(tc_nat)),X23)),c_Suc(X16)),X36),
c_0_67 ).
fof(c_0_475,axiom,
! [X29,X1,X27,X4] : hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X27)),X29) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X1,tc_Lambda_OdB,tc_Lambda_OdB),
c_0_68 ).
fof(c_0_476,axiom,
! [X4,X30,X9] : c_Nat_Ocompow(c_Suc(X4),X30,X9,X9) = c_Fun_Ocomp(X30,c_Nat_Ocompow(X4,X30,X9,X9),X9,X9,X9),
c_0_69 ).
fof(c_0_477,axiom,
! [X1,X27,X5] :
( c_Lambda_OdB_OVar(X5) != c_List_Ofoldl(c_Lambda_OdB_OApp,X27,X1,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OVar(X5) = X27 ),
c_0_70 ).
fof(c_0_478,axiom,
! [X1,X27,X3] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X27,X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X3)
| X27 = c_Lambda_OdB_OAbs(X3) ),
c_0_71 ).
fof(c_0_479,axiom,
! [X1,X27,X3] :
( c_Lambda_OdB_OAbs(X3) != c_List_Ofoldl(c_Lambda_OdB_OApp,X27,X1,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(X3) = X27 ),
c_0_72 ).
fof(c_0_480,plain,
! [X29,X27,X15,X16] :
( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),X27),X15)),X16) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X29),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,X27),X16)),X15)
| ~ c_HOL_Oord__class_Oless(X15,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_73]) ).
fof(c_0_481,plain,
! [X26,X29,X22,X23] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),X26),c_Type_Osko__Type__Xtyping__elims__2__1(X23,X22,X29,X26)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),hAPP(hAPP(c_Lambda_OdB_OApp,X29),X26)),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_74]) ).
fof(c_0_482,plain,
! [X28,X16,X22,X36,X37] :
( c_Type_Otypings(hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X22),X16),X36),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),X16),X28,tc_Lambda_OdB,tc_Lambda_OdB),X37)
| ~ c_Type_Otypings(X22,X28,X37) ),
inference(fof_simplification,[status(thm)],[c_0_75]) ).
fof(c_0_483,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_a____),v_T_H_H____)),
c_0_76 ).
fof(c_0_484,axiom,
! [X13,X4,X30,X9] : hAPP(X30,hAPP(c_Nat_Ocompow(X4,X30,X9,X9),X13)) = hAPP(c_Nat_Ocompow(X4,X30,X9,X9),hAPP(X30,X13)),
c_0_77 ).
fof(c_0_485,plain,
! [X28] :
( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),c_HOL_Ozero__class_Ozero(tc_nat)),X28,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_List_Olistsp(c_InductTermi_OIT,X28,tc_Lambda_OdB) ),
inference(fof_simplification,[status(thm)],[c_0_78]) ).
fof(c_0_486,plain,
! [X29,X27,X3,X16] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),X3),X16)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),X27),X16)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X3),X27)) ),
inference(fof_simplification,[status(thm)],[c_0_79]) ).
fof(c_0_487,plain,
! [X29,X27,X3,X16] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X29),X16)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X27),X29),X16)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X3),X27)) ),
inference(fof_simplification,[status(thm)],[c_0_80]) ).
fof(c_0_488,plain,
! [X29,X27,X3,X16] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),X3),X16)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),X27),X16)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X3),X27)) ),
inference(fof_simplification,[status(thm)],[c_0_81]) ).
fof(c_0_489,plain,
! [X29,X27,X53,X36,X23] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X53),hAPP(hAPP(c_Lambda_OdB_OApp,X27),X29)),X36))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X53),X29),X23))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X53),X27),hAPP(hAPP(c_Type_Otype_OFun,X23),X36))) ),
inference(fof_simplification,[status(thm)],[c_0_82]) ).
fof(c_0_490,plain,
! [X29,X27,X15,X16] :
( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),X27),X15)),X16) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X29),X16)),hAPP(hAPP(c_Lambda_Olift,X27),X16)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_83]) ).
fof(c_0_491,plain,
! [X29,X27,X3,X16] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X29),X16)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X27),X29),X16)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X3),X27)) ),
inference(fof_simplification,[status(thm)],[c_0_84]) ).
fof(c_0_492,axiom,
! [X47,X43,X9] : c_Fun_Ofcomp(c_Fun_Oid(X9),X47,X9,X9,X43) = X47,
c_0_85 ).
fof(c_0_493,axiom,
! [X30,X43,X9] : c_Fun_Ofcomp(X30,c_Fun_Oid(X43),X9,X43,X43) = X30,
c_0_86 ).
fof(c_0_494,axiom,
! [X30,X43,X9] : c_Fun_Ocomp(X30,c_Fun_Oid(X9),X9,X43,X9) = X30,
c_0_87 ).
fof(c_0_495,axiom,
! [X47,X43,X9] : c_Fun_Ocomp(c_Fun_Oid(X43),X47,X43,X43,X9) = X47,
c_0_88 ).
fof(c_0_496,plain,
! [X38,X29,X39,X27] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X27),X29)),hAPP(hAPP(c_Lambda_OdB_OApp,X39),X38)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X29),X38))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X27),X39)) ),
inference(fof_simplification,[status(thm)],[c_0_89]) ).
fof(c_0_497,plain,
! [X19,X6,X8] :
( ~ hBOOL(hAPP(X8,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X19),X6,tc_nat)))
| hBOOL(hAPP(X8,X19)) ),
inference(fof_simplification,[status(thm)],[c_0_90]) ).
fof(c_0_498,plain,
! [X13,X6,X8] :
( ~ hBOOL(hAPP(X8,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X13),X6,tc_nat)))
| hBOOL(hAPP(X8,X13)) ),
inference(fof_simplification,[status(thm)],[c_0_91]) ).
fof(c_0_499,axiom,
! [X26,X29,X27,X14] : hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,X29),X26)),X27),X14) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),X27),X14)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X26),X27),X14)),
c_0_92 ).
fof(c_0_500,plain,
! [X27,X3,X16] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,X3),X16)),hAPP(hAPP(c_Lambda_Olift,X27),X16)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X3),X27)) ),
inference(fof_simplification,[status(thm)],[c_0_93]) ).
fof(c_0_501,plain,
! [X38,X29,X27] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X27),X29)),hAPP(hAPP(c_Lambda_OdB_OApp,X27),X38)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X29),X38)) ),
inference(fof_simplification,[status(thm)],[c_0_94]) ).
fof(c_0_502,plain,
! [X29,X39,X27] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X27),X29)),hAPP(hAPP(c_Lambda_OdB_OApp,X39),X29)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X27),X39)) ),
inference(fof_simplification,[status(thm)],[c_0_95]) ).
fof(c_0_503,plain,
! [X4,X9] :
( ~ class_Ring__and__Field_Osemiring__1(X9)
| c_Nat_Osemiring__1__class_Oof__nat(X4,X9) = c_Nat_Osemiring__1__class_Oof__nat__aux(hAPP(hAPP(c_COMBC(X9,X9,X9),c_HOL_Oplus__class_Oplus(X9)),c_HOL_Oone__class_Oone(X9)),X4,c_HOL_Ozero__class_Ozero(X9),X9) ),
inference(fof_simplification,[status(thm)],[c_0_96]) ).
fof(c_0_504,axiom,
! [X29,X27] : hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X27)),X29)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X27),X29),c_HOL_Ozero__class_Ozero(tc_nat)))),
c_0_97 ).
fof(c_0_505,axiom,
! [X29,X27,X14] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(X29)),X27),X14) = c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),hAPP(hAPP(c_Lambda_Olift,X27),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)))),
c_0_98 ).
fof(c_0_506,plain,
! [X41,X11,X13,X3,X9] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X3,X9),X13),X41))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X3,X9),X11),X41))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X3,X9),X13),X11)) ),
inference(fof_simplification,[status(thm)],[c_0_99]) ).
fof(c_0_507,plain,
! [X19,X32,X6,X7,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X6)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X32),X19)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X32)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X6),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_100]) ).
fof(c_0_508,plain,
! [X38,X29,X22,X23] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),X38),X23))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),X29),X23))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X29),X38)) ),
inference(fof_simplification,[status(thm)],[c_0_101]) ).
fof(c_0_509,plain,
! [X29,X22,X23] :
( X23 = hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(X23,X22,X29)),c_Type_Osko__Type__Xtyping__elims__3__2(X23,X22,X29))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),c_Lambda_OdB_OAbs(X29)),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_102]) ).
fof(c_0_510,plain,
! [X26,X29,X27] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X26),X27)),hAPP(hAPP(c_Lambda_OdB_OApp,X26),X29)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X27),X29)) ),
inference(fof_simplification,[status(thm)],[c_0_103]) ).
fof(c_0_511,plain,
! [X26,X29,X27] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X27),X26)),hAPP(hAPP(c_Lambda_OdB_OApp,X29),X26)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X27),X29)) ),
inference(fof_simplification,[status(thm)],[c_0_104]) ).
fof(c_0_512,plain,
! [X27,X3,X16] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,X3),X16)),hAPP(hAPP(c_Lambda_Olift,X27),X16)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X3),X27)) ),
inference(fof_simplification,[status(thm)],[c_0_105]) ).
fof(c_0_513,plain,
! [X3,X32,X6,X7,X9] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X3,X9),X7),X32))
| ~ hBOOL(hAPP(hAPP(X3,X6),X32))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X3,X9),X7),X6)) ),
inference(fof_simplification,[status(thm)],[c_0_106]) ).
fof(c_0_514,plain,
! [X3,X32,X6,X7,X9] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X3,X9),X7),X32))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X3,X9),X6),X32))
| ~ hBOOL(hAPP(hAPP(X3,X7),X6)) ),
inference(fof_simplification,[status(thm)],[c_0_107]) ).
fof(c_0_515,plain,
! [X29,X14,X16] :
( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X29),X16)),c_Suc(X14)) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X29),X14)),X16)
| ~ c_HOL_Oord__class_Oless(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_108]) ).
fof(c_0_516,axiom,
! [X24,X25] : c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,X25),X24),tc_Type_Otype) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X25,tc_Type_Otype)),c_Nat_Osize__class_Osize(X24,tc_Type_Otype))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
c_0_109 ).
fof(c_0_517,axiom,
! [X4,X5] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X5,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X4))
| X5 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_110 ).
fof(c_0_518,plain,
! [X38,X29,X22,X23] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),X38),X23))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X29),X38))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),X29),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_111]) ).
fof(c_0_519,axiom,
! [X48,X42,X8,X44,X43,X9] : hAPP(hAPP(hAPP(c_COMBC(X43,X44,X9),X8),X42),X48) = hAPP(hAPP(X8,X48),X42),
c_0_112 ).
fof(c_0_520,plain,
! [X4,X17,X16,X9] :
( ~ class_Ring__and__Field_Osemiring__1(X9)
| c_Nat_Osemiring__1__class_Oof__nat__aux(X17,c_Suc(X4),X16,X9) = c_Nat_Osemiring__1__class_Oof__nat__aux(X17,X4,hAPP(X17,X16),X9) ),
inference(fof_simplification,[status(thm)],[c_0_113]) ).
fof(c_0_521,plain,
! [X32,X6,X7,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X6)),X32) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X32)),X6) ),
inference(fof_simplification,[status(thm)],[c_0_114]) ).
fof(c_0_522,plain,
! [X6,X7,X8] :
( hBOOL(hAPP(X8,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X7,X6,tc_nat)
| ~ hBOOL(hAPP(X8,c_HOL_Ominus__class_Ominus(X7,X6,tc_nat))) ),
inference(fof_simplification,[status(thm)],[c_0_115]) ).
fof(c_0_523,axiom,
! [X26,X29,X27,X14] : c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,X29),X26),X27,X14) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(X29,X27,X14)),c_Lambda_Osubstn(X26,X27,X14)),
c_0_116 ).
fof(c_0_524,axiom,
! [X29,X27,X4,X14] : c_Lambda_Oliftn(X4,hAPP(hAPP(c_Lambda_OdB_OApp,X27),X29),X14) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(X4,X27,X14)),c_Lambda_Oliftn(X4,X29,X14)),
c_0_117 ).
fof(c_0_525,plain,
! [X32,X6,X7,X9] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X9)
| c_HOL_Oord__class_Oless(X7,X6,X9)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X32),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X32),X6),X9) ),
inference(fof_simplification,[status(thm)],[c_0_118]) ).
fof(c_0_526,plain,
! [X32,X6,X7,X9] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X9)
| c_HOL_Oord__class_Oless(X7,X6,X9)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X32),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X6),X32),X9) ),
inference(fof_simplification,[status(thm)],[c_0_119]) ).
fof(c_0_527,plain,
! [X3,X15,X16] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),c_Lambda_OdB_OVar(X16)),X15)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_120]) ).
fof(c_0_528,plain,
! [X39,X27] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X27)),c_Lambda_OdB_OAbs(X39)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X27),X39)) ),
inference(fof_simplification,[status(thm)],[c_0_121]) ).
fof(c_0_529,plain,
! [X15,X16,X22,X23,X9] :
( hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(X9),X22),X16),X23),X15) = hAPP(X22,c_HOL_Ominus__class_Ominus(X15,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X16,X15,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_122]) ).
fof(c_0_530,plain,
! [X19,X32,X6,X7,X9] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X9)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X32),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X6),X19),X9)
| ~ c_HOL_Oord__class_Oless(X32,X19,X9)
| ~ c_HOL_Oord__class_Oless(X7,X6,X9) ),
inference(fof_simplification,[status(thm)],[c_0_123]) ).
fof(c_0_531,axiom,
! [X29,X27,X14] : hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,X27),X29)),X14) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X27),X14)),hAPP(hAPP(c_Lambda_Olift,X29),X14)),
c_0_124 ).
fof(c_0_532,plain,
! [X4,X5,X18] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X18,X4,tc_nat),c_HOL_Ominus__class_Ominus(X18,X5,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X18,tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_125]) ).
fof(c_0_533,plain,
! [X4,X5,X14] :
( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X4),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_126]) ).
fof(c_0_534,plain,
! [X32,X6,X7,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X6)),X32) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X6),X32)) ),
inference(fof_simplification,[status(thm)],[c_0_127]) ).
fof(c_0_535,plain,
! [X19,X32,X7,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X32),X19)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X32)),X19) ),
inference(fof_simplification,[status(thm)],[c_0_128]) ).
fof(c_0_536,plain,
! [X32,X6,X7,X9] :
( ~ class_OrderedGroup_Oab__semigroup__add(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X6)),X32) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X6),X32)) ),
inference(fof_simplification,[status(thm)],[c_0_129]) ).
fof(c_0_537,plain,
! [X32,X6,X7,X9] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X6)),X32) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X6),X32)) ),
inference(fof_simplification,[status(thm)],[c_0_130]) ).
fof(c_0_538,plain,
! [X41,X11,X13,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X11),X41)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X13),X11)),X41) ),
inference(fof_simplification,[status(thm)],[c_0_131]) ).
fof(c_0_539,plain,
! [X18,X14,X15,X16] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X18),tc_nat)
| ~ c_HOL_Oord__class_Oless(X14,X18,tc_nat)
| ~ c_HOL_Oord__class_Oless(X16,X15,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_132]) ).
fof(c_0_540,plain,
! [X14,X15,X16] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X14),X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X16,c_HOL_Ominus__class_Ominus(X15,X14,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_133]) ).
fof(c_0_541,axiom,
! [X24,X25] : c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X25),X24)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(X25)),c_Type_Otype_Otype__size(X24))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
c_0_134 ).
fof(c_0_542,plain,
! [X41,X11,X13,X26,X9] :
( ~ class_OrderedGroup_Oab__group__add(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X11),X41)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X11),X26)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X13),X41) = X26 ),
inference(fof_simplification,[status(thm)],[c_0_135]) ).
fof(c_0_543,plain,
! [X14,X15,X16] :
( c_HOL_Oord__class_Oless(X16,c_HOL_Ominus__class_Ominus(X15,X14,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X14),X15,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_136]) ).
fof(c_0_544,axiom,
! [X29,X27,X14] : hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X29),X14)),X27),X14) = X29,
c_0_137 ).
fof(c_0_545,axiom,
! [X29,X27,X4] : c_Lambda_Osubstn(X29,X27,X4) = hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),c_Lambda_Oliftn(X4,X27,c_HOL_Ozero__class_Ozero(tc_nat))),X4),
c_0_138 ).
fof(c_0_546,axiom,
! [X29,X27,X14] : c_Lambda_Osubstn(c_Lambda_OdB_OAbs(X29),X27,X14) = c_Lambda_OdB_OAbs(c_Lambda_Osubstn(X29,X27,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)))),
c_0_139 ).
fof(c_0_547,axiom,
! [X27,X4,X14] : c_Lambda_Oliftn(X4,c_Lambda_OdB_OAbs(X27),X14) = c_Lambda_OdB_OAbs(c_Lambda_Oliftn(X4,X27,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)))),
c_0_140 ).
fof(c_0_548,axiom,
! [X4,X5,X14] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4)),X14) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X14)),
c_0_141 ).
fof(c_0_549,plain,
! [X6,X7,X9] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X9)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X6),X9)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X9),X6,X9)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X9),X7,X9) ),
inference(fof_simplification,[status(thm)],[c_0_142]) ).
fof(c_0_550,plain,
! [X6,X7,X9] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X9)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X6),c_HOL_Ozero__class_Ozero(X9),X9)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X9),X9)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(X9),X9) ),
inference(fof_simplification,[status(thm)],[c_0_143]) ).
fof(c_0_551,plain,
! [X32,X6,X7,X9] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X9)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X32),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X32),X6),X9)
| ~ c_HOL_Oord__class_Oless(X7,X6,X9) ),
inference(fof_simplification,[status(thm)],[c_0_144]) ).
fof(c_0_552,plain,
! [X32,X6,X7,X9] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X9)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X32),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X32),X6),X9)
| ~ c_HOL_Oord__class_Oless(X7,X6,X9) ),
inference(fof_simplification,[status(thm)],[c_0_145]) ).
fof(c_0_553,plain,
! [X32,X6,X7,X9] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X9)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X32),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X6),X32),X9)
| ~ c_HOL_Oord__class_Oless(X7,X6,X9) ),
inference(fof_simplification,[status(thm)],[c_0_146]) ).
fof(c_0_554,plain,
! [X32,X6,X7,X9] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X9)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X32),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X6),X32),X9)
| ~ c_HOL_Oord__class_Oless(X7,X6,X9) ),
inference(fof_simplification,[status(thm)],[c_0_147]) ).
fof(c_0_555,plain,
! [X32,X6,X7,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X9)
| c_HOL_Oord__class_Oless(X6,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X32),X9)
| ~ c_HOL_Oord__class_Oless(X6,X32,X9)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X9),X7,X9) ),
inference(fof_simplification,[status(thm)],[c_0_148]) ).
fof(c_0_556,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_149]) ).
fof(c_0_557,plain,
! [X15,X16,X22,X23,X9] :
( hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(X9),X22),X16),X23),X15) = hAPP(X22,X15)
| ~ c_HOL_Oord__class_Oless(X15,X16,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_150]) ).
fof(c_0_558,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_151]) ).
fof(c_0_559,axiom,
! [X4,X5,X14] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X5),X4,tc_nat),c_Suc(X14),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),X14,tc_nat),
c_0_152 ).
fof(c_0_560,plain,
! [X16,X22,X23] :
( hAPP(X22,X16) = X23
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X22),c_Lambda_OdB_OVar(X16)),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_153]) ).
fof(c_0_561,plain,
! [X6,X7,X9] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X9)
| c_HOL_Oord__class_Oless(X7,X6,X9)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X7,X6,X9),c_HOL_Ozero__class_Ozero(X9),X9) ),
inference(fof_simplification,[status(thm)],[c_0_154]) ).
fof(c_0_562,plain,
! [X7,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X9)
| c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(X9),X9)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X7),c_HOL_Ozero__class_Ozero(X9),X9) ),
inference(fof_simplification,[status(thm)],[c_0_155]) ).
fof(c_0_563,plain,
! [X7,X9] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X9)
| c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(X9),X9)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X7),c_HOL_Ozero__class_Ozero(X9),X9) ),
inference(fof_simplification,[status(thm)],[c_0_156]) ).
fof(c_0_564,plain,
! [X7,X9] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X9)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X9),X7,X9)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X7),X9) ),
inference(fof_simplification,[status(thm)],[c_0_157]) ).
fof(c_0_565,plain,
! [X10,X11,X12,X13,X9] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X9)
| c_HOL_Ominus__class_Ominus(X13,X11,X9) != c_HOL_Ominus__class_Ominus(X12,X10,X9)
| c_HOL_Oord__class_Oless(X12,X10,X9)
| ~ c_HOL_Oord__class_Oless(X13,X11,X9) ),
inference(fof_simplification,[status(thm)],[c_0_158]) ).
fof(c_0_566,plain,
! [X10,X11,X12,X13,X9] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X9)
| c_HOL_Ominus__class_Ominus(X13,X11,X9) != c_HOL_Ominus__class_Ominus(X12,X10,X9)
| c_HOL_Oord__class_Oless(X13,X11,X9)
| ~ c_HOL_Oord__class_Oless(X12,X10,X9) ),
inference(fof_simplification,[status(thm)],[c_0_159]) ).
fof(c_0_567,axiom,
! [X27,X14] : hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(X27)),X14) = c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)))),
c_0_160 ).
fof(c_0_568,plain,
! [X4,X5,X14] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_161]) ).
fof(c_0_569,plain,
! [X14,X15,X16] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X14),tc_nat)
| ~ c_HOL_Oord__class_Oless(X16,X15,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_162]) ).
fof(c_0_570,plain,
! [X19,X32,X7,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X32),X19)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X32),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_163]) ).
fof(c_0_571,plain,
! [X32,X6,X7,X9] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X6),X32)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X32)) ),
inference(fof_simplification,[status(thm)],[c_0_164]) ).
fof(c_0_572,plain,
! [X41,X11,X13,X9] :
( ~ class_OrderedGroup_Oab__group__add(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X11),X41)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X13),X41)) ),
inference(fof_simplification,[status(thm)],[c_0_165]) ).
fof(c_0_573,plain,
! [X11,X13,X3,X9] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X3,X9),X13),X11))
| ~ hBOOL(hAPP(hAPP(X3,X13),X11)) ),
inference(fof_simplification,[status(thm)],[c_0_166]) ).
fof(c_0_574,axiom,
! [X14,X15,X16] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X16,X15,tc_nat),X14,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X16,X14,tc_nat),X15,tc_nat),
c_0_167 ).
fof(c_0_575,axiom,
! [X29,X4,X14] : c_Lambda_Oliftn(c_Suc(X4),X29,X14) = hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(X4,X29,X14)),X14),
c_0_168 ).
fof(c_0_576,plain,
! [X27,X14,X16] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X16)),X27),X14) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X16,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X14,X16,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_169]) ).
fof(c_0_577,plain,
! [X26,X15,X16] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X15)),X26),X16) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X15,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X16,X15,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_170]) ).
fof(c_0_578,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X4,X5,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_171]) ).
fof(c_0_579,axiom,
! [X14,X15,X16] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X16,X15,tc_nat),X14,tc_nat) = c_HOL_Ominus__class_Ominus(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X14),tc_nat),
c_0_172 ).
fof(c_0_580,axiom,
! [X4,X5,X14] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X4),tc_nat) = c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),
c_0_173 ).
fof(c_0_581,axiom,
! [X4,X5,X14] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X14),tc_nat) = c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),
c_0_174 ).
fof(c_0_582,plain,
! [X4,X5,X18,X14] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X18) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X4)
| ~ c_HOL_Oord__class_Oless(X14,X18,tc_nat)
| c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_175]) ).
fof(c_0_583,plain,
! [X14,X15,X16] :
( c_HOL_Oord__class_Oless(X16,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X15),X14,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_176]) ).
fof(c_0_584,plain,
! [X6,X7,X9] :
( ~ class_OrderedGroup_Ogroup__add(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),c_HOL_Ominus__class_Ominus(X7,X6,X9)),X6) = X7 ),
inference(fof_simplification,[status(thm)],[c_0_177]) ).
fof(c_0_585,axiom,
! [X41,X11,X13] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X41)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X41)),
c_0_178 ).
fof(c_0_586,plain,
! [X7,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X9)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X7),c_HOL_Ozero__class_Ozero(X9),X9)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(X9),X9) ),
inference(fof_simplification,[status(thm)],[c_0_179]) ).
fof(c_0_587,plain,
! [X7,X9] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X9)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X7),c_HOL_Ozero__class_Ozero(X9),X9)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(X9),X9) ),
inference(fof_simplification,[status(thm)],[c_0_180]) ).
fof(c_0_588,plain,
! [X7,X9] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X9)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X7),X9)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X9),X7,X9) ),
inference(fof_simplification,[status(thm)],[c_0_181]) ).
fof(c_0_589,plain,
! [X6,X7,X9] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X9)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X7,X6,X9),c_HOL_Ozero__class_Ozero(X9),X9)
| ~ c_HOL_Oord__class_Oless(X7,X6,X9) ),
inference(fof_simplification,[status(thm)],[c_0_182]) ).
fof(c_0_590,plain,
! [X17,X16,X9] :
( ~ class_Ring__and__Field_Osemiring__1(X9)
| c_Nat_Osemiring__1__class_Oof__nat__aux(X17,c_HOL_Ozero__class_Ozero(tc_nat),X16,X9) = X16 ),
inference(fof_simplification,[status(thm)],[c_0_183]) ).
fof(c_0_591,plain,
! [X27,X14,X16] :
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X16),X27,X14) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X16,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X14,X16,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_184]) ).
fof(c_0_592,plain,
! [X4,X16] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Suc(X16),tc_nat),X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_185]) ).
fof(c_0_593,axiom,
! [X30,X9] : c_Nat_Ocompow(c_HOL_Ozero__class_Ozero(tc_nat),X30,X9,X9) = c_Fun_Oid(X9),
c_0_186 ).
fof(c_0_594,axiom,
! [X13,X53] : hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X53),c_Lambda_OdB_OVar(X13)),hAPP(X53,X13))),
c_0_187 ).
fof(c_0_595,axiom,
! [X13,X22,X23,X9] : hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(X9),X22),X13),X23),X13) = X23,
c_0_188 ).
fof(c_0_596,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X4,X5,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_189]) ).
fof(c_0_597,plain,
! [X4,X5,X9] :
( ~ class_Ring__and__Field_Osemiring__1(X9)
| c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4),X9) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),c_Nat_Osemiring__1__class_Oof__nat(X5,X9)),c_Nat_Osemiring__1__class_Oof__nat(X4,X9)) ),
inference(fof_simplification,[status(thm)],[c_0_190]) ).
fof(c_0_598,plain,
! [X4,X14,X15] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X15,X4,tc_nat),X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(X15,X14,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_191]) ).
fof(c_0_599,axiom,
! [X5,X16] : c_HOL_Oord__class_Oless(X16,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X5)),tc_nat),
c_0_192 ).
fof(c_0_600,axiom,
! [X5,X16] : c_HOL_Oord__class_Oless(X16,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X16)),tc_nat),
c_0_193 ).
fof(c_0_601,axiom,
! [X13,X5] : c_HOL_Oord__class_Oless(X5,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X13)),tc_nat),
c_0_194 ).
fof(c_0_602,plain,
! [X29,X16] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X29),c_Lambda_OdB_OVar(X16))))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X29)) ),
inference(fof_simplification,[status(thm)],[c_0_195]) ).
fof(c_0_603,axiom,
c_Type_Otypings(hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____),v_as____,v_Ts____),
c_0_196 ).
fof(c_0_604,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_197]) ).
fof(c_0_605,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_198]) ).
fof(c_0_606,plain,
! [X41,X11,X13,X9] :
( ~ class_Orderings_Opreorder(X9)
| c_HOL_Oord__class_Oless(X13,X41,X9)
| ~ c_HOL_Oord__class_Oless(X11,X41,X9)
| ~ c_HOL_Oord__class_Oless(X13,X11,X9) ),
inference(fof_simplification,[status(thm)],[c_0_199]) ).
fof(c_0_607,plain,
! [X41,X11,X13,X9] :
( ~ class_Orderings_Oorder(X9)
| c_HOL_Oord__class_Oless(X41,X13,X9)
| ~ c_HOL_Oord__class_Oless(X41,X11,X9)
| ~ c_HOL_Oord__class_Oless(X11,X13,X9) ),
inference(fof_simplification,[status(thm)],[c_0_200]) ).
fof(c_0_608,plain,
! [X29,X27] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X27)),c_Lambda_OdB_OAbs(X29)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X27),X29)) ),
inference(fof_simplification,[status(thm)],[c_0_201]) ).
fof(c_0_609,plain,
! [X4,X5,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X9)
| c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X5,X9),c_Nat_Osemiring__1__class_Oof__nat(X4,X9),X9) ),
inference(fof_simplification,[status(thm)],[c_0_202]) ).
fof(c_0_610,plain,
! [X41,X11,X13] :
( c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X41),tc_nat)
| ~ c_HOL_Oord__class_Oless(X13,X11,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_203]) ).
fof(c_0_611,plain,
! [X41,X11,X13] :
( c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X41),tc_nat)
| ~ c_HOL_Oord__class_Oless(X13,X41,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_204]) ).
fof(c_0_612,plain,
! [X5,X15,X16] :
( c_HOL_Oord__class_Oless(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X5),tc_nat)
| ~ c_HOL_Oord__class_Oless(X16,X15,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_205]) ).
fof(c_0_613,plain,
! [X5,X15,X16] :
( c_HOL_Oord__class_Oless(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X15),tc_nat)
| ~ c_HOL_Oord__class_Oless(X16,X15,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_206]) ).
fof(c_0_614,plain,
! [X14,X15,X16] :
( c_HOL_Oord__class_Oless(c_Suc(X16),X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(X15,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(X16,X15,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_207]) ).
fof(c_0_615,plain,
! [X15,X16] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X16),X16,tc_nat),
inference(fof_simplification,[status(thm)],[c_0_208]) ).
fof(c_0_616,plain,
! [X15,X16] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X15),X16,tc_nat),
inference(fof_simplification,[status(thm)],[c_0_209]) ).
fof(c_0_617,plain,
! [X4] :
( c_Suc(c_HOL_Ominus__class_Ominus(X4,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X4
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_210]) ).
fof(c_0_618,axiom,
! [X4,X5] : c_HOL_Ominus__class_Ominus(X5,c_Suc(X4),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X5,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X4,tc_nat),
c_0_211 ).
fof(c_0_619,plain,
! [X29,X16] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X29),X16)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X29)) ),
inference(fof_simplification,[status(thm)],[c_0_212]) ).
fof(c_0_620,axiom,
! [X4,X14,X16] :
( c_Lambda_Oliftn(X4,c_Lambda_OdB_OVar(X16),X14) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X4))
| c_HOL_Oord__class_Oless(X16,X14,tc_nat) ),
c_0_213 ).
fof(c_0_621,plain,
! [X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X9)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),c_HOL_Oone__class_Oone(X9)),c_HOL_Oone__class_Oone(X9)),X9) ),
inference(fof_simplification,[status(thm)],[c_0_214]) ).
fof(c_0_622,axiom,
! [X4,X5] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Ominus__class_Ominus(X5,X4,tc_nat)) = X5
| c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
c_0_215 ).
fof(c_0_623,plain,
! [X4] :
( X4 = c_Suc(c_HOL_Ominus__class_Ominus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_216]) ).
fof(c_0_624,plain,
! [X4] :
( c_Suc(c_HOL_Ominus__class_Ominus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X4
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_217]) ).
fof(c_0_625,axiom,
! [X14,X16] :
( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X16)),X14) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),c_HOL_Oone__class_Oone(tc_nat)))
| c_HOL_Oord__class_Oless(X16,X14,tc_nat) ),
c_0_218 ).
fof(c_0_626,plain,
! [X4,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X9)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X9),c_Nat_Osemiring__1__class_Oof__nat(X4,X9),X9) ),
inference(fof_simplification,[status(thm)],[c_0_219]) ).
fof(c_0_627,plain,
! [X26,X15,X16] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X15)),X26),X16) = c_Lambda_OdB_OVar(X15)
| ~ c_HOL_Oord__class_Oless(X15,X16,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_220]) ).
fof(c_0_628,plain,
! [X4,X5,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X9)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X5,X9),c_Nat_Osemiring__1__class_Oof__nat(X4,X9),X9)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_221]) ).
fof(c_0_629,axiom,
! [X4,X5,X8] :
( hBOOL(hAPP(hAPP(X8,X4),X5))
| c_HOL_Oord__class_Oless(X4,X5,tc_nat)
| X5 = X4
| c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
c_0_222 ).
fof(c_0_630,axiom,
! [X3,X7,X9] : hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X3,X9),X7),X7)),
c_0_223 ).
fof(c_0_631,axiom,
! [X13,X3,X9] : hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X3,X9),X13),X13)),
c_0_224 ).
fof(c_0_632,plain,
! [X4,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X9)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X9),c_Nat_Osemiring__1__class_Oof__nat(X4,X9),X9)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_225]) ).
fof(c_0_633,plain,
! [X41,X11,X13,X9] :
( ~ class_Ring__and__Field_Oidom(X9)
| ~ class_Int_Onumber__ring(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X13),X11) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X13),X41)
| X11 = X41 ),
inference(fof_simplification,[status(thm)],[c_0_226]) ).
fof(c_0_634,plain,
! [X10,X12,X13,X9] :
( ~ class_OrderedGroup_Oab__group__add(X9)
| c_HOL_Ominus__class_Ominus(X13,X13,X9) != c_HOL_Ominus__class_Ominus(X12,X10,X9)
| X12 = X10 ),
inference(fof_simplification,[status(thm)],[c_0_227]) ).
fof(c_0_635,plain,
! [X11,X20,X13,X9] :
( ~ class_OrderedGroup_Oab__group__add(X9)
| c_HOL_Ominus__class_Ominus(X20,X11,X9) != c_HOL_Ominus__class_Ominus(X13,X13,X9)
| X20 = X11 ),
inference(fof_simplification,[status(thm)],[c_0_228]) ).
fof(c_0_636,plain,
! [X6,X7,X9] :
( ~ class_Orderings_Opreorder(X9)
| ~ c_HOL_Oord__class_Oless(X6,X7,X9)
| ~ c_HOL_Oord__class_Oless(X7,X6,X9) ),
inference(fof_simplification,[status(thm)],[c_0_229]) ).
fof(c_0_637,plain,
! [X11,X13,X9] :
( ~ class_Orderings_Opreorder(X9)
| ~ c_HOL_Oord__class_Oless(X11,X13,X9)
| ~ c_HOL_Oord__class_Oless(X13,X11,X9) ),
inference(fof_simplification,[status(thm)],[c_0_230]) ).
fof(c_0_638,plain,
! [X11,X13,X9] :
( ~ class_Orderings_Olinorder(X9)
| ~ c_HOL_Oord__class_Oless(X13,X11,X9)
| ~ c_HOL_Oord__class_Oless(X11,X13,X9) ),
inference(fof_simplification,[status(thm)],[c_0_231]) ).
fof(c_0_639,plain,
! [X6,X7,X9] :
( ~ class_Orderings_Oorder(X9)
| ~ c_HOL_Oord__class_Oless(X7,X6,X9)
| ~ c_HOL_Oord__class_Oless(X6,X7,X9) ),
inference(fof_simplification,[status(thm)],[c_0_232]) ).
fof(c_0_640,plain,
! [X4,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,c_Suc(X5),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_233]) ).
fof(c_0_641,axiom,
! [X4,X5] :
( c_HOL_Ominus__class_Ominus(X4,X5,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X5,X4,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X5 = X4 ),
c_0_234 ).
fof(c_0_642,plain,
! [X7,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X9)
| c_HOL_Oord__class_Oless(X7,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),c_HOL_Oone__class_Oone(X9)),X9) ),
inference(fof_simplification,[status(thm)],[c_0_235]) ).
fof(c_0_643,plain,
! [X32,X6,X7,X9] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X6),X7) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X32),X7)
| X6 = X32 ),
inference(fof_simplification,[status(thm)],[c_0_236]) ).
fof(c_0_644,plain,
! [X32,X6,X7,X9] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X6) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X32)
| X6 = X32 ),
inference(fof_simplification,[status(thm)],[c_0_237]) ).
fof(c_0_645,plain,
! [X32,X6,X7,X9] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X6) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X32)
| X6 = X32 ),
inference(fof_simplification,[status(thm)],[c_0_238]) ).
fof(c_0_646,axiom,
! [X13,X27] :
( c_HOL_Oord__class_Oless(X13,X13,tc_nat)
| c_Lambda_Osubstn(c_Lambda_OdB_OVar(X13),X27,X13) = c_Lambda_Oliftn(X13,X27,c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_239 ).
fof(c_0_647,axiom,
! [X27,X14,X16] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X16)),X27),X14) = c_Lambda_OdB_OVar(X16)
| X16 = X14
| c_HOL_Oord__class_Oless(X14,X16,tc_nat) ),
c_0_240 ).
fof(c_0_648,plain,
! [X6,X7,X9] :
( ~ class_OrderedGroup_Ogroup__add(X9)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X6),X6,X9) = X7 ),
inference(fof_simplification,[status(thm)],[c_0_241]) ).
fof(c_0_649,axiom,
! [X13,X27] :
( c_HOL_Oord__class_Oless(X13,X13,tc_nat)
| hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X13)),X27),X13) = X27 ),
c_0_242 ).
fof(c_0_650,axiom,
! [X4,X5] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),c_Suc(X5),tc_nat),
c_0_243 ).
fof(c_0_651,plain,
! [X29,X16] : ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X16)),X29)),
inference(fof_simplification,[status(thm)],[c_0_244]) ).
fof(c_0_652,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X5),c_Suc(X4),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_245]) ).
fof(c_0_653,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_ea______),v_ua______),v_T____)),
c_0_246 ).
fof(c_0_654,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_e____),v_u____),v_T____)),
c_0_247 ).
fof(c_0_655,axiom,
! [X4,X5] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X5)),X4) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4)),
c_0_248 ).
fof(c_0_656,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_Suc(X5),c_Suc(X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_249]) ).
fof(c_0_657,plain,
! [X13,X4] :
( c_HOL_Oord__class_Oless(c_Suc(X13),c_Suc(X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(X13,X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_250]) ).
fof(c_0_658,plain,
! [X4,X5] :
( X4 = X5
| ~ c_HOL_Oord__class_Oless(X4,c_Suc(X5),tc_nat)
| c_HOL_Oord__class_Oless(X4,X5,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_251]) ).
fof(c_0_659,plain,
! [X4,X5] :
( X5 = X4
| ~ c_HOL_Oord__class_Oless(X4,c_Suc(X5),tc_nat)
| c_HOL_Oord__class_Oless(X4,X5,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_252]) ).
fof(c_0_660,plain,
! [X4,X5] :
( X5 = X4
| c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,c_Suc(X4),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_253]) ).
fof(c_0_661,plain,
! [X4,X14,X16] :
( c_Lambda_Oliftn(X4,c_Lambda_OdB_OVar(X16),X14) = c_Lambda_OdB_OVar(X16)
| ~ c_HOL_Oord__class_Oless(X16,X14,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_254]) ).
fof(c_0_662,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_Suc(X5),X4,tc_nat)
| c_Suc(X5) = X4
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_255]) ).
fof(c_0_663,axiom,
! [X4,X5,X14] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X5) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X4)
| X5 = X4 ),
c_0_256 ).
fof(c_0_664,axiom,
! [X4,X5,X14] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X14) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X14)
| X5 = X4 ),
c_0_257 ).
fof(c_0_665,axiom,
! [X41,X11,X13] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X11) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X41)
| X11 = X41 ),
c_0_258 ).
fof(c_0_666,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X5),X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_259]) ).
fof(c_0_667,axiom,
! [X4,X5] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),c_Suc(X4)) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4)),
c_0_260 ).
fof(c_0_668,axiom,
! [X29,X27] : c_Lambda_Osubstn(X29,X27,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),X27),c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_261 ).
fof(c_0_669,axiom,
! [X4,X5] : c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X5),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_262 ).
fof(c_0_670,axiom,
! [X4,X5] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X5),X4,tc_nat) = X5,
c_0_263 ).
fof(c_0_671,axiom,
! [X4,X5] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4),X4,tc_nat) = X5,
c_0_264 ).
fof(c_0_672,plain,
! [X5,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X9)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X5,X9),c_HOL_Ozero__class_Ozero(X9),X9) ),
inference(fof_simplification,[status(thm)],[c_0_265]) ).
fof(c_0_673,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(X5,c_Suc(X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_266]) ).
fof(c_0_674,plain,
! [X14,X16] :
( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X16)),X14) = c_Lambda_OdB_OVar(X16)
| ~ c_HOL_Oord__class_Oless(X16,X14,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_267]) ).
fof(c_0_675,axiom,
! [X42,X8,X43,X9] : hAPP(c_COMBK(X8,X9,X43),X42) = X8,
c_0_268 ).
fof(c_0_676,axiom,
! [X27,X14,X16] :
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X16),X27,X14) = c_Lambda_OdB_OVar(X16)
| X16 = X14
| c_HOL_Oord__class_Oless(X14,X16,tc_nat) ),
c_0_269 ).
fof(c_0_677,plain,
! [X11,X13,X9] :
( ~ class_Orderings_Olinorder(X9)
| X13 = X11
| c_HOL_Oord__class_Oless(X13,X11,X9)
| c_HOL_Oord__class_Oless(X11,X13,X9) ),
inference(fof_simplification,[status(thm)],[c_0_270]) ).
fof(c_0_678,plain,
! [X11,X13,X9] :
( ~ class_Orderings_Olinorder(X9)
| c_HOL_Oord__class_Oless(X11,X13,X9)
| X13 = X11
| c_HOL_Oord__class_Oless(X13,X11,X9) ),
inference(fof_simplification,[status(thm)],[c_0_271]) ).
fof(c_0_679,plain,
! [X11,X13,X9] :
( ~ class_Orderings_Olinorder(X9)
| c_HOL_Oord__class_Oless(X11,X13,X9)
| c_HOL_Oord__class_Oless(X13,X11,X9)
| X13 = X11 ),
inference(fof_simplification,[status(thm)],[c_0_272]) ).
fof(c_0_680,plain,
! [X11,X13,X9] :
( ~ class_Orderings_Olinorder(X9)
| X13 = X11
| c_HOL_Oord__class_Oless(X11,X13,X9)
| c_HOL_Oord__class_Oless(X13,X11,X9) ),
inference(fof_simplification,[status(thm)],[c_0_273]) ).
fof(c_0_681,plain,
! [X11,X13,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X9)
| c_HOL_Oord__class_Oless(X11,X13,X9)
| c_HOL_Oord__class_Oless(X13,X11,X9)
| X13 = X11 ),
inference(fof_simplification,[status(thm)],[c_0_274]) ).
fof(c_0_682,axiom,
! [X56,X24,X57,X25] :
( hAPP(hAPP(c_Type_Otype_OFun,X25),X24) != hAPP(hAPP(c_Type_Otype_OFun,X57),X56)
| X25 = X57 ),
c_0_275 ).
fof(c_0_683,axiom,
! [X56,X24,X57,X25] :
( hAPP(hAPP(c_Type_Otype_OFun,X25),X24) != hAPP(hAPP(c_Type_Otype_OFun,X57),X56)
| X24 = X56 ),
c_0_276 ).
fof(c_0_684,axiom,
! [X45,X51,X46,X52] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X52),X51) != hAPP(hAPP(c_Lambda_OdB_OApp,X46),X45)
| X52 = X46 ),
c_0_277 ).
fof(c_0_685,axiom,
! [X45,X51,X46,X52] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X52),X51) != hAPP(hAPP(c_Lambda_OdB_OApp,X46),X45)
| X51 = X45 ),
c_0_278 ).
fof(c_0_686,axiom,
! [X4,X5] : c_HOL_Ominus__class_Ominus(c_Suc(X5),c_Suc(X4),tc_nat) = c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),
c_0_279 ).
fof(c_0_687,plain,
! [X5,X9] :
( ~ class_Ring__and__Field_Osemiring__1(X9)
| c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X5),X9) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),c_HOL_Oone__class_Oone(X9)),c_Nat_Osemiring__1__class_Oof__nat(X5,X9)) ),
inference(fof_simplification,[status(thm)],[c_0_280]) ).
fof(c_0_688,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(X4,c_Suc(X5),tc_nat)
| c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
c_0_281 ).
fof(c_0_689,axiom,
! [X13] :
( c_HOL_Oord__class_Oless(X13,X13,tc_nat)
| c_HOL_Oord__class_Oless(X13,c_Suc(X13),tc_nat) ),
c_0_282 ).
fof(c_0_690,plain,
! [X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X9)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X9),c_HOL_Ozero__class_Ozero(X9),X9) ),
inference(fof_simplification,[status(thm)],[c_0_283]) ).
fof(c_0_691,plain,
! [X32,X7,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X32) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X32),X7) ),
inference(fof_simplification,[status(thm)],[c_0_284]) ).
fof(c_0_692,plain,
! [X6,X7,X9] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X6) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X6),X7) ),
inference(fof_simplification,[status(thm)],[c_0_285]) ).
fof(c_0_693,plain,
! [X11,X13,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X13),X11) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X11),X13) ),
inference(fof_simplification,[status(thm)],[c_0_286]) ).
fof(c_0_694,axiom,
! [X26,X14] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X14)),X26),X14) = X26,
c_0_287 ).
fof(c_0_695,axiom,
! [X4,X5] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X5)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),c_Suc(X4)),
c_0_288 ).
fof(c_0_696,axiom,
! [X11,X13] :
( c_HOL_Oord__class_Oless(X11,X13,tc_nat)
| c_HOL_Oord__class_Oless(X13,X11,tc_nat)
| X13 = X11 ),
c_0_289 ).
fof(c_0_697,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(X4,X5,tc_nat)
| c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| X5 = X4 ),
c_0_290 ).
fof(c_0_698,plain,
! [X11,X13,X9] :
( ~ class_Ring__and__Field_Oidom(X9)
| ~ class_Int_Onumber__ring(X9)
| c_HOL_Ominus__class_Ominus(X13,X11,X9) != c_HOL_Ozero__class_Ozero(X9)
| X13 = X11 ),
inference(fof_simplification,[status(thm)],[c_0_291]) ).
fof(c_0_699,plain,
! [X4] :
( X4 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_292]) ).
fof(c_0_700,plain,
! [X13,X7,X9] :
( ~ class_Ring__and__Field_Oidom(X9)
| ~ class_Int_Onumber__ring(X9)
| X13 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X13),X7)
| X7 = c_HOL_Ozero__class_Ozero(X9) ),
inference(fof_simplification,[status(thm)],[c_0_293]) ).
fof(c_0_701,plain,
! [X6,X7,X9] :
( ~ class_OrderedGroup_Oab__group__add(X9)
| c_HOL_Ominus__class_Ominus(X7,X6,X9) != c_HOL_Ozero__class_Ozero(X9)
| X7 = X6 ),
inference(fof_simplification,[status(thm)],[c_0_294]) ).
fof(c_0_702,plain,
! [X6,X7,X9] :
( ~ class_OrderedGroup_Ogroup__add(X9)
| c_HOL_Ominus__class_Ominus(X7,X6,X9) != c_HOL_Ozero__class_Ozero(X9)
| X7 = X6 ),
inference(fof_simplification,[status(thm)],[c_0_295]) ).
fof(c_0_703,plain,
! [X7,X9] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),X7) != c_HOL_Ozero__class_Ozero(X9)
| X7 = c_HOL_Ozero__class_Ozero(X9) ),
inference(fof_simplification,[status(thm)],[c_0_296]) ).
fof(c_0_704,axiom,
! [X4,X5] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X5 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_297 ).
fof(c_0_705,axiom,
! [X4,X5] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4)
| X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X5 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_298 ).
fof(c_0_706,axiom,
! [X4,X5] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X5 = c_HOL_Ozero__class_Ozero(tc_nat)
| X5 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_299 ).
fof(c_0_707,axiom,
! [X4,X5] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_300 ).
fof(c_0_708,axiom,
! [X4,X5] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4)
| X5 = c_HOL_Ozero__class_Ozero(tc_nat)
| X5 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_301 ).
fof(c_0_709,axiom,
! [X4,X5] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4)
| X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_302 ).
fof(c_0_710,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(fof_simplification,[status(thm)],[c_0_303]) ).
fof(c_0_711,plain,
! [X13,X9] :
( ~ class_Orderings_Opreorder(X9)
| ~ c_HOL_Oord__class_Oless(X13,X13,X9) ),
inference(fof_simplification,[status(thm)],[c_0_304]) ).
fof(c_0_712,plain,
! [X13,X9] :
( ~ class_Orderings_Olinorder(X9)
| ~ c_HOL_Oord__class_Oless(X13,X13,X9) ),
inference(fof_simplification,[status(thm)],[c_0_305]) ).
fof(c_0_713,plain,
! [X13,X9] :
( ~ class_Orderings_Oorder(X9)
| ~ c_HOL_Oord__class_Oless(X13,X13,X9) ),
inference(fof_simplification,[status(thm)],[c_0_306]) ).
fof(c_0_714,axiom,
! [X4,X5] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X5),
c_0_307 ).
fof(c_0_715,axiom,
! [X4,X5] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X5 = c_HOL_Ozero__class_Ozero(tc_nat)
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_308 ).
fof(c_0_716,axiom,
! [X4,X5] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4)
| X5 = c_HOL_Ozero__class_Ozero(tc_nat)
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_309 ).
fof(c_0_717,plain,
! [X5] : ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(fof_simplification,[status(thm)],[c_0_310]) ).
fof(c_0_718,plain,
! [X4] : ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(fof_simplification,[status(thm)],[c_0_311]) ).
fof(c_0_719,plain,
! [X70,X71,X9] :
( X71 = X70
| ~ c_fequal(X71,X70,X9) ),
inference(fof_simplification,[status(thm)],[c_0_312]) ).
fof(c_0_720,plain,
! [X4] : ~ c_HOL_Oord__class_Oless(X4,X4,tc_nat),
inference(fof_simplification,[status(thm)],[c_0_313]) ).
fof(c_0_721,plain,
! [X13] : ~ c_HOL_Oord__class_Oless(X13,X13,tc_nat),
inference(fof_simplification,[status(thm)],[c_0_314]) ).
fof(c_0_722,plain,
! [X3] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X3)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_315]) ).
fof(c_0_723,plain,
! [X9] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),c_HOL_Ozero__class_Ozero(X9)),c_HOL_Ozero__class_Ozero(X9)) = c_HOL_Ozero__class_Ozero(X9) ),
inference(fof_simplification,[status(thm)],[c_0_316]) ).
fof(c_0_724,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_317 ).
fof(c_0_725,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_318 ).
fof(c_0_726,axiom,
! [X4,X5] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4) != c_HOL_Ozero__class_Ozero(tc_nat)
| X5 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_319 ).
fof(c_0_727,axiom,
! [X4,X5] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4) != c_HOL_Ozero__class_Ozero(tc_nat)
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_320 ).
fof(c_0_728,axiom,
! [X4,X5] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4) != X5
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_321 ).
fof(c_0_729,axiom,
! [X13,X7] :
( X13 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X7)
| X7 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_322 ).
fof(c_0_730,plain,
! [X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X9)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X9),c_HOL_Oone__class_Oone(X9),X9) ),
inference(fof_simplification,[status(thm)],[c_0_323]) ).
fof(c_0_731,plain,
! [X13,X9] :
( ~ class_Ring__and__Field_Oidom(X9)
| ~ class_Int_Onumber__ring(X9)
| X13 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X13),c_HOL_Ozero__class_Ozero(X9)) ),
inference(fof_simplification,[status(thm)],[c_0_324]) ).
fof(c_0_732,plain,
! [X13,X9] :
( ~ class_Ring__and__Field_Oidom(X9)
| ~ class_Int_Onumber__ring(X9)
| c_HOL_Ominus__class_Ominus(X13,X13,X9) = c_HOL_Ozero__class_Ozero(X9) ),
inference(fof_simplification,[status(thm)],[c_0_325]) ).
fof(c_0_733,plain,
! [X7,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),c_HOL_Ozero__class_Ozero(X9)),X7) = X7 ),
inference(fof_simplification,[status(thm)],[c_0_326]) ).
fof(c_0_734,plain,
! [X7,X9] :
( ~ class_OrderedGroup_Omonoid__add(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),c_HOL_Ozero__class_Ozero(X9)),X7) = X7 ),
inference(fof_simplification,[status(thm)],[c_0_327]) ).
fof(c_0_735,plain,
! [X7,X9] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),c_HOL_Ozero__class_Ozero(X9)),X7) = X7 ),
inference(fof_simplification,[status(thm)],[c_0_328]) ).
fof(c_0_736,plain,
! [X13,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),c_HOL_Ozero__class_Ozero(X9)),X13) = X13 ),
inference(fof_simplification,[status(thm)],[c_0_329]) ).
fof(c_0_737,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
c_0_330 ).
fof(c_0_738,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_331 ).
fof(c_0_739,plain,
! [X7,X9] :
( ~ class_OrderedGroup_Ogroup__add(X9)
| c_HOL_Ominus__class_Ominus(X7,c_HOL_Ozero__class_Ozero(X9),X9) = X7 ),
inference(fof_simplification,[status(thm)],[c_0_332]) ).
fof(c_0_740,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
c_0_333 ).
fof(c_0_741,plain,
! [X7,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),c_HOL_Ozero__class_Ozero(X9)) = X7 ),
inference(fof_simplification,[status(thm)],[c_0_334]) ).
fof(c_0_742,plain,
! [X7,X9] :
( ~ class_OrderedGroup_Omonoid__add(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),c_HOL_Ozero__class_Ozero(X9)) = X7 ),
inference(fof_simplification,[status(thm)],[c_0_335]) ).
fof(c_0_743,plain,
! [X7,X9] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X7),c_HOL_Ozero__class_Ozero(X9)) = X7 ),
inference(fof_simplification,[status(thm)],[c_0_336]) ).
fof(c_0_744,plain,
! [X13,X9] :
( ~ class_OrderedGroup_Oab__group__add(X9)
| c_HOL_Ominus__class_Ominus(X13,X13,X9) = c_HOL_Ozero__class_Ozero(X9) ),
inference(fof_simplification,[status(thm)],[c_0_337]) ).
fof(c_0_745,plain,
! [X13,X9] :
( ~ class_OrderedGroup_Ogroup__add(X9)
| c_HOL_Ominus__class_Ominus(X13,X13,X9) = c_HOL_Ozero__class_Ozero(X9) ),
inference(fof_simplification,[status(thm)],[c_0_338]) ).
fof(c_0_746,plain,
! [X7,X9] :
( ~ class_OrderedGroup_Ogroup__add(X9)
| c_HOL_Ominus__class_Ominus(X7,X7,X9) = c_HOL_Ozero__class_Ozero(X9) ),
inference(fof_simplification,[status(thm)],[c_0_339]) ).
fof(c_0_747,axiom,
! [X49,X51,X52] : hAPP(hAPP(c_Lambda_OdB_OApp,X52),X51) != c_Lambda_OdB_OAbs(X49),
c_0_340 ).
fof(c_0_748,axiom,
! [X49,X51,X52] : c_Lambda_OdB_OAbs(X49) != hAPP(hAPP(c_Lambda_OdB_OApp,X52),X51),
c_0_341 ).
fof(c_0_749,axiom,
! [X40,X45,X46] : c_Lambda_OdB_OVar(X40) != hAPP(hAPP(c_Lambda_OdB_OApp,X46),X45),
c_0_342 ).
fof(c_0_750,axiom,
! [X40,X45,X46] : hAPP(hAPP(c_Lambda_OdB_OApp,X46),X45) != c_Lambda_OdB_OVar(X40),
c_0_343 ).
fof(c_0_751,axiom,
! [X4] : c_HOL_Ominus__class_Ominus(c_Suc(X4),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X4,
c_0_344 ).
fof(c_0_752,axiom,
! [X4] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X4),tc_nat),
c_0_345 ).
fof(c_0_753,axiom,
! [X13] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X13),tc_nat),
c_0_346 ).
fof(c_0_754,axiom,
! [X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_347 ).
fof(c_0_755,axiom,
! [X13] : c_HOL_Oord__class_Oless(X13,c_Suc(X13),tc_nat),
c_0_348 ).
fof(c_0_756,axiom,
! [X4] : c_HOL_Oord__class_Oless(X4,c_Suc(X4),tc_nat),
c_0_349 ).
fof(c_0_757,axiom,
! [X29,X14] : c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X29,X14) = X29,
c_0_350 ).
fof(c_0_758,axiom,
! [X4] : c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_351 ).
fof(c_0_759,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),
c_0_352 ).
fof(c_0_760,axiom,
! [X5] : c_HOL_Ominus__class_Ominus(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X5,
c_0_353 ).
fof(c_0_761,axiom,
! [X4] : c_Suc(X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X4),
c_0_354 ).
fof(c_0_762,axiom,
! [X5] : c_HOL_Ominus__class_Ominus(X5,X5,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_355 ).
fof(c_0_763,axiom,
! [X13,X9] : c_fequal(X13,X13,X9),
c_0_356 ).
fof(c_0_764,axiom,
! [X3,X9] : c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(X3,X9),X9) = c_Transitive__Closure_Ortranclp(X3,X9),
c_0_357 ).
fof(c_0_765,plain,
! [X4,X5,X9] :
( ~ class_Nat_Osemiring__char__0(X9)
| c_Nat_Osemiring__1__class_Oof__nat(X5,X9) != c_Nat_Osemiring__1__class_Oof__nat(X4,X9)
| X5 = X4 ),
inference(fof_simplification,[status(thm)],[c_0_358]) ).
fof(c_0_766,axiom,
! [X4] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X4) = X4,
c_0_359 ).
fof(c_0_767,axiom,
! [X4] : c_Suc(X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),
c_0_360 ).
fof(c_0_768,axiom,
! [X5] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),c_HOL_Ozero__class_Ozero(tc_nat)) = X5,
c_0_361 ).
fof(c_0_769,axiom,
! [X13] : X13 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_362 ).
fof(c_0_770,axiom,
! [X4] : hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X4))),
c_0_363 ).
fof(c_0_771,plain,
! [X68,X69] :
( class_Orderings_Oorder(tc_fun(X68,X69))
| ~ class_Orderings_Oorder(X69) ),
inference(fof_simplification,[status(thm)],[c_0_364]) ).
fof(c_0_772,plain,
! [X68,X69] :
( class_Orderings_Opreorder(tc_fun(X68,X69))
| ~ class_Orderings_Opreorder(X69) ),
inference(fof_simplification,[status(thm)],[c_0_365]) ).
fof(c_0_773,plain,
! [X9] :
( ~ class_Ring__and__Field_Osemiring__1(X9)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X9) = c_HOL_Oone__class_Oone(X9) ),
inference(fof_simplification,[status(thm)],[c_0_366]) ).
fof(c_0_774,plain,
! [X9] :
( ~ class_Ring__and__Field_Osemiring__1(X9)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X9) = c_HOL_Ozero__class_Ozero(X9) ),
inference(fof_simplification,[status(thm)],[c_0_367]) ).
fof(c_0_775,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
c_0_368 ).
fof(c_0_776,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_ua______)),
c_0_369 ).
fof(c_0_777,axiom,
! [X13,X9] : hAPP(c_Fun_Oid(X9),X13) = X13,
c_0_370 ).
fof(c_0_778,plain,
! [X9] :
( ~ class_Ring__and__Field_Ozero__neq__one(X9)
| c_HOL_Ozero__class_Ozero(X9) != c_HOL_Oone__class_Oone(X9) ),
inference(fof_simplification,[status(thm)],[c_0_371]) ).
fof(c_0_779,plain,
! [X9] :
( ~ class_Ring__and__Field_Ozero__neq__one(X9)
| c_HOL_Oone__class_Oone(X9) != c_HOL_Ozero__class_Ozero(X9) ),
inference(fof_simplification,[status(thm)],[c_0_372]) ).
fof(c_0_780,axiom,
hAPP(c_Fun_Oid(t_a),v_x) = v_x,
c_0_373 ).
fof(c_0_781,axiom,
! [X33,X40] :
( c_Lambda_OdB_OVar(X40) != c_Lambda_OdB_OVar(X33)
| X40 = X33 ),
c_0_374 ).
fof(c_0_782,axiom,
! [X49,X50] :
( c_Lambda_OdB_OAbs(X50) != c_Lambda_OdB_OAbs(X49)
| X50 = X49 ),
c_0_375 ).
fof(c_0_783,axiom,
! [X11,X13] :
( c_Suc(X13) != c_Suc(X11)
| X13 = X11 ),
c_0_376 ).
fof(c_0_784,axiom,
! [X33,X40] :
( c_Suc(X40) != c_Suc(X33)
| X40 = X33 ),
c_0_377 ).
fof(c_0_785,axiom,
! [X40,X49] : c_Lambda_OdB_OAbs(X49) != c_Lambda_OdB_OVar(X40),
c_0_378 ).
fof(c_0_786,axiom,
! [X40,X49] : c_Lambda_OdB_OVar(X40) != c_Lambda_OdB_OAbs(X49),
c_0_379 ).
fof(c_0_787,axiom,
! [X33] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X33),
c_0_380 ).
fof(c_0_788,axiom,
! [X5] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X5),
c_0_381 ).
fof(c_0_789,axiom,
! [X5] : c_Suc(X5) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_382 ).
fof(c_0_790,axiom,
! [X33] : c_Suc(X33) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_383 ).
fof(c_0_791,axiom,
c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_384 ).
fof(c_0_792,axiom,
! [X4] : X4 != c_Suc(X4),
c_0_385 ).
fof(c_0_793,axiom,
! [X4] : c_Suc(X4) != X4,
c_0_386 ).
fof(c_0_794,axiom,
class_Orderings_Oorder(tc_bool),
c_0_387 ).
fof(c_0_795,axiom,
class_Orderings_Opreorder(tc_bool),
c_0_388 ).
fof(c_0_796,axiom,
class_Orderings_Oorder(tc_nat),
c_0_389 ).
fof(c_0_797,axiom,
class_Orderings_Olinorder(tc_nat),
c_0_390 ).
fof(c_0_798,axiom,
class_Orderings_Opreorder(tc_nat),
c_0_391 ).
fof(c_0_799,axiom,
class_Nat_Osemiring__char__0(tc_nat),
c_0_392 ).
fof(c_0_800,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
c_0_393 ).
fof(c_0_801,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
c_0_394 ).
fof(c_0_802,axiom,
class_OrderedGroup_Osemigroup__add(tc_nat),
c_0_395 ).
fof(c_0_803,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
c_0_396 ).
fof(c_0_804,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
c_0_397 ).
fof(c_0_805,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
c_0_398 ).
fof(c_0_806,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
c_0_399 ).
fof(c_0_807,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
c_0_400 ).
fof(c_0_808,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
c_0_401 ).
fof(c_0_809,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
c_0_402 ).
fof(c_0_810,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
c_0_403 ).
fof(c_0_811,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
c_0_404 ).
fof(c_0_812,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
c_0_405 ).
fof(c_0_813,axiom,
v_n____ = v_i____,
c_0_406 ).
fof(c_0_814,axiom,
c_List_Olistsp(hAPP(hAPP(c_COMBS(tc_Lambda_OdB,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_and),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_bool),tc_bool,tc_Lambda_OdB),c_All(tc_fun(tc_nat,tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_bool),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_fun(tc_nat,tc_Type_Otype)),c_All(tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_bool)),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_Type_Otype,tc_bool),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_bool),tc_bool,tc_Type_Otype),c_All(tc_Lambda_OdB)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_bool),tc_Type_Otype),hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_bool,tc_Lambda_OdB),c_All(tc_nat))))),hAPP(hAPP(c_COMBS(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_fun(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),c_COMBS(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Type_Otype),c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool),tc_Lambda_OdB)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Type_Otype),c_COMBS(tc_nat,tc_bool,tc_bool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_Type_Otype),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_nat),c_implies)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Type_Otype,tc_bool))),hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Lambda_OdB,tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype)),tc_fun(tc_nat,tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool)),tc_nat),c_Type_Otyping)),hAPP(hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_Type_Otype))),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Type_Otype,tc_fun(tc_nat,tc_Type_Otype))),c_Type_Oshift(tc_Type_Otype))),v_T____))))))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBS(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),c_COMBB(tc_bool,tc_bool,tc_nat)),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_implies),c_InductTermi_OIT))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBS(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_bool,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),c_COMBB(tc_bool,tc_bool,tc_nat))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_bool),tc_fun(tc_Lambda_OdB,tc_fun(tc_bool,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_implies)),hAPP(hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_Lambda_OdB,tc_Type_Otype,tc_bool)),c_Type_Otyping)),v_T____)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_nat,tc_Lambda_OdB),tc_fun(tc_nat,tc_bool),tc_Lambda_OdB),hAPP(c_COMBB(tc_Lambda_OdB,tc_bool,tc_nat),c_InductTermi_OIT))),c_Lambda_Osubst)))))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),c_Ex(tc_Type_Otype)),hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)))),v_bs____,tc_Lambda_OdB),
c_0_407 ).
fof(c_0_815,plain,
! [X38,X39,X40,X41,X42,X43,X44] :
( X42 = c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X44,X42,X41,X38),X44,tc_Type_Otype,tc_Type_Otype)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X41),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X40),X39,tc_Lambda_OdB,tc_Lambda_OdB)),X42))
| ~ c_Type_Otypings(X41,X39,X43)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X41),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X40),X39,tc_Lambda_OdB,tc_Lambda_OdB),X38,tc_Lambda_OdB,tc_Lambda_OdB)),X44)) ),
inference(variable_rename,[status(thm)],[c_0_408]) ).
fof(c_0_816,plain,
! [X38,X39,X40,X41,X42,X43,X44] :
( c_Type_Otypings(X41,X38,c_Type_Osko__Type__Xvar__app__types__1__1(X44,X42,X41,X38))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X41),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X40),X39,tc_Lambda_OdB,tc_Lambda_OdB)),X42))
| ~ c_Type_Otypings(X41,X39,X43)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X41),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X40),X39,tc_Lambda_OdB,tc_Lambda_OdB),X38,tc_Lambda_OdB,tc_Lambda_OdB)),X44)) ),
inference(variable_rename,[status(thm)],[c_0_409]) ).
fof(c_0_817,plain,
! [X37,X38,X39,X40,X41] :
( X41 = X40
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X39),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X38),X37,tc_Lambda_OdB,tc_Lambda_OdB)),X40))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X39),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X38),X37,tc_Lambda_OdB,tc_Lambda_OdB)),X41)) ),
inference(variable_rename,[status(thm)],[c_0_410]) ).
fof(c_0_818,plain,
! [X29,X30,X31,X32] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X31),c_Lambda_OdB_OVar(X30)),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X32,X31,X30,X29),X32,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X31),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X30),X29,tc_Lambda_OdB,tc_Lambda_OdB)),X32)) ),
inference(variable_rename,[status(thm)],[c_0_411]) ).
fof(c_0_819,plain,
! [X30,X31,X32,X33] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X32),X31),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X33,X32,X31,X30),X33,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X32),c_List_Ofoldl(c_Lambda_OdB_OApp,X31,X30,tc_Lambda_OdB,tc_Lambda_OdB)),X33)) ),
inference(variable_rename,[status(thm)],[c_0_412]) ).
fof(c_0_820,plain,
! [X30,X31,X32,X33] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X32),X31),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X33,X32,X31,X30),X33,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X32),c_List_Ofoldl(c_Lambda_OdB_OApp,X31,X30,tc_Lambda_OdB,tc_Lambda_OdB)),X33)) ),
inference(variable_rename,[status(thm)],[c_0_413]) ).
fof(c_0_821,plain,
! [X38,X39,X40,X41,X42] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X40),c_List_Ofoldl(c_Lambda_OdB_OApp,X39,X38,tc_Lambda_OdB,tc_Lambda_OdB)),X42))
| ~ c_Type_Otypings(X40,X38,X41)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X40),X39),c_List_Ofoldr(c_Type_Otype_OFun,X41,X42,tc_Type_Otype,tc_Type_Otype))) ),
inference(variable_rename,[status(thm)],[c_0_414]) ).
fof(c_0_822,plain,
! [X30,X31,X32,X33] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,X32,X31,tc_Lambda_OdB,tc_Lambda_OdB)),X30),X33) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X32),X30),X33),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),X30)),X33),X31,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(variable_rename,[status(thm)],[c_0_415]) ).
fof(c_0_823,plain,
! [X22,X23,X24] :
( X22 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X24),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X24,X23,X22),tc_Lambda_OdB,tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X24),X23,tc_Lambda_OdB,tc_Lambda_OdB)),X22)) ),
inference(variable_rename,[status(thm)],[c_0_416]) ).
fof(c_0_824,plain,
! [X29,X30,X31,X32] :
( c_Type_Otypings(X31,X29,c_Type_Osko__Type__Xvar__app__typesE__1__1(X32,X31,X30,X29))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X31),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X30),X29,tc_Lambda_OdB,tc_Lambda_OdB)),X32)) ),
inference(variable_rename,[status(thm)],[c_0_417]) ).
fof(c_0_825,plain,
! [X30,X31,X32,X33] :
( c_Type_Otypings(X32,X30,c_Type_Osko__Type__Xlist__app__typeD__1__1(X33,X32,X31,X30))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X32),c_List_Ofoldl(c_Lambda_OdB_OApp,X31,X30,tc_Lambda_OdB,tc_Lambda_OdB)),X33)) ),
inference(variable_rename,[status(thm)],[c_0_418]) ).
fof(c_0_826,plain,
! [X30,X31,X32,X33] :
( c_Type_Otypings(X32,X30,c_Type_Osko__Type__Xlist__app__typeE__1__1(X33,X32,X31,X30))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X32),c_List_Ofoldl(c_Lambda_OdB_OApp,X31,X30,tc_Lambda_OdB,tc_Lambda_OdB)),X33)) ),
inference(variable_rename,[status(thm)],[c_0_419]) ).
fof(c_0_827,plain,
! [X22,X23,X24] :
( c_ListOrder_Ostep1(c_Lambda_Obeta,X23,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X24,X23,X22),tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X24),X23,tc_Lambda_OdB,tc_Lambda_OdB)),X22)) ),
inference(variable_rename,[status(thm)],[c_0_420]) ).
fof(c_0_828,plain,
! [X4,X5,X6] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X6,X5,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X6,X4,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X5,X4,tc_Lambda_OdB) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_421])])]) ).
fof(c_0_829,plain,
! [X28,X29,X30] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X30,X28,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X29,X28,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X30),X29)) ),
inference(variable_rename,[status(thm)],[c_0_422]) ).
fof(c_0_830,plain,
! [X28,X29,X30] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X30,X28,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X29,X28,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X30),X29)) ),
inference(variable_rename,[status(thm)],[c_0_423]) ).
fof(c_0_831,axiom,
c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),v_u____)),v_i____),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
c_0_424 ).
fof(c_0_832,axiom,
c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),v_u____)),v_i____),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
c_0_425 ).
fof(c_0_833,plain,
! [X28,X29,X30] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X30)),X29),X28,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X29))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X30),X29),c_HOL_Ozero__class_Ozero(tc_nat)),X28,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(variable_rename,[status(thm)],[c_0_426]) ).
fof(c_0_834,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),c_Lambda_OdB_OVar(v_n____)),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)))),
c_0_427 ).
fof(c_0_835,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_H____)),
c_0_428 ).
fof(c_0_836,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_ea______),v_ia______),v_T____)),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_Ha______)),
c_0_429 ).
fof(c_0_837,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_e____),v_u____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)))),
c_0_430 ).
fof(c_0_838,plain,
! [X30,X31,X32] : hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,X31,X30,tc_Lambda_OdB,tc_Lambda_OdB)),X32) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X31),X32),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),X32),X30,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(variable_rename,[status(thm)],[c_0_431]) ).
fof(c_0_839,plain,
! [X38,X39,X40,X41,X42,X43] :
( c_Type_Otypings(X41,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),X38)),X40),X39,tc_Lambda_OdB,tc_Lambda_OdB),X42)
| ~ c_Type_Otypings(hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X41),X40),X43),X39,X42)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X41),X38),X43)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_432])])]) ).
fof(c_0_840,plain,
! [X56,X57,X58,X59,X60,X61,X62] : c_Fun_Ofcomp(c_Fun_Ofcomp(X58,X57,X62,X59,X60),X56,X62,X60,X61) = c_Fun_Ofcomp(X58,c_Fun_Ofcomp(X57,X56,X59,X60,X61),X62,X59,X61),
inference(variable_rename,[status(thm)],[c_0_433]) ).
fof(c_0_841,plain,
! [X56,X57,X58,X59,X60,X61,X62] : c_Fun_Ocomp(X58,c_Fun_Ocomp(X57,X56,X59,X60,X62),X60,X61,X62) = c_Fun_Ocomp(c_Fun_Ocomp(X58,X57,X60,X61,X59),X56,X59,X61,X62),
inference(variable_rename,[status(thm)],[c_0_434]) ).
fof(c_0_842,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
c_0_435 ).
fof(c_0_843,plain,
! [X30,X31,X32,X33] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X32),X31),hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X33,X32,X31,X30)),X33)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X32),hAPP(hAPP(c_Lambda_OdB_OApp,X31),X30)),X33)) ),
inference(variable_rename,[status(thm)],[c_0_436]) ).
fof(c_0_844,plain,
! [X61,X62,X63,X64,X65,X66,X67,X68,X69,X70,X71] :
( hAPP(X66,hAPP(X64,X62)) != hAPP(X65,hAPP(X63,X61))
| hAPP(c_Fun_Ocomp(X66,X64,X70,X71,X69),X62) = hAPP(c_Fun_Ocomp(X65,X63,X68,X71,X67),X61) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_437])])]) ).
fof(c_0_845,plain,
! [X5,X6] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X6),X5,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_List_Olistsp(c_InductTermi_OIT,X5,tc_Lambda_OdB) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_438])])]) ).
fof(c_0_846,plain,
! [X30,X31,X32] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X31),c_HOL_Ozero__class_Ozero(tc_nat)),c_Type_Osko__Type__Xtyping__elims__3__1(X32,X31,X30))),X30),c_Type_Osko__Type__Xtyping__elims__3__2(X32,X31,X30)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X31),c_Lambda_OdB_OAbs(X30)),X32)) ),
inference(variable_rename,[status(thm)],[c_0_439]) ).
fof(c_0_847,plain,
! [X68,X69,X70,X71,X72,X73] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X71),X68),X72))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X71),X70),X72)),X69),X73))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X71),hAPP(hAPP(hAPP(c_Lambda_Osubst,X69),X68),X70)),X73)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_440])])]) ).
fof(c_0_848,plain,
! [X56,X57,X58,X59,X60,X61,X62,X63,X64] :
( c_Fun_Ocomp(X60,X59,X62,X63,X64) != c_Fun_Ocomp(X58,X57,X61,X63,X64)
| hAPP(X60,hAPP(X59,X56)) = hAPP(X58,hAPP(X57,X56)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_441])])]) ).
fof(c_0_849,plain,
! [X45,X46,X47,X48,X49,X50,X51] :
( c_Fun_Ocomp(X48,X47,X49,X50,X51) != c_Fun_Ocomp(c_Fun_Oid(X50),X46,X50,X50,X51)
| hAPP(X48,hAPP(X47,X45)) = hAPP(X46,X45) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_442])])]) ).
fof(c_0_850,plain,
! [X6,X7,X8,X9] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X9),X7,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X8),X6,tc_Lambda_OdB,tc_Lambda_OdB)
| X9 = X8 ),
inference(variable_rename,[status(thm)],[c_0_443]) ).
fof(c_0_851,plain,
! [X6,X7,X8,X9] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X9),X7,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X8),X6,tc_Lambda_OdB,tc_Lambda_OdB)
| X7 = X6 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_444])])]) ).
fof(c_0_852,plain,
! [X28,X29,X30,X31] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X31),X30,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X29),X28,tc_Lambda_OdB,tc_Lambda_OdB)
| X31 = X29 ),
inference(variable_rename,[status(thm)],[c_0_445]) ).
fof(c_0_853,plain,
! [X28,X29,X30,X31] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X31),X30,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X29),X28,tc_Lambda_OdB,tc_Lambda_OdB)
| X30 = X28 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_446])])]) ).
fof(c_0_854,plain,
! [X32,X33,X34,X35] :
( ~ class_OrderedGroup_Osemigroup__add(X35)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X35),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X35),X34),X33),X32,X35,X35) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X35),X34),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X35),X33,X32,X35,X35)) ),
inference(variable_rename,[status(thm)],[c_0_447]) ).
fof(c_0_855,plain,
! [X29,X30,X31,X32] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X32),X29,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X31),X30,tc_Lambda_OdB,tc_Lambda_OdB),
inference(variable_rename,[status(thm)],[c_0_448]) ).
fof(c_0_856,plain,
! [X29,X30,X31] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X31,X29,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X30,X29,tc_Lambda_OdB,tc_Lambda_OdB)
| X31 = X30 ),
inference(variable_rename,[status(thm)],[c_0_449]) ).
fof(c_0_857,plain,
! [X35,X36,X37] :
( ~ class_OrderedGroup_Omonoid__add(X37)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X37),X36,X35,X37,X37) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X37),X36),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X37),X35,c_HOL_Ozero__class_Ozero(X37),X37,X37)) ),
inference(variable_rename,[status(thm)],[c_0_450]) ).
fof(c_0_858,plain,
! [X32,X33,X34] :
( ~ class_OrderedGroup_Omonoid__add(X34)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X34),X33),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X34),c_HOL_Ozero__class_Ozero(X34),X32,X34,X34)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X34),X33,X32,X34,X34) ),
inference(variable_rename,[status(thm)],[c_0_451]) ).
fof(c_0_859,plain,
! [X67,X68,X69,X70,X71,X72,X73] :
( v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X73),X72)
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X68),X67),X69)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X70),X67),X73))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X67))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X70),X69),X73)),X68),X71))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X68)) ),
inference(variable_rename,[status(thm)],[c_0_452]) ).
fof(c_0_860,plain,
! [X67,X68,X69,X70,X71,X72,X73] :
( v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X73),X72)
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X68),X67),X69)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X70),X67),X72))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X67))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X70),X69),X72)),X68),X71))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X68)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_453])])]) ).
fof(c_0_861,plain,
! [X64,X65,X66,X67] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),X64),X65)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X66),X64),v_T____))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X64))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X66),X65),v_T____)),v_b____),X67)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_454])])]) ).
fof(c_0_862,plain,
! [X64,X65,X66,X67] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),X64),X65)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X66),X64),v_T____))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X64))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X66),X65),v_T____)),v_b____),X67)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_455])])]) ).
fof(c_0_863,plain,
! [X48,X49,X50,X51,X52,X53] : c_List_Omap(X50,c_List_Omap(X49,X48,X51,X52),X52,X53) = c_List_Omap(c_Fun_Ocomp(X50,X49,X52,X53,X51),X48,X51,X53),
inference(variable_rename,[status(thm)],[c_0_456]) ).
fof(c_0_864,plain,
! [X54,X55,X56,X57] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X55),c_Lambda_OdB_OAbs(X54)),hAPP(hAPP(c_Type_Otype_OFun,X57),X56)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X55),c_HOL_Ozero__class_Ozero(tc_nat)),X57)),X54),X56)) ),
inference(variable_rename,[status(thm)],[c_0_457]) ).
fof(c_0_865,plain,
! [X30,X31,X32,X33,X34] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X32),hAPP(hAPP(c_Lambda_Olift,X30),X34)),c_Suc(X33))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X31),X30),X33)),X34) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X32),X31),X34)),X30),X33)
| ~ c_HOL_Oord__class_Oless(X34,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X33),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_458]) ).
fof(c_0_866,plain,
! [X30,X31,X32] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X31),c_HOL_Ozero__class_Ozero(tc_nat)),c_Type_Osko__Type__Xabs__typeE__1__1(X31,X30))),X30),c_Type_Osko__Type__Xabs__typeE__1__2(X31,X30)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X31),c_Lambda_OdB_OAbs(X30)),X32)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_459])])]) ).
fof(c_0_867,plain,
! [X45,X46,X47,X48] : hAPP(c_Fun_Ocomp(c_COMBK(X46,X48,X47),X45,X47,X48,t_a),v_x) = X46,
inference(variable_rename,[status(thm)],[c_0_460]) ).
fof(c_0_868,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_b____),v_sko__CHAINED__1(v_T____,v_b____,v_e____,v_i____))),
c_0_461 ).
fof(c_0_869,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_b____),v_sko__local__XCons__1__1(v_T____,v_b____,v_e____,v_i____))),
c_0_462 ).
fof(c_0_870,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_b____),v_sko__local__XCons__Xhyps__1__1(v_T____,v_b____,v_e____,v_i____))),
c_0_463 ).
fof(c_0_871,plain,
! [X31,X32,X33,X34] : c_Nat_Ocompow(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X32),X31),X33,X34,X34) = c_Fun_Ocomp(c_Nat_Ocompow(X32,X33,X34,X34),c_Nat_Ocompow(X31,X33,X34,X34),X34,X34,X34),
inference(variable_rename,[status(thm)],[c_0_464]) ).
fof(c_0_872,plain,
! [X48,X49,X50,X51,X52,X53] : hAPP(c_Fun_Ofcomp(X50,X49,X52,X51,X53),X48) = hAPP(X49,hAPP(X50,X48)),
inference(variable_rename,[status(thm)],[c_0_465]) ).
fof(c_0_873,plain,
! [X45,X46,X47,X48,X49,X50] : hAPP(X47,hAPP(X46,X45)) = hAPP(c_Fun_Ocomp(X47,X46,X48,X49,X50),X45),
inference(variable_rename,[status(thm)],[c_0_466]) ).
fof(c_0_874,plain,
! [X48,X49,X50,X51,X52,X53] : hAPP(c_Fun_Ocomp(X50,X49,X52,X53,X51),X48) = hAPP(X50,hAPP(X49,X48)),
inference(variable_rename,[status(thm)],[c_0_467]) ).
fof(c_0_875,plain,
! [X48,X49,X50,X51] : hAPP(c_Fun_Ofcomp(X49,X48,t_a,X50,X51),v_x) = hAPP(X48,hAPP(X49,v_x)),
inference(variable_rename,[status(thm)],[c_0_468]) ).
fof(c_0_876,plain,
! [X48,X49,X50,X51] : hAPP(c_Fun_Ocomp(X49,X48,X50,X51,t_a),v_x) = hAPP(X49,hAPP(X48,v_x)),
inference(variable_rename,[status(thm)],[c_0_469]) ).
fof(c_0_877,plain,
! [X35,X36] :
( ~ class_OrderedGroup_Omonoid__add(X36)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X36),c_HOL_Ozero__class_Ozero(X36),X35,X36,X36) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X36),X35,c_HOL_Ozero__class_Ozero(X36),X36,X36) ),
inference(variable_rename,[status(thm)],[c_0_470]) ).
fof(c_0_878,plain,
! [X35,X36,X37] :
( ~ class_OrderedGroup_Oab__semigroup__add(X37)
| c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X37),X35,X36,X37,X37) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X37),X36,X35,X37,X37) ),
inference(variable_rename,[status(thm)],[c_0_471]) ).
fof(c_0_879,axiom,
v_T____ = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
c_0_472 ).
fof(c_0_880,plain,
! [X37,X38,X39,X40,X41] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X39),X38),X40)),hAPP(hAPP(c_Lambda_Olift,X37),X38)),X41))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X39),X37),X41)) ),
inference(variable_rename,[status(thm)],[c_0_473]) ).
fof(c_0_881,plain,
! [X37,X38,X39,X40,X41] : hAPP(hAPP(hAPP(c_Type_Oshift(X41),hAPP(hAPP(hAPP(c_Type_Oshift(X41),X38),X37),X39)),c_HOL_Ozero__class_Ozero(tc_nat)),X40) = hAPP(hAPP(hAPP(c_Type_Oshift(X41),hAPP(hAPP(hAPP(c_Type_Oshift(X41),X38),c_HOL_Ozero__class_Ozero(tc_nat)),X40)),c_Suc(X37)),X39),
inference(variable_rename,[status(thm)],[c_0_474]) ).
fof(c_0_882,plain,
! [X30,X31,X32,X33] : hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X32)),X30) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X33),X31,tc_Lambda_OdB,tc_Lambda_OdB),
inference(variable_rename,[status(thm)],[c_0_475]) ).
fof(c_0_883,plain,
! [X31,X32,X33] : c_Nat_Ocompow(c_Suc(X31),X32,X33,X33) = c_Fun_Ocomp(X32,c_Nat_Ocompow(X31,X32,X33,X33),X33,X33,X33),
inference(variable_rename,[status(thm)],[c_0_476]) ).
fof(c_0_884,plain,
! [X28,X29,X30] :
( c_Lambda_OdB_OVar(X30) != c_List_Ofoldl(c_Lambda_OdB_OApp,X29,X28,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OVar(X30) = X29 ),
inference(variable_rename,[status(thm)],[c_0_477]) ).
fof(c_0_885,plain,
! [X28,X29,X30] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X29,X28,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X30)
| X29 = c_Lambda_OdB_OAbs(X30) ),
inference(variable_rename,[status(thm)],[c_0_478]) ).
fof(c_0_886,plain,
! [X28,X29,X30] :
( c_Lambda_OdB_OAbs(X30) != c_List_Ofoldl(c_Lambda_OdB_OApp,X29,X28,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(X30) = X29 ),
inference(variable_rename,[status(thm)],[c_0_479]) ).
fof(c_0_887,plain,
! [X30,X31,X32,X33] :
( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X30),X31),X32)),X33) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X30),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X33),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,X31),X33)),X32)
| ~ c_HOL_Oord__class_Oless(X32,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X33),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_480]) ).
fof(c_0_888,plain,
! [X30,X31,X32,X33] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X32),X30),c_Type_Osko__Type__Xtyping__elims__2__1(X33,X32,X31,X30)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X32),hAPP(hAPP(c_Lambda_OdB_OApp,X31),X30)),X33)) ),
inference(variable_rename,[status(thm)],[c_0_481]) ).
fof(c_0_889,plain,
! [X38,X39,X40,X41,X42] :
( c_Type_Otypings(hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X40),X39),X41),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),X39),X38,tc_Lambda_OdB,tc_Lambda_OdB),X42)
| ~ c_Type_Otypings(X40,X38,X42) ),
inference(variable_rename,[status(thm)],[c_0_482]) ).
fof(c_0_890,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_a____),v_T_H_H____)),
c_0_483 ).
fof(c_0_891,plain,
! [X31,X32,X33,X34] : hAPP(X33,hAPP(c_Nat_Ocompow(X32,X33,X34,X34),X31)) = hAPP(c_Nat_Ocompow(X32,X33,X34,X34),hAPP(X33,X31)),
inference(variable_rename,[status(thm)],[c_0_484]) ).
fof(c_0_892,plain,
! [X29] :
( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),c_HOL_Ozero__class_Ozero(tc_nat)),X29,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_List_Olistsp(c_InductTermi_OIT,X29,tc_Lambda_OdB) ),
inference(variable_rename,[status(thm)],[c_0_485]) ).
fof(c_0_893,plain,
! [X30,X31,X32,X33] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X30),X32),X33)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X30),X31),X33)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X32),X31)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_486])])]) ).
fof(c_0_894,plain,
! [X30,X31,X32,X33] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X32),X30),X33)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X31),X30),X33)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X32),X31)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_487])])]) ).
fof(c_0_895,plain,
! [X30,X31,X32,X33] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X30),X32),X33)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X30),X31),X33)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X32),X31)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_488])])]) ).
fof(c_0_896,plain,
! [X54,X55,X56,X57,X58] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X56),hAPP(hAPP(c_Lambda_OdB_OApp,X55),X54)),X57))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X56),X54),X58))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X56),X55),hAPP(hAPP(c_Type_Otype_OFun,X58),X57))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_489])])]) ).
fof(c_0_897,plain,
! [X30,X31,X32,X33] :
( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X30),X31),X32)),X33) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X30),X33)),hAPP(hAPP(c_Lambda_Olift,X31),X33)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X32),c_HOL_Oone__class_Oone(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X33,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X32),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_490]) ).
fof(c_0_898,plain,
! [X30,X31,X32,X33] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(hAPP(c_Lambda_Osubst,X32),X30),X33)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X31),X30),X33)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X32),X31)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_491])])]) ).
fof(c_0_899,plain,
! [X48,X49,X50] : c_Fun_Ofcomp(c_Fun_Oid(X50),X48,X50,X50,X49) = X48,
inference(variable_rename,[status(thm)],[c_0_492]) ).
fof(c_0_900,plain,
! [X44,X45,X46] : c_Fun_Ofcomp(X44,c_Fun_Oid(X45),X46,X45,X45) = X44,
inference(variable_rename,[status(thm)],[c_0_493]) ).
fof(c_0_901,plain,
! [X44,X45,X46] : c_Fun_Ocomp(X44,c_Fun_Oid(X46),X46,X45,X46) = X44,
inference(variable_rename,[status(thm)],[c_0_494]) ).
fof(c_0_902,plain,
! [X48,X49,X50] : c_Fun_Ocomp(c_Fun_Oid(X49),X48,X49,X49,X50) = X48,
inference(variable_rename,[status(thm)],[c_0_495]) ).
fof(c_0_903,plain,
! [X40,X41,X42,X43] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X43),X41)),hAPP(hAPP(c_Lambda_OdB_OApp,X42),X40)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X41),X40))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X43),X42)) ),
inference(variable_rename,[status(thm)],[c_0_496]) ).
fof(c_0_904,plain,
! [X20,X21,X22] :
( ~ hBOOL(hAPP(X22,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X21),X20),X21,tc_nat)))
| hBOOL(hAPP(X22,X20)) ),
inference(variable_rename,[status(thm)],[c_0_497]) ).
fof(c_0_905,plain,
! [X14,X15,X16] :
( ~ hBOOL(hAPP(X16,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X14),X15,tc_nat)))
| hBOOL(hAPP(X16,X14)) ),
inference(variable_rename,[status(thm)],[c_0_498]) ).
fof(c_0_906,plain,
! [X30,X31,X32,X33] : hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,X31),X30)),X32),X33) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X31),X32),X33)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X30),X32),X33)),
inference(variable_rename,[status(thm)],[c_0_499]) ).
fof(c_0_907,plain,
! [X28,X29,X30] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,X29),X30)),hAPP(hAPP(c_Lambda_Olift,X28),X30)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X29),X28)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_500])])]) ).
fof(c_0_908,plain,
! [X39,X40,X41] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X41),X40)),hAPP(hAPP(c_Lambda_OdB_OApp,X41),X39)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X40),X39)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_501])])]) ).
fof(c_0_909,plain,
! [X40,X41,X42] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X42),X40)),hAPP(hAPP(c_Lambda_OdB_OApp,X41),X40)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X42),X41)) ),
inference(variable_rename,[status(thm)],[c_0_502]) ).
fof(c_0_910,plain,
! [X10,X11] :
( ~ class_Ring__and__Field_Osemiring__1(X11)
| c_Nat_Osemiring__1__class_Oof__nat(X10,X11) = c_Nat_Osemiring__1__class_Oof__nat__aux(hAPP(hAPP(c_COMBC(X11,X11,X11),c_HOL_Oplus__class_Oplus(X11)),c_HOL_Oone__class_Oone(X11)),X10,c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_503]) ).
fof(c_0_911,plain,
! [X30,X31] : hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X31)),X30)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X31),X30),c_HOL_Ozero__class_Ozero(tc_nat)))),
inference(variable_rename,[status(thm)],[c_0_504]) ).
fof(c_0_912,plain,
! [X30,X31,X32] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(X30)),X31),X32) = c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,X30),hAPP(hAPP(c_Lambda_Olift,X31),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X32),c_HOL_Oone__class_Oone(tc_nat)))),
inference(variable_rename,[status(thm)],[c_0_505]) ).
fof(c_0_913,plain,
! [X42,X43,X44,X45,X46] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X45,X46),X44),X42))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X45,X46),X43),X42))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X45,X46),X44),X43)) ),
inference(variable_rename,[status(thm)],[c_0_506]) ).
fof(c_0_914,plain,
! [X33,X34,X35,X36,X37] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X37)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X37),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X37),X36),X35)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X37),X34),X33)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X37),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X37),X36),X34)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X37),X35),X33)) ),
inference(variable_rename,[status(thm)],[c_0_507]) ).
fof(c_0_915,plain,
! [X39,X40,X41,X42] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X41),X39),X42))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X41),X40),X42))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X40),X39)) ),
inference(variable_rename,[status(thm)],[c_0_508]) ).
fof(c_0_916,plain,
! [X30,X31,X32] :
( X32 = hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(X32,X31,X30)),c_Type_Osko__Type__Xtyping__elims__3__2(X32,X31,X30))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X31),c_Lambda_OdB_OAbs(X30)),X32)) ),
inference(variable_rename,[status(thm)],[c_0_509]) ).
fof(c_0_917,plain,
! [X30,X31,X32] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X30),X32)),hAPP(hAPP(c_Lambda_OdB_OApp,X30),X31)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X32),X31)) ),
inference(variable_rename,[status(thm)],[c_0_510]) ).
fof(c_0_918,plain,
! [X30,X31,X32] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X32),X30)),hAPP(hAPP(c_Lambda_OdB_OApp,X31),X30)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X32),X31)) ),
inference(variable_rename,[status(thm)],[c_0_511]) ).
fof(c_0_919,plain,
! [X28,X29,X30] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,X29),X30)),hAPP(hAPP(c_Lambda_Olift,X28),X30)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X29),X28)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_512])])]) ).
fof(c_0_920,plain,
! [X33,X34,X35,X36,X37] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X33,X37),X36),X34))
| ~ hBOOL(hAPP(hAPP(X33,X35),X34))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X33,X37),X36),X35)) ),
inference(variable_rename,[status(thm)],[c_0_513]) ).
fof(c_0_921,plain,
! [X33,X34,X35,X36,X37] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X33,X37),X36),X34))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X33,X37),X35),X34))
| ~ hBOOL(hAPP(hAPP(X33,X36),X35)) ),
inference(variable_rename,[status(thm)],[c_0_514]) ).
fof(c_0_922,plain,
! [X30,X31,X32] :
( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X30),X32)),c_Suc(X31)) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X30),X31)),X32)
| ~ c_HOL_Oord__class_Oless(X32,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X31),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_515]) ).
fof(c_0_923,plain,
! [X26,X27] : c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,X27),X26),tc_Type_Otype) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X27,tc_Type_Otype)),c_Nat_Osize__class_Osize(X26,tc_Type_Otype))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
inference(variable_rename,[status(thm)],[c_0_516]) ).
fof(c_0_924,plain,
! [X6,X7] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X6) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X7,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X6))
| X7 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_517]) ).
fof(c_0_925,plain,
! [X39,X40,X41,X42] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X41),X39),X42))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X40),X39))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X41),X40),X42)) ),
inference(variable_rename,[status(thm)],[c_0_518]) ).
fof(c_0_926,plain,
! [X49,X50,X51,X52,X53,X54] : hAPP(hAPP(hAPP(c_COMBC(X53,X52,X54),X51),X50),X49) = hAPP(hAPP(X51,X49),X50),
inference(variable_rename,[status(thm)],[c_0_519]) ).
fof(c_0_927,plain,
! [X18,X19,X20,X21] :
( ~ class_Ring__and__Field_Osemiring__1(X21)
| c_Nat_Osemiring__1__class_Oof__nat__aux(X19,c_Suc(X18),X20,X21) = c_Nat_Osemiring__1__class_Oof__nat__aux(X19,X18,hAPP(X19,X20),X21) ),
inference(variable_rename,[status(thm)],[c_0_520]) ).
fof(c_0_928,plain,
! [X33,X34,X35,X36] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X36)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X35),X34)),X33) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X35),X33)),X34) ),
inference(variable_rename,[status(thm)],[c_0_521]) ).
fof(c_0_929,plain,
! [X9,X10,X11] :
( hBOOL(hAPP(X11,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X10,X9,tc_nat)
| ~ hBOOL(hAPP(X11,c_HOL_Ominus__class_Ominus(X10,X9,tc_nat))) ),
inference(variable_rename,[status(thm)],[c_0_522]) ).
fof(c_0_930,plain,
! [X30,X31,X32,X33] : c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,X31),X30),X32,X33) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(X31,X32,X33)),c_Lambda_Osubstn(X30,X32,X33)),
inference(variable_rename,[status(thm)],[c_0_523]) ).
fof(c_0_931,plain,
! [X30,X31,X32,X33] : c_Lambda_Oliftn(X32,hAPP(hAPP(c_Lambda_OdB_OApp,X31),X30),X33) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(X32,X31,X33)),c_Lambda_Oliftn(X32,X30,X33)),
inference(variable_rename,[status(thm)],[c_0_524]) ).
fof(c_0_932,plain,
! [X33,X34,X35,X36] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X36)
| c_HOL_Oord__class_Oless(X35,X34,X36)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X33),X35),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X33),X34),X36) ),
inference(variable_rename,[status(thm)],[c_0_525]) ).
fof(c_0_933,plain,
! [X33,X34,X35,X36] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X36)
| c_HOL_Oord__class_Oless(X35,X34,X36)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X35),X33),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X34),X33),X36) ),
inference(variable_rename,[status(thm)],[c_0_526]) ).
fof(c_0_934,plain,
! [X17,X18,X19] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X17),c_Lambda_OdB_OVar(X19)),X18)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X17)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_527])])]) ).
fof(c_0_935,plain,
! [X40,X41] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X41)),c_Lambda_OdB_OAbs(X40)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X41),X40)) ),
inference(variable_rename,[status(thm)],[c_0_528]) ).
fof(c_0_936,plain,
! [X24,X25,X26,X27,X28] :
( hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(X28),X26),X25),X27),X24) = hAPP(X26,c_HOL_Ominus__class_Ominus(X24,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X25,X24,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_529])])]) ).
fof(c_0_937,plain,
! [X33,X34,X35,X36,X37] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X37)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X37),X36),X34),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X37),X35),X33),X37)
| ~ c_HOL_Oord__class_Oless(X34,X33,X37)
| ~ c_HOL_Oord__class_Oless(X36,X35,X37) ),
inference(variable_rename,[status(thm)],[c_0_530]) ).
fof(c_0_938,plain,
! [X30,X31,X32] : hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,X31),X30)),X32) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X31),X32)),hAPP(hAPP(c_Lambda_Olift,X30),X32)),
inference(variable_rename,[status(thm)],[c_0_531]) ).
fof(c_0_939,plain,
! [X19,X20,X21] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X21,X19,tc_nat),c_HOL_Ominus__class_Ominus(X21,X20,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X20,X21,tc_nat)
| ~ c_HOL_Oord__class_Oless(X20,X19,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_532]) ).
fof(c_0_940,plain,
! [X15,X16,X17] :
( c_HOL_Oord__class_Oless(X16,X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X15),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_533])])]) ).
fof(c_0_941,plain,
! [X33,X34,X35,X36] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X36)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X35),X34)),X33) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X35),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X34),X33)) ),
inference(variable_rename,[status(thm)],[c_0_534]) ).
fof(c_0_942,plain,
! [X33,X34,X35,X36] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X36)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X35),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X34),X33)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X35),X34)),X33) ),
inference(variable_rename,[status(thm)],[c_0_535]) ).
fof(c_0_943,plain,
! [X33,X34,X35,X36] :
( ~ class_OrderedGroup_Oab__semigroup__add(X36)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X35),X34)),X33) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X35),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X34),X33)) ),
inference(variable_rename,[status(thm)],[c_0_536]) ).
fof(c_0_944,plain,
! [X33,X34,X35,X36] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X36)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X35),X34)),X33) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X35),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X34),X33)) ),
inference(variable_rename,[status(thm)],[c_0_537]) ).
fof(c_0_945,plain,
! [X42,X43,X44,X45] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X45)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X45),X44),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X45),X43),X42)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X45),X44),X43)),X42) ),
inference(variable_rename,[status(thm)],[c_0_538]) ).
fof(c_0_946,plain,
! [X19,X20,X21,X22] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X20),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X21),X19),tc_nat)
| ~ c_HOL_Oord__class_Oless(X20,X19,tc_nat)
| ~ c_HOL_Oord__class_Oless(X22,X21,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_539]) ).
fof(c_0_947,plain,
! [X17,X18,X19] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X19),X17),X18,tc_nat)
| ~ c_HOL_Oord__class_Oless(X19,c_HOL_Ominus__class_Ominus(X18,X17,tc_nat),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_540]) ).
fof(c_0_948,plain,
! [X26,X27] : c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X27),X26)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(X27)),c_Type_Otype_Otype__size(X26))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
inference(variable_rename,[status(thm)],[c_0_541]) ).
fof(c_0_949,plain,
! [X42,X43,X44,X45,X46] :
( ~ class_OrderedGroup_Oab__group__add(X46)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X46),X44),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X46),X43),X42)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X46),X43),X45)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X46),X44),X42) = X45 ),
inference(variable_rename,[status(thm)],[c_0_542]) ).
fof(c_0_950,plain,
! [X17,X18,X19] :
( c_HOL_Oord__class_Oless(X19,c_HOL_Ominus__class_Ominus(X18,X17,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X19),X17),X18,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_543]) ).
fof(c_0_951,plain,
! [X30,X31,X32] : hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X30),X32)),X31),X32) = X30,
inference(variable_rename,[status(thm)],[c_0_544]) ).
fof(c_0_952,plain,
! [X30,X31,X32] : c_Lambda_Osubstn(X30,X31,X32) = hAPP(hAPP(hAPP(c_Lambda_Osubst,X30),c_Lambda_Oliftn(X32,X31,c_HOL_Ozero__class_Ozero(tc_nat))),X32),
inference(variable_rename,[status(thm)],[c_0_545]) ).
fof(c_0_953,plain,
! [X30,X31,X32] : c_Lambda_Osubstn(c_Lambda_OdB_OAbs(X30),X31,X32) = c_Lambda_OdB_OAbs(c_Lambda_Osubstn(X30,X31,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X32),c_HOL_Oone__class_Oone(tc_nat)))),
inference(variable_rename,[status(thm)],[c_0_546]) ).
fof(c_0_954,plain,
! [X28,X29,X30] : c_Lambda_Oliftn(X29,c_Lambda_OdB_OAbs(X28),X30) = c_Lambda_OdB_OAbs(c_Lambda_Oliftn(X29,X28,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X30),c_HOL_Oone__class_Oone(tc_nat)))),
inference(variable_rename,[status(thm)],[c_0_547]) ).
fof(c_0_955,plain,
! [X15,X16,X17] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X15)),X17) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X17)),
inference(variable_rename,[status(thm)],[c_0_548]) ).
fof(c_0_956,plain,
! [X10,X11,X12] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X12),X11),X10),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X10,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_549]) ).
fof(c_0_957,plain,
! [X10,X11,X12] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X12)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X12),X11),X10),c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_550]) ).
fof(c_0_958,plain,
! [X33,X34,X35,X36] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X36)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X33),X35),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X33),X34),X36)
| ~ c_HOL_Oord__class_Oless(X35,X34,X36) ),
inference(variable_rename,[status(thm)],[c_0_551]) ).
fof(c_0_959,plain,
! [X33,X34,X35,X36] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X36)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X33),X35),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X33),X34),X36)
| ~ c_HOL_Oord__class_Oless(X35,X34,X36) ),
inference(variable_rename,[status(thm)],[c_0_552]) ).
fof(c_0_960,plain,
! [X33,X34,X35,X36] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X36)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X35),X33),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X34),X33),X36)
| ~ c_HOL_Oord__class_Oless(X35,X34,X36) ),
inference(variable_rename,[status(thm)],[c_0_553]) ).
fof(c_0_961,plain,
! [X33,X34,X35,X36] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X36)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X35),X33),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X34),X33),X36)
| ~ c_HOL_Oord__class_Oless(X35,X34,X36) ),
inference(variable_rename,[status(thm)],[c_0_554]) ).
fof(c_0_962,plain,
! [X33,X34,X35,X36] :
( ~ class_Ring__and__Field_Oordered__semidom(X36)
| c_HOL_Oord__class_Oless(X34,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X35),X33),X36)
| ~ c_HOL_Oord__class_Oless(X34,X33,X36)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X36),X35,X36) ),
inference(variable_rename,[status(thm)],[c_0_555]) ).
fof(c_0_963,plain,
! [X6,X7] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X6),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_556])])]) ).
fof(c_0_964,plain,
! [X24,X25,X26,X27,X28] :
( hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(X28),X26),X25),X27),X24) = hAPP(X26,X24)
| ~ c_HOL_Oord__class_Oless(X24,X25,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_557])])]) ).
fof(c_0_965,plain,
! [X6,X7] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_558]) ).
fof(c_0_966,plain,
! [X15,X16,X17] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X16),X15,tc_nat),c_Suc(X17),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X16,X15,tc_nat),X17,tc_nat),
inference(variable_rename,[status(thm)],[c_0_559]) ).
fof(c_0_967,plain,
! [X24,X25,X26] :
( hAPP(X25,X24) = X26
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X25),c_Lambda_OdB_OVar(X24)),X26)) ),
inference(variable_rename,[status(thm)],[c_0_560]) ).
fof(c_0_968,plain,
! [X10,X11,X12] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X12)
| c_HOL_Oord__class_Oless(X11,X10,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X11,X10,X12),c_HOL_Ozero__class_Ozero(X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_561]) ).
fof(c_0_969,plain,
! [X10,X11] :
( ~ class_Ring__and__Field_Oordered__idom(X11)
| c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X11),X10),X10),c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_562]) ).
fof(c_0_970,plain,
! [X10,X11] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X11)
| c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X11),X10),X10),c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_563]) ).
fof(c_0_971,plain,
! [X10,X11] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X11)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),X10,X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X11),X10),X10),X11) ),
inference(variable_rename,[status(thm)],[c_0_564]) ).
fof(c_0_972,plain,
! [X14,X15,X16,X17,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X18)
| c_HOL_Ominus__class_Ominus(X17,X15,X18) != c_HOL_Ominus__class_Ominus(X16,X14,X18)
| c_HOL_Oord__class_Oless(X16,X14,X18)
| ~ c_HOL_Oord__class_Oless(X17,X15,X18) ),
inference(variable_rename,[status(thm)],[c_0_565]) ).
fof(c_0_973,plain,
! [X14,X15,X16,X17,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X18)
| c_HOL_Ominus__class_Ominus(X17,X15,X18) != c_HOL_Ominus__class_Ominus(X16,X14,X18)
| c_HOL_Oord__class_Oless(X17,X15,X18)
| ~ c_HOL_Oord__class_Oless(X16,X14,X18) ),
inference(variable_rename,[status(thm)],[c_0_566]) ).
fof(c_0_974,plain,
! [X28,X29] : hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(X28)),X29) = c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,X28),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X29),c_HOL_Oone__class_Oone(tc_nat)))),
inference(variable_rename,[status(thm)],[c_0_567]) ).
fof(c_0_975,plain,
! [X15,X16,X17] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X15),tc_nat)
| ~ c_HOL_Oord__class_Oless(X16,X15,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_568])])]) ).
fof(c_0_976,plain,
! [X17,X18,X19] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X19),X17),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17),tc_nat)
| ~ c_HOL_Oord__class_Oless(X19,X18,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_569]) ).
fof(c_0_977,plain,
! [X33,X34,X35,X36] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X36)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X35),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X34),X33)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X34),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X35),X33)) ),
inference(variable_rename,[status(thm)],[c_0_570]) ).
fof(c_0_978,plain,
! [X33,X34,X35,X36] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X36)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X35),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X34),X33)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X34),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X35),X33)) ),
inference(variable_rename,[status(thm)],[c_0_571]) ).
fof(c_0_979,plain,
! [X42,X43,X44,X45] :
( ~ class_OrderedGroup_Oab__group__add(X45)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X45),X44),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X45),X43),X42)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X45),X43),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X45),X44),X42)) ),
inference(variable_rename,[status(thm)],[c_0_572]) ).
fof(c_0_980,plain,
! [X14,X15,X16,X17] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X16,X17),X15),X14))
| ~ hBOOL(hAPP(hAPP(X16,X15),X14)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_573])])]) ).
fof(c_0_981,plain,
! [X17,X18,X19] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X19,X18,tc_nat),X17,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X19,X17,tc_nat),X18,tc_nat),
inference(variable_rename,[status(thm)],[c_0_574]) ).
fof(c_0_982,plain,
! [X30,X31,X32] : c_Lambda_Oliftn(c_Suc(X31),X30,X32) = hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(X31,X30,X32)),X32),
inference(variable_rename,[status(thm)],[c_0_575]) ).
fof(c_0_983,plain,
! [X28,X29,X30] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X30)),X28),X29) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X30,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X29,X30,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_576]) ).
fof(c_0_984,plain,
! [X27,X28,X29] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X28)),X27),X29) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X28,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X29,X28,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_577]) ).
fof(c_0_985,plain,
! [X6,X7] :
( c_HOL_Oord__class_Oless(X7,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X6,X7,tc_nat),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_578]) ).
fof(c_0_986,plain,
! [X17,X18,X19] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X19,X18,tc_nat),X17,tc_nat) = c_HOL_Ominus__class_Ominus(X19,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17),tc_nat),
inference(variable_rename,[status(thm)],[c_0_579]) ).
fof(c_0_987,plain,
! [X15,X16,X17] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X15),tc_nat) = c_HOL_Ominus__class_Ominus(X16,X15,tc_nat),
inference(variable_rename,[status(thm)],[c_0_580]) ).
fof(c_0_988,plain,
! [X15,X16,X17] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X17),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X17),tc_nat) = c_HOL_Ominus__class_Ominus(X16,X15,tc_nat),
inference(variable_rename,[status(thm)],[c_0_581]) ).
fof(c_0_989,plain,
! [X19,X20,X21,X22] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X21) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X19)
| ~ c_HOL_Oord__class_Oless(X22,X21,tc_nat)
| c_HOL_Oord__class_Oless(X20,X19,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_582]) ).
fof(c_0_990,plain,
! [X17,X18,X19] :
( c_HOL_Oord__class_Oless(X19,X17,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X19),X18),X17,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_583]) ).
fof(c_0_991,plain,
! [X10,X11,X12] :
( ~ class_OrderedGroup_Ogroup__add(X12)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X12),c_HOL_Ominus__class_Ominus(X11,X10,X12)),X10) = X11 ),
inference(variable_rename,[status(thm)],[c_0_584]) ).
fof(c_0_992,plain,
! [X42,X43,X44] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X44),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X43),X42)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X43),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X44),X42)),
inference(variable_rename,[status(thm)],[c_0_585]) ).
fof(c_0_993,plain,
! [X10,X11] :
( ~ class_Ring__and__Field_Oordered__idom(X11)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X11),X10),X10),c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_586]) ).
fof(c_0_994,plain,
! [X10,X11] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X11)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X11),X10),X10),c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_587]) ).
fof(c_0_995,plain,
! [X10,X11] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X11)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X11),X10),X10),X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_588]) ).
fof(c_0_996,plain,
! [X10,X11,X12] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X12)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X11,X10,X12),c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_589]) ).
fof(c_0_997,plain,
! [X18,X19,X20] :
( ~ class_Ring__and__Field_Osemiring__1(X20)
| c_Nat_Osemiring__1__class_Oof__nat__aux(X18,c_HOL_Ozero__class_Ozero(tc_nat),X19,X20) = X19 ),
inference(variable_rename,[status(thm)],[c_0_590]) ).
fof(c_0_998,plain,
! [X28,X29,X30] :
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X30),X28,X29) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X30,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X29,X30,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_591]) ).
fof(c_0_999,plain,
! [X17,X18] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X17,c_Suc(X18),tc_nat),X17,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_592])])]) ).
fof(c_0_1000,plain,
! [X31,X32] : c_Nat_Ocompow(c_HOL_Ozero__class_Ozero(tc_nat),X31,X32,X32) = c_Fun_Oid(X32),
inference(variable_rename,[status(thm)],[c_0_593]) ).
fof(c_0_1001,plain,
! [X54,X55] : hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X55),c_Lambda_OdB_OVar(X54)),hAPP(X55,X54))),
inference(variable_rename,[status(thm)],[c_0_594]) ).
fof(c_0_1002,plain,
! [X24,X25,X26,X27] : hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(X27),X25),X24),X26),X24) = X26,
inference(variable_rename,[status(thm)],[c_0_595]) ).
fof(c_0_1003,plain,
! [X6,X7] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X6,X7,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,X6,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_596]) ).
fof(c_0_1004,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Osemiring__1(X12)
| c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X10),X12) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X12),c_Nat_Osemiring__1__class_Oof__nat(X11,X12)),c_Nat_Osemiring__1__class_Oof__nat(X10,X12)) ),
inference(variable_rename,[status(thm)],[c_0_597]) ).
fof(c_0_1005,plain,
! [X16,X17,X18] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X18,X16,tc_nat),X17,tc_nat)
| ~ c_HOL_Oord__class_Oless(X18,X17,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_598]) ).
fof(c_0_1006,plain,
! [X17,X18] : c_HOL_Oord__class_Oless(X18,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17)),tc_nat),
inference(variable_rename,[status(thm)],[c_0_599]) ).
fof(c_0_1007,plain,
! [X17,X18] : c_HOL_Oord__class_Oless(X18,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X18)),tc_nat),
inference(variable_rename,[status(thm)],[c_0_600]) ).
fof(c_0_1008,plain,
! [X14,X15] : c_HOL_Oord__class_Oless(X15,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X14)),tc_nat),
inference(variable_rename,[status(thm)],[c_0_601]) ).
fof(c_0_1009,plain,
! [X30,X31] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X30),c_Lambda_OdB_OVar(X31))))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X30)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_602])])]) ).
fof(c_0_1010,axiom,
c_Type_Otypings(hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____),v_as____,v_Ts____),
c_0_603 ).
fof(c_0_1011,plain,
! [X6,X7] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X6),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_604])])]) ).
fof(c_0_1012,plain,
! [X6,X7] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X6),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_605]) ).
fof(c_0_1013,plain,
! [X42,X43,X44,X45] :
( ~ class_Orderings_Opreorder(X45)
| c_HOL_Oord__class_Oless(X44,X42,X45)
| ~ c_HOL_Oord__class_Oless(X43,X42,X45)
| ~ c_HOL_Oord__class_Oless(X44,X43,X45) ),
inference(variable_rename,[status(thm)],[c_0_606]) ).
fof(c_0_1014,plain,
! [X42,X43,X44,X45] :
( ~ class_Orderings_Oorder(X45)
| c_HOL_Oord__class_Oless(X42,X44,X45)
| ~ c_HOL_Oord__class_Oless(X42,X43,X45)
| ~ c_HOL_Oord__class_Oless(X43,X44,X45) ),
inference(variable_rename,[status(thm)],[c_0_607]) ).
fof(c_0_1015,plain,
! [X30,X31] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X31)),c_Lambda_OdB_OAbs(X30)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X31),X30)) ),
inference(variable_rename,[status(thm)],[c_0_608]) ).
fof(c_0_1016,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__semidom(X12)
| c_HOL_Oord__class_Oless(X11,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X11,X12),c_Nat_Osemiring__1__class_Oof__nat(X10,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_609]) ).
fof(c_0_1017,plain,
! [X42,X43,X44] :
( c_HOL_Oord__class_Oless(X44,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X43),X42),tc_nat)
| ~ c_HOL_Oord__class_Oless(X44,X43,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_610]) ).
fof(c_0_1018,plain,
! [X42,X43,X44] :
( c_HOL_Oord__class_Oless(X44,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X43),X42),tc_nat)
| ~ c_HOL_Oord__class_Oless(X44,X42,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_611]) ).
fof(c_0_1019,plain,
! [X17,X18,X19] :
( c_HOL_Oord__class_Oless(X19,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17),tc_nat)
| ~ c_HOL_Oord__class_Oless(X19,X18,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_612]) ).
fof(c_0_1020,plain,
! [X17,X18,X19] :
( c_HOL_Oord__class_Oless(X19,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X18),tc_nat)
| ~ c_HOL_Oord__class_Oless(X19,X18,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_613]) ).
fof(c_0_1021,plain,
! [X17,X18,X19] :
( c_HOL_Oord__class_Oless(c_Suc(X19),X17,tc_nat)
| ~ c_HOL_Oord__class_Oless(X18,X17,tc_nat)
| ~ c_HOL_Oord__class_Oless(X19,X18,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_614]) ).
fof(c_0_1022,plain,
! [X17,X18] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X18),X18,tc_nat),
inference(variable_rename,[status(thm)],[c_0_615]) ).
fof(c_0_1023,plain,
! [X17,X18] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17),X18,tc_nat),
inference(variable_rename,[status(thm)],[c_0_616]) ).
fof(c_0_1024,plain,
! [X5] :
( c_Suc(c_HOL_Ominus__class_Ominus(X5,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X5
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_617]) ).
fof(c_0_1025,plain,
! [X6,X7] : c_HOL_Ominus__class_Ominus(X7,c_Suc(X6),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X7,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X6,tc_nat),
inference(variable_rename,[status(thm)],[c_0_618]) ).
fof(c_0_1026,plain,
! [X30,X31] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X30),X31)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X30)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_619])])]) ).
fof(c_0_1027,plain,
! [X17,X18,X19] :
( c_Lambda_Oliftn(X17,c_Lambda_OdB_OVar(X19),X18) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X19),X17))
| c_HOL_Oord__class_Oless(X19,X18,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_620]) ).
fof(c_0_1028,plain,
! [X10] :
( ~ class_Ring__and__Field_Oordered__semidom(X10)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X10),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X10),c_HOL_Oone__class_Oone(X10)),c_HOL_Oone__class_Oone(X10)),X10) ),
inference(variable_rename,[status(thm)],[c_0_621]) ).
fof(c_0_1029,plain,
! [X6,X7] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),c_HOL_Ominus__class_Ominus(X7,X6,tc_nat)) = X7
| c_HOL_Oord__class_Oless(X7,X6,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_622]) ).
fof(c_0_1030,plain,
! [X5] :
( X5 = c_Suc(c_HOL_Ominus__class_Ominus(X5,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_623]) ).
fof(c_0_1031,plain,
! [X5] :
( c_Suc(c_HOL_Ominus__class_Ominus(X5,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X5
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_624]) ).
fof(c_0_1032,plain,
! [X17,X18] :
( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X18)),X17) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),c_HOL_Oone__class_Oone(tc_nat)))
| c_HOL_Oord__class_Oless(X18,X17,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_625]) ).
fof(c_0_1033,plain,
! [X10,X11] :
( ~ class_Ring__and__Field_Oordered__semidom(X11)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),c_Nat_Osemiring__1__class_Oof__nat(X10,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_626]) ).
fof(c_0_1034,plain,
! [X27,X28,X29] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X28)),X27),X29) = c_Lambda_OdB_OVar(X28)
| ~ c_HOL_Oord__class_Oless(X28,X29,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_627]) ).
fof(c_0_1035,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__semidom(X12)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X11,X12),c_Nat_Osemiring__1__class_Oof__nat(X10,X12),X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_628]) ).
fof(c_0_1036,plain,
! [X9,X10,X11] :
( hBOOL(hAPP(hAPP(X11,X9),X10))
| c_HOL_Oord__class_Oless(X9,X10,tc_nat)
| X10 = X9
| c_HOL_Oord__class_Oless(X10,X9,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_629])])]) ).
fof(c_0_1037,plain,
! [X10,X11,X12] : hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X12),X11),X11)),
inference(variable_rename,[status(thm)],[c_0_630]) ).
fof(c_0_1038,plain,
! [X14,X15,X16] : hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X15,X16),X14),X14)),
inference(variable_rename,[status(thm)],[c_0_631]) ).
fof(c_0_1039,plain,
! [X10,X11] :
( ~ class_Ring__and__Field_Oordered__semidom(X11)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),c_Nat_Osemiring__1__class_Oof__nat(X10,X11),X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_632]) ).
fof(c_0_1040,plain,
! [X42,X43,X44,X45] :
( ~ class_Ring__and__Field_Oidom(X45)
| ~ class_Int_Onumber__ring(X45)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X45),X44),X43) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X45),X44),X42)
| X43 = X42 ),
inference(variable_rename,[status(thm)],[c_0_633]) ).
fof(c_0_1041,plain,
! [X14,X15,X16,X17] :
( ~ class_OrderedGroup_Oab__group__add(X17)
| c_HOL_Ominus__class_Ominus(X16,X16,X17) != c_HOL_Ominus__class_Ominus(X15,X14,X17)
| X15 = X14 ),
inference(variable_rename,[status(thm)],[c_0_634]) ).
fof(c_0_1042,plain,
! [X21,X22,X23,X24] :
( ~ class_OrderedGroup_Oab__group__add(X24)
| c_HOL_Ominus__class_Ominus(X22,X21,X24) != c_HOL_Ominus__class_Ominus(X23,X23,X24)
| X22 = X21 ),
inference(variable_rename,[status(thm)],[c_0_635]) ).
fof(c_0_1043,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Opreorder(X12)
| ~ c_HOL_Oord__class_Oless(X10,X11,X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_636]) ).
fof(c_0_1044,plain,
! [X14,X15,X16] :
( ~ class_Orderings_Opreorder(X16)
| ~ c_HOL_Oord__class_Oless(X14,X15,X16)
| ~ c_HOL_Oord__class_Oless(X15,X14,X16) ),
inference(variable_rename,[status(thm)],[c_0_637]) ).
fof(c_0_1045,plain,
! [X14,X15,X16] :
( ~ class_Orderings_Olinorder(X16)
| ~ c_HOL_Oord__class_Oless(X15,X14,X16)
| ~ c_HOL_Oord__class_Oless(X14,X15,X16) ),
inference(variable_rename,[status(thm)],[c_0_638]) ).
fof(c_0_1046,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Oorder(X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12)
| ~ c_HOL_Oord__class_Oless(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_639]) ).
fof(c_0_1047,plain,
! [X6,X7] :
( ~ c_HOL_Oord__class_Oless(X7,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(X6,c_Suc(X7),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_640]) ).
fof(c_0_1048,plain,
! [X6,X7] :
( c_HOL_Ominus__class_Ominus(X6,X7,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X7,X6,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X7 = X6 ),
inference(variable_rename,[status(thm)],[c_0_641]) ).
fof(c_0_1049,plain,
! [X10,X11] :
( ~ class_Ring__and__Field_Oordered__semidom(X11)
| c_HOL_Oord__class_Oless(X10,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X11),X10),c_HOL_Oone__class_Oone(X11)),X11) ),
inference(variable_rename,[status(thm)],[c_0_642]) ).
fof(c_0_1050,plain,
! [X33,X34,X35,X36] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X36)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X34),X35) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X33),X35)
| X34 = X33 ),
inference(variable_rename,[status(thm)],[c_0_643]) ).
fof(c_0_1051,plain,
! [X33,X34,X35,X36] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X36)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X35),X34) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X35),X33)
| X34 = X33 ),
inference(variable_rename,[status(thm)],[c_0_644]) ).
fof(c_0_1052,plain,
! [X33,X34,X35,X36] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X36)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X35),X34) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X35),X33)
| X34 = X33 ),
inference(variable_rename,[status(thm)],[c_0_645]) ).
fof(c_0_1053,plain,
! [X28,X29] :
( c_HOL_Oord__class_Oless(X28,X28,tc_nat)
| c_Lambda_Osubstn(c_Lambda_OdB_OVar(X28),X29,X28) = c_Lambda_Oliftn(X28,X29,c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_646])])]) ).
fof(c_0_1054,plain,
! [X28,X29,X30] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X30)),X28),X29) = c_Lambda_OdB_OVar(X30)
| X30 = X29
| c_HOL_Oord__class_Oless(X29,X30,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_647]) ).
fof(c_0_1055,plain,
! [X10,X11,X12] :
( ~ class_OrderedGroup_Ogroup__add(X12)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X12),X11),X10),X10,X12) = X11 ),
inference(variable_rename,[status(thm)],[c_0_648]) ).
fof(c_0_1056,plain,
! [X28,X29] :
( c_HOL_Oord__class_Oless(X28,X28,tc_nat)
| hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X28)),X29),X28) = X29 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_649])])]) ).
fof(c_0_1057,plain,
! [X6,X7] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),c_Suc(X7),tc_nat),
inference(variable_rename,[status(thm)],[c_0_650]) ).
fof(c_0_1058,plain,
! [X30,X31] : ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X31)),X30)),
inference(variable_rename,[status(thm)],[c_0_651]) ).
fof(c_0_1059,plain,
! [X6,X7] :
( c_HOL_Oord__class_Oless(X7,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X7),c_Suc(X6),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_652]) ).
fof(c_0_1060,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_ea______),v_ua______),v_T____)),
c_0_653 ).
fof(c_0_1061,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_e____),v_u____),v_T____)),
c_0_654 ).
fof(c_0_1062,plain,
! [X6,X7] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X7)),X6) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X6)),
inference(variable_rename,[status(thm)],[c_0_655]) ).
fof(c_0_1063,plain,
! [X6,X7] :
( c_HOL_Oord__class_Oless(c_Suc(X7),c_Suc(X6),tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,X6,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_656]) ).
fof(c_0_1064,plain,
! [X14,X15] :
( c_HOL_Oord__class_Oless(c_Suc(X14),c_Suc(X15),tc_nat)
| ~ c_HOL_Oord__class_Oless(X14,X15,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_657]) ).
fof(c_0_1065,plain,
! [X6,X7] :
( X6 = X7
| ~ c_HOL_Oord__class_Oless(X6,c_Suc(X7),tc_nat)
| c_HOL_Oord__class_Oless(X6,X7,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_658]) ).
fof(c_0_1066,plain,
! [X6,X7] :
( X7 = X6
| ~ c_HOL_Oord__class_Oless(X6,c_Suc(X7),tc_nat)
| c_HOL_Oord__class_Oless(X6,X7,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_659]) ).
fof(c_0_1067,plain,
! [X6,X7] :
( X7 = X6
| c_HOL_Oord__class_Oless(X7,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,c_Suc(X6),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_660]) ).
fof(c_0_1068,plain,
! [X17,X18,X19] :
( c_Lambda_Oliftn(X17,c_Lambda_OdB_OVar(X19),X18) = c_Lambda_OdB_OVar(X19)
| ~ c_HOL_Oord__class_Oless(X19,X18,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_661]) ).
fof(c_0_1069,plain,
! [X6,X7] :
( c_HOL_Oord__class_Oless(c_Suc(X7),X6,tc_nat)
| c_Suc(X7) = X6
| ~ c_HOL_Oord__class_Oless(X7,X6,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_662]) ).
fof(c_0_1070,plain,
! [X15,X16,X17] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X16) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X15)
| X16 = X15 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_663])])]) ).
fof(c_0_1071,plain,
! [X15,X16,X17] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X17) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X17)
| X16 = X15 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_664])])]) ).
fof(c_0_1072,plain,
! [X42,X43,X44] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X44),X43) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X44),X42)
| X43 = X42 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_665])])]) ).
fof(c_0_1073,plain,
! [X6,X7] :
( c_HOL_Oord__class_Oless(X7,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X7),X6,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_666]) ).
fof(c_0_1074,plain,
! [X6,X7] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_Suc(X6)) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X6)),
inference(variable_rename,[status(thm)],[c_0_667]) ).
fof(c_0_1075,plain,
! [X30,X31] : c_Lambda_Osubstn(X30,X31,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,X30),X31),c_HOL_Ozero__class_Ozero(tc_nat)),
inference(variable_rename,[status(thm)],[c_0_668]) ).
fof(c_0_1076,plain,
! [X6,X7] : c_HOL_Ominus__class_Ominus(X6,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_669]) ).
fof(c_0_1077,plain,
! [X6,X7] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7),X6,tc_nat) = X7,
inference(variable_rename,[status(thm)],[c_0_670]) ).
fof(c_0_1078,plain,
! [X6,X7] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X6),X6,tc_nat) = X7,
inference(variable_rename,[status(thm)],[c_0_671]) ).
fof(c_0_1079,plain,
! [X10,X11] :
( ~ class_Ring__and__Field_Oordered__semidom(X11)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X10,X11),c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_672]) ).
fof(c_0_1080,plain,
! [X6,X7] :
( c_HOL_Oord__class_Oless(X7,c_Suc(X6),tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,X6,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_673]) ).
fof(c_0_1081,plain,
! [X17,X18] :
( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X18)),X17) = c_Lambda_OdB_OVar(X18)
| ~ c_HOL_Oord__class_Oless(X18,X17,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_674]) ).
fof(c_0_1082,plain,
! [X44,X45,X46,X47] : hAPP(c_COMBK(X45,X47,X46),X44) = X45,
inference(variable_rename,[status(thm)],[c_0_675]) ).
fof(c_0_1083,plain,
! [X28,X29,X30] :
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X30),X28,X29) = c_Lambda_OdB_OVar(X30)
| X30 = X29
| c_HOL_Oord__class_Oless(X29,X30,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_676]) ).
fof(c_0_1084,plain,
! [X14,X15,X16] :
( ~ class_Orderings_Olinorder(X16)
| X15 = X14
| c_HOL_Oord__class_Oless(X15,X14,X16)
| c_HOL_Oord__class_Oless(X14,X15,X16) ),
inference(variable_rename,[status(thm)],[c_0_677]) ).
fof(c_0_1085,plain,
! [X14,X15,X16] :
( ~ class_Orderings_Olinorder(X16)
| c_HOL_Oord__class_Oless(X14,X15,X16)
| X15 = X14
| c_HOL_Oord__class_Oless(X15,X14,X16) ),
inference(variable_rename,[status(thm)],[c_0_678]) ).
fof(c_0_1086,plain,
! [X14,X15,X16] :
( ~ class_Orderings_Olinorder(X16)
| c_HOL_Oord__class_Oless(X14,X15,X16)
| c_HOL_Oord__class_Oless(X15,X14,X16)
| X15 = X14 ),
inference(variable_rename,[status(thm)],[c_0_679]) ).
fof(c_0_1087,plain,
! [X14,X15,X16] :
( ~ class_Orderings_Olinorder(X16)
| X15 = X14
| c_HOL_Oord__class_Oless(X14,X15,X16)
| c_HOL_Oord__class_Oless(X15,X14,X16) ),
inference(variable_rename,[status(thm)],[c_0_680]) ).
fof(c_0_1088,plain,
! [X14,X15,X16] :
( ~ class_Ring__and__Field_Oordered__idom(X16)
| c_HOL_Oord__class_Oless(X14,X15,X16)
| c_HOL_Oord__class_Oless(X15,X14,X16)
| X15 = X14 ),
inference(variable_rename,[status(thm)],[c_0_681]) ).
fof(c_0_1089,plain,
! [X58,X59,X60,X61] :
( hAPP(hAPP(c_Type_Otype_OFun,X61),X59) != hAPP(hAPP(c_Type_Otype_OFun,X60),X58)
| X61 = X60 ),
inference(variable_rename,[status(thm)],[c_0_682]) ).
fof(c_0_1090,plain,
! [X58,X59,X60,X61] :
( hAPP(hAPP(c_Type_Otype_OFun,X61),X59) != hAPP(hAPP(c_Type_Otype_OFun,X60),X58)
| X59 = X58 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_683])])]) ).
fof(c_0_1091,plain,
! [X53,X54,X55,X56] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X56),X54) != hAPP(hAPP(c_Lambda_OdB_OApp,X55),X53)
| X56 = X55 ),
inference(variable_rename,[status(thm)],[c_0_684]) ).
fof(c_0_1092,plain,
! [X53,X54,X55,X56] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X56),X54) != hAPP(hAPP(c_Lambda_OdB_OApp,X55),X53)
| X54 = X53 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_685])])]) ).
fof(c_0_1093,plain,
! [X6,X7] : c_HOL_Ominus__class_Ominus(c_Suc(X7),c_Suc(X6),tc_nat) = c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),
inference(variable_rename,[status(thm)],[c_0_686]) ).
fof(c_0_1094,plain,
! [X10,X11] :
( ~ class_Ring__and__Field_Osemiring__1(X11)
| c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X10),X11) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X11),c_HOL_Oone__class_Oone(X11)),c_Nat_Osemiring__1__class_Oof__nat(X10,X11)) ),
inference(variable_rename,[status(thm)],[c_0_687]) ).
fof(c_0_1095,plain,
! [X6,X7] :
( c_HOL_Oord__class_Oless(X6,c_Suc(X7),tc_nat)
| c_HOL_Oord__class_Oless(X7,X6,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_688]) ).
fof(c_0_1096,plain,
! [X14] :
( c_HOL_Oord__class_Oless(X14,X14,tc_nat)
| c_HOL_Oord__class_Oless(X14,c_Suc(X14),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_689]) ).
fof(c_0_1097,plain,
! [X10] :
( ~ class_Ring__and__Field_Oordered__semidom(X10)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X10),c_HOL_Ozero__class_Ozero(X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_690]) ).
fof(c_0_1098,plain,
! [X33,X34,X35] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X35)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X35),X34),X33) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X35),X33),X34) ),
inference(variable_rename,[status(thm)],[c_0_691]) ).
fof(c_0_1099,plain,
! [X10,X11,X12] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X12)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X12),X11),X10) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X12),X10),X11) ),
inference(variable_rename,[status(thm)],[c_0_692]) ).
fof(c_0_1100,plain,
! [X14,X15,X16] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X16)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X16),X15),X14) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X16),X14),X15) ),
inference(variable_rename,[status(thm)],[c_0_693]) ).
fof(c_0_1101,plain,
! [X27,X28] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X28)),X27),X28) = X27,
inference(variable_rename,[status(thm)],[c_0_694]) ).
fof(c_0_1102,plain,
! [X6,X7] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X7)),X6) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_Suc(X6)),
inference(variable_rename,[status(thm)],[c_0_695]) ).
fof(c_0_1103,plain,
! [X14,X15] :
( c_HOL_Oord__class_Oless(X14,X15,tc_nat)
| c_HOL_Oord__class_Oless(X15,X14,tc_nat)
| X15 = X14 ),
inference(variable_rename,[status(thm)],[c_0_696]) ).
fof(c_0_1104,plain,
! [X6,X7] :
( c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| c_HOL_Oord__class_Oless(X7,X6,tc_nat)
| X7 = X6 ),
inference(variable_rename,[status(thm)],[c_0_697]) ).
fof(c_0_1105,plain,
! [X14,X15,X16] :
( ~ class_Ring__and__Field_Oidom(X16)
| ~ class_Int_Onumber__ring(X16)
| c_HOL_Ominus__class_Ominus(X15,X14,X16) != c_HOL_Ozero__class_Ozero(X16)
| X15 = X14 ),
inference(variable_rename,[status(thm)],[c_0_698]) ).
fof(c_0_1106,plain,
! [X5] :
( X5 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_699]) ).
fof(c_0_1107,plain,
! [X14,X15,X16] :
( ~ class_Ring__and__Field_Oidom(X16)
| ~ class_Int_Onumber__ring(X16)
| X14 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X16),X14),X15)
| X15 = c_HOL_Ozero__class_Ozero(X16) ),
inference(variable_rename,[status(thm)],[c_0_700]) ).
fof(c_0_1108,plain,
! [X10,X11,X12] :
( ~ class_OrderedGroup_Oab__group__add(X12)
| c_HOL_Ominus__class_Ominus(X11,X10,X12) != c_HOL_Ozero__class_Ozero(X12)
| X11 = X10 ),
inference(variable_rename,[status(thm)],[c_0_701]) ).
fof(c_0_1109,plain,
! [X10,X11,X12] :
( ~ class_OrderedGroup_Ogroup__add(X12)
| c_HOL_Ominus__class_Ominus(X11,X10,X12) != c_HOL_Ozero__class_Ozero(X12)
| X11 = X10 ),
inference(variable_rename,[status(thm)],[c_0_702]) ).
fof(c_0_1110,plain,
! [X10,X11] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X11)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X11),X10),X10) != c_HOL_Ozero__class_Ozero(X11)
| X10 = c_HOL_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[c_0_703]) ).
fof(c_0_1111,plain,
! [X6,X7] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X6) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X6 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X7 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(variable_rename,[status(thm)],[c_0_704]) ).
fof(c_0_1112,plain,
! [X6,X7] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X6)
| X6 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X7 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(variable_rename,[status(thm)],[c_0_705]) ).
fof(c_0_1113,plain,
! [X6,X7] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X6) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X7 = c_HOL_Ozero__class_Ozero(tc_nat)
| X7 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(variable_rename,[status(thm)],[c_0_706]) ).
fof(c_0_1114,plain,
! [X6,X7] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X6) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X6 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_707])])]) ).
fof(c_0_1115,plain,
! [X6,X7] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X6)
| X7 = c_HOL_Ozero__class_Ozero(tc_nat)
| X7 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(variable_rename,[status(thm)],[c_0_708]) ).
fof(c_0_1116,plain,
! [X6,X7] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X6)
| X6 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_709])])]) ).
fof(c_0_1117,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_710 ).
fof(c_0_1118,plain,
! [X14,X15] :
( ~ class_Orderings_Opreorder(X15)
| ~ c_HOL_Oord__class_Oless(X14,X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_711]) ).
fof(c_0_1119,plain,
! [X14,X15] :
( ~ class_Orderings_Olinorder(X15)
| ~ c_HOL_Oord__class_Oless(X14,X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_712]) ).
fof(c_0_1120,plain,
! [X14,X15] :
( ~ class_Orderings_Oorder(X15)
| ~ c_HOL_Oord__class_Oless(X14,X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_713]) ).
fof(c_0_1121,plain,
! [X6,X7] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X6) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7),
inference(variable_rename,[status(thm)],[c_0_714]) ).
fof(c_0_1122,plain,
! [X6,X7] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X6) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X7 = c_HOL_Ozero__class_Ozero(tc_nat)
| X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_715]) ).
fof(c_0_1123,plain,
! [X6,X7] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X6)
| X7 = c_HOL_Ozero__class_Ozero(tc_nat)
| X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_716]) ).
fof(c_0_1124,plain,
! [X6] : ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_717]) ).
fof(c_0_1125,plain,
! [X5] : ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_718]) ).
fof(c_0_1126,plain,
! [X72,X73,X74] :
( X73 = X72
| ~ c_fequal(X73,X72,X74) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_719])])]) ).
fof(c_0_1127,plain,
! [X5] : ~ c_HOL_Oord__class_Oless(X5,X5,tc_nat),
inference(variable_rename,[status(thm)],[c_0_720]) ).
fof(c_0_1128,plain,
! [X14] : ~ c_HOL_Oord__class_Oless(X14,X14,tc_nat),
inference(variable_rename,[status(thm)],[c_0_721]) ).
fof(c_0_1129,plain,
! [X4] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X4)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X4)) ),
inference(variable_rename,[status(thm)],[c_0_722]) ).
fof(c_0_1130,plain,
! [X10] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X10)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X10),c_HOL_Ozero__class_Ozero(X10)),c_HOL_Ozero__class_Ozero(X10)) = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_723]) ).
fof(c_0_1131,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_724 ).
fof(c_0_1132,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_725 ).
fof(c_0_1133,plain,
! [X6,X7] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X6) != c_HOL_Ozero__class_Ozero(tc_nat)
| X7 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_726]) ).
fof(c_0_1134,plain,
! [X6,X7] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X6) != c_HOL_Ozero__class_Ozero(tc_nat)
| X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_727])])]) ).
fof(c_0_1135,plain,
! [X6,X7] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X6) != X7
| X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_728])])]) ).
fof(c_0_1136,plain,
! [X14,X15] :
( X14 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X15)
| X15 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_729]) ).
fof(c_0_1137,plain,
! [X10] :
( ~ class_Ring__and__Field_Oordered__semidom(X10)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X10),c_HOL_Oone__class_Oone(X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_730]) ).
fof(c_0_1138,plain,
! [X14,X15] :
( ~ class_Ring__and__Field_Oidom(X15)
| ~ class_Int_Onumber__ring(X15)
| X14 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),c_HOL_Ozero__class_Ozero(X15)) ),
inference(variable_rename,[status(thm)],[c_0_731]) ).
fof(c_0_1139,plain,
! [X14,X15] :
( ~ class_Ring__and__Field_Oidom(X15)
| ~ class_Int_Onumber__ring(X15)
| c_HOL_Ominus__class_Ominus(X14,X14,X15) = c_HOL_Ozero__class_Ozero(X15) ),
inference(variable_rename,[status(thm)],[c_0_732]) ).
fof(c_0_1140,plain,
! [X10,X11] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X11)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X11),c_HOL_Ozero__class_Ozero(X11)),X10) = X10 ),
inference(variable_rename,[status(thm)],[c_0_733]) ).
fof(c_0_1141,plain,
! [X10,X11] :
( ~ class_OrderedGroup_Omonoid__add(X11)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X11),c_HOL_Ozero__class_Ozero(X11)),X10) = X10 ),
inference(variable_rename,[status(thm)],[c_0_734]) ).
fof(c_0_1142,plain,
! [X10,X11] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X11)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X11),c_HOL_Ozero__class_Ozero(X11)),X10) = X10 ),
inference(variable_rename,[status(thm)],[c_0_735]) ).
fof(c_0_1143,plain,
! [X14,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X15)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),c_HOL_Ozero__class_Ozero(X15)),X14) = X14 ),
inference(variable_rename,[status(thm)],[c_0_736]) ).
fof(c_0_1144,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
c_0_737 ).
fof(c_0_1145,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_738 ).
fof(c_0_1146,plain,
! [X10,X11] :
( ~ class_OrderedGroup_Ogroup__add(X11)
| c_HOL_Ominus__class_Ominus(X10,c_HOL_Ozero__class_Ozero(X11),X11) = X10 ),
inference(variable_rename,[status(thm)],[c_0_739]) ).
fof(c_0_1147,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
c_0_740 ).
fof(c_0_1148,plain,
! [X10,X11] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X11)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X11),X10),c_HOL_Ozero__class_Ozero(X11)) = X10 ),
inference(variable_rename,[status(thm)],[c_0_741]) ).
fof(c_0_1149,plain,
! [X10,X11] :
( ~ class_OrderedGroup_Omonoid__add(X11)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X11),X10),c_HOL_Ozero__class_Ozero(X11)) = X10 ),
inference(variable_rename,[status(thm)],[c_0_742]) ).
fof(c_0_1150,plain,
! [X10,X11] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X11)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X11),X10),c_HOL_Ozero__class_Ozero(X11)) = X10 ),
inference(variable_rename,[status(thm)],[c_0_743]) ).
fof(c_0_1151,plain,
! [X14,X15] :
( ~ class_OrderedGroup_Oab__group__add(X15)
| c_HOL_Ominus__class_Ominus(X14,X14,X15) = c_HOL_Ozero__class_Ozero(X15) ),
inference(variable_rename,[status(thm)],[c_0_744]) ).
fof(c_0_1152,plain,
! [X14,X15] :
( ~ class_OrderedGroup_Ogroup__add(X15)
| c_HOL_Ominus__class_Ominus(X14,X14,X15) = c_HOL_Ozero__class_Ozero(X15) ),
inference(variable_rename,[status(thm)],[c_0_745]) ).
fof(c_0_1153,plain,
! [X10,X11] :
( ~ class_OrderedGroup_Ogroup__add(X11)
| c_HOL_Ominus__class_Ominus(X10,X10,X11) = c_HOL_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[c_0_746]) ).
fof(c_0_1154,plain,
! [X53,X54,X55] : hAPP(hAPP(c_Lambda_OdB_OApp,X55),X54) != c_Lambda_OdB_OAbs(X53),
inference(variable_rename,[status(thm)],[c_0_747]) ).
fof(c_0_1155,plain,
! [X53,X54,X55] : c_Lambda_OdB_OAbs(X53) != hAPP(hAPP(c_Lambda_OdB_OApp,X55),X54),
inference(variable_rename,[status(thm)],[c_0_748]) ).
fof(c_0_1156,plain,
! [X47,X48,X49] : c_Lambda_OdB_OVar(X47) != hAPP(hAPP(c_Lambda_OdB_OApp,X49),X48),
inference(variable_rename,[status(thm)],[c_0_749]) ).
fof(c_0_1157,plain,
! [X47,X48,X49] : hAPP(hAPP(c_Lambda_OdB_OApp,X49),X48) != c_Lambda_OdB_OVar(X47),
inference(variable_rename,[status(thm)],[c_0_750]) ).
fof(c_0_1158,plain,
! [X5] : c_HOL_Ominus__class_Ominus(c_Suc(X5),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X5,
inference(variable_rename,[status(thm)],[c_0_751]) ).
fof(c_0_1159,plain,
! [X5] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X5),tc_nat),
inference(variable_rename,[status(thm)],[c_0_752]) ).
fof(c_0_1160,plain,
! [X14] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X14),tc_nat),
inference(variable_rename,[status(thm)],[c_0_753]) ).
fof(c_0_1161,plain,
! [X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| X5 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_754]) ).
fof(c_0_1162,plain,
! [X14] : c_HOL_Oord__class_Oless(X14,c_Suc(X14),tc_nat),
inference(variable_rename,[status(thm)],[c_0_755]) ).
fof(c_0_1163,plain,
! [X5] : c_HOL_Oord__class_Oless(X5,c_Suc(X5),tc_nat),
inference(variable_rename,[status(thm)],[c_0_756]) ).
fof(c_0_1164,plain,
! [X30,X31] : c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X30,X31) = X30,
inference(variable_rename,[status(thm)],[c_0_757]) ).
fof(c_0_1165,plain,
! [X5] : c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_758]) ).
fof(c_0_1166,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),
c_0_759 ).
fof(c_0_1167,plain,
! [X6] : c_HOL_Ominus__class_Ominus(X6,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X6,
inference(variable_rename,[status(thm)],[c_0_760]) ).
fof(c_0_1168,plain,
! [X5] : c_Suc(X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X5),
inference(variable_rename,[status(thm)],[c_0_761]) ).
fof(c_0_1169,plain,
! [X6] : c_HOL_Ominus__class_Ominus(X6,X6,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_762]) ).
fof(c_0_1170,plain,
! [X14,X15] : c_fequal(X14,X14,X15),
inference(variable_rename,[status(thm)],[c_0_763]) ).
fof(c_0_1171,plain,
! [X10,X11] : c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(X10,X11),X11) = c_Transitive__Closure_Ortranclp(X10,X11),
inference(variable_rename,[status(thm)],[c_0_764]) ).
fof(c_0_1172,plain,
! [X10,X11,X12] :
( ~ class_Nat_Osemiring__char__0(X12)
| c_Nat_Osemiring__1__class_Oof__nat(X11,X12) != c_Nat_Osemiring__1__class_Oof__nat(X10,X12)
| X11 = X10 ),
inference(variable_rename,[status(thm)],[c_0_765]) ).
fof(c_0_1173,plain,
! [X5] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X5) = X5,
inference(variable_rename,[status(thm)],[c_0_766]) ).
fof(c_0_1174,plain,
! [X5] : c_Suc(X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),c_HOL_Oone__class_Oone(tc_nat)),
inference(variable_rename,[status(thm)],[c_0_767]) ).
fof(c_0_1175,plain,
! [X6] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),c_HOL_Ozero__class_Ozero(tc_nat)) = X6,
inference(variable_rename,[status(thm)],[c_0_768]) ).
fof(c_0_1176,plain,
! [X14] : X14 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Ozero__class_Ozero(tc_nat)),
inference(variable_rename,[status(thm)],[c_0_769]) ).
fof(c_0_1177,plain,
! [X5] : hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X5))),
inference(variable_rename,[status(thm)],[c_0_770]) ).
fof(c_0_1178,plain,
! [X70,X71] :
( class_Orderings_Oorder(tc_fun(X70,X71))
| ~ class_Orderings_Oorder(X71) ),
inference(variable_rename,[status(thm)],[c_0_771]) ).
fof(c_0_1179,plain,
! [X70,X71] :
( class_Orderings_Opreorder(tc_fun(X70,X71))
| ~ class_Orderings_Opreorder(X71) ),
inference(variable_rename,[status(thm)],[c_0_772]) ).
fof(c_0_1180,plain,
! [X10] :
( ~ class_Ring__and__Field_Osemiring__1(X10)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X10) = c_HOL_Oone__class_Oone(X10) ),
inference(variable_rename,[status(thm)],[c_0_773]) ).
fof(c_0_1181,plain,
! [X10] :
( ~ class_Ring__and__Field_Osemiring__1(X10)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X10) = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_774]) ).
fof(c_0_1182,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
c_0_775 ).
fof(c_0_1183,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_ua______)),
c_0_776 ).
fof(c_0_1184,plain,
! [X14,X15] : hAPP(c_Fun_Oid(X15),X14) = X14,
inference(variable_rename,[status(thm)],[c_0_777]) ).
fof(c_0_1185,plain,
! [X10] :
( ~ class_Ring__and__Field_Ozero__neq__one(X10)
| c_HOL_Ozero__class_Ozero(X10) != c_HOL_Oone__class_Oone(X10) ),
inference(variable_rename,[status(thm)],[c_0_778]) ).
fof(c_0_1186,plain,
! [X10] :
( ~ class_Ring__and__Field_Ozero__neq__one(X10)
| c_HOL_Oone__class_Oone(X10) != c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_779]) ).
fof(c_0_1187,axiom,
hAPP(c_Fun_Oid(t_a),v_x) = v_x,
c_0_780 ).
fof(c_0_1188,plain,
! [X41,X42] :
( c_Lambda_OdB_OVar(X42) != c_Lambda_OdB_OVar(X41)
| X42 = X41 ),
inference(variable_rename,[status(thm)],[c_0_781]) ).
fof(c_0_1189,plain,
! [X51,X52] :
( c_Lambda_OdB_OAbs(X52) != c_Lambda_OdB_OAbs(X51)
| X52 = X51 ),
inference(variable_rename,[status(thm)],[c_0_782]) ).
fof(c_0_1190,plain,
! [X14,X15] :
( c_Suc(X15) != c_Suc(X14)
| X15 = X14 ),
inference(variable_rename,[status(thm)],[c_0_783]) ).
fof(c_0_1191,plain,
! [X41,X42] :
( c_Suc(X42) != c_Suc(X41)
| X42 = X41 ),
inference(variable_rename,[status(thm)],[c_0_784]) ).
fof(c_0_1192,plain,
! [X50,X51] : c_Lambda_OdB_OAbs(X51) != c_Lambda_OdB_OVar(X50),
inference(variable_rename,[status(thm)],[c_0_785]) ).
fof(c_0_1193,plain,
! [X50,X51] : c_Lambda_OdB_OVar(X50) != c_Lambda_OdB_OAbs(X51),
inference(variable_rename,[status(thm)],[c_0_786]) ).
fof(c_0_1194,plain,
! [X34] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X34),
inference(variable_rename,[status(thm)],[c_0_787]) ).
fof(c_0_1195,plain,
! [X6] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X6),
inference(variable_rename,[status(thm)],[c_0_788]) ).
fof(c_0_1196,plain,
! [X6] : c_Suc(X6) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_789]) ).
fof(c_0_1197,plain,
! [X34] : c_Suc(X34) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_790]) ).
fof(c_0_1198,axiom,
c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_791 ).
fof(c_0_1199,plain,
! [X5] : X5 != c_Suc(X5),
inference(variable_rename,[status(thm)],[c_0_792]) ).
fof(c_0_1200,plain,
! [X5] : c_Suc(X5) != X5,
inference(variable_rename,[status(thm)],[c_0_793]) ).
fof(c_0_1201,axiom,
class_Orderings_Oorder(tc_bool),
c_0_794 ).
fof(c_0_1202,axiom,
class_Orderings_Opreorder(tc_bool),
c_0_795 ).
fof(c_0_1203,axiom,
class_Orderings_Oorder(tc_nat),
c_0_796 ).
fof(c_0_1204,axiom,
class_Orderings_Olinorder(tc_nat),
c_0_797 ).
fof(c_0_1205,axiom,
class_Orderings_Opreorder(tc_nat),
c_0_798 ).
fof(c_0_1206,axiom,
class_Nat_Osemiring__char__0(tc_nat),
c_0_799 ).
fof(c_0_1207,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
c_0_800 ).
fof(c_0_1208,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
c_0_801 ).
fof(c_0_1209,axiom,
class_OrderedGroup_Osemigroup__add(tc_nat),
c_0_802 ).
fof(c_0_1210,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
c_0_803 ).
fof(c_0_1211,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
c_0_804 ).
fof(c_0_1212,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
c_0_805 ).
fof(c_0_1213,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
c_0_806 ).
fof(c_0_1214,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
c_0_807 ).
fof(c_0_1215,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
c_0_808 ).
fof(c_0_1216,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
c_0_809 ).
fof(c_0_1217,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
c_0_810 ).
fof(c_0_1218,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
c_0_811 ).
fof(c_0_1219,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
c_0_812 ).
fof(c_0_1220,axiom,
v_n____ = v_i____,
c_0_813 ).
cnf(c_0_1221,plain,
c_List_Olistsp(hAPP(hAPP(c_COMBS(tc_Lambda_OdB,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_and),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_bool),tc_bool,tc_Lambda_OdB),c_All(tc_fun(tc_nat,tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_bool),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_fun(tc_nat,tc_Type_Otype)),c_All(tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_bool)),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_Type_Otype,tc_bool),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_bool),tc_bool,tc_Type_Otype),c_All(tc_Lambda_OdB)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_bool),tc_Type_Otype),hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_bool,tc_Lambda_OdB),c_All(tc_nat))))),hAPP(hAPP(c_COMBS(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_fun(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),c_COMBS(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Type_Otype),c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool),tc_Lambda_OdB)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Type_Otype),c_COMBS(tc_nat,tc_bool,tc_bool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_Type_Otype),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_nat),c_implies)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Type_Otype,tc_bool))),hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Lambda_OdB,tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype)),tc_fun(tc_nat,tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool)),tc_nat),c_Type_Otyping)),hAPP(hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_Type_Otype))),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Type_Otype,tc_fun(tc_nat,tc_Type_Otype))),c_Type_Oshift(tc_Type_Otype))),v_T____))))))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBS(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),c_COMBB(tc_bool,tc_bool,tc_nat)),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_implies),c_InductTermi_OIT))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBS(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_bool,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),c_COMBB(tc_bool,tc_bool,tc_nat))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_bool),tc_fun(tc_Lambda_OdB,tc_fun(tc_bool,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_implies)),hAPP(hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_Lambda_OdB,tc_Type_Otype,tc_bool)),c_Type_Otyping)),v_T____)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_nat,tc_Lambda_OdB),tc_fun(tc_nat,tc_bool),tc_Lambda_OdB),hAPP(c_COMBB(tc_Lambda_OdB,tc_bool,tc_nat),c_InductTermi_OIT))),c_Lambda_Osubst)))))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),c_Ex(tc_Type_Otype)),hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)))),v_bs____,tc_Lambda_OdB),
inference(split_conjunct,[status(thm)],[c_0_814]) ).
cnf(c_0_1222,plain,
( X7 = c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4),X5,tc_Type_Otype,tc_Type_Otype)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB)),X5))
| ~ c_Type_Otypings(X1,X3,X6)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)),X7)) ),
inference(split_conjunct,[status(thm)],[c_0_815]) ).
cnf(c_0_1223,plain,
( c_Type_Otypings(X1,X4,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB)),X5))
| ~ c_Type_Otypings(X1,X3,X6)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)),X7)) ),
inference(split_conjunct,[status(thm)],[c_0_816]) ).
cnf(c_0_1224,plain,
( X4 = X5
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)),X4))
| ~ hBOOL(hAPP(hAPP(hAPP(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_817]) ).
cnf(c_0_1225,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OVar(X2)),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_818]) ).
cnf(c_0_1226,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_819]) ).
cnf(c_0_1227,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_820]) ).
cnf(c_0_1228,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X5,tc_Lambda_OdB,tc_Lambda_OdB)),X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),c_List_Ofoldr(c_Type_Otype_OFun,X3,X4,tc_Type_Otype,tc_Type_Otype)))
| ~ c_Type_Otypings(X1,X5,X3) ),
inference(split_conjunct,[status(thm)],[c_0_821]) ).
cnf(c_0_1229,plain,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3),X4) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),X3)),X4),X2,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(split_conjunct,[status(thm)],[c_0_822]) ).
cnf(c_0_1230,plain,
( X3 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X1,X2,X3),tc_Lambda_OdB,tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_823]) ).
cnf(c_0_1231,plain,
( c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xvar__app__typesE__1__1(X4,X1,X2,X3))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_824]) ).
cnf(c_0_1232,plain,
( c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xlist__app__typeD__1__1(X4,X1,X2,X3))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_825]) ).
cnf(c_0_1233,plain,
( c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xlist__app__typeE__1__1(X4,X1,X2,X3))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_826]) ).
cnf(c_0_1234,plain,
( c_ListOrder_Ostep1(c_Lambda_Obeta,X2,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X1,X2,X3),tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_827]) ).
cnf(c_0_1235,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_828]) ).
cnf(c_0_1236,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_829]) ).
cnf(c_0_1237,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_830]) ).
cnf(c_0_1238,plain,
c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),v_u____)),v_i____),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
inference(split_conjunct,[status(thm)],[c_0_831]) ).
cnf(c_0_1239,plain,
c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),v_u____)),v_i____),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
inference(split_conjunct,[status(thm)],[c_0_832]) ).
cnf(c_0_1240,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_833]) ).
cnf(c_0_1241,plain,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),c_Lambda_OdB_OVar(v_n____)),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)))),
inference(split_conjunct,[status(thm)],[c_0_834]) ).
cnf(c_0_1242,plain,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_H____)),
inference(split_conjunct,[status(thm)],[c_0_835]) ).
cnf(c_0_1243,plain,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_ea______),v_ia______),v_T____)),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_Ha______)),
inference(split_conjunct,[status(thm)],[c_0_836]) ).
cnf(c_0_1244,plain,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_e____),v_u____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)))),
inference(split_conjunct,[status(thm)],[c_0_837]) ).
cnf(c_0_1245,plain,
hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X1),X3),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),X3),X2,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(split_conjunct,[status(thm)],[c_0_838]) ).
cnf(c_0_1246,plain,
( c_Type_Otypings(X1,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),X2)),X4),X5,tc_Lambda_OdB,tc_Lambda_OdB),X6)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),X3))
| ~ c_Type_Otypings(hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X4),X3),X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_839]) ).
cnf(c_0_1247,plain,
c_Fun_Ofcomp(c_Fun_Ofcomp(X1,X2,X3,X4,X5),X6,X3,X5,X7) = c_Fun_Ofcomp(X1,c_Fun_Ofcomp(X2,X6,X4,X5,X7),X3,X4,X7),
inference(split_conjunct,[status(thm)],[c_0_840]) ).
cnf(c_0_1248,plain,
c_Fun_Ocomp(X1,c_Fun_Ocomp(X2,X3,X4,X5,X6),X5,X7,X6) = c_Fun_Ocomp(c_Fun_Ocomp(X1,X2,X5,X7,X4),X3,X4,X7,X6),
inference(split_conjunct,[status(thm)],[c_0_841]) ).
cnf(c_0_1249,plain,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
inference(split_conjunct,[status(thm)],[c_0_842]) ).
cnf(c_0_1250,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X4,X1,X2,X3)),X4)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_843]) ).
cnf(c_0_1251,plain,
( hAPP(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6) = hAPP(c_Fun_Ocomp(X7,X8,X9,X4,X10),X11)
| hAPP(X1,hAPP(X2,X6)) != hAPP(X7,hAPP(X8,X11)) ),
inference(split_conjunct,[status(thm)],[c_0_844]) ).
cnf(c_0_1252,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_845]) ).
cnf(c_0_1253,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),c_HOL_Ozero__class_Ozero(tc_nat)),c_Type_Osko__Type__Xtyping__elims__3__1(X3,X1,X2))),X2),c_Type_Osko__Type__Xtyping__elims__3__2(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OAbs(X2)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_846]) ).
cnf(c_0_1254,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4)),X5))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X4),X6)),X2),X5))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X3),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_847]) ).
cnf(c_0_1255,plain,
( hAPP(X1,hAPP(X2,X3)) = hAPP(X4,hAPP(X5,X3))
| c_Fun_Ocomp(X1,X2,X6,X7,X8) != c_Fun_Ocomp(X4,X5,X9,X7,X8) ),
inference(split_conjunct,[status(thm)],[c_0_848]) ).
cnf(c_0_1256,plain,
( hAPP(X1,hAPP(X2,X3)) = hAPP(X4,X3)
| c_Fun_Ocomp(X1,X2,X5,X6,X7) != c_Fun_Ocomp(c_Fun_Oid(X6),X4,X6,X6,X7) ),
inference(split_conjunct,[status(thm)],[c_0_849]) ).
cnf(c_0_1257,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_850]) ).
cnf(c_0_1258,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_851]) ).
cnf(c_0_1259,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_852]) ).
cnf(c_0_1260,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_853]) ).
cnf(c_0_1261,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_854]) ).
cnf(c_0_1262,plain,
c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB),
inference(split_conjunct,[status(thm)],[c_0_855]) ).
cnf(c_0_1263,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_856]) ).
cnf(c_0_1264,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_857]) ).
cnf(c_0_1265,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_858]) ).
cnf(c_0_1266,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X6),X3)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X2),X3),X4)),X1),X5))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X2),X6),X4))
| v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X4),X7) ),
inference(split_conjunct,[status(thm)],[c_0_859]) ).
cnf(c_0_1267,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X6),X3)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X2),X3),X4)),X1),X5))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X2),X6),X4))
| v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X7),X4) ),
inference(split_conjunct,[status(thm)],[c_0_860]) ).
cnf(c_0_1268,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),X4),X2)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X2),v_T____)),v_b____),X3))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X4),v_T____)) ),
inference(split_conjunct,[status(thm)],[c_0_861]) ).
cnf(c_0_1269,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),X4),X2)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X2),v_T____)),v_b____),X3))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X4),v_T____)) ),
inference(split_conjunct,[status(thm)],[c_0_862]) ).
cnf(c_0_1270,plain,
c_List_Omap(X1,c_List_Omap(X2,X3,X4,X5),X5,X6) = c_List_Omap(c_Fun_Ocomp(X1,X2,X5,X6,X4),X3,X4,X6),
inference(split_conjunct,[status(thm)],[c_0_863]) ).
cnf(c_0_1271,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OAbs(X3)),hAPP(hAPP(c_Type_Otype_OFun,X2),X4)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),c_HOL_Ozero__class_Ozero(tc_nat)),X2)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_864]) ).
cnf(c_0_1272,plain,
( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),hAPP(hAPP(c_Lambda_Olift,X4),X1)),c_Suc(X2))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X5),X4),X2)),X1) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X5),X1)),X4),X2)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_865]) ).
cnf(c_0_1273,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),c_HOL_Ozero__class_Ozero(tc_nat)),c_Type_Osko__Type__Xabs__typeE__1__1(X1,X2))),X2),c_Type_Osko__Type__Xabs__typeE__1__2(X1,X2)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OAbs(X2)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_866]) ).
cnf(c_0_1274,plain,
hAPP(c_Fun_Ocomp(c_COMBK(X1,X2,X3),X4,X3,X2,t_a),v_x) = X1,
inference(split_conjunct,[status(thm)],[c_0_867]) ).
cnf(c_0_1275,plain,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_b____),v_sko__CHAINED__1(v_T____,v_b____,v_e____,v_i____))),
inference(split_conjunct,[status(thm)],[c_0_868]) ).
cnf(c_0_1276,plain,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_b____),v_sko__local__XCons__1__1(v_T____,v_b____,v_e____,v_i____))),
inference(split_conjunct,[status(thm)],[c_0_869]) ).
cnf(c_0_1277,plain,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_b____),v_sko__local__XCons__Xhyps__1__1(v_T____,v_b____,v_e____,v_i____))),
inference(split_conjunct,[status(thm)],[c_0_870]) ).
cnf(c_0_1278,plain,
c_Nat_Ocompow(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,X4,X4) = c_Fun_Ocomp(c_Nat_Ocompow(X1,X3,X4,X4),c_Nat_Ocompow(X2,X3,X4,X4),X4,X4,X4),
inference(split_conjunct,[status(thm)],[c_0_871]) ).
cnf(c_0_1279,plain,
hAPP(c_Fun_Ofcomp(X1,X2,X3,X4,X5),X6) = hAPP(X2,hAPP(X1,X6)),
inference(split_conjunct,[status(thm)],[c_0_872]) ).
cnf(c_0_1280,plain,
hAPP(X1,hAPP(X2,X3)) = hAPP(c_Fun_Ocomp(X1,X2,X4,X5,X6),X3),
inference(split_conjunct,[status(thm)],[c_0_873]) ).
cnf(c_0_1281,plain,
hAPP(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
inference(split_conjunct,[status(thm)],[c_0_874]) ).
cnf(c_0_1282,plain,
hAPP(c_Fun_Ofcomp(X1,X2,t_a,X3,X4),v_x) = hAPP(X2,hAPP(X1,v_x)),
inference(split_conjunct,[status(thm)],[c_0_875]) ).
cnf(c_0_1283,plain,
hAPP(c_Fun_Ocomp(X1,X2,X3,X4,t_a),v_x) = hAPP(X1,hAPP(X2,v_x)),
inference(split_conjunct,[status(thm)],[c_0_876]) ).
cnf(c_0_1284,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_877]) ).
cnf(c_0_1285,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_878]) ).
cnf(c_0_1286,plain,
v_T____ = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
inference(split_conjunct,[status(thm)],[c_0_879]) ).
cnf(c_0_1287,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X4),X5)),hAPP(hAPP(c_Lambda_Olift,X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_880]) ).
cnf(c_0_1288,plain,
hAPP(hAPP(hAPP(c_Type_Oshift(X1),hAPP(hAPP(hAPP(c_Type_Oshift(X1),X2),X3),X4)),c_HOL_Ozero__class_Ozero(tc_nat)),X5) = hAPP(hAPP(hAPP(c_Type_Oshift(X1),hAPP(hAPP(hAPP(c_Type_Oshift(X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X5)),c_Suc(X3)),X4),
inference(split_conjunct,[status(thm)],[c_0_881]) ).
cnf(c_0_1289,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB),
inference(split_conjunct,[status(thm)],[c_0_882]) ).
cnf(c_0_1290,plain,
c_Nat_Ocompow(c_Suc(X1),X2,X3,X3) = c_Fun_Ocomp(X2,c_Nat_Ocompow(X1,X2,X3,X3),X3,X3,X3),
inference(split_conjunct,[status(thm)],[c_0_883]) ).
cnf(c_0_1291,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_884]) ).
cnf(c_0_1292,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_885]) ).
cnf(c_0_1293,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_886]) ).
cnf(c_0_1294,plain,
( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X4),X1)),X2) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,X4),X2)),X1)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_887]) ).
cnf(c_0_1295,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X3),c_Type_Osko__Type__Xtyping__elims__2__1(X4,X1,X2,X3)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_888]) ).
cnf(c_0_1296,plain,
( c_Type_Otypings(hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X4),X5),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),X4),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3)
| ~ c_Type_Otypings(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_889]) ).
cnf(c_0_1297,plain,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_a____),v_T_H_H____)),
inference(split_conjunct,[status(thm)],[c_0_890]) ).
cnf(c_0_1298,plain,
hAPP(X1,hAPP(c_Nat_Ocompow(X2,X1,X3,X3),X4)) = hAPP(c_Nat_Ocompow(X2,X1,X3,X3),hAPP(X1,X4)),
inference(split_conjunct,[status(thm)],[c_0_891]) ).
cnf(c_0_1299,plain,
( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),c_HOL_Ozero__class_Ozero(tc_nat)),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_892]) ).
cnf(c_0_1300,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_893]) ).
cnf(c_0_1301,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_894]) ).
cnf(c_0_1302,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_895]) ).
cnf(c_0_1303,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X5)),X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),hAPP(hAPP(c_Type_Otype_OFun,X3),X4)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X5),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_896]) ).
cnf(c_0_1304,plain,
( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X4),X2)),X1) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X3),X1)),hAPP(hAPP(c_Lambda_Olift,X4),X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_897]) ).
cnf(c_0_1305,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_898]) ).
cnf(c_0_1306,plain,
c_Fun_Ofcomp(c_Fun_Oid(X1),X2,X1,X1,X3) = X2,
inference(split_conjunct,[status(thm)],[c_0_899]) ).
cnf(c_0_1307,plain,
c_Fun_Ofcomp(X1,c_Fun_Oid(X2),X3,X2,X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_900]) ).
cnf(c_0_1308,plain,
c_Fun_Ocomp(X1,c_Fun_Oid(X2),X2,X3,X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_901]) ).
cnf(c_0_1309,plain,
c_Fun_Ocomp(c_Fun_Oid(X1),X2,X1,X1,X3) = X2,
inference(split_conjunct,[status(thm)],[c_0_902]) ).
cnf(c_0_1310,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_903]) ).
cnf(c_0_1311,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_904]) ).
cnf(c_0_1312,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_905]) ).
cnf(c_0_1313,plain,
hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),X3),X4) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4)),
inference(split_conjunct,[status(thm)],[c_0_906]) ).
cnf(c_0_1314,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_907]) ).
cnf(c_0_1315,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_908]) ).
cnf(c_0_1316,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_909]) ).
cnf(c_0_1317,plain,
( c_Nat_Osemiring__1__class_Oof__nat(X1,X2) = c_Nat_Osemiring__1__class_Oof__nat__aux(hAPP(hAPP(c_COMBC(X2,X2,X2),c_HOL_Oplus__class_Oplus(X2)),c_HOL_Oone__class_Oone(X2)),X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Osemiring__1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_910]) ).
cnf(c_0_1318,plain,
hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)))),
inference(split_conjunct,[status(thm)],[c_0_911]) ).
cnf(c_0_1319,plain,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(X1)),X2),X3) = c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),hAPP(hAPP(c_Lambda_Olift,X2),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)))),
inference(split_conjunct,[status(thm)],[c_0_912]) ).
cnf(c_0_1320,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_913]) ).
cnf(c_0_1321,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_914]) ).
cnf(c_0_1322,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X3),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X3),X1),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_915]) ).
cnf(c_0_1323,plain,
( X3 = hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(X3,X1,X2)),c_Type_Osko__Type__Xtyping__elims__3__2(X3,X1,X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OAbs(X2)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_916]) ).
cnf(c_0_1324,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_917]) ).
cnf(c_0_1325,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_918]) ).
cnf(c_0_1326,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_919]) ).
cnf(c_0_1327,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_920]) ).
cnf(c_0_1328,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_921]) ).
cnf(c_0_1329,plain,
( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X3),X1)),c_Suc(X2)) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X3),X2)),X1)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_922]) ).
cnf(c_0_1330,plain,
c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,X1),X2),tc_Type_Otype) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X1,tc_Type_Otype)),c_Nat_Osize__class_Osize(X2,tc_Type_Otype))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
inference(split_conjunct,[status(thm)],[c_0_923]) ).
cnf(c_0_1331,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_924]) ).
cnf(c_0_1332,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_925]) ).
cnf(c_0_1333,plain,
hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
inference(split_conjunct,[status(thm)],[c_0_926]) ).
cnf(c_0_1334,plain,
( c_Nat_Osemiring__1__class_Oof__nat__aux(X1,c_Suc(X2),X3,X4) = c_Nat_Osemiring__1__class_Oof__nat__aux(X1,X2,hAPP(X1,X3),X4)
| ~ class_Ring__and__Field_Osemiring__1(X4) ),
inference(split_conjunct,[status(thm)],[c_0_927]) ).
cnf(c_0_1335,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_928]) ).
cnf(c_0_1336,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_929]) ).
cnf(c_0_1337,plain,
c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),X3,X4) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(X1,X3,X4)),c_Lambda_Osubstn(X2,X3,X4)),
inference(split_conjunct,[status(thm)],[c_0_930]) ).
cnf(c_0_1338,plain,
c_Lambda_Oliftn(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(X1,X2,X4)),c_Lambda_Oliftn(X1,X3,X4)),
inference(split_conjunct,[status(thm)],[c_0_931]) ).
cnf(c_0_1339,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_932]) ).
cnf(c_0_1340,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_933]) ).
cnf(c_0_1341,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_934]) ).
cnf(c_0_1342,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_935]) ).
cnf(c_0_1343,plain,
( hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(X3),X4),X1),X5),X2) = hAPP(X4,c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_936]) ).
cnf(c_0_1344,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_937]) ).
cnf(c_0_1345,plain,
hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),X3) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X1),X3)),hAPP(hAPP(c_Lambda_Olift,X2),X3)),
inference(split_conjunct,[status(thm)],[c_0_938]) ).
cnf(c_0_1346,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_939]) ).
cnf(c_0_1347,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_940]) ).
cnf(c_0_1348,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_941]) ).
cnf(c_0_1349,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_942]) ).
cnf(c_0_1350,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_943]) ).
cnf(c_0_1351,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_944]) ).
cnf(c_0_1352,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_945]) ).
cnf(c_0_1353,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_946]) ).
cnf(c_0_1354,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_947]) ).
cnf(c_0_1355,plain,
c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X1),X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(X1)),c_Type_Otype_Otype__size(X2))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
inference(split_conjunct,[status(thm)],[c_0_948]) ).
cnf(c_0_1356,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_949]) ).
cnf(c_0_1357,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_950]) ).
cnf(c_0_1358,plain,
hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X1),X2)),X3),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_951]) ).
cnf(c_0_1359,plain,
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(split_conjunct,[status(thm)],[c_0_952]) ).
cnf(c_0_1360,plain,
c_Lambda_Osubstn(c_Lambda_OdB_OAbs(X1),X2,X3) = c_Lambda_OdB_OAbs(c_Lambda_Osubstn(X1,X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)))),
inference(split_conjunct,[status(thm)],[c_0_953]) ).
cnf(c_0_1361,plain,
c_Lambda_Oliftn(X1,c_Lambda_OdB_OAbs(X2),X3) = c_Lambda_OdB_OAbs(c_Lambda_Oliftn(X1,X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)))),
inference(split_conjunct,[status(thm)],[c_0_954]) ).
cnf(c_0_1362,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3)),
inference(split_conjunct,[status(thm)],[c_0_955]) ).
cnf(c_0_1363,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_956]) ).
cnf(c_0_1364,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_957]) ).
cnf(c_0_1365,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_958]) ).
cnf(c_0_1366,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_959]) ).
cnf(c_0_1367,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_960]) ).
cnf(c_0_1368,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_961]) ).
cnf(c_0_1369,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_962]) ).
cnf(c_0_1370,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_963]) ).
cnf(c_0_1371,plain,
( hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(X3),X4),X2),X5),X1) = hAPP(X4,X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_964]) ).
cnf(c_0_1372,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_965]) ).
cnf(c_0_1373,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X1),X2,tc_nat),c_Suc(X3),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_966]) ).
cnf(c_0_1374,plain,
( hAPP(X1,X2) = X3
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OVar(X2)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_967]) ).
cnf(c_0_1375,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_968]) ).
cnf(c_0_1376,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_969]) ).
cnf(c_0_1377,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_970]) ).
cnf(c_0_1378,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_971]) ).
cnf(c_0_1379,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_972]) ).
cnf(c_0_1380,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_973]) ).
cnf(c_0_1381,plain,
hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(X1)),X2) = c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)))),
inference(split_conjunct,[status(thm)],[c_0_974]) ).
cnf(c_0_1382,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_975]) ).
cnf(c_0_1383,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_976]) ).
cnf(c_0_1384,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_977]) ).
cnf(c_0_1385,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_978]) ).
cnf(c_0_1386,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_979]) ).
cnf(c_0_1387,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_980]) ).
cnf(c_0_1388,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_981]) ).
cnf(c_0_1389,plain,
c_Lambda_Oliftn(c_Suc(X1),X2,X3) = hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(X1,X2,X3)),X3),
inference(split_conjunct,[status(thm)],[c_0_982]) ).
cnf(c_0_1390,plain,
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X2)),X3),X1) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_983]) ).
cnf(c_0_1391,plain,
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X2)),X3),X1) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_984]) ).
cnf(c_0_1392,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_985]) ).
cnf(c_0_1393,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_986]) ).
cnf(c_0_1394,plain,
c_HOL_Ominus__class_Ominus(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_Ominus__class_Ominus(X2,X3,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_987]) ).
cnf(c_0_1395,plain,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_988]) ).
cnf(c_0_1396,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_989]) ).
cnf(c_0_1397,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_990]) ).
cnf(c_0_1398,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_991]) ).
cnf(c_0_1399,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3)),
inference(split_conjunct,[status(thm)],[c_0_992]) ).
cnf(c_0_1400,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_993]) ).
cnf(c_0_1401,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_994]) ).
cnf(c_0_1402,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_995]) ).
cnf(c_0_1403,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_996]) ).
cnf(c_0_1404,plain,
( c_Nat_Osemiring__1__class_Oof__nat__aux(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2,X3) = X2
| ~ class_Ring__and__Field_Osemiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_997]) ).
cnf(c_0_1405,plain,
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_998]) ).
cnf(c_0_1406,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Suc(X2),tc_nat),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_999]) ).
cnf(c_0_1407,plain,
c_Nat_Ocompow(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2,X2) = c_Fun_Oid(X2),
inference(split_conjunct,[status(thm)],[c_0_1000]) ).
cnf(c_0_1408,plain,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OVar(X2)),hAPP(X1,X2))),
inference(split_conjunct,[status(thm)],[c_0_1001]) ).
cnf(c_0_1409,plain,
hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(X1),X2),X3),X4),X3) = X4,
inference(split_conjunct,[status(thm)],[c_0_1002]) ).
cnf(c_0_1410,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_1003]) ).
cnf(c_0_1411,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_1004]) ).
cnf(c_0_1412,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_1005]) ).
cnf(c_0_1413,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1006]) ).
cnf(c_0_1414,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1)),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1007]) ).
cnf(c_0_1415,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1008]) ).
cnf(c_0_1416,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_1009]) ).
cnf(c_0_1417,plain,
c_Type_Otypings(hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____),v_as____,v_Ts____),
inference(split_conjunct,[status(thm)],[c_0_1010]) ).
cnf(c_0_1418,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_1011]) ).
cnf(c_0_1419,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_1012]) ).
cnf(c_0_1420,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_1013]) ).
cnf(c_0_1421,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_1014]) ).
cnf(c_0_1422,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_1015]) ).
cnf(c_0_1423,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_1016]) ).
cnf(c_0_1424,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_1017]) ).
cnf(c_0_1425,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_1018]) ).
cnf(c_0_1426,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_1019]) ).
cnf(c_0_1427,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_1020]) ).
cnf(c_0_1428,plain,
( c_HOL_Oord__class_Oless(c_Suc(X1),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1021]) ).
cnf(c_0_1429,plain,
~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X2,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1022]) ).
cnf(c_0_1430,plain,
~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X1,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1023]) ).
cnf(c_0_1431,plain,
( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1024]) ).
cnf(c_0_1432,plain,
c_HOL_Ominus__class_Ominus(X1,c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1025]) ).
cnf(c_0_1433,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_1026]) ).
cnf(c_0_1434,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_1027]) ).
cnf(c_0_1435,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1)),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1028]) ).
cnf(c_0_1436,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_1029]) ).
cnf(c_0_1437,plain,
( X1 = c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1030]) ).
cnf(c_0_1438,plain,
( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1031]) ).
cnf(c_0_1439,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X1)),X2) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat))) ),
inference(split_conjunct,[status(thm)],[c_0_1032]) ).
cnf(c_0_1440,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_1033]) ).
cnf(c_0_1441,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_1034]) ).
cnf(c_0_1442,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_1035]) ).
cnf(c_0_1443,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_1036]) ).
cnf(c_0_1444,plain,
hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3)),
inference(split_conjunct,[status(thm)],[c_0_1037]) ).
cnf(c_0_1445,plain,
hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3)),
inference(split_conjunct,[status(thm)],[c_0_1038]) ).
cnf(c_0_1446,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_1039]) ).
cnf(c_0_1447,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_1040]) ).
cnf(c_0_1448,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_1041]) ).
cnf(c_0_1449,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_1042]) ).
cnf(c_0_1450,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_1043]) ).
cnf(c_0_1451,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_1044]) ).
cnf(c_0_1452,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_1045]) ).
cnf(c_0_1453,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_1046]) ).
cnf(c_0_1454,plain,
( ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1047]) ).
cnf(c_0_1455,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_1048]) ).
cnf(c_0_1456,plain,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Oone__class_Oone(X2)),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1049]) ).
cnf(c_0_1457,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_1050]) ).
cnf(c_0_1458,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_1051]) ).
cnf(c_0_1459,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_1052]) ).
cnf(c_0_1460,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_1053]) ).
cnf(c_0_1461,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_1054]) ).
cnf(c_0_1462,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_1055]) ).
cnf(c_0_1463,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_1056]) ).
cnf(c_0_1464,plain,
c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_Suc(X1),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1057]) ).
cnf(c_0_1465,plain,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X1)),X2)),
inference(split_conjunct,[status(thm)],[c_0_1058]) ).
cnf(c_0_1466,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1059]) ).
cnf(c_0_1467,plain,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_ea______),v_ua______),v_T____)),
inference(split_conjunct,[status(thm)],[c_0_1060]) ).
cnf(c_0_1468,plain,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_e____),v_u____),v_T____)),
inference(split_conjunct,[status(thm)],[c_0_1061]) ).
cnf(c_0_1469,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X1)),X2) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_1062]) ).
cnf(c_0_1470,plain,
( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1063]) ).
cnf(c_0_1471,plain,
( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1064]) ).
cnf(c_0_1472,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1065]) ).
cnf(c_0_1473,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1066]) ).
cnf(c_0_1474,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1067]) ).
cnf(c_0_1475,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_1068]) ).
cnf(c_0_1476,plain,
( c_Suc(X1) = X2
| c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1069]) ).
cnf(c_0_1477,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_1070]) ).
cnf(c_0_1478,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_1071]) ).
cnf(c_0_1479,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_1072]) ).
cnf(c_0_1480,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1073]) ).
cnf(c_0_1481,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_Suc(X2)) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_1074]) ).
cnf(c_0_1482,plain,
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(split_conjunct,[status(thm)],[c_0_1075]) ).
cnf(c_0_1483,plain,
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(split_conjunct,[status(thm)],[c_0_1076]) ).
cnf(c_0_1484,plain,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X1,tc_nat) = X2,
inference(split_conjunct,[status(thm)],[c_0_1077]) ).
cnf(c_0_1485,plain,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X2,tc_nat) = X1,
inference(split_conjunct,[status(thm)],[c_0_1078]) ).
cnf(c_0_1486,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_1079]) ).
cnf(c_0_1487,plain,
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1080]) ).
cnf(c_0_1488,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_1081]) ).
cnf(c_0_1489,plain,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
inference(split_conjunct,[status(thm)],[c_0_1082]) ).
cnf(c_0_1490,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_1083]) ).
cnf(c_0_1491,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_1084]) ).
cnf(c_0_1492,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_1085]) ).
cnf(c_0_1493,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_1086]) ).
cnf(c_0_1494,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_1087]) ).
cnf(c_0_1495,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_1088]) ).
cnf(c_0_1496,plain,
( X1 = X2
| hAPP(hAPP(c_Type_Otype_OFun,X1),X3) != hAPP(hAPP(c_Type_Otype_OFun,X2),X4) ),
inference(split_conjunct,[status(thm)],[c_0_1089]) ).
cnf(c_0_1497,plain,
( X1 = X2
| hAPP(hAPP(c_Type_Otype_OFun,X3),X1) != hAPP(hAPP(c_Type_Otype_OFun,X4),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1090]) ).
cnf(c_0_1498,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_1091]) ).
cnf(c_0_1499,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_1092]) ).
cnf(c_0_1500,plain,
c_HOL_Ominus__class_Ominus(c_Suc(X1),c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1093]) ).
cnf(c_0_1501,plain,
( c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X1),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Oone__class_Oone(X2)),c_Nat_Osemiring__1__class_Oof__nat(X1,X2))
| ~ class_Ring__and__Field_Osemiring__1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1094]) ).
cnf(c_0_1502,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1095]) ).
cnf(c_0_1503,plain,
( c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1096]) ).
cnf(c_0_1504,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1097]) ).
cnf(c_0_1505,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_1098]) ).
cnf(c_0_1506,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_1099]) ).
cnf(c_0_1507,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_1100]) ).
cnf(c_0_1508,plain,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1) = X2,
inference(split_conjunct,[status(thm)],[c_0_1101]) ).
cnf(c_0_1509,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X1)),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_Suc(X2)),
inference(split_conjunct,[status(thm)],[c_0_1102]) ).
cnf(c_0_1510,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_1103]) ).
cnf(c_0_1511,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_1104]) ).
cnf(c_0_1512,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_1105]) ).
cnf(c_0_1513,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1106]) ).
cnf(c_0_1514,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_1107]) ).
cnf(c_0_1515,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_1108]) ).
cnf(c_0_1516,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_1109]) ).
cnf(c_0_1517,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_1110]) ).
cnf(c_0_1518,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_1111]) ).
cnf(c_0_1519,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1112]) ).
cnf(c_0_1520,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_1113]) ).
cnf(c_0_1521,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_1114]) ).
cnf(c_0_1522,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1115]) ).
cnf(c_0_1523,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_1116]) ).
cnf(c_0_1524,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1117]) ).
cnf(c_0_1525,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1118]) ).
cnf(c_0_1526,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1119]) ).
cnf(c_0_1527,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1120]) ).
cnf(c_0_1528,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),
inference(split_conjunct,[status(thm)],[c_0_1121]) ).
cnf(c_0_1529,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_1122]) ).
cnf(c_0_1530,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_1123]) ).
cnf(c_0_1531,plain,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1124]) ).
cnf(c_0_1532,plain,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1125]) ).
cnf(c_0_1533,plain,
( X1 = X2
| ~ c_fequal(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1126]) ).
cnf(c_0_1534,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1127]) ).
cnf(c_0_1535,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1128]) ).
cnf(c_0_1536,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1129]) ).
cnf(c_0_1537,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_1130]) ).
cnf(c_0_1538,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_1131]) ).
cnf(c_0_1539,plain,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_1132]) ).
cnf(c_0_1540,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_1133]) ).
cnf(c_0_1541,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_1134]) ).
cnf(c_0_1542,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_1135]) ).
cnf(c_0_1543,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_1136]) ).
cnf(c_0_1544,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1137]) ).
cnf(c_0_1545,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_1138]) ).
cnf(c_0_1546,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_1139]) ).
cnf(c_0_1547,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_1140]) ).
cnf(c_0_1548,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_1141]) ).
cnf(c_0_1549,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_1142]) ).
cnf(c_0_1550,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_1143]) ).
cnf(c_0_1551,plain,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
inference(split_conjunct,[status(thm)],[c_0_1144]) ).
cnf(c_0_1552,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_1145]) ).
cnf(c_0_1553,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_1146]) ).
cnf(c_0_1554,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1147]) ).
cnf(c_0_1555,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_1148]) ).
cnf(c_0_1556,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_1149]) ).
cnf(c_0_1557,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_1150]) ).
cnf(c_0_1558,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_1151]) ).
cnf(c_0_1559,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_1152]) ).
cnf(c_0_1560,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_1153]) ).
cnf(c_0_1561,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OAbs(X3),
inference(split_conjunct,[status(thm)],[c_0_1154]) ).
cnf(c_0_1562,plain,
c_Lambda_OdB_OAbs(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_1155]) ).
cnf(c_0_1563,plain,
c_Lambda_OdB_OVar(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_1156]) ).
cnf(c_0_1564,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OVar(X3),
inference(split_conjunct,[status(thm)],[c_0_1157]) ).
cnf(c_0_1565,plain,
c_HOL_Ominus__class_Ominus(c_Suc(X1),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1,
inference(split_conjunct,[status(thm)],[c_0_1158]) ).
cnf(c_0_1566,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1159]) ).
cnf(c_0_1567,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1160]) ).
cnf(c_0_1568,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_1161]) ).
cnf(c_0_1569,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1162]) ).
cnf(c_0_1570,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1163]) ).
cnf(c_0_1571,plain,
c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_1164]) ).
cnf(c_0_1572,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1165]) ).
cnf(c_0_1573,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),
inference(split_conjunct,[status(thm)],[c_0_1166]) ).
cnf(c_0_1574,plain,
c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
inference(split_conjunct,[status(thm)],[c_0_1167]) ).
cnf(c_0_1575,plain,
c_Suc(X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X1),
inference(split_conjunct,[status(thm)],[c_0_1168]) ).
cnf(c_0_1576,plain,
c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1169]) ).
cnf(c_0_1577,plain,
c_fequal(X1,X1,X2),
inference(split_conjunct,[status(thm)],[c_0_1170]) ).
cnf(c_0_1578,plain,
c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(X1,X2),X2) = c_Transitive__Closure_Ortranclp(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_1171]) ).
cnf(c_0_1579,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_1172]) ).
cnf(c_0_1580,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_1173]) ).
cnf(c_0_1581,plain,
c_Suc(X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_1174]) ).
cnf(c_0_1582,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)) = X1,
inference(split_conjunct,[status(thm)],[c_0_1175]) ).
cnf(c_0_1583,plain,
X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_1176]) ).
cnf(c_0_1584,plain,
hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X1))),
inference(split_conjunct,[status(thm)],[c_0_1177]) ).
cnf(c_0_1585,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1178]) ).
cnf(c_0_1586,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1179]) ).
cnf(c_0_1587,plain,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1180]) ).
cnf(c_0_1588,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_1181]) ).
cnf(c_0_1589,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
inference(split_conjunct,[status(thm)],[c_0_1182]) ).
cnf(c_0_1590,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_ua______)),
inference(split_conjunct,[status(thm)],[c_0_1183]) ).
cnf(c_0_1591,plain,
hAPP(c_Fun_Oid(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_1184]) ).
cnf(c_0_1592,plain,
( c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1185]) ).
cnf(c_0_1593,plain,
( c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1186]) ).
cnf(c_0_1594,plain,
hAPP(c_Fun_Oid(t_a),v_x) = v_x,
inference(split_conjunct,[status(thm)],[c_0_1187]) ).
cnf(c_0_1595,plain,
( X1 = X2
| c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1188]) ).
cnf(c_0_1596,plain,
( X1 = X2
| c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1189]) ).
cnf(c_0_1597,plain,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1190]) ).
cnf(c_0_1598,plain,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1191]) ).
cnf(c_0_1599,plain,
c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OVar(X2),
inference(split_conjunct,[status(thm)],[c_0_1192]) ).
cnf(c_0_1600,plain,
c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OAbs(X2),
inference(split_conjunct,[status(thm)],[c_0_1193]) ).
cnf(c_0_1601,plain,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
inference(split_conjunct,[status(thm)],[c_0_1194]) ).
cnf(c_0_1602,plain,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
inference(split_conjunct,[status(thm)],[c_0_1195]) ).
cnf(c_0_1603,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1196]) ).
cnf(c_0_1604,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1197]) ).
cnf(c_0_1605,plain,
c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_1198]) ).
cnf(c_0_1606,plain,
X1 != c_Suc(X1),
inference(split_conjunct,[status(thm)],[c_0_1199]) ).
cnf(c_0_1607,plain,
c_Suc(X1) != X1,
inference(split_conjunct,[status(thm)],[c_0_1200]) ).
cnf(c_0_1608,plain,
class_Orderings_Oorder(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_1201]) ).
cnf(c_0_1609,plain,
class_Orderings_Opreorder(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_1202]) ).
cnf(c_0_1610,plain,
class_Orderings_Oorder(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1203]) ).
cnf(c_0_1611,plain,
class_Orderings_Olinorder(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1204]) ).
cnf(c_0_1612,plain,
class_Orderings_Opreorder(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1205]) ).
cnf(c_0_1613,plain,
class_Nat_Osemiring__char__0(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1206]) ).
cnf(c_0_1614,plain,
class_OrderedGroup_Omonoid__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1207]) ).
cnf(c_0_1615,plain,
class_Ring__and__Field_Osemiring__1(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1208]) ).
cnf(c_0_1616,plain,
class_OrderedGroup_Osemigroup__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1209]) ).
cnf(c_0_1617,plain,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1210]) ).
cnf(c_0_1618,plain,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1211]) ).
cnf(c_0_1619,plain,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1212]) ).
cnf(c_0_1620,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1213]) ).
cnf(c_0_1621,plain,
class_Ring__and__Field_Oordered__semidom(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1214]) ).
cnf(c_0_1622,plain,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1215]) ).
cnf(c_0_1623,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1216]) ).
cnf(c_0_1624,plain,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1217]) ).
cnf(c_0_1625,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1218]) ).
cnf(c_0_1626,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1219]) ).
cnf(c_0_1627,plain,
v_n____ = v_i____,
inference(split_conjunct,[status(thm)],[c_0_1220]) ).
cnf(c_0_1628,plain,
c_List_Olistsp(hAPP(hAPP(c_COMBS(tc_Lambda_OdB,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_and),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_bool),tc_bool,tc_Lambda_OdB),c_All(tc_fun(tc_nat,tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_bool),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_fun(tc_nat,tc_Type_Otype)),c_All(tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_bool)),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_Type_Otype,tc_bool),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_bool),tc_bool,tc_Type_Otype),c_All(tc_Lambda_OdB)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_bool),tc_Type_Otype),hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_bool,tc_Lambda_OdB),c_All(tc_nat))))),hAPP(hAPP(c_COMBS(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_fun(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),c_COMBS(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Type_Otype),c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool),tc_Lambda_OdB)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Type_Otype),c_COMBS(tc_nat,tc_bool,tc_bool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_Type_Otype),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_nat),c_implies)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Type_Otype,tc_bool))),hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Lambda_OdB,tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype)),tc_fun(tc_nat,tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool)),tc_nat),c_Type_Otyping)),hAPP(hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_Type_Otype))),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Type_Otype,tc_fun(tc_nat,tc_Type_Otype))),c_Type_Oshift(tc_Type_Otype))),v_T____))))))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBS(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),c_COMBB(tc_bool,tc_bool,tc_nat)),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_implies),c_InductTermi_OIT))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBS(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_bool,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),c_COMBB(tc_bool,tc_bool,tc_nat))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_bool),tc_fun(tc_Lambda_OdB,tc_fun(tc_bool,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_implies)),hAPP(hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_Lambda_OdB,tc_Type_Otype,tc_bool)),c_Type_Otyping)),v_T____)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_nat,tc_Lambda_OdB),tc_fun(tc_nat,tc_bool),tc_Lambda_OdB),hAPP(c_COMBB(tc_Lambda_OdB,tc_bool,tc_nat),c_InductTermi_OIT))),c_Lambda_Osubst)))))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),c_Ex(tc_Type_Otype)),hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)))),v_bs____,tc_Lambda_OdB),
c_0_1221,
[final] ).
cnf(c_0_1629,plain,
( c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4),X5,tc_Type_Otype,tc_Type_Otype) = X7
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB)),X5))
| ~ c_Type_Otypings(X1,X3,X6)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)),X7)) ),
c_0_1222,
[final] ).
cnf(c_0_1630,plain,
( c_Type_Otypings(X1,X4,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB)),X5))
| ~ c_Type_Otypings(X1,X3,X6)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)),X7)) ),
c_0_1223,
[final] ).
cnf(c_0_1631,plain,
( X4 = X5
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)),X4))
| ~ hBOOL(hAPP(hAPP(hAPP(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_1224,
[final] ).
cnf(c_0_1632,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OVar(X2)),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(hAPP(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_0_1225,
[final] ).
cnf(c_0_1633,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)),X4)) ),
c_0_1226,
[final] ).
cnf(c_0_1634,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)),X4)) ),
c_0_1227,
[final] ).
cnf(c_0_1635,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X5,tc_Lambda_OdB,tc_Lambda_OdB)),X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),c_List_Ofoldr(c_Type_Otype_OFun,X3,X4,tc_Type_Otype,tc_Type_Otype)))
| ~ c_Type_Otypings(X1,X5,X3) ),
c_0_1228,
[final] ).
cnf(c_0_1636,plain,
c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),X3)),X4),X2,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3),X4),
c_0_1229,
[final] ).
cnf(c_0_1637,plain,
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X1,X2,X3),tc_Lambda_OdB,tc_Lambda_OdB) = X3
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
c_0_1230,
[final] ).
cnf(c_0_1638,plain,
( c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xvar__app__typesE__1__1(X4,X1,X2,X3))
| ~ hBOOL(hAPP(hAPP(hAPP(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_0_1231,
[final] ).
cnf(c_0_1639,plain,
( c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xlist__app__typeD__1__1(X4,X1,X2,X3))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)),X4)) ),
c_0_1232,
[final] ).
cnf(c_0_1640,plain,
( c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xlist__app__typeE__1__1(X4,X1,X2,X3))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)),X4)) ),
c_0_1233,
[final] ).
cnf(c_0_1641,plain,
( c_ListOrder_Ostep1(c_Lambda_Obeta,X2,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X1,X2,X3),tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
c_0_1234,
[final] ).
cnf(c_0_1642,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_1235,
[final] ).
cnf(c_0_1643,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_1236,
[final] ).
cnf(c_0_1644,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_1237,
[final] ).
cnf(c_0_1645,plain,
c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),v_u____)),v_i____),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
c_0_1238,
[final] ).
cnf(c_0_1646,plain,
c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),v_u____)),v_i____),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
c_0_1239,
[final] ).
cnf(c_0_1647,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_1240,
[final] ).
cnf(c_0_1648,plain,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),c_Lambda_OdB_OVar(v_n____)),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)))),
c_0_1241,
[final] ).
cnf(c_0_1649,plain,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_H____)),
c_0_1242,
[final] ).
cnf(c_0_1650,plain,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_ea______),v_ia______),v_T____)),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_Ha______)),
c_0_1243,
[final] ).
cnf(c_0_1651,plain,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_e____),v_u____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)))),
c_0_1244,
[final] ).
cnf(c_0_1652,plain,
c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X1),X3),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),X3),X2,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3),
c_0_1245,
[final] ).
cnf(c_0_1653,plain,
( c_Type_Otypings(X1,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),X2)),X4),X5,tc_Lambda_OdB,tc_Lambda_OdB),X6)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),X3))
| ~ c_Type_Otypings(hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X4),X3),X5,X6) ),
c_0_1246,
[final] ).
cnf(c_0_1654,plain,
c_Fun_Ofcomp(c_Fun_Ofcomp(X1,X2,X3,X4,X5),X6,X3,X5,X7) = c_Fun_Ofcomp(X1,c_Fun_Ofcomp(X2,X6,X4,X5,X7),X3,X4,X7),
c_0_1247,
[final] ).
cnf(c_0_1655,plain,
c_Fun_Ocomp(X1,c_Fun_Ocomp(X2,X3,X4,X5,X6),X5,X7,X6) = c_Fun_Ocomp(c_Fun_Ocomp(X1,X2,X5,X7,X4),X3,X4,X7,X6),
c_0_1248,
[final] ).
cnf(c_0_1656,plain,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
c_0_1249,
[final] ).
cnf(c_0_1657,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X4,X1,X2,X3)),X4)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)),X4)) ),
c_0_1250,
[final] ).
cnf(c_0_1658,plain,
( hAPP(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6) = hAPP(c_Fun_Ocomp(X7,X8,X9,X4,X10),X11)
| hAPP(X1,hAPP(X2,X6)) != hAPP(X7,hAPP(X8,X11)) ),
c_0_1251,
[final] ).
cnf(c_0_1659,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_1252,
[final] ).
cnf(c_0_1660,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),c_HOL_Ozero__class_Ozero(tc_nat)),c_Type_Osko__Type__Xtyping__elims__3__1(X3,X1,X2))),X2),c_Type_Osko__Type__Xtyping__elims__3__2(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OAbs(X2)),X3)) ),
c_0_1253,
[final] ).
cnf(c_0_1661,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4)),X5))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X4),X6)),X2),X5))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X3),X6)) ),
c_0_1254,
[final] ).
cnf(c_0_1662,plain,
( hAPP(X1,hAPP(X2,X3)) = hAPP(X4,hAPP(X5,X3))
| c_Fun_Ocomp(X1,X2,X6,X7,X8) != c_Fun_Ocomp(X4,X5,X9,X7,X8) ),
c_0_1255,
[final] ).
cnf(c_0_1663,plain,
( hAPP(X1,hAPP(X2,X3)) = hAPP(X4,X3)
| c_Fun_Ocomp(X1,X2,X5,X6,X7) != c_Fun_Ocomp(c_Fun_Oid(X6),X4,X6,X6,X7) ),
c_0_1256,
[final] ).
cnf(c_0_1664,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_1257,
[final] ).
cnf(c_0_1665,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_1258,
[final] ).
cnf(c_0_1666,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_1259,
[final] ).
cnf(c_0_1667,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_1260,
[final] ).
cnf(c_0_1668,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_1261,
[final] ).
cnf(c_0_1669,plain,
c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB),
c_0_1262,
[final] ).
cnf(c_0_1670,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_1263,
[final] ).
cnf(c_0_1671,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_1264,
[final] ).
cnf(c_0_1672,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_1265,
[final] ).
cnf(c_0_1673,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X6),X3)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X2),X3),X4)),X1),X5))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X2),X6),X4))
| hAPP(hAPP(c_Type_Otype_OFun,X4),X7) != v_T____ ),
c_0_1266,
[final] ).
cnf(c_0_1674,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X6),X3)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X2),X3),X4)),X1),X5))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X2),X6),X4))
| hAPP(hAPP(c_Type_Otype_OFun,X7),X4) != v_T____ ),
c_0_1267,
[final] ).
cnf(c_0_1675,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),X4),X2)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X2),v_T____)),v_b____),X3))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X4),v_T____)) ),
c_0_1268,
[final] ).
cnf(c_0_1676,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),X4),X2)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X2),v_T____)),v_b____),X3))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X4),v_T____)) ),
c_0_1269,
[final] ).
cnf(c_0_1677,plain,
c_List_Omap(X1,c_List_Omap(X2,X3,X4,X5),X5,X6) = c_List_Omap(c_Fun_Ocomp(X1,X2,X5,X6,X4),X3,X4,X6),
c_0_1270,
[final] ).
cnf(c_0_1678,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OAbs(X3)),hAPP(hAPP(c_Type_Otype_OFun,X2),X4)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),c_HOL_Ozero__class_Ozero(tc_nat)),X2)),X3),X4)) ),
c_0_1271,
[final] ).
cnf(c_0_1679,plain,
( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),hAPP(hAPP(c_Lambda_Olift,X4),X1)),c_Suc(X2))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X5),X4),X2)),X1) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X5),X1)),X4),X2)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
c_0_1272,
[final] ).
cnf(c_0_1680,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),c_HOL_Ozero__class_Ozero(tc_nat)),c_Type_Osko__Type__Xabs__typeE__1__1(X1,X2))),X2),c_Type_Osko__Type__Xabs__typeE__1__2(X1,X2)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OAbs(X2)),X3)) ),
c_0_1273,
[final] ).
cnf(c_0_1681,plain,
hAPP(c_Fun_Ocomp(c_COMBK(X1,X2,X3),X4,X3,X2,t_a),v_x) = X1,
c_0_1274,
[final] ).
cnf(c_0_1682,plain,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_b____),v_sko__CHAINED__1(v_T____,v_b____,v_e____,v_i____))),
c_0_1275,
[final] ).
cnf(c_0_1683,plain,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_b____),v_sko__local__XCons__1__1(v_T____,v_b____,v_e____,v_i____))),
c_0_1276,
[final] ).
cnf(c_0_1684,plain,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_b____),v_sko__local__XCons__Xhyps__1__1(v_T____,v_b____,v_e____,v_i____))),
c_0_1277,
[final] ).
cnf(c_0_1685,plain,
c_Fun_Ocomp(c_Nat_Ocompow(X1,X3,X4,X4),c_Nat_Ocompow(X2,X3,X4,X4),X4,X4,X4) = c_Nat_Ocompow(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,X4,X4),
c_0_1278,
[final] ).
cnf(c_0_1686,plain,
hAPP(c_Fun_Ofcomp(X1,X2,X3,X4,X5),X6) = hAPP(X2,hAPP(X1,X6)),
c_0_1279,
[final] ).
cnf(c_0_1687,plain,
hAPP(c_Fun_Ocomp(X1,X2,X4,X5,X6),X3) = hAPP(X1,hAPP(X2,X3)),
c_0_1280,
[final] ).
cnf(c_0_1688,plain,
hAPP(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
c_0_1281,
[final] ).
cnf(c_0_1689,plain,
hAPP(c_Fun_Ofcomp(X1,X2,t_a,X3,X4),v_x) = hAPP(X2,hAPP(X1,v_x)),
c_0_1282,
[final] ).
cnf(c_0_1690,plain,
hAPP(c_Fun_Ocomp(X1,X2,X3,X4,t_a),v_x) = hAPP(X1,hAPP(X2,v_x)),
c_0_1283,
[final] ).
cnf(c_0_1691,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_1284,
[final] ).
cnf(c_0_1692,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_1285,
[final] ).
cnf(c_0_1693,plain,
hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) = v_T____,
c_0_1286,
[final] ).
cnf(c_0_1694,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X4),X5)),hAPP(hAPP(c_Lambda_Olift,X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),X3)) ),
c_0_1287,
[final] ).
cnf(c_0_1695,plain,
hAPP(hAPP(hAPP(c_Type_Oshift(X1),hAPP(hAPP(hAPP(c_Type_Oshift(X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X5)),c_Suc(X3)),X4) = hAPP(hAPP(hAPP(c_Type_Oshift(X1),hAPP(hAPP(hAPP(c_Type_Oshift(X1),X2),X3),X4)),c_HOL_Ozero__class_Ozero(tc_nat)),X5),
c_0_1288,
[final] ).
cnf(c_0_1696,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB),
c_0_1289,
[final] ).
cnf(c_0_1697,plain,
c_Fun_Ocomp(X2,c_Nat_Ocompow(X1,X2,X3,X3),X3,X3,X3) = c_Nat_Ocompow(c_Suc(X1),X2,X3,X3),
c_0_1290,
[final] ).
cnf(c_0_1698,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_1291,
[final] ).
cnf(c_0_1699,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_1292,
[final] ).
cnf(c_0_1700,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_1293,
[final] ).
cnf(c_0_1701,plain,
( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,X4),X2)),X1) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X4),X1)),X2)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
c_0_1294,
[final] ).
cnf(c_0_1702,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X3),c_Type_Osko__Type__Xtyping__elims__2__1(X4,X1,X2,X3)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)),X4)) ),
c_0_1295,
[final] ).
cnf(c_0_1703,plain,
( c_Type_Otypings(hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X4),X5),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),X4),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3)
| ~ c_Type_Otypings(X1,X2,X3) ),
c_0_1296,
[final] ).
cnf(c_0_1704,plain,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_a____),v_T_H_H____)),
c_0_1297,
[final] ).
cnf(c_0_1705,plain,
hAPP(c_Nat_Ocompow(X2,X1,X3,X3),hAPP(X1,X4)) = hAPP(X1,hAPP(c_Nat_Ocompow(X2,X1,X3,X3),X4)),
c_0_1298,
[final] ).
cnf(c_0_1706,plain,
( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB) ),
c_0_1299,
[final] ).
cnf(c_0_1707,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_1300,
[final] ).
cnf(c_0_1708,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_1301,
[final] ).
cnf(c_0_1709,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_1302,
[final] ).
cnf(c_0_1710,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X5)),X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),hAPP(hAPP(c_Type_Otype_OFun,X3),X4)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X5),X3)) ),
c_0_1303,
[final] ).
cnf(c_0_1711,plain,
( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X3),X1)),hAPP(hAPP(c_Lambda_Olift,X4),X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat))) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X4),X2)),X1)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
c_0_1304,
[final] ).
cnf(c_0_1712,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_1305,
[final] ).
cnf(c_0_1713,plain,
c_Fun_Ofcomp(c_Fun_Oid(X1),X2,X1,X1,X3) = X2,
c_0_1306,
[final] ).
cnf(c_0_1714,plain,
c_Fun_Ofcomp(X1,c_Fun_Oid(X2),X3,X2,X2) = X1,
c_0_1307,
[final] ).
cnf(c_0_1715,plain,
c_Fun_Ocomp(X1,c_Fun_Oid(X2),X2,X3,X2) = X1,
c_0_1308,
[final] ).
cnf(c_0_1716,plain,
c_Fun_Ocomp(c_Fun_Oid(X1),X2,X1,X1,X3) = X2,
c_0_1309,
[final] ).
cnf(c_0_1717,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_1310,
[final] ).
cnf(c_0_1718,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_1311,
[final] ).
cnf(c_0_1719,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_1312,
[final] ).
cnf(c_0_1720,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),X3),X4),
c_0_1313,
[final] ).
cnf(c_0_1721,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_1314,
[final] ).
cnf(c_0_1722,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_1315,
[final] ).
cnf(c_0_1723,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_1316,
[final] ).
cnf(c_0_1724,plain,
( c_Nat_Osemiring__1__class_Oof__nat__aux(hAPP(hAPP(c_COMBC(X2,X2,X2),c_HOL_Oplus__class_Oplus(X2)),c_HOL_Oone__class_Oone(X2)),X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_Nat_Osemiring__1__class_Oof__nat(X1,X2)
| ~ class_Ring__and__Field_Osemiring__1(X2) ),
c_0_1317,
[final] ).
cnf(c_0_1725,plain,
hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)))),
c_0_1318,
[final] ).
cnf(c_0_1726,plain,
c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),hAPP(hAPP(c_Lambda_Olift,X2),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)))) = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(X1)),X2),X3),
c_0_1319,
[final] ).
cnf(c_0_1727,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_1320,
[final] ).
cnf(c_0_1728,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_1321,
[final] ).
cnf(c_0_1729,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X3),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X3),X1),X4)) ),
c_0_1322,
[final] ).
cnf(c_0_1730,plain,
( hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(X3,X1,X2)),c_Type_Osko__Type__Xtyping__elims__3__2(X3,X1,X2)) = X3
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OAbs(X2)),X3)) ),
c_0_1323,
[final] ).
cnf(c_0_1731,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_1324,
[final] ).
cnf(c_0_1732,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_1325,
[final] ).
cnf(c_0_1733,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_1326,
[final] ).
cnf(c_0_1734,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_1327,
[final] ).
cnf(c_0_1735,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_1328,
[final] ).
cnf(c_0_1736,plain,
( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X3),X1)),c_Suc(X2)) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X3),X2)),X1)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
c_0_1329,
[final] ).
cnf(c_0_1737,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X1,tc_Type_Otype)),c_Nat_Osize__class_Osize(X2,tc_Type_Otype))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,X1),X2),tc_Type_Otype),
c_0_1330,
[final] ).
cnf(c_0_1738,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
c_0_1331,
[final] ).
cnf(c_0_1739,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X2),X4)) ),
c_0_1332,
[final] ).
cnf(c_0_1740,plain,
hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
c_0_1333,
[final] ).
cnf(c_0_1741,plain,
( c_Nat_Osemiring__1__class_Oof__nat__aux(X1,X2,hAPP(X1,X3),X4) = c_Nat_Osemiring__1__class_Oof__nat__aux(X1,c_Suc(X2),X3,X4)
| ~ class_Ring__and__Field_Osemiring__1(X4) ),
c_0_1334,
[final] ).
cnf(c_0_1742,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_1335,
[final] ).
cnf(c_0_1743,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_1336,
[final] ).
cnf(c_0_1744,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(X1,X3,X4)),c_Lambda_Osubstn(X2,X3,X4)) = c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),X3,X4),
c_0_1337,
[final] ).
cnf(c_0_1745,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(X1,X2,X4)),c_Lambda_Oliftn(X1,X3,X4)) = c_Lambda_Oliftn(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4),
c_0_1338,
[final] ).
cnf(c_0_1746,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_1339,
[final] ).
cnf(c_0_1747,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_1340,
[final] ).
cnf(c_0_1748,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_1341,
[final] ).
cnf(c_0_1749,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_1342,
[final] ).
cnf(c_0_1750,plain,
( hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(X3),X4),X1),X5),X2) = hAPP(X4,c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1343,
[final] ).
cnf(c_0_1751,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_1344,
[final] ).
cnf(c_0_1752,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X1),X3)),hAPP(hAPP(c_Lambda_Olift,X2),X3)) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),X3),
c_0_1345,
[final] ).
cnf(c_0_1753,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_1346,
[final] ).
cnf(c_0_1754,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_1347,
[final] ).
cnf(c_0_1755,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_1348,
[final] ).
cnf(c_0_1756,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_1349,
[final] ).
cnf(c_0_1757,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_1350,
[final] ).
cnf(c_0_1758,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_1351,
[final] ).
cnf(c_0_1759,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_1352,
[final] ).
cnf(c_0_1760,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_1353,
[final] ).
cnf(c_0_1761,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_1354,
[final] ).
cnf(c_0_1762,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(X1)),c_Type_Otype_Otype__size(X2))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X1),X2)),
c_0_1355,
[final] ).
cnf(c_0_1763,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_1356,
[final] ).
cnf(c_0_1764,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_1357,
[final] ).
cnf(c_0_1765,plain,
hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X1),X2)),X3),X2) = X1,
c_0_1358,
[final] ).
cnf(c_0_1766,plain,
hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),c_Lambda_Oliftn(X3,X2,c_HOL_Ozero__class_Ozero(tc_nat))),X3) = c_Lambda_Osubstn(X1,X2,X3),
c_0_1359,
[final] ).
cnf(c_0_1767,plain,
c_Lambda_OdB_OAbs(c_Lambda_Osubstn(X1,X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)))) = c_Lambda_Osubstn(c_Lambda_OdB_OAbs(X1),X2,X3),
c_0_1360,
[final] ).
cnf(c_0_1768,plain,
c_Lambda_OdB_OAbs(c_Lambda_Oliftn(X1,X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)))) = c_Lambda_Oliftn(X1,c_Lambda_OdB_OAbs(X2),X3),
c_0_1361,
[final] ).
cnf(c_0_1769,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3)),
c_0_1362,
[final] ).
cnf(c_0_1770,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_1363,
[final] ).
cnf(c_0_1771,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_1364,
[final] ).
cnf(c_0_1772,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_1365,
[final] ).
cnf(c_0_1773,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_1366,
[final] ).
cnf(c_0_1774,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_1367,
[final] ).
cnf(c_0_1775,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_1368,
[final] ).
cnf(c_0_1776,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_1369,
[final] ).
cnf(c_0_1777,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_1370,
[final] ).
cnf(c_0_1778,plain,
( hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(X3),X4),X2),X5),X1) = hAPP(X4,X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1371,
[final] ).
cnf(c_0_1779,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_1372,
[final] ).
cnf(c_0_1780,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X1),X2,tc_nat),c_Suc(X3),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),
c_0_1373,
[final] ).
cnf(c_0_1781,plain,
( hAPP(X1,X2) = X3
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OVar(X2)),X3)) ),
c_0_1374,
[final] ).
cnf(c_0_1782,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_1375,
[final] ).
cnf(c_0_1783,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_1376,
[final] ).
cnf(c_0_1784,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_1377,
[final] ).
cnf(c_0_1785,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_1378,
[final] ).
cnf(c_0_1786,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_1379,
[final] ).
cnf(c_0_1787,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_1380,
[final] ).
cnf(c_0_1788,plain,
c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)))) = hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(X1)),X2),
c_0_1381,
[final] ).
cnf(c_0_1789,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_1382,
[final] ).
cnf(c_0_1790,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_1383,
[final] ).
cnf(c_0_1791,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_1384,
[final] ).
cnf(c_0_1792,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_1385,
[final] ).
cnf(c_0_1793,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_1386,
[final] ).
cnf(c_0_1794,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
c_0_1387,
[final] ).
cnf(c_0_1795,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat),
c_0_1388,
[final] ).
cnf(c_0_1796,plain,
hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(X1,X2,X3)),X3) = c_Lambda_Oliftn(c_Suc(X1),X2,X3),
c_0_1389,
[final] ).
cnf(c_0_1797,plain,
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X2)),X3),X1) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1390,
[final] ).
cnf(c_0_1798,plain,
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X2)),X3),X1) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1391,
[final] ).
cnf(c_0_1799,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_1392,
[final] ).
cnf(c_0_1800,plain,
c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),
c_0_1393,
[final] ).
cnf(c_0_1801,plain,
c_HOL_Ominus__class_Ominus(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_Ominus__class_Ominus(X2,X3,tc_nat),
c_0_1394,
[final] ).
cnf(c_0_1802,plain,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),
c_0_1395,
[final] ).
cnf(c_0_1803,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_1396,
[final] ).
cnf(c_0_1804,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_1397,
[final] ).
cnf(c_0_1805,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_1398,
[final] ).
cnf(c_0_1806,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3)),
c_0_1399,
[final] ).
cnf(c_0_1807,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_1400,
[final] ).
cnf(c_0_1808,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_1401,
[final] ).
cnf(c_0_1809,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_1402,
[final] ).
cnf(c_0_1810,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_1403,
[final] ).
cnf(c_0_1811,plain,
( c_Nat_Osemiring__1__class_Oof__nat__aux(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2,X3) = X2
| ~ class_Ring__and__Field_Osemiring__1(X3) ),
c_0_1404,
[final] ).
cnf(c_0_1812,plain,
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1405,
[final] ).
cnf(c_0_1813,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Suc(X2),tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
c_0_1406,
[final] ).
cnf(c_0_1814,plain,
c_Nat_Ocompow(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2,X2) = c_Fun_Oid(X2),
c_0_1407,
[final] ).
cnf(c_0_1815,plain,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OVar(X2)),hAPP(X1,X2))),
c_0_1408,
[final] ).
cnf(c_0_1816,plain,
hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(X1),X2),X3),X4),X3) = X4,
c_0_1409,
[final] ).
cnf(c_0_1817,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_1410,
[final] ).
cnf(c_0_1818,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_1411,
[final] ).
cnf(c_0_1819,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_1412,
[final] ).
cnf(c_0_1820,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),tc_nat),
c_0_1413,
[final] ).
cnf(c_0_1821,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1)),tc_nat),
c_0_1414,
[final] ).
cnf(c_0_1822,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),tc_nat),
c_0_1415,
[final] ).
cnf(c_0_1823,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_1416,
[final] ).
cnf(c_0_1824,plain,
c_Type_Otypings(hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____),v_as____,v_Ts____),
c_0_1417,
[final] ).
cnf(c_0_1825,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_1418,
[final] ).
cnf(c_0_1826,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_1419,
[final] ).
cnf(c_0_1827,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_1420,
[final] ).
cnf(c_0_1828,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_1421,
[final] ).
cnf(c_0_1829,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_1422,
[final] ).
cnf(c_0_1830,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_1423,
[final] ).
cnf(c_0_1831,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_1424,
[final] ).
cnf(c_0_1832,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_1425,
[final] ).
cnf(c_0_1833,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_1426,
[final] ).
cnf(c_0_1834,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_1427,
[final] ).
cnf(c_0_1835,plain,
( c_HOL_Oord__class_Oless(c_Suc(X1),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
c_0_1428,
[final] ).
cnf(c_0_1836,plain,
~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X2,tc_nat),
c_0_1429,
[final] ).
cnf(c_0_1837,plain,
~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X1,tc_nat),
c_0_1430,
[final] ).
cnf(c_0_1838,plain,
( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
c_0_1431,
[final] ).
cnf(c_0_1839,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) = c_HOL_Ominus__class_Ominus(X1,c_Suc(X2),tc_nat),
c_0_1432,
[final] ).
cnf(c_0_1840,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X1),X2)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
c_0_1433,
[final] ).
cnf(c_0_1841,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_1434,
[final] ).
cnf(c_0_1842,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1)),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_1435,
[final] ).
cnf(c_0_1843,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_1436,
[final] ).
cnf(c_0_1844,plain,
( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
c_0_1437,
[final] ).
cnf(c_0_1845,plain,
( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
c_0_1438,
[final] ).
cnf(c_0_1846,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X1)),X2) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat))) ),
c_0_1439,
[final] ).
cnf(c_0_1847,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_1440,
[final] ).
cnf(c_0_1848,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_1441,
[final] ).
cnf(c_0_1849,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_1442,
[final] ).
cnf(c_0_1850,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_1443,
[final] ).
cnf(c_0_1851,plain,
hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3)),
c_0_1444,
[final] ).
cnf(c_0_1852,plain,
hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3)),
c_0_1445,
[final] ).
cnf(c_0_1853,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_1446,
[final] ).
cnf(c_0_1854,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_1447,
[final] ).
cnf(c_0_1855,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_1448,
[final] ).
cnf(c_0_1856,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_1449,
[final] ).
cnf(c_0_1857,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_1450,
[final] ).
cnf(c_0_1858,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_1451,
[final] ).
cnf(c_0_1859,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1452,
[final] ).
cnf(c_0_1860,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1453,
[final] ).
cnf(c_0_1861,plain,
( ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
c_0_1454,
[final] ).
cnf(c_0_1862,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_1455,
[final] ).
cnf(c_0_1863,plain,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Oone__class_Oone(X2)),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
c_0_1456,
[final] ).
cnf(c_0_1864,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_1457,
[final] ).
cnf(c_0_1865,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_1458,
[final] ).
cnf(c_0_1866,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_1459,
[final] ).
cnf(c_0_1867,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_1460,
[final] ).
cnf(c_0_1868,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_1461,
[final] ).
cnf(c_0_1869,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_1462,
[final] ).
cnf(c_0_1870,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_1463,
[final] ).
cnf(c_0_1871,plain,
c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_Suc(X1),tc_nat),
c_0_1464,
[final] ).
cnf(c_0_1872,plain,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X1)),X2)),
c_0_1465,
[final] ).
cnf(c_0_1873,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat) ),
c_0_1466,
[final] ).
cnf(c_0_1874,plain,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_ea______),v_ua______),v_T____)),
c_0_1467,
[final] ).
cnf(c_0_1875,plain,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_e____),v_u____),v_T____)),
c_0_1468,
[final] ).
cnf(c_0_1876,plain,
c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X1)),X2),
c_0_1469,
[final] ).
cnf(c_0_1877,plain,
( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1470,
[final] ).
cnf(c_0_1878,plain,
( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1471,
[final] ).
cnf(c_0_1879,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
c_0_1472,
[final] ).
cnf(c_0_1880,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
c_0_1473,
[final] ).
cnf(c_0_1881,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
c_0_1474,
[final] ).
cnf(c_0_1882,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_1475,
[final] ).
cnf(c_0_1883,plain,
( c_Suc(X1) = X2
| c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1476,
[final] ).
cnf(c_0_1884,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_1477,
[final] ).
cnf(c_0_1885,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_1478,
[final] ).
cnf(c_0_1886,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_1479,
[final] ).
cnf(c_0_1887,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat) ),
c_0_1480,
[final] ).
cnf(c_0_1888,plain,
c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_Suc(X2)),
c_0_1481,
[final] ).
cnf(c_0_1889,plain,
hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Osubstn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_1482,
[final] ).
cnf(c_0_1890,plain,
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),
c_0_1483,
[final] ).
cnf(c_0_1891,plain,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X1,tc_nat) = X2,
c_0_1484,
[final] ).
cnf(c_0_1892,plain,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X2,tc_nat) = X1,
c_0_1485,
[final] ).
cnf(c_0_1893,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_1486,
[final] ).
cnf(c_0_1894,plain,
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1487,
[final] ).
cnf(c_0_1895,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_1488,
[final] ).
cnf(c_0_1896,plain,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
c_0_1489,
[final] ).
cnf(c_0_1897,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_1490,
[final] ).
cnf(c_0_1898,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_1491,
[final] ).
cnf(c_0_1899,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_1492,
[final] ).
cnf(c_0_1900,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_1493,
[final] ).
cnf(c_0_1901,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_1494,
[final] ).
cnf(c_0_1902,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_1495,
[final] ).
cnf(c_0_1903,plain,
( X1 = X2
| hAPP(hAPP(c_Type_Otype_OFun,X1),X3) != hAPP(hAPP(c_Type_Otype_OFun,X2),X4) ),
c_0_1496,
[final] ).
cnf(c_0_1904,plain,
( X1 = X2
| hAPP(hAPP(c_Type_Otype_OFun,X3),X1) != hAPP(hAPP(c_Type_Otype_OFun,X4),X2) ),
c_0_1497,
[final] ).
cnf(c_0_1905,plain,
( X1 = X2
| hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4) ),
c_0_1498,
[final] ).
cnf(c_0_1906,plain,
( X1 = X2
| hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X4),X2) ),
c_0_1499,
[final] ).
cnf(c_0_1907,plain,
c_HOL_Ominus__class_Ominus(c_Suc(X1),c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),
c_0_1500,
[final] ).
cnf(c_0_1908,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Oone__class_Oone(X2)),c_Nat_Osemiring__1__class_Oof__nat(X1,X2)) = c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X1),X2)
| ~ class_Ring__and__Field_Osemiring__1(X2) ),
c_0_1501,
[final] ).
cnf(c_0_1909,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
c_0_1502,
[final] ).
cnf(c_0_1910,plain,
( c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
c_0_1503,
[final] ).
cnf(c_0_1911,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_1504,
[final] ).
cnf(c_0_1912,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_1505,
[final] ).
cnf(c_0_1913,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_1506,
[final] ).
cnf(c_0_1914,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_1507,
[final] ).
cnf(c_0_1915,plain,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1) = X2,
c_0_1508,
[final] ).
cnf(c_0_1916,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X1)),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_Suc(X2)),
c_0_1509,
[final] ).
cnf(c_0_1917,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
c_0_1510,
[final] ).
cnf(c_0_1918,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
c_0_1511,
[final] ).
cnf(c_0_1919,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_1512,
[final] ).
cnf(c_0_1920,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
c_0_1513,
[final] ).
cnf(c_0_1921,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_1514,
[final] ).
cnf(c_0_1922,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_1515,
[final] ).
cnf(c_0_1923,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
c_0_1516,
[final] ).
cnf(c_0_1924,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_1517,
[final] ).
cnf(c_0_1925,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_1518,
[final] ).
cnf(c_0_1926,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_1519,
[final] ).
cnf(c_0_1927,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_1520,
[final] ).
cnf(c_0_1928,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_1521,
[final] ).
cnf(c_0_1929,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_1522,
[final] ).
cnf(c_0_1930,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_1523,
[final] ).
cnf(c_0_1931,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_1524,
[final] ).
cnf(c_0_1932,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
c_0_1525,
[final] ).
cnf(c_0_1933,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_1526,
[final] ).
cnf(c_0_1934,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
c_0_1527,
[final] ).
cnf(c_0_1935,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),
c_0_1528,
[final] ).
cnf(c_0_1936,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_1529,
[final] ).
cnf(c_0_1937,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_1530,
[final] ).
cnf(c_0_1938,plain,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_1531,
[final] ).
cnf(c_0_1939,plain,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_1532,
[final] ).
cnf(c_0_1940,plain,
( X1 = X2
| ~ c_fequal(X1,X2,X3) ),
c_0_1533,
[final] ).
cnf(c_0_1941,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
c_0_1534,
[final] ).
cnf(c_0_1942,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
c_0_1535,
[final] ).
cnf(c_0_1943,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
c_0_1536,
[final] ).
cnf(c_0_1944,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_1537,
[final] ).
cnf(c_0_1945,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_1538,
[final] ).
cnf(c_0_1946,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_1539,
[final] ).
cnf(c_0_1947,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_1540,
[final] ).
cnf(c_0_1948,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_1541,
[final] ).
cnf(c_0_1949,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != X2 ),
c_0_1542,
[final] ).
cnf(c_0_1950,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != X2 ),
c_0_1543,
[final] ).
cnf(c_0_1951,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_1544,
[final] ).
cnf(c_0_1952,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_1545,
[final] ).
cnf(c_0_1953,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_1546,
[final] ).
cnf(c_0_1954,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_1547,
[final] ).
cnf(c_0_1955,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
c_0_1548,
[final] ).
cnf(c_0_1956,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_1549,
[final] ).
cnf(c_0_1957,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_1550,
[final] ).
cnf(c_0_1958,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_1551,
[final] ).
cnf(c_0_1959,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_1552,
[final] ).
cnf(c_0_1960,plain,
( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_1553,
[final] ).
cnf(c_0_1961,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
c_0_1554,
[final] ).
cnf(c_0_1962,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_1555,
[final] ).
cnf(c_0_1963,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
c_0_1556,
[final] ).
cnf(c_0_1964,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_1557,
[final] ).
cnf(c_0_1965,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
c_0_1558,
[final] ).
cnf(c_0_1966,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_1559,
[final] ).
cnf(c_0_1967,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_1560,
[final] ).
cnf(c_0_1968,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OAbs(X3),
c_0_1561,
[final] ).
cnf(c_0_1969,plain,
c_Lambda_OdB_OAbs(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
c_0_1562,
[final] ).
cnf(c_0_1970,plain,
c_Lambda_OdB_OVar(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
c_0_1563,
[final] ).
cnf(c_0_1971,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OVar(X3),
c_0_1564,
[final] ).
cnf(c_0_1972,plain,
c_HOL_Ominus__class_Ominus(c_Suc(X1),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1,
c_0_1565,
[final] ).
cnf(c_0_1973,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
c_0_1566,
[final] ).
cnf(c_0_1974,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
c_0_1567,
[final] ).
cnf(c_0_1975,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_1568,
[final] ).
cnf(c_0_1976,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
c_0_1569,
[final] ).
cnf(c_0_1977,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
c_0_1570,
[final] ).
cnf(c_0_1978,plain,
c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = X1,
c_0_1571,
[final] ).
cnf(c_0_1979,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1572,
[final] ).
cnf(c_0_1980,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),
c_0_1573,
[final] ).
cnf(c_0_1981,plain,
c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
c_0_1574,
[final] ).
cnf(c_0_1982,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X1) = c_Suc(X1),
c_0_1575,
[final] ).
cnf(c_0_1983,plain,
c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1576,
[final] ).
cnf(c_0_1984,plain,
c_fequal(X1,X1,X2),
c_0_1577,
[final] ).
cnf(c_0_1985,plain,
c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(X1,X2),X2) = c_Transitive__Closure_Ortranclp(X1,X2),
c_0_1578,
[final] ).
cnf(c_0_1986,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_1579,
[final] ).
cnf(c_0_1987,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1) = X1,
c_0_1580,
[final] ).
cnf(c_0_1988,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)) = c_Suc(X1),
c_0_1581,
[final] ).
cnf(c_0_1989,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)) = X1,
c_0_1582,
[final] ).
cnf(c_0_1990,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)) = X1,
c_0_1583,
[final] ).
cnf(c_0_1991,plain,
hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X1))),
c_0_1584,
[final] ).
cnf(c_0_1992,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
c_0_1585,
[final] ).
cnf(c_0_1993,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
c_0_1586,
[final] ).
cnf(c_0_1994,plain,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
c_0_1587,
[final] ).
cnf(c_0_1995,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_1588,
[final] ).
cnf(c_0_1996,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
c_0_1589,
[final] ).
cnf(c_0_1997,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_ua______)),
c_0_1590,
[final] ).
cnf(c_0_1998,plain,
hAPP(c_Fun_Oid(X1),X2) = X2,
c_0_1591,
[final] ).
cnf(c_0_1999,plain,
( c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
c_0_1592,
[final] ).
cnf(c_0_2000,plain,
( c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
c_0_1593,
[final] ).
cnf(c_0_2001,plain,
hAPP(c_Fun_Oid(t_a),v_x) = v_x,
c_0_1594,
[final] ).
cnf(c_0_2002,plain,
( X1 = X2
| c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
c_0_1595,
[final] ).
cnf(c_0_2003,plain,
( X1 = X2
| c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
c_0_1596,
[final] ).
cnf(c_0_2004,plain,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
c_0_1597,
[final] ).
cnf(c_0_2005,plain,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
c_0_1598,
[final] ).
cnf(c_0_2006,plain,
c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OVar(X2),
c_0_1599,
[final] ).
cnf(c_0_2007,plain,
c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OAbs(X2),
c_0_1600,
[final] ).
cnf(c_0_2008,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1601,
[final] ).
cnf(c_0_2009,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1602,
[final] ).
cnf(c_0_2010,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1603,
[final] ).
cnf(c_0_2011,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1604,
[final] ).
cnf(c_0_2012,plain,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat),
c_0_1605,
[final] ).
cnf(c_0_2013,plain,
c_Suc(X1) != X1,
c_0_1606,
[final] ).
cnf(c_0_2014,plain,
c_Suc(X1) != X1,
c_0_1607,
[final] ).
cnf(c_0_2015,plain,
class_Orderings_Oorder(tc_bool),
c_0_1608,
[final] ).
cnf(c_0_2016,plain,
class_Orderings_Opreorder(tc_bool),
c_0_1609,
[final] ).
cnf(c_0_2017,plain,
class_Orderings_Oorder(tc_nat),
c_0_1610,
[final] ).
cnf(c_0_2018,plain,
class_Orderings_Olinorder(tc_nat),
c_0_1611,
[final] ).
cnf(c_0_2019,plain,
class_Orderings_Opreorder(tc_nat),
c_0_1612,
[final] ).
cnf(c_0_2020,plain,
class_Nat_Osemiring__char__0(tc_nat),
c_0_1613,
[final] ).
cnf(c_0_2021,plain,
class_OrderedGroup_Omonoid__add(tc_nat),
c_0_1614,
[final] ).
cnf(c_0_2022,plain,
class_Ring__and__Field_Osemiring__1(tc_nat),
c_0_1615,
[final] ).
cnf(c_0_2023,plain,
class_OrderedGroup_Osemigroup__add(tc_nat),
c_0_1616,
[final] ).
cnf(c_0_2024,plain,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
c_0_1617,
[final] ).
cnf(c_0_2025,plain,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
c_0_1618,
[final] ).
cnf(c_0_2026,plain,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
c_0_1619,
[final] ).
cnf(c_0_2027,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
c_0_1620,
[final] ).
cnf(c_0_2028,plain,
class_Ring__and__Field_Oordered__semidom(tc_nat),
c_0_1621,
[final] ).
cnf(c_0_2029,plain,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
c_0_1622,
[final] ).
cnf(c_0_2030,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
c_0_1623,
[final] ).
cnf(c_0_2031,plain,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
c_0_1624,
[final] ).
cnf(c_0_2032,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
c_0_1625,
[final] ).
cnf(c_0_2033,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
c_0_1626,
[final] ).
cnf(c_0_2034,plain,
v_i____ = v_n____,
c_0_1627,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_1629_0,axiom,
( c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4),X5,tc_Type_Otype,tc_Type_Otype) = X7
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB)),X5))
| ~ c_Type_Otypings(X1,X3,X6)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_1629]) ).
cnf(c_0_1629_1,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB)),X5))
| c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4),X5,tc_Type_Otype,tc_Type_Otype) = X7
| ~ c_Type_Otypings(X1,X3,X6)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_1629]) ).
cnf(c_0_1629_2,axiom,
( ~ c_Type_Otypings(X1,X3,X6)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB)),X5))
| c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4),X5,tc_Type_Otype,tc_Type_Otype) = X7
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_1629]) ).
cnf(c_0_1629_3,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)),X7))
| ~ c_Type_Otypings(X1,X3,X6)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB)),X5))
| c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4),X5,tc_Type_Otype,tc_Type_Otype) = X7 ),
inference(literals_permutation,[status(thm)],[c_0_1629]) ).
cnf(c_0_1630_0,axiom,
( c_Type_Otypings(X1,X4,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB)),X5))
| ~ c_Type_Otypings(X1,X3,X6)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_1630]) ).
cnf(c_0_1630_1,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB)),X5))
| c_Type_Otypings(X1,X4,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4))
| ~ c_Type_Otypings(X1,X3,X6)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_1630]) ).
cnf(c_0_1630_2,axiom,
( ~ c_Type_Otypings(X1,X3,X6)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB)),X5))
| c_Type_Otypings(X1,X4,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_1630]) ).
cnf(c_0_1630_3,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)),X7))
| ~ c_Type_Otypings(X1,X3,X6)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB)),X5))
| c_Type_Otypings(X1,X4,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1630]) ).
cnf(c_0_1631_0,axiom,
( X4 = X5
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)),X4))
| ~ hBOOL(hAPP(hAPP(hAPP(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_1631]) ).
cnf(c_0_1631_1,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(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
| ~ hBOOL(hAPP(hAPP(hAPP(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_1631]) ).
cnf(c_0_1631_2,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)),X5))
| ~ hBOOL(hAPP(hAPP(hAPP(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_1631]) ).
cnf(c_0_1632_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OVar(X2)),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1632]) ).
cnf(c_0_1632_1,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)),X4))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OVar(X2)),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype))) ),
inference(literals_permutation,[status(thm)],[c_0_1632]) ).
cnf(c_0_1633_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1633]) ).
cnf(c_0_1633_1,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)),X4))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype))) ),
inference(literals_permutation,[status(thm)],[c_0_1633]) ).
cnf(c_0_1634_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1634]) ).
cnf(c_0_1634_1,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)),X4))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype))) ),
inference(literals_permutation,[status(thm)],[c_0_1634]) ).
cnf(c_0_1635_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X5,tc_Lambda_OdB,tc_Lambda_OdB)),X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),c_List_Ofoldr(c_Type_Otype_OFun,X3,X4,tc_Type_Otype,tc_Type_Otype)))
| ~ c_Type_Otypings(X1,X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1635]) ).
cnf(c_0_1635_1,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),c_List_Ofoldr(c_Type_Otype_OFun,X3,X4,tc_Type_Otype,tc_Type_Otype)))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X5,tc_Lambda_OdB,tc_Lambda_OdB)),X4))
| ~ c_Type_Otypings(X1,X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1635]) ).
cnf(c_0_1635_2,axiom,
( ~ c_Type_Otypings(X1,X5,X3)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),c_List_Ofoldr(c_Type_Otype_OFun,X3,X4,tc_Type_Otype,tc_Type_Otype)))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X5,tc_Lambda_OdB,tc_Lambda_OdB)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1635]) ).
cnf(c_0_1637_0,axiom,
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X1,X2,X3),tc_Lambda_OdB,tc_Lambda_OdB) = X3
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1637]) ).
cnf(c_0_1637_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3))
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X1,X2,X3),tc_Lambda_OdB,tc_Lambda_OdB) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_1637]) ).
cnf(c_0_1638_0,axiom,
( c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xvar__app__typesE__1__1(X4,X1,X2,X3))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1638]) ).
cnf(c_0_1638_1,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(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_Otypings(X1,X3,c_Type_Osko__Type__Xvar__app__typesE__1__1(X4,X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1638]) ).
cnf(c_0_1639_0,axiom,
( c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xlist__app__typeD__1__1(X4,X1,X2,X3))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1639]) ).
cnf(c_0_1639_1,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)),X4))
| c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xlist__app__typeD__1__1(X4,X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1639]) ).
cnf(c_0_1640_0,axiom,
( c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xlist__app__typeE__1__1(X4,X1,X2,X3))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1640]) ).
cnf(c_0_1640_1,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)),X4))
| c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xlist__app__typeE__1__1(X4,X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1640]) ).
cnf(c_0_1641_0,axiom,
( c_ListOrder_Ostep1(c_Lambda_Obeta,X2,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X1,X2,X3),tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1641]) ).
cnf(c_0_1641_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3))
| c_ListOrder_Ostep1(c_Lambda_Obeta,X2,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X1,X2,X3),tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1641]) ).
cnf(c_0_1642_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_1642]) ).
cnf(c_0_1642_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_1642]) ).
cnf(c_0_1643_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_1643]) ).
cnf(c_0_1643_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_1643]) ).
cnf(c_0_1644_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_1644]) ).
cnf(c_0_1644_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_1644]) ).
cnf(c_0_1647_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_1647]) ).
cnf(c_0_1647_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_1647]) ).
cnf(c_0_1647_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_1647]) ).
cnf(c_0_1653_0,axiom,
( c_Type_Otypings(X1,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),X2)),X4),X5,tc_Lambda_OdB,tc_Lambda_OdB),X6)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),X3))
| ~ c_Type_Otypings(hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X4),X3),X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1653]) ).
cnf(c_0_1653_1,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),X3))
| c_Type_Otypings(X1,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),X2)),X4),X5,tc_Lambda_OdB,tc_Lambda_OdB),X6)
| ~ c_Type_Otypings(hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X4),X3),X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1653]) ).
cnf(c_0_1653_2,axiom,
( ~ c_Type_Otypings(hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X4),X3),X5,X6)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),X3))
| c_Type_Otypings(X1,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),X2)),X4),X5,tc_Lambda_OdB,tc_Lambda_OdB),X6) ),
inference(literals_permutation,[status(thm)],[c_0_1653]) ).
cnf(c_0_1657_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X4,X1,X2,X3)),X4)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1657]) ).
cnf(c_0_1657_1,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)),X4))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X4,X1,X2,X3)),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_1657]) ).
cnf(c_0_1658_0,axiom,
( hAPP(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6) = hAPP(c_Fun_Ocomp(X7,X8,X9,X4,X10),X11)
| hAPP(X1,hAPP(X2,X6)) != hAPP(X7,hAPP(X8,X11)) ),
inference(literals_permutation,[status(thm)],[c_0_1658]) ).
cnf(c_0_1658_1,axiom,
( hAPP(X1,hAPP(X2,X6)) != hAPP(X7,hAPP(X8,X11))
| hAPP(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6) = hAPP(c_Fun_Ocomp(X7,X8,X9,X4,X10),X11) ),
inference(literals_permutation,[status(thm)],[c_0_1658]) ).
cnf(c_0_1659_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_1659]) ).
cnf(c_0_1659_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_1659]) ).
cnf(c_0_1660_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),c_HOL_Ozero__class_Ozero(tc_nat)),c_Type_Osko__Type__Xtyping__elims__3__1(X3,X1,X2))),X2),c_Type_Osko__Type__Xtyping__elims__3__2(X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OAbs(X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1660]) ).
cnf(c_0_1660_1,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OAbs(X2)),X3))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),c_HOL_Ozero__class_Ozero(tc_nat)),c_Type_Osko__Type__Xtyping__elims__3__1(X3,X1,X2))),X2),c_Type_Osko__Type__Xtyping__elims__3__2(X3,X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1660]) ).
cnf(c_0_1661_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4)),X5))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X4),X6)),X2),X5))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X3),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_1661]) ).
cnf(c_0_1661_1,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X4),X6)),X2),X5))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4)),X5))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X3),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_1661]) ).
cnf(c_0_1661_2,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X3),X6))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X4),X6)),X2),X5))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1661]) ).
cnf(c_0_1662_0,axiom,
( hAPP(X1,hAPP(X2,X3)) = hAPP(X4,hAPP(X5,X3))
| c_Fun_Ocomp(X1,X2,X6,X7,X8) != c_Fun_Ocomp(X4,X5,X9,X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1662]) ).
cnf(c_0_1662_1,axiom,
( c_Fun_Ocomp(X1,X2,X6,X7,X8) != c_Fun_Ocomp(X4,X5,X9,X7,X8)
| hAPP(X1,hAPP(X2,X3)) = hAPP(X4,hAPP(X5,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1662]) ).
cnf(c_0_1663_0,axiom,
( hAPP(X1,hAPP(X2,X3)) = hAPP(X4,X3)
| c_Fun_Ocomp(X1,X2,X5,X6,X7) != c_Fun_Ocomp(c_Fun_Oid(X6),X4,X6,X6,X7) ),
inference(literals_permutation,[status(thm)],[c_0_1663]) ).
cnf(c_0_1663_1,axiom,
( c_Fun_Ocomp(X1,X2,X5,X6,X7) != c_Fun_Ocomp(c_Fun_Oid(X6),X4,X6,X6,X7)
| hAPP(X1,hAPP(X2,X3)) = hAPP(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1663]) ).
cnf(c_0_1664_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_1664]) ).
cnf(c_0_1664_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_1664]) ).
cnf(c_0_1665_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_1665]) ).
cnf(c_0_1665_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_1665]) ).
cnf(c_0_1666_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_1666]) ).
cnf(c_0_1666_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_1666]) ).
cnf(c_0_1667_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_1667]) ).
cnf(c_0_1667_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_1667]) ).
cnf(c_0_1668_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_1668]) ).
cnf(c_0_1668_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_1668]) ).
cnf(c_0_1670_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_1670]) ).
cnf(c_0_1670_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_1670]) ).
cnf(c_0_1671_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_1671]) ).
cnf(c_0_1671_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_1671]) ).
cnf(c_0_1672_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_1672]) ).
cnf(c_0_1672_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_1672]) ).
cnf(c_0_1673_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X6),X3)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X2),X3),X4)),X1),X5))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X2),X6),X4))
| hAPP(hAPP(c_Type_Otype_OFun,X4),X7) != v_T____ ),
inference(literals_permutation,[status(thm)],[c_0_1673]) ).
cnf(c_0_1673_1,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X6),X3)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X2),X3),X4)),X1),X5))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X2),X6),X4))
| hAPP(hAPP(c_Type_Otype_OFun,X4),X7) != v_T____ ),
inference(literals_permutation,[status(thm)],[c_0_1673]) ).
cnf(c_0_1673_2,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X2),X3),X4)),X1),X5))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X6),X3)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X2),X6),X4))
| hAPP(hAPP(c_Type_Otype_OFun,X4),X7) != v_T____ ),
inference(literals_permutation,[status(thm)],[c_0_1673]) ).
cnf(c_0_1673_3,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X2),X3),X4)),X1),X5))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X6),X3)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X2),X6),X4))
| hAPP(hAPP(c_Type_Otype_OFun,X4),X7) != v_T____ ),
inference(literals_permutation,[status(thm)],[c_0_1673]) ).
cnf(c_0_1673_4,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X2),X6),X4))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X2),X3),X4)),X1),X5))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X6),X3)))
| hAPP(hAPP(c_Type_Otype_OFun,X4),X7) != v_T____ ),
inference(literals_permutation,[status(thm)],[c_0_1673]) ).
cnf(c_0_1673_5,axiom,
( hAPP(hAPP(c_Type_Otype_OFun,X4),X7) != v_T____
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X2),X6),X4))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X2),X3),X4)),X1),X5))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X6),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1673]) ).
cnf(c_0_1674_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X6),X3)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X2),X3),X4)),X1),X5))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X2),X6),X4))
| hAPP(hAPP(c_Type_Otype_OFun,X7),X4) != v_T____ ),
inference(literals_permutation,[status(thm)],[c_0_1674]) ).
cnf(c_0_1674_1,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X6),X3)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X2),X3),X4)),X1),X5))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X2),X6),X4))
| hAPP(hAPP(c_Type_Otype_OFun,X7),X4) != v_T____ ),
inference(literals_permutation,[status(thm)],[c_0_1674]) ).
cnf(c_0_1674_2,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X2),X3),X4)),X1),X5))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X6),X3)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X2),X6),X4))
| hAPP(hAPP(c_Type_Otype_OFun,X7),X4) != v_T____ ),
inference(literals_permutation,[status(thm)],[c_0_1674]) ).
cnf(c_0_1674_3,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X2),X3),X4)),X1),X5))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X6),X3)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X2),X6),X4))
| hAPP(hAPP(c_Type_Otype_OFun,X7),X4) != v_T____ ),
inference(literals_permutation,[status(thm)],[c_0_1674]) ).
cnf(c_0_1674_4,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X2),X6),X4))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X2),X3),X4)),X1),X5))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X6),X3)))
| hAPP(hAPP(c_Type_Otype_OFun,X7),X4) != v_T____ ),
inference(literals_permutation,[status(thm)],[c_0_1674]) ).
cnf(c_0_1674_5,axiom,
( hAPP(hAPP(c_Type_Otype_OFun,X7),X4) != v_T____
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X2),X6),X4))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X2),X3),X4)),X1),X5))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X6),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1674]) ).
cnf(c_0_1675_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),X4),X2)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X2),v_T____)),v_b____),X3))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X4),v_T____)) ),
inference(literals_permutation,[status(thm)],[c_0_1675]) ).
cnf(c_0_1675_1,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X2),v_T____)),v_b____),X3))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),X4),X2)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X4),v_T____)) ),
inference(literals_permutation,[status(thm)],[c_0_1675]) ).
cnf(c_0_1675_2,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X2),v_T____)),v_b____),X3))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),X4),X2)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X4),v_T____)) ),
inference(literals_permutation,[status(thm)],[c_0_1675]) ).
cnf(c_0_1675_3,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X4),v_T____))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X2),v_T____)),v_b____),X3))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),X4),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1675]) ).
cnf(c_0_1676_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),X4),X2)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X2),v_T____)),v_b____),X3))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X4),v_T____)) ),
inference(literals_permutation,[status(thm)],[c_0_1676]) ).
cnf(c_0_1676_1,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X2),v_T____)),v_b____),X3))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),X4),X2)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X4),v_T____)) ),
inference(literals_permutation,[status(thm)],[c_0_1676]) ).
cnf(c_0_1676_2,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X2),v_T____)),v_b____),X3))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),X4),X2)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X4),v_T____)) ),
inference(literals_permutation,[status(thm)],[c_0_1676]) ).
cnf(c_0_1676_3,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X4),v_T____))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X2),v_T____)),v_b____),X3))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),X4),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1676]) ).
cnf(c_0_1678_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OAbs(X3)),hAPP(hAPP(c_Type_Otype_OFun,X2),X4)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),c_HOL_Ozero__class_Ozero(tc_nat)),X2)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1678]) ).
cnf(c_0_1678_1,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),c_HOL_Ozero__class_Ozero(tc_nat)),X2)),X3),X4))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OAbs(X3)),hAPP(hAPP(c_Type_Otype_OFun,X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_1678]) ).
cnf(c_0_1679_0,axiom,
( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),hAPP(hAPP(c_Lambda_Olift,X4),X1)),c_Suc(X2))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X5),X4),X2)),X1) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X5),X1)),X4),X2)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1679]) ).
cnf(c_0_1679_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),hAPP(hAPP(c_Lambda_Olift,X4),X1)),c_Suc(X2))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X5),X4),X2)),X1) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X5),X1)),X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1679]) ).
cnf(c_0_1680_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),c_HOL_Ozero__class_Ozero(tc_nat)),c_Type_Osko__Type__Xabs__typeE__1__1(X1,X2))),X2),c_Type_Osko__Type__Xabs__typeE__1__2(X1,X2)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OAbs(X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1680]) ).
cnf(c_0_1680_1,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OAbs(X2)),X3))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),c_HOL_Ozero__class_Ozero(tc_nat)),c_Type_Osko__Type__Xabs__typeE__1__1(X1,X2))),X2),c_Type_Osko__Type__Xabs__typeE__1__2(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1680]) ).
cnf(c_0_1691_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_1691]) ).
cnf(c_0_1691_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_1691]) ).
cnf(c_0_1692_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_1692]) ).
cnf(c_0_1692_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_1692]) ).
cnf(c_0_1694_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X4),X5)),hAPP(hAPP(c_Lambda_Olift,X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1694]) ).
cnf(c_0_1694_1,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),X3))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X4),X5)),hAPP(hAPP(c_Lambda_Olift,X2),X4)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1694]) ).
cnf(c_0_1698_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_1698]) ).
cnf(c_0_1698_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_1698]) ).
cnf(c_0_1699_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_1699]) ).
cnf(c_0_1699_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_1699]) ).
cnf(c_0_1700_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_1700]) ).
cnf(c_0_1700_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_1700]) ).
cnf(c_0_1701_0,axiom,
( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,X4),X2)),X1) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X4),X1)),X2)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1701]) ).
cnf(c_0_1701_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,X4),X2)),X1) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X4),X1)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1701]) ).
cnf(c_0_1702_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X3),c_Type_Osko__Type__Xtyping__elims__2__1(X4,X1,X2,X3)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1702]) ).
cnf(c_0_1702_1,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)),X4))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X3),c_Type_Osko__Type__Xtyping__elims__2__1(X4,X1,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1702]) ).
cnf(c_0_1703_0,axiom,
( c_Type_Otypings(hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X4),X5),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),X4),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3)
| ~ c_Type_Otypings(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1703]) ).
cnf(c_0_1703_1,axiom,
( ~ c_Type_Otypings(X1,X2,X3)
| c_Type_Otypings(hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X4),X5),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),X4),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1703]) ).
cnf(c_0_1706_0,axiom,
( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),c_HOL_Ozero__class_Ozero(tc_nat)),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_1706]) ).
cnf(c_0_1706_1,axiom,
( ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB)
| c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1706]) ).
cnf(c_0_1707_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_1707]) ).
cnf(c_0_1707_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_1707]) ).
cnf(c_0_1708_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_1708]) ).
cnf(c_0_1708_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_1708]) ).
cnf(c_0_1709_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_1709]) ).
cnf(c_0_1709_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_1709]) ).
cnf(c_0_1710_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X5)),X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),hAPP(hAPP(c_Type_Otype_OFun,X3),X4)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X5),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1710]) ).
cnf(c_0_1710_1,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),hAPP(hAPP(c_Type_Otype_OFun,X3),X4)))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X5)),X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X5),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1710]) ).
cnf(c_0_1710_2,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X5),X3))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),hAPP(hAPP(c_Type_Otype_OFun,X3),X4)))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X5)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1710]) ).
cnf(c_0_1711_0,axiom,
( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X3),X1)),hAPP(hAPP(c_Lambda_Olift,X4),X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat))) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X4),X2)),X1)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1711]) ).
cnf(c_0_1711_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X3),X1)),hAPP(hAPP(c_Lambda_Olift,X4),X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat))) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X4),X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1711]) ).
cnf(c_0_1712_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_1712]) ).
cnf(c_0_1712_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_1712]) ).
cnf(c_0_1717_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_1717]) ).
cnf(c_0_1717_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_1717]) ).
cnf(c_0_1717_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_1717]) ).
cnf(c_0_1718_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_1718]) ).
cnf(c_0_1718_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_1718]) ).
cnf(c_0_1719_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_1719]) ).
cnf(c_0_1719_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_1719]) ).
cnf(c_0_1721_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_1721]) ).
cnf(c_0_1721_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_1721]) ).
cnf(c_0_1722_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_1722]) ).
cnf(c_0_1722_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_1722]) ).
cnf(c_0_1723_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_1723]) ).
cnf(c_0_1723_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_1723]) ).
cnf(c_0_1724_0,axiom,
( c_Nat_Osemiring__1__class_Oof__nat__aux(hAPP(hAPP(c_COMBC(X2,X2,X2),c_HOL_Oplus__class_Oplus(X2)),c_HOL_Oone__class_Oone(X2)),X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_Nat_Osemiring__1__class_Oof__nat(X1,X2)
| ~ class_Ring__and__Field_Osemiring__1(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1724]) ).
cnf(c_0_1724_1,axiom,
( ~ class_Ring__and__Field_Osemiring__1(X2)
| c_Nat_Osemiring__1__class_Oof__nat__aux(hAPP(hAPP(c_COMBC(X2,X2,X2),c_HOL_Oplus__class_Oplus(X2)),c_HOL_Oone__class_Oone(X2)),X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_Nat_Osemiring__1__class_Oof__nat(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1724]) ).
cnf(c_0_1727_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_1727]) ).
cnf(c_0_1727_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_1727]) ).
cnf(c_0_1727_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_1727]) ).
cnf(c_0_1728_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_1728]) ).
cnf(c_0_1728_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_1728]) ).
cnf(c_0_1729_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X3),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X3),X1),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1729]) ).
cnf(c_0_1729_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X3),X2),X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X3),X1),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1729]) ).
cnf(c_0_1729_2,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X3),X1),X4))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X3),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1729]) ).
cnf(c_0_1730_0,axiom,
( hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(X3,X1,X2)),c_Type_Osko__Type__Xtyping__elims__3__2(X3,X1,X2)) = X3
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OAbs(X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1730]) ).
cnf(c_0_1730_1,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OAbs(X2)),X3))
| hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(X3,X1,X2)),c_Type_Osko__Type__Xtyping__elims__3__2(X3,X1,X2)) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_1730]) ).
cnf(c_0_1731_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_1731]) ).
cnf(c_0_1731_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_1731]) ).
cnf(c_0_1732_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_1732]) ).
cnf(c_0_1732_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_1732]) ).
cnf(c_0_1733_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_1733]) ).
cnf(c_0_1733_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_1733]) ).
cnf(c_0_1734_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_1734]) ).
cnf(c_0_1734_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_1734]) ).
cnf(c_0_1734_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_1734]) ).
cnf(c_0_1735_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_1735]) ).
cnf(c_0_1735_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_1735]) ).
cnf(c_0_1735_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_1735]) ).
cnf(c_0_1736_0,axiom,
( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X3),X1)),c_Suc(X2)) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X3),X2)),X1)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1736]) ).
cnf(c_0_1736_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X3),X1)),c_Suc(X2)) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X3),X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1736]) ).
cnf(c_0_1738_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1738]) ).
cnf(c_0_1738_1,axiom,
( c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1738]) ).
cnf(c_0_1739_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1739]) ).
cnf(c_0_1739_1,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),X3))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1739]) ).
cnf(c_0_1739_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X2),X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),X3))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1739]) ).
cnf(c_0_1741_0,axiom,
( c_Nat_Osemiring__1__class_Oof__nat__aux(X1,X2,hAPP(X1,X3),X4) = c_Nat_Osemiring__1__class_Oof__nat__aux(X1,c_Suc(X2),X3,X4)
| ~ class_Ring__and__Field_Osemiring__1(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1741]) ).
cnf(c_0_1741_1,axiom,
( ~ class_Ring__and__Field_Osemiring__1(X4)
| c_Nat_Osemiring__1__class_Oof__nat__aux(X1,X2,hAPP(X1,X3),X4) = c_Nat_Osemiring__1__class_Oof__nat__aux(X1,c_Suc(X2),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1741]) ).
cnf(c_0_1742_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_1742]) ).
cnf(c_0_1742_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_1742]) ).
cnf(c_0_1743_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_1743]) ).
cnf(c_0_1743_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_1743]) ).
cnf(c_0_1743_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_1743]) ).
cnf(c_0_1746_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_1746]) ).
cnf(c_0_1746_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_1746]) ).
cnf(c_0_1746_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_1746]) ).
cnf(c_0_1747_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_1747]) ).
cnf(c_0_1747_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_1747]) ).
cnf(c_0_1747_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_1747]) ).
cnf(c_0_1748_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_1748]) ).
cnf(c_0_1748_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_1748]) ).
cnf(c_0_1749_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_1749]) ).
cnf(c_0_1749_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_1749]) ).
cnf(c_0_1750_0,axiom,
( hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(X3),X4),X1),X5),X2) = hAPP(X4,c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1750]) ).
cnf(c_0_1750_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(X3),X4),X1),X5),X2) = hAPP(X4,c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1750]) ).
cnf(c_0_1751_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_1751]) ).
cnf(c_0_1751_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_1751]) ).
cnf(c_0_1751_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_1751]) ).
cnf(c_0_1751_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_1751]) ).
cnf(c_0_1753_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_1753]) ).
cnf(c_0_1753_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_1753]) ).
cnf(c_0_1753_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_1753]) ).
cnf(c_0_1754_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_1754]) ).
cnf(c_0_1754_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_1754]) ).
cnf(c_0_1755_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_1755]) ).
cnf(c_0_1755_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_1755]) ).
cnf(c_0_1756_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_1756]) ).
cnf(c_0_1756_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_1756]) ).
cnf(c_0_1757_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_1757]) ).
cnf(c_0_1757_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_1757]) ).
cnf(c_0_1758_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_1758]) ).
cnf(c_0_1758_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_1758]) ).
cnf(c_0_1759_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_1759]) ).
cnf(c_0_1759_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_1759]) ).
cnf(c_0_1760_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_1760]) ).
cnf(c_0_1760_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_1760]) ).
cnf(c_0_1760_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_1760]) ).
cnf(c_0_1761_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_1761]) ).
cnf(c_0_1761_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_1761]) ).
cnf(c_0_1763_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_1763]) ).
cnf(c_0_1763_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_1763]) ).
cnf(c_0_1763_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_1763]) ).
cnf(c_0_1764_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_1764]) ).
cnf(c_0_1764_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_1764]) ).
cnf(c_0_1770_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_1770]) ).
cnf(c_0_1770_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_1770]) ).
cnf(c_0_1770_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_1770]) ).
cnf(c_0_1770_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_1770]) ).
cnf(c_0_1771_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_1771]) ).
cnf(c_0_1771_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_1771]) ).
cnf(c_0_1771_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_1771]) ).
cnf(c_0_1771_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_1771]) ).
cnf(c_0_1772_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_1772]) ).
cnf(c_0_1772_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_1772]) ).
cnf(c_0_1772_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_1772]) ).
cnf(c_0_1773_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_1773]) ).
cnf(c_0_1773_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_1773]) ).
cnf(c_0_1773_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_1773]) ).
cnf(c_0_1774_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_1774]) ).
cnf(c_0_1774_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_1774]) ).
cnf(c_0_1774_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_1774]) ).
cnf(c_0_1775_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_1775]) ).
cnf(c_0_1775_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_1775]) ).
cnf(c_0_1775_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_1775]) ).
cnf(c_0_1776_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_1776]) ).
cnf(c_0_1776_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_1776]) ).
cnf(c_0_1776_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_1776]) ).
cnf(c_0_1776_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_1776]) ).
cnf(c_0_1777_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_1777]) ).
cnf(c_0_1777_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_1777]) ).
cnf(c_0_1777_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_1777]) ).
cnf(c_0_1778_0,axiom,
( hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(X3),X4),X2),X5),X1) = hAPP(X4,X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1778]) ).
cnf(c_0_1778_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(X3),X4),X2),X5),X1) = hAPP(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1778]) ).
cnf(c_0_1779_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_1779]) ).
cnf(c_0_1779_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_1779]) ).
cnf(c_0_1779_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_1779]) ).
cnf(c_0_1781_0,axiom,
( hAPP(X1,X2) = X3
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OVar(X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1781]) ).
cnf(c_0_1781_1,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OVar(X2)),X3))
| hAPP(X1,X2) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_1781]) ).
cnf(c_0_1782_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_1782]) ).
cnf(c_0_1782_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_1782]) ).
cnf(c_0_1782_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_1782]) ).
cnf(c_0_1783_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_1783]) ).
cnf(c_0_1783_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_1783]) ).
cnf(c_0_1783_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_1783]) ).
cnf(c_0_1784_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_1784]) ).
cnf(c_0_1784_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_1784]) ).
cnf(c_0_1784_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_1784]) ).
cnf(c_0_1785_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_1785]) ).
cnf(c_0_1785_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_1785]) ).
cnf(c_0_1785_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_1785]) ).
cnf(c_0_1786_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_1786]) ).
cnf(c_0_1786_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_1786]) ).
cnf(c_0_1786_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_1786]) ).
cnf(c_0_1786_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_1786]) ).
cnf(c_0_1787_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_1787]) ).
cnf(c_0_1787_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_1787]) ).
cnf(c_0_1787_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_1787]) ).
cnf(c_0_1787_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_1787]) ).
cnf(c_0_1789_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_1789]) ).
cnf(c_0_1789_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_1789]) ).
cnf(c_0_1790_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_1790]) ).
cnf(c_0_1790_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_1790]) ).
cnf(c_0_1791_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_1791]) ).
cnf(c_0_1791_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_1791]) ).
cnf(c_0_1792_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_1792]) ).
cnf(c_0_1792_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_1792]) ).
cnf(c_0_1793_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_1793]) ).
cnf(c_0_1793_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_1793]) ).
cnf(c_0_1794_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_1794]) ).
cnf(c_0_1794_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_1794]) ).
cnf(c_0_1797_0,axiom,
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X2)),X3),X1) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1797]) ).
cnf(c_0_1797_1,axiom,
( ~ 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(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1797]) ).
cnf(c_0_1798_0,axiom,
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X2)),X3),X1) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1798]) ).
cnf(c_0_1798_1,axiom,
( ~ 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(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1798]) ).
cnf(c_0_1799_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_1799]) ).
cnf(c_0_1799_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_1799]) ).
cnf(c_0_1803_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_1803]) ).
cnf(c_0_1803_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_1803]) ).
cnf(c_0_1803_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_1803]) ).
cnf(c_0_1804_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_1804]) ).
cnf(c_0_1804_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_1804]) ).
cnf(c_0_1805_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_1805]) ).
cnf(c_0_1805_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_1805]) ).
cnf(c_0_1807_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_1807]) ).
cnf(c_0_1807_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_1807]) ).
cnf(c_0_1807_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_1807]) ).
cnf(c_0_1808_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_1808]) ).
cnf(c_0_1808_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_1808]) ).
cnf(c_0_1808_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_1808]) ).
cnf(c_0_1809_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_1809]) ).
cnf(c_0_1809_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_1809]) ).
cnf(c_0_1809_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_1809]) ).
cnf(c_0_1810_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_1810]) ).
cnf(c_0_1810_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_1810]) ).
cnf(c_0_1810_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_1810]) ).
cnf(c_0_1811_0,axiom,
( c_Nat_Osemiring__1__class_Oof__nat__aux(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2,X3) = X2
| ~ class_Ring__and__Field_Osemiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1811]) ).
cnf(c_0_1811_1,axiom,
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_Nat_Osemiring__1__class_Oof__nat__aux(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2,X3) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1811]) ).
cnf(c_0_1812_0,axiom,
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1812]) ).
cnf(c_0_1812_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Lambda_Osubstn(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1812]) ).
cnf(c_0_1813_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Suc(X2),tc_nat),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_1813]) ).
cnf(c_0_1813_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(X1,c_Suc(X2),tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1813]) ).
cnf(c_0_1817_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_1817]) ).
cnf(c_0_1817_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_1817]) ).
cnf(c_0_1818_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_1818]) ).
cnf(c_0_1818_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_1818]) ).
cnf(c_0_1819_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_1819]) ).
cnf(c_0_1819_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_1819]) ).
cnf(c_0_1823_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_1823]) ).
cnf(c_0_1823_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_1823]) ).
cnf(c_0_1825_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_1825]) ).
cnf(c_0_1825_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_1825]) ).
cnf(c_0_1826_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_1826]) ).
cnf(c_0_1826_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_1826]) ).
cnf(c_0_1827_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_1827]) ).
cnf(c_0_1827_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_1827]) ).
cnf(c_0_1827_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_1827]) ).
cnf(c_0_1827_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_1827]) ).
cnf(c_0_1828_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_1828]) ).
cnf(c_0_1828_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_1828]) ).
cnf(c_0_1828_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_1828]) ).
cnf(c_0_1828_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_1828]) ).
cnf(c_0_1829_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_1829]) ).
cnf(c_0_1829_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_1829]) ).
cnf(c_0_1830_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_1830]) ).
cnf(c_0_1830_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_1830]) ).
cnf(c_0_1830_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_1830]) ).
cnf(c_0_1831_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_1831]) ).
cnf(c_0_1831_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_1831]) ).
cnf(c_0_1832_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_1832]) ).
cnf(c_0_1832_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_1832]) ).
cnf(c_0_1833_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_1833]) ).
cnf(c_0_1833_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_1833]) ).
cnf(c_0_1834_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_1834]) ).
cnf(c_0_1834_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_1834]) ).
cnf(c_0_1835_0,axiom,
( c_HOL_Oord__class_Oless(c_Suc(X1),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1835]) ).
cnf(c_0_1835_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X1),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1835]) ).
cnf(c_0_1835_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X1),X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1835]) ).
cnf(c_0_1838_0,axiom,
( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1838]) ).
cnf(c_0_1838_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_Suc(c_HOL_Ominus__class_Ominus(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1838]) ).
cnf(c_0_1840_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_1840]) ).
cnf(c_0_1840_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_1840]) ).
cnf(c_0_1841_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_1841]) ).
cnf(c_0_1841_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_1841]) ).
cnf(c_0_1842_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1)),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1842]) ).
cnf(c_0_1842_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1842]) ).
cnf(c_0_1843_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_1843]) ).
cnf(c_0_1843_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_1843]) ).
cnf(c_0_1844_0,axiom,
( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1844]) ).
cnf(c_0_1844_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1844]) ).
cnf(c_0_1845_0,axiom,
( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1845]) ).
cnf(c_0_1845_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1845]) ).
cnf(c_0_1846_0,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(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat))) ),
inference(literals_permutation,[status(thm)],[c_0_1846]) ).
cnf(c_0_1846_1,axiom,
( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X1)),X2) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)))
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1846]) ).
cnf(c_0_1847_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_1847]) ).
cnf(c_0_1847_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_1847]) ).
cnf(c_0_1847_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_1847]) ).
cnf(c_0_1848_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_1848]) ).
cnf(c_0_1848_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_1848]) ).
cnf(c_0_1849_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_1849]) ).
cnf(c_0_1849_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_1849]) ).
cnf(c_0_1849_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_1849]) ).
cnf(c_0_1850_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_1850]) ).
cnf(c_0_1850_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_1850]) ).
cnf(c_0_1850_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_1850]) ).
cnf(c_0_1850_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_1850]) ).
cnf(c_0_1853_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_1853]) ).
cnf(c_0_1853_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_1853]) ).
cnf(c_0_1853_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_1853]) ).
cnf(c_0_1854_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_1854]) ).
cnf(c_0_1854_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_1854]) ).
cnf(c_0_1854_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_1854]) ).
cnf(c_0_1854_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_1854]) ).
cnf(c_0_1855_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_1855]) ).
cnf(c_0_1855_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_1855]) ).
cnf(c_0_1855_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_1855]) ).
cnf(c_0_1856_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_1856]) ).
cnf(c_0_1856_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_1856]) ).
cnf(c_0_1856_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_1856]) ).
cnf(c_0_1857_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_1857]) ).
cnf(c_0_1857_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_1857]) ).
cnf(c_0_1857_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_1857]) ).
cnf(c_0_1858_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_1858]) ).
cnf(c_0_1858_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_1858]) ).
cnf(c_0_1858_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_1858]) ).
cnf(c_0_1859_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_1859]) ).
cnf(c_0_1859_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_1859]) ).
cnf(c_0_1859_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_1859]) ).
cnf(c_0_1860_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_1860]) ).
cnf(c_0_1860_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_1860]) ).
cnf(c_0_1860_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_1860]) ).
cnf(c_0_1861_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1861]) ).
cnf(c_0_1861_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1861]) ).
cnf(c_0_1862_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_1862]) ).
cnf(c_0_1862_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_1862]) ).
cnf(c_0_1862_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_1862]) ).
cnf(c_0_1863_0,axiom,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Oone__class_Oone(X2)),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1863]) ).
cnf(c_0_1863_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Oone__class_Oone(X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1863]) ).
cnf(c_0_1864_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_1864]) ).
cnf(c_0_1864_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_1864]) ).
cnf(c_0_1864_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_1864]) ).
cnf(c_0_1865_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_1865]) ).
cnf(c_0_1865_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_1865]) ).
cnf(c_0_1865_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_1865]) ).
cnf(c_0_1866_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_1866]) ).
cnf(c_0_1866_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_1866]) ).
cnf(c_0_1866_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_1866]) ).
cnf(c_0_1867_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_1867]) ).
cnf(c_0_1867_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_1867]) ).
cnf(c_0_1868_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_1868]) ).
cnf(c_0_1868_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_1868]) ).
cnf(c_0_1868_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_1868]) ).
cnf(c_0_1869_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_1869]) ).
cnf(c_0_1869_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_1869]) ).
cnf(c_0_1870_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_1870]) ).
cnf(c_0_1870_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_1870]) ).
cnf(c_0_1873_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1873]) ).
cnf(c_0_1873_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1873]) ).
cnf(c_0_1877_0,axiom,
( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1877]) ).
cnf(c_0_1877_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1877]) ).
cnf(c_0_1878_0,axiom,
( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1878]) ).
cnf(c_0_1878_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1878]) ).
cnf(c_0_1879_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1879]) ).
cnf(c_0_1879_1,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1879]) ).
cnf(c_0_1879_2,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1879]) ).
cnf(c_0_1880_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1880]) ).
cnf(c_0_1880_1,axiom,
( X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1880]) ).
cnf(c_0_1880_2,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1880]) ).
cnf(c_0_1881_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1881]) ).
cnf(c_0_1881_1,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1881]) ).
cnf(c_0_1881_2,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1881]) ).
cnf(c_0_1882_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_1882]) ).
cnf(c_0_1882_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_1882]) ).
cnf(c_0_1883_0,axiom,
( c_Suc(X1) = X2
| c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1883]) ).
cnf(c_0_1883_1,axiom,
( c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
| c_Suc(X1) = X2
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1883]) ).
cnf(c_0_1883_2,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
| c_Suc(X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1883]) ).
cnf(c_0_1884_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_1884]) ).
cnf(c_0_1884_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_1884]) ).
cnf(c_0_1885_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_1885]) ).
cnf(c_0_1885_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_1885]) ).
cnf(c_0_1886_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_1886]) ).
cnf(c_0_1886_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_1886]) ).
cnf(c_0_1887_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1887]) ).
cnf(c_0_1887_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1887]) ).
cnf(c_0_1893_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_1893]) ).
cnf(c_0_1893_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_1893]) ).
cnf(c_0_1894_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1894]) ).
cnf(c_0_1894_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1894]) ).
cnf(c_0_1895_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_1895]) ).
cnf(c_0_1895_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_1895]) ).
cnf(c_0_1897_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_1897]) ).
cnf(c_0_1897_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_1897]) ).
cnf(c_0_1897_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_1897]) ).
cnf(c_0_1898_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_1898]) ).
cnf(c_0_1898_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_1898]) ).
cnf(c_0_1898_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_1898]) ).
cnf(c_0_1898_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_1898]) ).
cnf(c_0_1899_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_1899]) ).
cnf(c_0_1899_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_1899]) ).
cnf(c_0_1899_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_1899]) ).
cnf(c_0_1899_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_1899]) ).
cnf(c_0_1900_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_1900]) ).
cnf(c_0_1900_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_1900]) ).
cnf(c_0_1900_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_1900]) ).
cnf(c_0_1900_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_1900]) ).
cnf(c_0_1901_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_1901]) ).
cnf(c_0_1901_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_1901]) ).
cnf(c_0_1901_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_1901]) ).
cnf(c_0_1901_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_1901]) ).
cnf(c_0_1902_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_1902]) ).
cnf(c_0_1902_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_1902]) ).
cnf(c_0_1902_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_1902]) ).
cnf(c_0_1902_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_1902]) ).
cnf(c_0_1903_0,axiom,
( X1 = X2
| hAPP(hAPP(c_Type_Otype_OFun,X1),X3) != hAPP(hAPP(c_Type_Otype_OFun,X2),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1903]) ).
cnf(c_0_1903_1,axiom,
( hAPP(hAPP(c_Type_Otype_OFun,X1),X3) != hAPP(hAPP(c_Type_Otype_OFun,X2),X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1903]) ).
cnf(c_0_1904_0,axiom,
( X1 = X2
| hAPP(hAPP(c_Type_Otype_OFun,X3),X1) != hAPP(hAPP(c_Type_Otype_OFun,X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1904]) ).
cnf(c_0_1904_1,axiom,
( hAPP(hAPP(c_Type_Otype_OFun,X3),X1) != hAPP(hAPP(c_Type_Otype_OFun,X4),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1904]) ).
cnf(c_0_1905_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_1905]) ).
cnf(c_0_1905_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_1905]) ).
cnf(c_0_1906_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_1906]) ).
cnf(c_0_1906_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_1906]) ).
cnf(c_0_1908_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Oone__class_Oone(X2)),c_Nat_Osemiring__1__class_Oof__nat(X1,X2)) = c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X1),X2)
| ~ class_Ring__and__Field_Osemiring__1(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1908]) ).
cnf(c_0_1908_1,axiom,
( ~ class_Ring__and__Field_Osemiring__1(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Oone__class_Oone(X2)),c_Nat_Osemiring__1__class_Oof__nat(X1,X2)) = c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1908]) ).
cnf(c_0_1909_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1909]) ).
cnf(c_0_1909_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1909]) ).
cnf(c_0_1910_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1910]) ).
cnf(c_0_1910_1,axiom,
( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1910]) ).
cnf(c_0_1911_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1911]) ).
cnf(c_0_1911_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1911]) ).
cnf(c_0_1912_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_1912]) ).
cnf(c_0_1912_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_1912]) ).
cnf(c_0_1913_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_1913]) ).
cnf(c_0_1913_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_1913]) ).
cnf(c_0_1914_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_1914]) ).
cnf(c_0_1914_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_1914]) ).
cnf(c_0_1917_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_1917]) ).
cnf(c_0_1917_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_1917]) ).
cnf(c_0_1917_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_1917]) ).
cnf(c_0_1918_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_1918]) ).
cnf(c_0_1918_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_1918]) ).
cnf(c_0_1918_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_1918]) ).
cnf(c_0_1919_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_1919]) ).
cnf(c_0_1919_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_1919]) ).
cnf(c_0_1919_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_1919]) ).
cnf(c_0_1919_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_1919]) ).
cnf(c_0_1920_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1920]) ).
cnf(c_0_1920_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1920]) ).
cnf(c_0_1921_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_1921]) ).
cnf(c_0_1921_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_1921]) ).
cnf(c_0_1921_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_1921]) ).
cnf(c_0_1921_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_1921]) ).
cnf(c_0_1922_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_1922]) ).
cnf(c_0_1922_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_1922]) ).
cnf(c_0_1922_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_1922]) ).
cnf(c_0_1923_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_1923]) ).
cnf(c_0_1923_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_1923]) ).
cnf(c_0_1923_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_1923]) ).
cnf(c_0_1924_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_1924]) ).
cnf(c_0_1924_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_1924]) ).
cnf(c_0_1924_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_1924]) ).
cnf(c_0_1925_0,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1925]) ).
cnf(c_0_1925_1,axiom,
( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1925]) ).
cnf(c_0_1925_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1925]) ).
cnf(c_0_1926_0,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1926]) ).
cnf(c_0_1926_1,axiom,
( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1926]) ).
cnf(c_0_1926_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1926]) ).
cnf(c_0_1927_0,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1927]) ).
cnf(c_0_1927_1,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1927]) ).
cnf(c_0_1927_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1927]) ).
cnf(c_0_1928_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1928]) ).
cnf(c_0_1928_1,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1928]) ).
cnf(c_0_1928_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1928]) ).
cnf(c_0_1929_0,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1929]) ).
cnf(c_0_1929_1,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1929]) ).
cnf(c_0_1929_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1929]) ).
cnf(c_0_1930_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1930]) ).
cnf(c_0_1930_1,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1930]) ).
cnf(c_0_1930_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1930]) ).
cnf(c_0_1932_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1932]) ).
cnf(c_0_1932_1,axiom,
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1932]) ).
cnf(c_0_1933_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1933]) ).
cnf(c_0_1933_1,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1933]) ).
cnf(c_0_1934_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1934]) ).
cnf(c_0_1934_1,axiom,
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1934]) ).
cnf(c_0_1936_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1936]) ).
cnf(c_0_1936_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1936]) ).
cnf(c_0_1936_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1936]) ).
cnf(c_0_1937_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1937]) ).
cnf(c_0_1937_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1937]) ).
cnf(c_0_1937_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1937]) ).
cnf(c_0_1940_0,axiom,
( X1 = X2
| ~ c_fequal(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1940]) ).
cnf(c_0_1940_1,axiom,
( ~ c_fequal(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1940]) ).
cnf(c_0_1943_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_1943]) ).
cnf(c_0_1943_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_1943]) ).
cnf(c_0_1944_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_1944]) ).
cnf(c_0_1944_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_1944]) ).
cnf(c_0_1947_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_1947]) ).
cnf(c_0_1947_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_1947]) ).
cnf(c_0_1948_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_1948]) ).
cnf(c_0_1948_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_1948]) ).
cnf(c_0_1949_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_1949]) ).
cnf(c_0_1949_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_1949]) ).
cnf(c_0_1950_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_1950]) ).
cnf(c_0_1950_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_1950]) ).
cnf(c_0_1951_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1951]) ).
cnf(c_0_1951_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1951]) ).
cnf(c_0_1952_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_1952]) ).
cnf(c_0_1952_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_1952]) ).
cnf(c_0_1952_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_1952]) ).
cnf(c_0_1953_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_1953]) ).
cnf(c_0_1953_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_1953]) ).
cnf(c_0_1953_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_1953]) ).
cnf(c_0_1954_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_1954]) ).
cnf(c_0_1954_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_1954]) ).
cnf(c_0_1955_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_1955]) ).
cnf(c_0_1955_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_1955]) ).
cnf(c_0_1956_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_1956]) ).
cnf(c_0_1956_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_1956]) ).
cnf(c_0_1957_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_1957]) ).
cnf(c_0_1957_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_1957]) ).
cnf(c_0_1960_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_1960]) ).
cnf(c_0_1960_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_1960]) ).
cnf(c_0_1962_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_1962]) ).
cnf(c_0_1962_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_1962]) ).
cnf(c_0_1963_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_1963]) ).
cnf(c_0_1963_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_1963]) ).
cnf(c_0_1964_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_1964]) ).
cnf(c_0_1964_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_1964]) ).
cnf(c_0_1965_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_1965]) ).
cnf(c_0_1965_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_1965]) ).
cnf(c_0_1966_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_1966]) ).
cnf(c_0_1966_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_1966]) ).
cnf(c_0_1967_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_1967]) ).
cnf(c_0_1967_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_1967]) ).
cnf(c_0_1975_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_1975]) ).
cnf(c_0_1975_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_1975]) ).
cnf(c_0_1986_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_1986]) ).
cnf(c_0_1986_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_1986]) ).
cnf(c_0_1986_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_1986]) ).
cnf(c_0_1992_0,axiom,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1992]) ).
cnf(c_0_1992_1,axiom,
( ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1992]) ).
cnf(c_0_1993_0,axiom,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1993]) ).
cnf(c_0_1993_1,axiom,
( ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1993]) ).
cnf(c_0_1994_0,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1994]) ).
cnf(c_0_1994_1,axiom,
( ~ class_Ring__and__Field_Osemiring__1(X1)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X1) = c_HOL_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1994]) ).
cnf(c_0_1995_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_1995]) ).
cnf(c_0_1995_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_1995]) ).
cnf(c_0_1999_0,axiom,
( c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1999]) ).
cnf(c_0_1999_1,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1999]) ).
cnf(c_0_2000_0,axiom,
( c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2000]) ).
cnf(c_0_2000_1,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2000]) ).
cnf(c_0_2002_0,axiom,
( X1 = X2
| c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2002]) ).
cnf(c_0_2002_1,axiom,
( c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2002]) ).
cnf(c_0_2003_0,axiom,
( X1 = X2
| c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2003]) ).
cnf(c_0_2003_1,axiom,
( c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2003]) ).
cnf(c_0_2004_0,axiom,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2004]) ).
cnf(c_0_2004_1,axiom,
( c_Suc(X1) != c_Suc(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2004]) ).
cnf(c_0_2005_0,axiom,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2005]) ).
cnf(c_0_2005_1,axiom,
( c_Suc(X1) != c_Suc(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2005]) ).
cnf(c_0_1669_0,axiom,
c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB),
inference(literals_permutation,[status(thm)],[c_0_1669]) ).
cnf(c_0_1696_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB),
inference(literals_permutation,[status(thm)],[c_0_1696]) ).
cnf(c_0_1836_0,axiom,
~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X2,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1836]) ).
cnf(c_0_1837_0,axiom,
~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X1,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1837]) ).
cnf(c_0_1872_0,axiom,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X1)),X2)),
inference(literals_permutation,[status(thm)],[c_0_1872]) ).
cnf(c_0_1931_0,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1931]) ).
cnf(c_0_1938_0,axiom,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1938]) ).
cnf(c_0_1939_0,axiom,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1939]) ).
cnf(c_0_1941_0,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1941]) ).
cnf(c_0_1942_0,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1942]) ).
cnf(c_0_1968_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OAbs(X3),
inference(literals_permutation,[status(thm)],[c_0_1968]) ).
cnf(c_0_1969_0,axiom,
c_Lambda_OdB_OAbs(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
inference(literals_permutation,[status(thm)],[c_0_1969]) ).
cnf(c_0_1970_0,axiom,
c_Lambda_OdB_OVar(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
inference(literals_permutation,[status(thm)],[c_0_1970]) ).
cnf(c_0_1971_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OVar(X3),
inference(literals_permutation,[status(thm)],[c_0_1971]) ).
cnf(c_0_2006_0,axiom,
c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OVar(X2),
inference(literals_permutation,[status(thm)],[c_0_2006]) ).
cnf(c_0_2007_0,axiom,
c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OAbs(X2),
inference(literals_permutation,[status(thm)],[c_0_2007]) ).
cnf(c_0_2008_0,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2008]) ).
cnf(c_0_2009_0,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2009]) ).
cnf(c_0_2010_0,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2010]) ).
cnf(c_0_2011_0,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2011]) ).
cnf(c_0_2013_0,axiom,
c_Suc(X1) != X1,
inference(literals_permutation,[status(thm)],[c_0_2013]) ).
cnf(c_0_2014_0,axiom,
c_Suc(X1) != X1,
inference(literals_permutation,[status(thm)],[c_0_2014]) ).
cnf(c_0_1628_0,axiom,
c_List_Olistsp(hAPP(hAPP(c_COMBS(tc_Lambda_OdB,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_and),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_bool),tc_bool,tc_Lambda_OdB),c_All(tc_fun(tc_nat,tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_bool),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_fun(tc_nat,tc_Type_Otype)),c_All(tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_bool)),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_Type_Otype,tc_bool),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_bool),tc_bool,tc_Type_Otype),c_All(tc_Lambda_OdB)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_bool),tc_Type_Otype),hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_bool,tc_Lambda_OdB),c_All(tc_nat))))),hAPP(hAPP(c_COMBS(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_fun(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),c_COMBS(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Type_Otype),c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool),tc_Lambda_OdB)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Type_Otype),c_COMBS(tc_nat,tc_bool,tc_bool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_Type_Otype),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_nat),c_implies)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Type_Otype,tc_bool))),hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Lambda_OdB,tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype)),tc_fun(tc_nat,tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool)),tc_nat),c_Type_Otyping)),hAPP(hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_Type_Otype))),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Type_Otype,tc_fun(tc_nat,tc_Type_Otype))),c_Type_Oshift(tc_Type_Otype))),v_T____))))))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBS(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),c_COMBB(tc_bool,tc_bool,tc_nat)),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_implies),c_InductTermi_OIT))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBS(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_bool,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),c_COMBB(tc_bool,tc_bool,tc_nat))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_bool),tc_fun(tc_Lambda_OdB,tc_fun(tc_bool,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_implies)),hAPP(hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_Lambda_OdB,tc_Type_Otype,tc_bool)),c_Type_Otyping)),v_T____)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_nat,tc_Lambda_OdB),tc_fun(tc_nat,tc_bool),tc_Lambda_OdB),hAPP(c_COMBB(tc_Lambda_OdB,tc_bool,tc_nat),c_InductTermi_OIT))),c_Lambda_Osubst)))))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),c_Ex(tc_Type_Otype)),hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)))),v_bs____,tc_Lambda_OdB),
inference(literals_permutation,[status(thm)],[c_0_1628]) ).
cnf(c_0_1636_0,axiom,
c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),X3)),X4),X2,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3),X4),
inference(literals_permutation,[status(thm)],[c_0_1636]) ).
cnf(c_0_1645_0,axiom,
c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),v_u____)),v_i____),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
inference(literals_permutation,[status(thm)],[c_0_1645]) ).
cnf(c_0_1646_0,axiom,
c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),v_u____)),v_i____),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
inference(literals_permutation,[status(thm)],[c_0_1646]) ).
cnf(c_0_1648_0,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),c_Lambda_OdB_OVar(v_n____)),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)))),
inference(literals_permutation,[status(thm)],[c_0_1648]) ).
cnf(c_0_1649_0,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_H____)),
inference(literals_permutation,[status(thm)],[c_0_1649]) ).
cnf(c_0_1650_0,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_ea______),v_ia______),v_T____)),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_Ha______)),
inference(literals_permutation,[status(thm)],[c_0_1650]) ).
cnf(c_0_1651_0,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_e____),v_u____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)))),
inference(literals_permutation,[status(thm)],[c_0_1651]) ).
cnf(c_0_1652_0,axiom,
c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X1),X3),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),X3),X2,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3),
inference(literals_permutation,[status(thm)],[c_0_1652]) ).
cnf(c_0_1654_0,axiom,
c_Fun_Ofcomp(c_Fun_Ofcomp(X1,X2,X3,X4,X5),X6,X3,X5,X7) = c_Fun_Ofcomp(X1,c_Fun_Ofcomp(X2,X6,X4,X5,X7),X3,X4,X7),
inference(literals_permutation,[status(thm)],[c_0_1654]) ).
cnf(c_0_1655_0,axiom,
c_Fun_Ocomp(X1,c_Fun_Ocomp(X2,X3,X4,X5,X6),X5,X7,X6) = c_Fun_Ocomp(c_Fun_Ocomp(X1,X2,X5,X7,X4),X3,X4,X7,X6),
inference(literals_permutation,[status(thm)],[c_0_1655]) ).
cnf(c_0_1656_0,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
inference(literals_permutation,[status(thm)],[c_0_1656]) ).
cnf(c_0_1677_0,axiom,
c_List_Omap(X1,c_List_Omap(X2,X3,X4,X5),X5,X6) = c_List_Omap(c_Fun_Ocomp(X1,X2,X5,X6,X4),X3,X4,X6),
inference(literals_permutation,[status(thm)],[c_0_1677]) ).
cnf(c_0_1681_0,axiom,
hAPP(c_Fun_Ocomp(c_COMBK(X1,X2,X3),X4,X3,X2,t_a),v_x) = X1,
inference(literals_permutation,[status(thm)],[c_0_1681]) ).
cnf(c_0_1682_0,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_b____),v_sko__CHAINED__1(v_T____,v_b____,v_e____,v_i____))),
inference(literals_permutation,[status(thm)],[c_0_1682]) ).
cnf(c_0_1683_0,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_b____),v_sko__local__XCons__1__1(v_T____,v_b____,v_e____,v_i____))),
inference(literals_permutation,[status(thm)],[c_0_1683]) ).
cnf(c_0_1684_0,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_b____),v_sko__local__XCons__Xhyps__1__1(v_T____,v_b____,v_e____,v_i____))),
inference(literals_permutation,[status(thm)],[c_0_1684]) ).
cnf(c_0_1685_0,axiom,
c_Fun_Ocomp(c_Nat_Ocompow(X1,X3,X4,X4),c_Nat_Ocompow(X2,X3,X4,X4),X4,X4,X4) = c_Nat_Ocompow(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,X4,X4),
inference(literals_permutation,[status(thm)],[c_0_1685]) ).
cnf(c_0_1686_0,axiom,
hAPP(c_Fun_Ofcomp(X1,X2,X3,X4,X5),X6) = hAPP(X2,hAPP(X1,X6)),
inference(literals_permutation,[status(thm)],[c_0_1686]) ).
cnf(c_0_1687_0,axiom,
hAPP(c_Fun_Ocomp(X1,X2,X4,X5,X6),X3) = hAPP(X1,hAPP(X2,X3)),
inference(literals_permutation,[status(thm)],[c_0_1687]) ).
cnf(c_0_1688_0,axiom,
hAPP(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
inference(literals_permutation,[status(thm)],[c_0_1688]) ).
cnf(c_0_1689_0,axiom,
hAPP(c_Fun_Ofcomp(X1,X2,t_a,X3,X4),v_x) = hAPP(X2,hAPP(X1,v_x)),
inference(literals_permutation,[status(thm)],[c_0_1689]) ).
cnf(c_0_1690_0,axiom,
hAPP(c_Fun_Ocomp(X1,X2,X3,X4,t_a),v_x) = hAPP(X1,hAPP(X2,v_x)),
inference(literals_permutation,[status(thm)],[c_0_1690]) ).
cnf(c_0_1693_0,axiom,
hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) = v_T____,
inference(literals_permutation,[status(thm)],[c_0_1693]) ).
cnf(c_0_1695_0,axiom,
hAPP(hAPP(hAPP(c_Type_Oshift(X1),hAPP(hAPP(hAPP(c_Type_Oshift(X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X5)),c_Suc(X3)),X4) = hAPP(hAPP(hAPP(c_Type_Oshift(X1),hAPP(hAPP(hAPP(c_Type_Oshift(X1),X2),X3),X4)),c_HOL_Ozero__class_Ozero(tc_nat)),X5),
inference(literals_permutation,[status(thm)],[c_0_1695]) ).
cnf(c_0_1697_0,axiom,
c_Fun_Ocomp(X2,c_Nat_Ocompow(X1,X2,X3,X3),X3,X3,X3) = c_Nat_Ocompow(c_Suc(X1),X2,X3,X3),
inference(literals_permutation,[status(thm)],[c_0_1697]) ).
cnf(c_0_1704_0,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_a____),v_T_H_H____)),
inference(literals_permutation,[status(thm)],[c_0_1704]) ).
cnf(c_0_1705_0,axiom,
hAPP(c_Nat_Ocompow(X2,X1,X3,X3),hAPP(X1,X4)) = hAPP(X1,hAPP(c_Nat_Ocompow(X2,X1,X3,X3),X4)),
inference(literals_permutation,[status(thm)],[c_0_1705]) ).
cnf(c_0_1713_0,axiom,
c_Fun_Ofcomp(c_Fun_Oid(X1),X2,X1,X1,X3) = X2,
inference(literals_permutation,[status(thm)],[c_0_1713]) ).
cnf(c_0_1714_0,axiom,
c_Fun_Ofcomp(X1,c_Fun_Oid(X2),X3,X2,X2) = X1,
inference(literals_permutation,[status(thm)],[c_0_1714]) ).
cnf(c_0_1715_0,axiom,
c_Fun_Ocomp(X1,c_Fun_Oid(X2),X2,X3,X2) = X1,
inference(literals_permutation,[status(thm)],[c_0_1715]) ).
cnf(c_0_1716_0,axiom,
c_Fun_Ocomp(c_Fun_Oid(X1),X2,X1,X1,X3) = X2,
inference(literals_permutation,[status(thm)],[c_0_1716]) ).
cnf(c_0_1720_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),X3),X4),
inference(literals_permutation,[status(thm)],[c_0_1720]) ).
cnf(c_0_1725_0,axiom,
hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)))),
inference(literals_permutation,[status(thm)],[c_0_1725]) ).
cnf(c_0_1726_0,axiom,
c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),hAPP(hAPP(c_Lambda_Olift,X2),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)))) = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(X1)),X2),X3),
inference(literals_permutation,[status(thm)],[c_0_1726]) ).
cnf(c_0_1737_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X1,tc_Type_Otype)),c_Nat_Osize__class_Osize(X2,tc_Type_Otype))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,X1),X2),tc_Type_Otype),
inference(literals_permutation,[status(thm)],[c_0_1737]) ).
cnf(c_0_1740_0,axiom,
hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
inference(literals_permutation,[status(thm)],[c_0_1740]) ).
cnf(c_0_1744_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(X1,X3,X4)),c_Lambda_Osubstn(X2,X3,X4)) = c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),X3,X4),
inference(literals_permutation,[status(thm)],[c_0_1744]) ).
cnf(c_0_1745_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(X1,X2,X4)),c_Lambda_Oliftn(X1,X3,X4)) = c_Lambda_Oliftn(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4),
inference(literals_permutation,[status(thm)],[c_0_1745]) ).
cnf(c_0_1752_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X1),X3)),hAPP(hAPP(c_Lambda_Olift,X2),X3)) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),X3),
inference(literals_permutation,[status(thm)],[c_0_1752]) ).
cnf(c_0_1762_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(X1)),c_Type_Otype_Otype__size(X2))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X1),X2)),
inference(literals_permutation,[status(thm)],[c_0_1762]) ).
cnf(c_0_1765_0,axiom,
hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X1),X2)),X3),X2) = X1,
inference(literals_permutation,[status(thm)],[c_0_1765]) ).
cnf(c_0_1766_0,axiom,
hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),c_Lambda_Oliftn(X3,X2,c_HOL_Ozero__class_Ozero(tc_nat))),X3) = c_Lambda_Osubstn(X1,X2,X3),
inference(literals_permutation,[status(thm)],[c_0_1766]) ).
cnf(c_0_1767_0,axiom,
c_Lambda_OdB_OAbs(c_Lambda_Osubstn(X1,X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)))) = c_Lambda_Osubstn(c_Lambda_OdB_OAbs(X1),X2,X3),
inference(literals_permutation,[status(thm)],[c_0_1767]) ).
cnf(c_0_1768_0,axiom,
c_Lambda_OdB_OAbs(c_Lambda_Oliftn(X1,X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)))) = c_Lambda_Oliftn(X1,c_Lambda_OdB_OAbs(X2),X3),
inference(literals_permutation,[status(thm)],[c_0_1768]) ).
cnf(c_0_1769_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3)),
inference(literals_permutation,[status(thm)],[c_0_1769]) ).
cnf(c_0_1780_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X1),X2,tc_nat),c_Suc(X3),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1780]) ).
cnf(c_0_1788_0,axiom,
c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)))) = hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(X1)),X2),
inference(literals_permutation,[status(thm)],[c_0_1788]) ).
cnf(c_0_1795_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1795]) ).
cnf(c_0_1796_0,axiom,
hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(X1,X2,X3)),X3) = c_Lambda_Oliftn(c_Suc(X1),X2,X3),
inference(literals_permutation,[status(thm)],[c_0_1796]) ).
cnf(c_0_1800_0,axiom,
c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1800]) ).
cnf(c_0_1801_0,axiom,
c_HOL_Ominus__class_Ominus(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_Ominus__class_Ominus(X2,X3,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1801]) ).
cnf(c_0_1802_0,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1802]) ).
cnf(c_0_1806_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3)),
inference(literals_permutation,[status(thm)],[c_0_1806]) ).
cnf(c_0_1814_0,axiom,
c_Nat_Ocompow(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2,X2) = c_Fun_Oid(X2),
inference(literals_permutation,[status(thm)],[c_0_1814]) ).
cnf(c_0_1815_0,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OVar(X2)),hAPP(X1,X2))),
inference(literals_permutation,[status(thm)],[c_0_1815]) ).
cnf(c_0_1816_0,axiom,
hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(X1),X2),X3),X4),X3) = X4,
inference(literals_permutation,[status(thm)],[c_0_1816]) ).
cnf(c_0_1820_0,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1820]) ).
cnf(c_0_1821_0,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1)),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1821]) ).
cnf(c_0_1822_0,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1822]) ).
cnf(c_0_1824_0,axiom,
c_Type_Otypings(hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____),v_as____,v_Ts____),
inference(literals_permutation,[status(thm)],[c_0_1824]) ).
cnf(c_0_1839_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) = c_HOL_Ominus__class_Ominus(X1,c_Suc(X2),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1839]) ).
cnf(c_0_1851_0,axiom,
hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3)),
inference(literals_permutation,[status(thm)],[c_0_1851]) ).
cnf(c_0_1852_0,axiom,
hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3)),
inference(literals_permutation,[status(thm)],[c_0_1852]) ).
cnf(c_0_1871_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_Suc(X1),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1871]) ).
cnf(c_0_1874_0,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_ea______),v_ua______),v_T____)),
inference(literals_permutation,[status(thm)],[c_0_1874]) ).
cnf(c_0_1875_0,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_e____),v_u____),v_T____)),
inference(literals_permutation,[status(thm)],[c_0_1875]) ).
cnf(c_0_1876_0,axiom,
c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X1)),X2),
inference(literals_permutation,[status(thm)],[c_0_1876]) ).
cnf(c_0_1888_0,axiom,
c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_Suc(X2)),
inference(literals_permutation,[status(thm)],[c_0_1888]) ).
cnf(c_0_1889_0,axiom,
hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Osubstn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),
inference(literals_permutation,[status(thm)],[c_0_1889]) ).
cnf(c_0_1890_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(literals_permutation,[status(thm)],[c_0_1890]) ).
cnf(c_0_1891_0,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X1,tc_nat) = X2,
inference(literals_permutation,[status(thm)],[c_0_1891]) ).
cnf(c_0_1892_0,axiom,
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_1892]) ).
cnf(c_0_1896_0,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
inference(literals_permutation,[status(thm)],[c_0_1896]) ).
cnf(c_0_1907_0,axiom,
c_HOL_Ominus__class_Ominus(c_Suc(X1),c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1907]) ).
cnf(c_0_1915_0,axiom,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1) = X2,
inference(literals_permutation,[status(thm)],[c_0_1915]) ).
cnf(c_0_1916_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X1)),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_Suc(X2)),
inference(literals_permutation,[status(thm)],[c_0_1916]) ).
cnf(c_0_1935_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),
inference(literals_permutation,[status(thm)],[c_0_1935]) ).
cnf(c_0_1945_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(literals_permutation,[status(thm)],[c_0_1945]) ).
cnf(c_0_1946_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(literals_permutation,[status(thm)],[c_0_1946]) ).
cnf(c_0_1958_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(literals_permutation,[status(thm)],[c_0_1958]) ).
cnf(c_0_1959_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(literals_permutation,[status(thm)],[c_0_1959]) ).
cnf(c_0_1961_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1961]) ).
cnf(c_0_1972_0,axiom,
c_HOL_Ominus__class_Ominus(c_Suc(X1),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1,
inference(literals_permutation,[status(thm)],[c_0_1972]) ).
cnf(c_0_1973_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1973]) ).
cnf(c_0_1974_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1974]) ).
cnf(c_0_1976_0,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1976]) ).
cnf(c_0_1977_0,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1977]) ).
cnf(c_0_1978_0,axiom,
c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = X1,
inference(literals_permutation,[status(thm)],[c_0_1978]) ).
cnf(c_0_1979_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(literals_permutation,[status(thm)],[c_0_1979]) ).
cnf(c_0_1980_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(literals_permutation,[status(thm)],[c_0_1980]) ).
cnf(c_0_1981_0,axiom,
c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
inference(literals_permutation,[status(thm)],[c_0_1981]) ).
cnf(c_0_1982_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X1) = c_Suc(X1),
inference(literals_permutation,[status(thm)],[c_0_1982]) ).
cnf(c_0_1983_0,axiom,
c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1983]) ).
cnf(c_0_1984_0,axiom,
c_fequal(X1,X1,X2),
inference(literals_permutation,[status(thm)],[c_0_1984]) ).
cnf(c_0_1985_0,axiom,
c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(X1,X2),X2) = c_Transitive__Closure_Ortranclp(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_1985]) ).
cnf(c_0_1987_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_1987]) ).
cnf(c_0_1988_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)) = c_Suc(X1),
inference(literals_permutation,[status(thm)],[c_0_1988]) ).
cnf(c_0_1989_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)) = X1,
inference(literals_permutation,[status(thm)],[c_0_1989]) ).
cnf(c_0_1990_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)) = X1,
inference(literals_permutation,[status(thm)],[c_0_1990]) ).
cnf(c_0_1991_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X1))),
inference(literals_permutation,[status(thm)],[c_0_1991]) ).
cnf(c_0_1996_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
inference(literals_permutation,[status(thm)],[c_0_1996]) ).
cnf(c_0_1997_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_ua______)),
inference(literals_permutation,[status(thm)],[c_0_1997]) ).
cnf(c_0_1998_0,axiom,
hAPP(c_Fun_Oid(X1),X2) = X2,
inference(literals_permutation,[status(thm)],[c_0_1998]) ).
cnf(c_0_2001_0,axiom,
hAPP(c_Fun_Oid(t_a),v_x) = v_x,
inference(literals_permutation,[status(thm)],[c_0_2001]) ).
cnf(c_0_2012_0,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2012]) ).
cnf(c_0_2015_0,axiom,
class_Orderings_Oorder(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_2015]) ).
cnf(c_0_2016_0,axiom,
class_Orderings_Opreorder(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_2016]) ).
cnf(c_0_2017_0,axiom,
class_Orderings_Oorder(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2017]) ).
cnf(c_0_2018_0,axiom,
class_Orderings_Olinorder(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2018]) ).
cnf(c_0_2019_0,axiom,
class_Orderings_Opreorder(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2019]) ).
cnf(c_0_2020_0,axiom,
class_Nat_Osemiring__char__0(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2020]) ).
cnf(c_0_2021_0,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2021]) ).
cnf(c_0_2022_0,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2022]) ).
cnf(c_0_2023_0,axiom,
class_OrderedGroup_Osemigroup__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2023]) ).
cnf(c_0_2024_0,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2024]) ).
cnf(c_0_2025_0,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2025]) ).
cnf(c_0_2026_0,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2026]) ).
cnf(c_0_2027_0,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2027]) ).
cnf(c_0_2028_0,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2028]) ).
cnf(c_0_2029_0,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2029]) ).
cnf(c_0_2030_0,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2030]) ).
cnf(c_0_2031_0,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2031]) ).
cnf(c_0_2032_0,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2032]) ).
cnf(c_0_2033_0,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2033]) ).
cnf(c_0_2034_0,axiom,
v_i____ = v_n____,
inference(literals_permutation,[status(thm)],[c_0_2034]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_001,negated_conjecture,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),v_b____),v_xa)),
file('<stdin>',cls_conjecture_0) ).
fof(c_0_1_002,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_xb),v_xc))),
file('<stdin>',cls_conjecture_3) ).
fof(c_0_2_003,negated_conjecture,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____)),
file('<stdin>',cls_conjecture_2) ).
fof(c_0_3_004,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,v_xb)),
file('<stdin>',cls_conjecture_1) ).
fof(c_0_4_005,negated_conjecture,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),v_b____),v_xa)),
c_0_0 ).
fof(c_0_5_006,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_xb),v_xc))),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_6_007,negated_conjecture,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____)),
c_0_2 ).
fof(c_0_7_008,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,v_xb)),
c_0_3 ).
fof(c_0_8_009,negated_conjecture,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),v_b____),v_xa)),
c_0_4 ).
fof(c_0_9_010,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_xb),v_xc))),
c_0_5 ).
fof(c_0_10_011,negated_conjecture,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____)),
c_0_6 ).
fof(c_0_11_012,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,v_xb)),
c_0_7 ).
cnf(c_0_12_013,negated_conjecture,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),v_b____),v_xa)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13_014,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_xb),v_xc))),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14_015,negated_conjecture,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15_016,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,v_xb)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16_017,negated_conjecture,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),v_b____),v_xa)),
c_0_12,
[final] ).
cnf(c_0_17_018,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_xb),v_xc))),
c_0_13,
[final] ).
cnf(c_0_18_019,negated_conjecture,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____)),
c_0_14,
[final] ).
cnf(c_0_19_020,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,v_xb)),
c_0_15,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_693,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),X0),X1)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X2),X1),v_T____)),v_b____),X3))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X0))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X2),X0),v_T____)) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_d8084e.p',c_0_1676_3) ).
cnf(c_1788,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),X0),X1)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X2),X1),v_T____)),v_b____),X3))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X0))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X2),X0),v_T____)) ),
inference(copy,[status(esa)],[c_693]) ).
cnf(c_24060,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X0),X1),v_T____)),v_b____),X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X0),v_xb),v_T____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_xb),X1)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,v_xb)) ),
inference(instantiation,[status(thm)],[c_1788]) ).
cnf(c_54587,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),X0),v_T____)),v_b____),X1))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_xb),X0)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,v_xb)) ),
inference(instantiation,[status(thm)],[c_24060]) ).
cnf(c_56463,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),v_b____),v_xa))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_xb),v_xc)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,v_xb)) ),
inference(instantiation,[status(thm)],[c_54587]) ).
cnf(c_786,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_xb),v_xc))),
file('/export/starexec/sandbox/tmp/iprover_modulo_d8084e.p',c_0_17) ).
cnf(c_787,negated_conjecture,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),v_b____),v_xa)),
file('/export/starexec/sandbox/tmp/iprover_modulo_d8084e.p',c_0_16) ).
cnf(c_788,negated_conjecture,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____)),
file('/export/starexec/sandbox/tmp/iprover_modulo_d8084e.p',c_0_18) ).
cnf(c_789,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,v_xb)),
file('/export/starexec/sandbox/tmp/iprover_modulo_d8084e.p',c_0_19) ).
cnf(contradiction,plain,
$false,
inference(minisat,[status(thm)],[c_56463,c_786,c_787,c_788,c_789]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL806-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13 % Command : iprover_modulo %s %d
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 4 11:48:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % Running in mono-core mode
% 0.19/0.47 % Orienting using strategy Equiv(ClausalAll)
% 0.19/0.47 % Orientation found
% 0.19/0.47 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_c5dc42.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_d8084e.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_9ad091 | grep -v "SZS"
% 0.19/0.49
% 0.19/0.49 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.19/0.49
% 0.19/0.49 %
% 0.19/0.49 % ------ iProver source info
% 0.19/0.49
% 0.19/0.49 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.19/0.49 % git: non_committed_changes: true
% 0.19/0.49 % git: last_make_outside_of_git: true
% 0.19/0.49
% 0.19/0.49 %
% 0.19/0.49 % ------ Input Options
% 0.19/0.49
% 0.19/0.49 % --out_options all
% 0.19/0.49 % --tptp_safe_out true
% 0.19/0.49 % --problem_path ""
% 0.19/0.49 % --include_path ""
% 0.19/0.49 % --clausifier .//eprover
% 0.19/0.49 % --clausifier_options --tstp-format
% 0.19/0.49 % --stdin false
% 0.19/0.49 % --dbg_backtrace false
% 0.19/0.49 % --dbg_dump_prop_clauses false
% 0.19/0.49 % --dbg_dump_prop_clauses_file -
% 0.19/0.49 % --dbg_out_stat false
% 0.19/0.49
% 0.19/0.49 % ------ General Options
% 0.19/0.49
% 0.19/0.49 % --fof false
% 0.19/0.49 % --time_out_real 150.
% 0.19/0.49 % --time_out_prep_mult 0.2
% 0.19/0.49 % --time_out_virtual -1.
% 0.19/0.49 % --schedule none
% 0.19/0.49 % --ground_splitting input
% 0.19/0.49 % --splitting_nvd 16
% 0.19/0.49 % --non_eq_to_eq false
% 0.19/0.49 % --prep_gs_sim true
% 0.19/0.49 % --prep_unflatten false
% 0.19/0.49 % --prep_res_sim true
% 0.19/0.49 % --prep_upred true
% 0.19/0.49 % --res_sim_input true
% 0.19/0.49 % --clause_weak_htbl true
% 0.19/0.49 % --gc_record_bc_elim false
% 0.19/0.49 % --symbol_type_check false
% 0.19/0.49 % --clausify_out false
% 0.19/0.49 % --large_theory_mode false
% 0.19/0.49 % --prep_sem_filter none
% 0.19/0.49 % --prep_sem_filter_out false
% 0.19/0.49 % --preprocessed_out false
% 0.19/0.49 % --sub_typing false
% 0.19/0.49 % --brand_transform false
% 0.19/0.49 % --pure_diseq_elim true
% 0.19/0.49 % --min_unsat_core false
% 0.19/0.49 % --pred_elim true
% 0.19/0.49 % --add_important_lit false
% 0.19/0.49 % --soft_assumptions false
% 0.19/0.49 % --reset_solvers false
% 0.19/0.49 % --bc_imp_inh []
% 0.19/0.49 % --conj_cone_tolerance 1.5
% 0.19/0.49 % --prolific_symb_bound 500
% 0.19/0.49 % --lt_threshold 2000
% 0.19/0.49
% 0.19/0.49 % ------ SAT Options
% 0.19/0.49
% 0.19/0.49 % --sat_mode false
% 0.19/0.49 % --sat_fm_restart_options ""
% 0.19/0.49 % --sat_gr_def false
% 0.19/0.49 % --sat_epr_types true
% 0.19/0.49 % --sat_non_cyclic_types false
% 0.19/0.49 % --sat_finite_models false
% 0.19/0.49 % --sat_fm_lemmas false
% 0.19/0.49 % --sat_fm_prep false
% 0.19/0.49 % --sat_fm_uc_incr true
% 0.19/0.49 % --sat_out_model small
% 0.19/0.49 % --sat_out_clauses false
% 0.19/0.49
% 0.19/0.49 % ------ QBF Options
% 0.19/0.49
% 0.19/0.49 % --qbf_mode false
% 0.19/0.49 % --qbf_elim_univ true
% 0.19/0.49 % --qbf_sk_in true
% 0.19/0.49 % --qbf_pred_elim true
% 0.19/0.49 % --qbf_split 32
% 0.19/0.49
% 0.19/0.49 % ------ BMC1 Options
% 0.19/0.49
% 0.19/0.49 % --bmc1_incremental false
% 0.19/0.49 % --bmc1_axioms reachable_all
% 0.19/0.49 % --bmc1_min_bound 0
% 0.19/0.49 % --bmc1_max_bound -1
% 0.19/0.49 % --bmc1_max_bound_default -1
% 0.19/0.49 % --bmc1_symbol_reachability true
% 0.19/0.49 % --bmc1_property_lemmas false
% 0.19/0.49 % --bmc1_k_induction false
% 0.19/0.49 % --bmc1_non_equiv_states false
% 0.19/0.49 % --bmc1_deadlock false
% 0.19/0.49 % --bmc1_ucm false
% 0.19/0.49 % --bmc1_add_unsat_core none
% 0.19/0.49 % --bmc1_unsat_core_children false
% 0.19/0.49 % --bmc1_unsat_core_extrapolate_axioms false
% 0.19/0.49 % --bmc1_out_stat full
% 0.19/0.49 % --bmc1_ground_init false
% 0.19/0.49 % --bmc1_pre_inst_next_state false
% 0.19/0.49 % --bmc1_pre_inst_state false
% 0.19/0.49 % --bmc1_pre_inst_reach_state false
% 0.19/0.49 % --bmc1_out_unsat_core false
% 0.19/0.49 % --bmc1_aig_witness_out false
% 0.19/0.49 % --bmc1_verbose false
% 0.19/0.49 % --bmc1_dump_clauses_tptp false
% 150.26/150.50 % --bmc1_dump_unsat_core_tptp false
% 150.26/150.50 % --bmc1_dump_file -
% 150.26/150.50 % --bmc1_ucm_expand_uc_limit 128
% 150.26/150.50 % --bmc1_ucm_n_expand_iterations 6
% 150.26/150.50 % --bmc1_ucm_extend_mode 1
% 150.26/150.50 % --bmc1_ucm_init_mode 2
% 150.26/150.50 % --bmc1_ucm_cone_mode none
% 150.26/150.50 % --bmc1_ucm_reduced_relation_type 0
% 150.26/150.50 % --bmc1_ucm_relax_model 4
% 150.26/150.50 % --bmc1_ucm_full_tr_after_sat true
% 150.26/150.50 % --bmc1_ucm_expand_neg_assumptions false
% 150.26/150.50 % --bmc1_ucm_layered_model none
% 150.26/150.50 % --bmc1_ucm_max_lemma_size 10
% 150.26/150.50
% 150.26/150.50 % ------ AIG Options
% 150.26/150.50
% 150.26/150.50 % --aig_mode false
% 150.26/150.50
% 150.26/150.50 % ------ Instantiation Options
% 150.26/150.50
% 150.26/150.50 % --instantiation_flag true
% 150.26/150.50 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 150.26/150.50 % --inst_solver_per_active 750
% 150.26/150.50 % --inst_solver_calls_frac 0.5
% 150.26/150.50 % --inst_passive_queue_type priority_queues
% 150.26/150.50 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 150.26/150.50 % --inst_passive_queues_freq [25;2]
% 150.26/150.50 % --inst_dismatching true
% 150.26/150.50 % --inst_eager_unprocessed_to_passive true
% 150.26/150.50 % --inst_prop_sim_given true
% 150.26/150.50 % --inst_prop_sim_new false
% 150.26/150.50 % --inst_orphan_elimination true
% 150.26/150.50 % --inst_learning_loop_flag true
% 150.26/150.50 % --inst_learning_start 3000
% 150.26/150.50 % --inst_learning_factor 2
% 150.26/150.50 % --inst_start_prop_sim_after_learn 3
% 150.26/150.50 % --inst_sel_renew solver
% 150.26/150.50 % --inst_lit_activity_flag true
% 150.26/150.50 % --inst_out_proof true
% 150.26/150.50
% 150.26/150.50 % ------ Resolution Options
% 150.26/150.50
% 150.26/150.50 % --resolution_flag true
% 150.26/150.50 % --res_lit_sel kbo_max
% 150.26/150.50 % --res_to_prop_solver none
% 150.26/150.50 % --res_prop_simpl_new false
% 150.26/150.50 % --res_prop_simpl_given false
% 150.26/150.50 % --res_passive_queue_type priority_queues
% 150.26/150.50 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 150.26/150.50 % --res_passive_queues_freq [15;5]
% 150.26/150.50 % --res_forward_subs full
% 150.26/150.50 % --res_backward_subs full
% 150.26/150.50 % --res_forward_subs_resolution true
% 150.26/150.50 % --res_backward_subs_resolution true
% 150.26/150.50 % --res_orphan_elimination false
% 150.26/150.50 % --res_time_limit 1000.
% 150.26/150.50 % --res_out_proof true
% 150.26/150.50 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_c5dc42.s
% 150.26/150.50 % --modulo true
% 150.26/150.50
% 150.26/150.50 % ------ Combination Options
% 150.26/150.50
% 150.26/150.50 % --comb_res_mult 1000
% 150.26/150.50 % --comb_inst_mult 300
% 150.26/150.50 % ------
% 150.26/150.50
% 150.26/150.50 % ------ Parsing...% successful
% 150.26/150.50
% 150.26/150.50 % ------ 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 %
% 150.26/150.50
% 150.26/150.50 % ------ Proving...
% 150.26/150.50 % ------ Problem Properties
% 150.26/150.50
% 150.26/150.50 %
% 150.26/150.50 % EPR false
% 150.26/150.50 % Horn false
% 150.26/150.50 % Has equality true
% 150.26/150.50
% 150.26/150.50 % % ------ Input Options Time Limit: Unbounded
% 150.26/150.50
% 150.26/150.50
% 150.26/150.50 Compiling...
% 150.26/150.50 Loading plugin: done.
% 150.26/150.50 %
% 150.26/150.50
% 150.26/150.50
% 150.26/150.50 % Time Out Real
% 150.26/150.50
% 150.26/150.50 % ------ Statistics
% 150.26/150.50
% 150.26/150.50 % ------ General
% 150.26/150.50
% 150.26/150.50 % num_of_input_clauses: 790
% 150.26/150.50 % num_of_input_neg_conjectures: 4
% 150.26/150.50 % num_of_splits: 0
% 150.26/150.50 % num_of_split_atoms: 0
% 150.26/150.50 % num_of_sem_filtered_clauses: 0
% 150.26/150.50 % num_of_subtypes: 0
% 150.26/150.50 % monotx_restored_types: 0
% 150.26/150.50 % sat_num_of_epr_types: 0
% 150.26/150.50 % sat_num_of_non_cyclic_types: 0
% 150.26/150.50 % sat_guarded_non_collapsed_types: 0
% 150.26/150.50 % is_epr: 0
% 150.26/150.50 % is_horn: 0
% 150.26/150.50 % has_eq: 1
% 150.26/150.50 % num_pure_diseq_elim: 0
% 150.26/150.50 % simp_replaced_by: 0
% 150.26/150.50 % res_preprocessed: 8
% 150.26/150.50 % prep_upred: 0
% 150.26/150.50 % prep_unflattend: 0
% 150.26/150.50 % pred_elim_cands: 0
% 150.26/150.50 % pred_elim: 0
% 150.26/150.50 % pred_elim_cl: 0
% 150.26/150.50 % pred_elim_cycles: 0
% 150.26/150.50 % forced_gc_time: 0
% 150.26/150.50 % gc_basic_clause_elim: 0
% 150.26/150.50 % parsing_time: 0.052
% 150.26/150.50 % sem_filter_time: 0.
% 150.26/150.50 % pred_elim_time: 0.
% 150.26/150.50 % out_proof_time: 0.
% 150.26/150.50 % monotx_time: 0.
% 150.26/150.50 % subtype_inf_time: 0.
% 150.26/150.50 % unif_index_cands_time: 0.
% 150.26/150.50 % unif_index_add_time: 0.
% 150.26/150.50 % total_time: 150.026
% 150.26/150.50 % num_of_symbols: 133
% 150.26/150.50 % num_of_terms: 3954
% 150.26/150.50
% 150.26/150.50 % ------ Propositional Solver
% 150.26/150.50
% 150.26/150.50 % prop_solver_calls: 1
% 150.26/150.50 % prop_fast_solver_calls: 12
% 150.26/150.50 % prop_num_of_clauses: 765
% 150.26/150.50 % prop_preprocess_simplified: 2325
% 150.26/150.50 % prop_fo_subsumed: 0
% 150.26/150.50 % prop_solver_time: 0.
% 150.26/150.50 % prop_fast_solver_time: 0.
% 150.26/150.50 % prop_unsat_core_time: 0.
% 150.26/150.50
% 150.26/150.50 % ------ QBF
% 150.26/150.50
% 150.26/150.50 % qbf_q_res: 0
% 150.26/150.50 % qbf_num_tautologies: 0
% 150.26/150.50 % qbf_prep_cycles: 0
% 150.26/150.50
% 150.26/150.50 % ------ BMC1
% 150.26/150.50
% 150.26/150.50 % bmc1_current_bound: -1
% 150.26/150.50 % bmc1_last_solved_bound: -1
% 150.26/150.50 % bmc1_unsat_core_size: -1
% 150.26/150.50 % bmc1_unsat_core_parents_size: -1
% 150.26/150.50 % bmc1_merge_next_fun: 0
% 150.26/150.50 % bmc1_unsat_core_clauses_time: 0.
% 150.26/150.50
% 150.26/150.50 % ------ Instantiation
% 150.26/150.50
% 150.26/150.50 % inst_num_of_clauses: 716
% 150.26/150.50 % inst_num_in_passive: 0
% 150.26/150.50 % inst_num_in_active: 0
% 150.26/150.50 % inst_num_in_unprocessed: 790
% 150.26/150.50 % inst_num_of_loops: 0
% 150.26/150.50 % inst_num_of_learning_restarts: 0
% 150.26/150.50 % inst_num_moves_active_passive: 0
% 150.26/150.50 % inst_lit_activity: 0
% 150.26/150.50 % inst_lit_activity_moves: 0
% 150.26/150.50 % inst_num_tautologies: 0
% 150.26/150.50 % inst_num_prop_implied: 0
% 150.26/150.50 % inst_num_existing_simplified: 0
% 150.26/150.50 % inst_num_eq_res_simplified: 0
% 150.26/150.50 % inst_num_child_elim: 0
% 150.26/150.50 % inst_num_of_dismatching_blockings: 0
% 150.26/150.50 % inst_num_of_non_proper_insts: 0
% 150.26/150.50 % inst_num_of_duplicates: 0
% 150.26/150.50 % inst_inst_num_from_inst_to_res: 0
% 150.26/150.50 % inst_dismatching_checking_time: 0.
% 150.26/150.50
% 150.26/150.50 % ------ Resolution
% 150.26/150.50
% 150.26/150.50 % res_num_of_clauses: 634
% 150.26/150.50 % res_num_in_passive: 0
% 150.26/150.50 % res_num_in_active: 266
% 150.26/150.50 % res_num_of_loops: 0
% 150.26/150.50 % res_forward_subset_subsumed: 373
% 150.26/150.50 % res_backward_subset_subsumed: 0
% 150.26/150.50 % res_forward_subsumed: 0
% 150.26/150.50 % res_backward_subsumed: 0
% 150.26/150.50 % res_forward_subsumption_resolution: 0
% 150.26/150.50 % res_backward_subsumption_resolution: 0
% 150.26/150.50 % res_clause_to_clause_subsumption: 0
% 150.26/150.50 % res_orphan_elimination: 0
% 150.26/150.50 % res_tautology_del: 0
% 150.26/150.50 % res_num_eq_res_simplified: 0
% 150.26/150.50 % res_num_sel_changes: 0
% 150.26/150.50 % res_moves_from_active_to_pass: 0
% 150.26/150.50
% 150.26/150.50 % Status Unknown
% 150.35/150.61 % Orienting using strategy ClausalAll
% 150.35/150.61 % Orientation found
% 150.35/150.61 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_c5dc42.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_d8084e.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_755af5 | grep -v "SZS"
% 150.35/150.63
% 150.35/150.63 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 150.35/150.63
% 150.35/150.63 %
% 150.35/150.63 % ------ iProver source info
% 150.35/150.63
% 150.35/150.63 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 150.35/150.63 % git: non_committed_changes: true
% 150.35/150.63 % git: last_make_outside_of_git: true
% 150.35/150.63
% 150.35/150.63 %
% 150.35/150.63 % ------ Input Options
% 150.35/150.63
% 150.35/150.63 % --out_options all
% 150.35/150.63 % --tptp_safe_out true
% 150.35/150.63 % --problem_path ""
% 150.35/150.63 % --include_path ""
% 150.35/150.63 % --clausifier .//eprover
% 150.35/150.63 % --clausifier_options --tstp-format
% 150.35/150.63 % --stdin false
% 150.35/150.63 % --dbg_backtrace false
% 150.35/150.63 % --dbg_dump_prop_clauses false
% 150.35/150.63 % --dbg_dump_prop_clauses_file -
% 150.35/150.63 % --dbg_out_stat false
% 150.35/150.63
% 150.35/150.63 % ------ General Options
% 150.35/150.63
% 150.35/150.63 % --fof false
% 150.35/150.63 % --time_out_real 150.
% 150.35/150.63 % --time_out_prep_mult 0.2
% 150.35/150.63 % --time_out_virtual -1.
% 150.35/150.63 % --schedule none
% 150.35/150.63 % --ground_splitting input
% 150.35/150.63 % --splitting_nvd 16
% 150.35/150.63 % --non_eq_to_eq false
% 150.35/150.63 % --prep_gs_sim true
% 150.35/150.63 % --prep_unflatten false
% 150.35/150.63 % --prep_res_sim true
% 150.35/150.63 % --prep_upred true
% 150.35/150.63 % --res_sim_input true
% 150.35/150.63 % --clause_weak_htbl true
% 150.35/150.63 % --gc_record_bc_elim false
% 150.35/150.63 % --symbol_type_check false
% 150.35/150.63 % --clausify_out false
% 150.35/150.63 % --large_theory_mode false
% 150.35/150.63 % --prep_sem_filter none
% 150.35/150.63 % --prep_sem_filter_out false
% 150.35/150.63 % --preprocessed_out false
% 150.35/150.63 % --sub_typing false
% 150.35/150.63 % --brand_transform false
% 150.35/150.63 % --pure_diseq_elim true
% 150.35/150.63 % --min_unsat_core false
% 150.35/150.63 % --pred_elim true
% 150.35/150.63 % --add_important_lit false
% 150.35/150.63 % --soft_assumptions false
% 150.35/150.63 % --reset_solvers false
% 150.35/150.63 % --bc_imp_inh []
% 150.35/150.63 % --conj_cone_tolerance 1.5
% 150.35/150.63 % --prolific_symb_bound 500
% 150.35/150.63 % --lt_threshold 2000
% 150.35/150.63
% 150.35/150.63 % ------ SAT Options
% 150.35/150.63
% 150.35/150.63 % --sat_mode false
% 150.35/150.63 % --sat_fm_restart_options ""
% 150.35/150.63 % --sat_gr_def false
% 150.35/150.63 % --sat_epr_types true
% 150.35/150.63 % --sat_non_cyclic_types false
% 150.35/150.63 % --sat_finite_models false
% 150.35/150.63 % --sat_fm_lemmas false
% 150.35/150.63 % --sat_fm_prep false
% 150.35/150.63 % --sat_fm_uc_incr true
% 150.35/150.63 % --sat_out_model small
% 150.35/150.63 % --sat_out_clauses false
% 150.35/150.63
% 150.35/150.63 % ------ QBF Options
% 150.35/150.63
% 150.35/150.63 % --qbf_mode false
% 150.35/150.63 % --qbf_elim_univ true
% 150.35/150.63 % --qbf_sk_in true
% 150.35/150.63 % --qbf_pred_elim true
% 150.35/150.63 % --qbf_split 32
% 150.35/150.63
% 150.35/150.63 % ------ BMC1 Options
% 150.35/150.63
% 150.35/150.63 % --bmc1_incremental false
% 150.35/150.63 % --bmc1_axioms reachable_all
% 150.35/150.63 % --bmc1_min_bound 0
% 150.35/150.63 % --bmc1_max_bound -1
% 150.35/150.63 % --bmc1_max_bound_default -1
% 150.35/150.63 % --bmc1_symbol_reachability true
% 150.35/150.63 % --bmc1_property_lemmas false
% 150.35/150.63 % --bmc1_k_induction false
% 150.35/150.63 % --bmc1_non_equiv_states false
% 150.35/150.63 % --bmc1_deadlock false
% 150.35/150.63 % --bmc1_ucm false
% 150.35/150.63 % --bmc1_add_unsat_core none
% 150.35/150.63 % --bmc1_unsat_core_children false
% 150.35/150.63 % --bmc1_unsat_core_extrapolate_axioms false
% 150.35/150.63 % --bmc1_out_stat full
% 150.35/150.63 % --bmc1_ground_init false
% 150.35/150.63 % --bmc1_pre_inst_next_state false
% 150.35/150.63 % --bmc1_pre_inst_state false
% 150.35/150.63 % --bmc1_pre_inst_reach_state false
% 150.35/150.63 % --bmc1_out_unsat_core false
% 150.35/150.63 % --bmc1_aig_witness_out false
% 150.35/150.63 % --bmc1_verbose false
% 150.35/150.63 % --bmc1_dump_clauses_tptp false
% 153.61/153.82 % --bmc1_dump_unsat_core_tptp false
% 153.61/153.82 % --bmc1_dump_file -
% 153.61/153.82 % --bmc1_ucm_expand_uc_limit 128
% 153.61/153.82 % --bmc1_ucm_n_expand_iterations 6
% 153.61/153.82 % --bmc1_ucm_extend_mode 1
% 153.61/153.82 % --bmc1_ucm_init_mode 2
% 153.61/153.82 % --bmc1_ucm_cone_mode none
% 153.61/153.82 % --bmc1_ucm_reduced_relation_type 0
% 153.61/153.82 % --bmc1_ucm_relax_model 4
% 153.61/153.82 % --bmc1_ucm_full_tr_after_sat true
% 153.61/153.82 % --bmc1_ucm_expand_neg_assumptions false
% 153.61/153.82 % --bmc1_ucm_layered_model none
% 153.61/153.82 % --bmc1_ucm_max_lemma_size 10
% 153.61/153.82
% 153.61/153.82 % ------ AIG Options
% 153.61/153.82
% 153.61/153.82 % --aig_mode false
% 153.61/153.82
% 153.61/153.82 % ------ Instantiation Options
% 153.61/153.82
% 153.61/153.82 % --instantiation_flag true
% 153.61/153.82 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 153.61/153.82 % --inst_solver_per_active 750
% 153.61/153.82 % --inst_solver_calls_frac 0.5
% 153.61/153.82 % --inst_passive_queue_type priority_queues
% 153.61/153.82 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 153.61/153.82 % --inst_passive_queues_freq [25;2]
% 153.61/153.82 % --inst_dismatching true
% 153.61/153.82 % --inst_eager_unprocessed_to_passive true
% 153.61/153.82 % --inst_prop_sim_given true
% 153.61/153.82 % --inst_prop_sim_new false
% 153.61/153.82 % --inst_orphan_elimination true
% 153.61/153.82 % --inst_learning_loop_flag true
% 153.61/153.82 % --inst_learning_start 3000
% 153.61/153.82 % --inst_learning_factor 2
% 153.61/153.82 % --inst_start_prop_sim_after_learn 3
% 153.61/153.82 % --inst_sel_renew solver
% 153.61/153.82 % --inst_lit_activity_flag true
% 153.61/153.82 % --inst_out_proof true
% 153.61/153.82
% 153.61/153.82 % ------ Resolution Options
% 153.61/153.82
% 153.61/153.82 % --resolution_flag true
% 153.61/153.82 % --res_lit_sel kbo_max
% 153.61/153.82 % --res_to_prop_solver none
% 153.61/153.82 % --res_prop_simpl_new false
% 153.61/153.82 % --res_prop_simpl_given false
% 153.61/153.82 % --res_passive_queue_type priority_queues
% 153.61/153.82 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 153.61/153.82 % --res_passive_queues_freq [15;5]
% 153.61/153.82 % --res_forward_subs full
% 153.61/153.82 % --res_backward_subs full
% 153.61/153.82 % --res_forward_subs_resolution true
% 153.61/153.82 % --res_backward_subs_resolution true
% 153.61/153.82 % --res_orphan_elimination false
% 153.61/153.82 % --res_time_limit 1000.
% 153.61/153.82 % --res_out_proof true
% 153.61/153.82 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_c5dc42.s
% 153.61/153.82 % --modulo true
% 153.61/153.82
% 153.61/153.82 % ------ Combination Options
% 153.61/153.82
% 153.61/153.82 % --comb_res_mult 1000
% 153.61/153.82 % --comb_inst_mult 300
% 153.61/153.82 % ------
% 153.61/153.82
% 153.61/153.82 % ------ Parsing...% successful
% 153.61/153.82
% 153.61/153.82 % ------ 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 %
% 153.61/153.82
% 153.61/153.82 % ------ Proving...
% 153.61/153.82 % ------ Problem Properties
% 153.61/153.82
% 153.61/153.82 %
% 153.61/153.82 % EPR false
% 153.61/153.82 % Horn false
% 153.61/153.82 % Has equality true
% 153.61/153.82
% 153.61/153.82 % % ------ Input Options Time Limit: Unbounded
% 153.61/153.82
% 153.61/153.82
% 153.61/153.82 Compiling...
% 153.61/153.82 Loading plugin: done.
% 153.61/153.82 Compiling...
% 153.61/153.82 Loading plugin: done.
% 153.61/153.82 Compiling...
% 153.61/153.82 Loading plugin: done.
% 153.61/153.82 Compiling...
% 153.61/153.82 Loading plugin: done.
% 153.61/153.82 Compiling...
% 153.61/153.82 Loading plugin: done.
% 153.61/153.82 Compiling...
% 153.61/153.82 Loading plugin: done.
% 153.61/153.82 Compiling...
% 153.61/153.82 Loading plugin: done.
% 153.61/153.82 Compiling...
% 153.61/153.82 Loading plugin: done.
% 153.61/153.82 Compiling...
% 153.61/153.82 Loading plugin: done.
% 153.61/153.82 Compiling...
% 153.61/153.82 Loading plugin: done.
% 153.61/153.82 Compiling...
% 153.61/153.82 Loading plugin: done.
% 153.61/153.82 Compiling...
% 153.61/153.82 Loading plugin: done.
% 153.61/153.82 Compiling...
% 153.61/153.82 Loading plugin: done.
% 153.61/153.82 Compiling...
% 153.61/153.82 Loading plugin: done.
% 153.61/153.82 Compiling...
% 153.61/153.82 Loading plugin: done.
% 153.61/153.82 Compiling...
% 153.61/153.82 Loading plugin: done.
% 153.61/153.82 Compiling...
% 153.61/153.82 Loading plugin: done.
% 153.61/153.82 % % ------ Current options:
% 153.61/153.82
% 153.61/153.82 % ------ Input Options
% 153.61/153.82
% 153.61/153.82 % --out_options all
% 153.61/153.82 % --tptp_safe_out true
% 153.61/153.82 % --problem_path ""
% 153.61/153.82 % --include_path ""
% 153.61/153.82 % --clausifier .//eprover
% 153.61/153.82 % --clausifier_options --tstp-format
% 153.61/153.82 % --stdin false
% 153.61/153.82 % --dbg_backtrace false
% 153.61/153.82 % --dbg_dump_prop_clauses false
% 153.61/153.82 % --dbg_dump_prop_clauses_file -
% 153.61/153.82 % --dbg_out_stat false
% 153.61/153.82
% 153.61/153.82 % ------ General Options
% 153.61/153.82
% 153.61/153.82 % --fof false
% 153.61/153.82 % --time_out_real 150.
% 153.61/153.82 % --time_out_prep_mult 0.2
% 153.61/153.82 % --time_out_virtual -1.
% 153.61/153.82 % --schedule none
% 153.61/153.82 % --ground_splitting input
% 153.61/153.82 % --splitting_nvd 16
% 153.61/153.82 % --non_eq_to_eq false
% 153.61/153.82 % --prep_gs_sim true
% 153.61/153.82 % --prep_unflatten false
% 153.61/153.82 % --prep_res_sim true
% 153.61/153.82 % --prep_upred true
% 153.61/153.82 % --res_sim_input true
% 153.61/153.82 % --clause_weak_htbl true
% 153.61/153.82 % --gc_record_bc_elim false
% 153.61/153.82 % --symbol_type_check false
% 153.61/153.82 % --clausify_out false
% 153.61/153.82 % --large_theory_mode false
% 153.61/153.82 % --prep_sem_filter none
% 153.61/153.82 % --prep_sem_filter_out false
% 153.61/153.82 % --preprocessed_out false
% 153.61/153.82 % --sub_typing false
% 153.61/153.82 % --brand_transform false
% 153.61/153.82 % --pure_diseq_elim true
% 153.61/153.82 % --min_unsat_core false
% 153.61/153.82 % --pred_elim true
% 153.61/153.82 % --add_important_lit false
% 153.61/153.82 % --soft_assumptions false
% 153.61/153.82 % --reset_solvers false
% 153.61/153.82 % --bc_imp_inh []
% 153.61/153.82 % --conj_cone_tolerance 1.5
% 153.61/153.82 % --prolific_symb_bound 500
% 153.61/153.82 % --lt_threshold 2000
% 153.61/153.82
% 153.61/153.82 % ------ SAT Options
% 153.61/153.82
% 153.61/153.82 % --sat_mode false
% 153.61/153.82 % --sat_fm_restart_options ""
% 153.61/153.82 % --sat_gr_def false
% 153.61/153.82 % --sat_epr_types true
% 153.61/153.82 % --sat_non_cyclic_types false
% 153.61/153.82 % --sat_finite_models false
% 153.61/153.82 % --sat_fm_lemmas false
% 153.61/153.82 % --sat_fm_prep false
% 153.61/153.82 % --sat_fm_uc_incr true
% 153.61/153.82 % --sat_out_model small
% 153.61/153.82 % --sat_out_clauses false
% 153.61/153.82
% 153.61/153.82 % ------ QBF Options
% 153.61/153.82
% 153.61/153.82 % --qbf_mode false
% 153.61/153.82 % --qbf_elim_univ true
% 153.61/153.82 % --qbf_sk_in true
% 153.61/153.82 % --qbf_pred_elim true
% 153.61/153.82 % --qbf_split 32
% 153.61/153.82
% 153.61/153.82 % ------ BMC1 Options
% 153.61/153.82
% 153.61/153.82 % --bmc1_incremental false
% 153.61/153.82 % --bmc1_axioms reachable_all
% 153.61/153.82 % --bmc1_min_bound 0
% 153.61/153.82 % --bmc1_max_bound -1
% 153.61/153.82 % --bmc1_max_bound_default -1
% 153.61/153.82 % --bmc1_symbol_reachability true
% 153.61/153.82 % --bmc1_property_lemmas false
% 153.61/153.82 % --bmc1_k_induction false
% 153.61/153.82 % --bmc1_non_equiv_states false
% 153.61/153.82 % --bmc1_deadlock false
% 153.61/153.82 % --bmc1_ucm false
% 153.61/153.82 % --bmc1_add_unsat_core none
% 153.61/153.82 % --bmc1_unsat_core_children false
% 153.61/153.82 % --bmc1_unsat_core_extrapolate_axioms false
% 153.61/153.82 % --bmc1_out_stat full
% 153.61/153.82 % --bmc1_ground_init false
% 153.61/153.82 % --bmc1_pre_inst_next_state false
% 153.61/153.82 % --bmc1_pre_inst_state false
% 153.61/153.82 % --bmc1_pre_inst_reach_state false
% 153.61/153.82 % --bmc1_out_unsat_core false
% 153.61/153.82 % --bmc1_aig_witness_out false
% 153.61/153.82 % --bmc1_verbose false
% 153.61/153.82 % --bmc1_dump_clauses_tptp false
% 153.61/153.82 % --bmc1_dump_unsat_core_tptp false
% 153.61/153.82 % --bmc1_dump_file -
% 153.61/153.82 % --bmc1_ucm_expand_uc_limit 128
% 153.61/153.82 % --bmc1_ucm_n_expand_iterations 6
% 153.61/153.82 % --bmc1_ucm_extend_mode 1
% 153.61/153.82 % --bmc1_ucm_init_mode 2
% 153.61/153.82 % --bmc1_ucm_cone_mode none
% 153.61/153.82 % --bmc1_ucm_reduced_relation_type 0
% 153.61/153.82 % --bmc1_ucm_relax_model 4
% 153.61/153.82 % --bmc1_ucm_full_tr_after_sat true
% 153.61/153.82 % --bmc1_ucm_expand_neg_assumptions false
% 153.61/153.82 % --bmc1_ucm_layered_model none
% 153.61/153.82 % --bmc1_ucm_max_lemma_size 10
% 153.61/153.82
% 153.61/153.82 % ------ AIG Options
% 153.61/153.82
% 153.61/153.82 % --aig_mode false
% 174.89/175.09
% 174.89/175.09 % ------ Instantiation Options
% 174.89/175.09
% 174.89/175.09 % --instantiation_flag true
% 174.89/175.09 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 174.89/175.09 % --inst_solver_per_active 750
% 174.89/175.09 % --inst_solver_calls_frac 0.5
% 174.89/175.09 % --inst_passive_queue_type priority_queues
% 174.89/175.09 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 174.89/175.09 % --inst_passive_queues_freq [25;2]
% 174.89/175.09 % --inst_dismatching true
% 174.89/175.09 % --inst_eager_unprocessed_to_passive true
% 174.89/175.09 % --inst_prop_sim_given true
% 174.89/175.09 % --inst_prop_sim_new false
% 174.89/175.09 % --inst_orphan_elimination true
% 174.89/175.09 % --inst_learning_loop_flag true
% 174.89/175.09 % --inst_learning_start 3000
% 174.89/175.09 % --inst_learning_factor 2
% 174.89/175.09 % --inst_start_prop_sim_after_learn 3
% 174.89/175.09 % --inst_sel_renew solver
% 174.89/175.09 % --inst_lit_activity_flag true
% 174.89/175.09 % --inst_out_proof true
% 174.89/175.09
% 174.89/175.09 % ------ Resolution Options
% 174.89/175.09
% 174.89/175.09 % --resolution_flag true
% 174.89/175.09 % --res_lit_sel kbo_max
% 174.89/175.09 % --res_to_prop_solver none
% 174.89/175.09 % --res_prop_simpl_new false
% 174.89/175.09 % --res_prop_simpl_given false
% 174.89/175.09 % --res_passive_queue_type priority_queues
% 174.89/175.09 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 174.89/175.09 % --res_passive_queues_freq [15;5]
% 174.89/175.09 % --res_forward_subs full
% 174.89/175.09 % --res_backward_subs full
% 174.89/175.09 % --res_forward_subs_resolution true
% 174.89/175.09 % --res_backward_subs_resolution true
% 174.89/175.09 % --res_orphan_elimination false
% 174.89/175.09 % --res_time_limit 1000.
% 174.89/175.09 % --res_out_proof true
% 174.89/175.09 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_c5dc42.s
% 174.89/175.09 % --modulo true
% 174.89/175.09
% 174.89/175.09 % ------ Combination Options
% 174.89/175.09
% 174.89/175.09 % --comb_res_mult 1000
% 174.89/175.09 % --comb_inst_mult 300
% 174.89/175.09 % ------
% 174.89/175.09
% 174.89/175.09
% 174.89/175.09
% 174.89/175.09 % ------ Proving...
% 174.89/175.09 %
% 174.89/175.09
% 174.89/175.09
% 174.89/175.09 % ------ Statistics
% 174.89/175.09
% 174.89/175.09 % ------ General
% 174.89/175.09
% 174.89/175.09 % num_of_input_clauses: 790
% 174.89/175.09 % num_of_input_neg_conjectures: 4
% 174.89/175.09 % num_of_splits: 0
% 174.89/175.09 % num_of_split_atoms: 0
% 174.89/175.09 % num_of_sem_filtered_clauses: 0
% 174.89/175.09 % num_of_subtypes: 0
% 174.89/175.09 % monotx_restored_types: 0
% 174.89/175.09 % sat_num_of_epr_types: 0
% 174.89/175.09 % sat_num_of_non_cyclic_types: 0
% 174.89/175.09 % sat_guarded_non_collapsed_types: 0
% 174.89/175.09 % is_epr: 0
% 174.89/175.09 % is_horn: 0
% 174.89/175.09 % has_eq: 1
% 174.89/175.09 % num_pure_diseq_elim: 0
% 174.89/175.09 % simp_replaced_by: 0
% 174.89/175.09 % res_preprocessed: 8
% 174.89/175.09 % prep_upred: 0
% 174.89/175.09 % prep_unflattend: 0
% 174.89/175.09 % pred_elim_cands: 0
% 174.89/175.09 % pred_elim: 0
% 174.89/175.09 % pred_elim_cl: 0
% 174.89/175.09 % pred_elim_cycles: 0
% 174.89/175.09 % forced_gc_time: 0
% 174.89/175.09 % gc_basic_clause_elim: 0
% 174.89/175.09 % parsing_time: 0.024
% 174.89/175.09 % sem_filter_time: 0.
% 174.89/175.09 % pred_elim_time: 0.
% 174.89/175.09 % out_proof_time: 0.
% 174.89/175.09 % monotx_time: 0.
% 174.89/175.09 % subtype_inf_time: 0.
% 174.89/175.09 % unif_index_cands_time: 0.026
% 174.89/175.09 % unif_index_add_time: 0.022
% 174.89/175.09 % total_time: 24.468
% 174.89/175.09 % num_of_symbols: 133
% 174.89/175.09 % num_of_terms: 140740
% 174.89/175.09
% 174.89/175.09 % ------ Propositional Solver
% 174.89/175.09
% 174.89/175.09 % prop_solver_calls: 4
% 174.89/175.09 % prop_fast_solver_calls: 12
% 174.89/175.09 % prop_num_of_clauses: 2296
% 174.89/175.09 % prop_preprocess_simplified: 5857
% 174.89/175.09 % prop_fo_subsumed: 0
% 174.89/175.09 % prop_solver_time: 0.
% 174.89/175.09 % prop_fast_solver_time: 0.
% 174.89/175.09 % prop_unsat_core_time: 0.
% 174.89/175.09
% 174.89/175.09 % ------ QBF
% 174.89/175.09
% 174.89/175.09 % qbf_q_res: 0
% 174.89/175.09 % qbf_num_tautologies: 0
% 174.89/175.09 % qbf_prep_cycles: 0
% 174.89/175.09
% 174.89/175.09 % ------ BMC1
% 174.89/175.09
% 174.89/175.09 % bmc1_current_bound: -1
% 174.89/175.09 % bmc1_last_solved_bound: -1
% 174.89/175.09 % bmc1_unsat_core_size: -1
% 174.89/175.09 % bmc1_unsat_core_parents_size: -1
% 174.89/175.09 % bmc1_merge_next_fun: 0
% 174.89/175.09 % bmc1_unsat_core_clauses_time: 0.
% 174.89/175.09
% 174.89/175.09 % ------ Instantiation
% 174.89/175.09
% 174.89/175.09 % inst_num_of_clauses: 1619
% 174.89/175.09 % inst_num_in_passive: 1124
% 174.89/175.09 % inst_num_in_active: 493
% 174.89/175.09 % inst_num_in_unprocessed: 0
% 174.89/175.09 % inst_num_of_loops: 515
% 174.89/175.09 % inst_num_of_learning_restarts: 0
% 174.89/175.09 % inst_num_moves_active_passive: 20
% 174.89/175.09 % inst_lit_activity: 260
% 174.89/175.09 % inst_lit_activity_moves: 0
% 174.89/175.09 % inst_num_tautologies: 0
% 174.89/175.09 % inst_num_prop_implied: 0
% 174.89/175.09 % inst_num_existing_simplified: 0
% 174.89/175.09 % inst_num_eq_res_simplified: 0
% 174.89/175.09 % inst_num_child_elim: 0
% 174.89/175.09 % inst_num_of_dismatching_blockings: 250
% 174.89/175.09 % inst_num_of_non_proper_insts: 789
% 174.89/175.09 % inst_num_of_duplicates: 1411
% 174.89/175.09 % inst_inst_num_from_inst_to_res: 0
% 174.89/175.09 % inst_dismatching_checking_time: 0.001
% 174.89/175.09
% 174.89/175.09 % ------ Resolution
% 174.89/175.09
% 174.89/175.09 % res_num_of_clauses: 18476
% 174.89/175.09 % res_num_in_passive: 15840
% 174.89/175.09 % res_num_in_active: 2207
% 174.89/175.09 % res_num_of_loops: 2000
% 174.89/175.09 % res_forward_subset_subsumed: 998
% 174.89/175.09 % res_backward_subset_subsumed: 0
% 174.89/175.09 % res_forward_subsumed: 122
% 174.89/175.09 % res_backward_subsumed: 0
% 174.89/175.09 % res_forward_subsumption_resolution: 1
% 174.89/175.09 % res_backward_subsumption_resolution: 0
% 174.89/175.09 % res_clause_to_clause_subsumption: 23918
% 174.89/175.09 % res_orphan_elimination: 0
% 174.89/175.09 % res_tautology_del: 0
% 174.89/175.09 % res_num_eq_res_simplified: 0
% 174.89/175.09 % res_num_sel_changes: 0
% 174.89/175.09 % res_moves_from_active_to_pass: 0
% 174.89/175.09
% 174.89/175.09 % Status Unsatisfiable
% 174.89/175.09 % SZS status Unsatisfiable
% 174.89/175.09 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------