%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : LCL759-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 12:21:52 PM UTC 2026
% Result : Unsatisfiable 154.21s 154.58s
% Output : CNFRefutation 154.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 641
% Syntax : Number of formulae : 4651 ( 952 unt; 0 def)
% Number of atoms : 11195 (3593 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 12538 (5994 ~;6544 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 49 ( 47 usr; 1 prp; 0-3 aty)
% Number of functors : 44 ( 44 usr; 12 con; 0-6 aty)
% Number of variables : 12443 ( 836 sgn4953 !; 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,
! [X12,X41,X6,X9] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,X6,X41,tc_Lambda_OdB,tc_Lambda_OdB)),X12),X9) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X6),X12),X9),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X12,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X9,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X41,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
file('<stdin>',cls_subst__map_0) ).
fof(c_0_1,axiom,
! [X12,X41,X9,X10,X42,X26] :
( c_Type_Otypings(X10,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X12,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X9,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X41,tc_Lambda_OdB,tc_Lambda_OdB),X42)
| ~ c_Type_Otypings(c_Type_Oshift(X10,X9,X26,tc_Type_Otype),X41,X42)
| ~ c_Type_Otyping(X10,X12,X26) ),
file('<stdin>',cls_substs__lemma_0) ).
fof(c_0_2,axiom,
! [X50,X7,X23] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X23)),X7),X50,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X7))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X23),X7),c_HOL_Ozero__class_Ozero(tc_nat)),X50,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('<stdin>',cls_Beta_0) ).
fof(c_0_3,axiom,
! [X41,X6,X9] : hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,X6,X41,tc_Lambda_OdB,tc_Lambda_OdB)),X9) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X6),X9),c_List_Omap(c_COMBC(c_Lambda_Olift,X9,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X41,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
file('<stdin>',cls_lift__map_0) ).
fof(c_0_4,axiom,
! [X41,X9,X10,X25,X26] :
( X26 = X25
| ~ c_Type_Otyping(X10,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X9),X41,tc_Lambda_OdB,tc_Lambda_OdB),X25)
| ~ c_Type_Otyping(X10,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X9),X41,tc_Lambda_OdB,tc_Lambda_OdB),X26) ),
file('<stdin>',cls_var__app__type__eq_0) ).
fof(c_0_5,axiom,
! [X56,X57,X27,X58,X39,X3] : c_COMBB(X27,X57,X56,X39,X3,X58) = hAPP(X27,hAPP(X57,X56)),
file('<stdin>',cls_ATP__Linkup_OCOMBB__def_0) ).
fof(c_0_6,axiom,
! [X41,X9,X10,X25,X42] :
( c_Type_Otypings(c_Type_Oshift(X10,X9,X25,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,X9,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X41,tc_Lambda_OdB,tc_Lambda_OdB),X42)
| ~ c_Type_Otypings(X10,X41,X42) ),
file('<stdin>',cls_lift__types_0) ).
fof(c_0_7,axiom,
! [X41] :
( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X41,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_List_Olistsp(c_InductTermi_OIT,X41,tc_Lambda_OdB) ),
file('<stdin>',cls_lifts__IT_0) ).
fof(c_0_8,axiom,
! [X51,X4] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X51,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_List_Olistsp(c_InductTermi_OIT,X51,tc_Lambda_OdB) ),
file('<stdin>',cls_IT_OVar_0) ).
fof(c_0_9,axiom,
! [X50,X7,X23] :
( c_Lambda_Obeta(c_List_Ofoldl(c_Lambda_OdB_OApp,X23,X50,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X50,tc_Lambda_OdB,tc_Lambda_OdB))
| ~ c_Lambda_Obeta(X23,X7) ),
file('<stdin>',cls_apps__preserves__beta_0) ).
fof(c_0_10,axiom,
! [X50,X7,X51,X23] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X23),X51,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X7),X50,tc_Lambda_OdB,tc_Lambda_OdB)
| X51 = X50 ),
file('<stdin>',cls_Abs__apps__eq__Abs__apps__conv_1) ).
fof(c_0_11,axiom,
! [X50,X7,X51,X23] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X23),X51,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X7),X50,tc_Lambda_OdB,tc_Lambda_OdB)
| X23 = X7 ),
file('<stdin>',cls_Abs__apps__eq__Abs__apps__conv_0) ).
fof(c_0_12,axiom,
! [X50,X51,X4,X5] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X51,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X50,tc_Lambda_OdB,tc_Lambda_OdB)
| X51 = X50 ),
file('<stdin>',cls_Var__apps__eq__Var__apps__conv_1) ).
fof(c_0_13,axiom,
! [X50,X51,X4,X5] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X51,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X50,tc_Lambda_OdB,tc_Lambda_OdB)
| X5 = X4 ),
file('<stdin>',cls_Var__apps__eq__Var__apps__conv_0) ).
fof(c_0_14,axiom,
! [X40,X15,X16,X3] :
( ~ class_OrderedGroup_Osemigroup__add(X3)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X15),X40,X3,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X15,X40,X3,X3)) ),
file('<stdin>',cls_foldl__assoc_0) ).
fof(c_0_15,axiom,
! [X41,X50,X23,X4] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X41,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X23),X50,tc_Lambda_OdB,tc_Lambda_OdB),
file('<stdin>',cls_Var__apps__neq__Abs__apps_0) ).
fof(c_0_16,axiom,
! [X41,X7,X23] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X23,X41,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X41,tc_Lambda_OdB,tc_Lambda_OdB)
| X23 = X7 ),
file('<stdin>',cls_apps__eq__tail__conv_0) ).
fof(c_0_17,axiom,
! [X40,X16,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3),X40,X3,X3)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X16,X40,X3,X3) ),
file('<stdin>',cls_foldl__absorb0_0) ).
fof(c_0_18,axiom,
! [X13,X8,X9,X27] :
( ~ c_HOL_Oord__class_Oless(X8,X13,tc_nat)
| X13 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ hBOOL(hAPP(X27,c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X13,X9,tc_nat)),X8),X13,tc_nat)))
| hBOOL(hAPP(X27,X9)) ),
file('<stdin>',cls_split__div_1) ).
fof(c_0_19,axiom,
! [X13,X8,X9,X27] :
( ~ c_HOL_Oord__class_Oless(X8,X13,tc_nat)
| X13 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ hBOOL(hAPP(X27,c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X13,X9,tc_nat)),X8),X13,tc_nat)))
| hBOOL(hAPP(X27,X8)) ),
file('<stdin>',cls_split__mod_1) ).
fof(c_0_20,axiom,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X1,X3)),c_Divides_Odiv__class_Omod(X2,X1,X3))),X11) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X11) ),
file('<stdin>',cls_div__mod__equality_0) ).
fof(c_0_21,axiom,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X2,X1,X3),X3)),c_Divides_Odiv__class_Omod(X2,X1,X3))),X11) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X11) ),
file('<stdin>',cls_div__mod__equality2_0) ).
fof(c_0_22,axiom,
! [X22,X12,X6,X8,X9] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X6),hAPP(hAPP(c_Lambda_Olift,X22),X9)),c_Suc(X8))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X12),X22),X8)),X9) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X6),X12),X9)),X22),X8)
| ~ c_HOL_Oord__class_Oless(X9,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
file('<stdin>',cls_subst__subst_0) ).
fof(c_0_23,axiom,
! [X11,X1,X2] : c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),X11,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(X2,X11,tc_nat)),c_Divides_Odiv__class_Odiv(X1,X11,tc_nat))),c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(X2,X11,tc_nat)),c_Divides_Odiv__class_Omod(X1,X11,tc_nat)),X11,tc_nat)),
file('<stdin>',cls_div__add1__eq_0) ).
fof(c_0_24,axiom,
! [X56,X57,X27,X58,X39,X3] : hAPP(c_COMBC(X27,X57,X39,X58,X3),X56) = hAPP(hAPP(X27,X56),X57),
file('<stdin>',cls_ATP__Linkup_OCOMBC__def_0) ).
fof(c_0_25,axiom,
! [X56,X57,X27,X58,X39,X3] : hAPP(c_COMBC(X27,X57,X39,X58,X3),X56) = hAPP(hAPP(X27,X56),X57),
file('<stdin>',cls_COMBC__def_0) ).
fof(c_0_26,axiom,
! [X6,X7,X23] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X23),X7) != c_List_Ofoldl(c_Lambda_OdB_OApp,X6,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,X23),X7) = X6 ),
file('<stdin>',cls_App__eq__foldl__conv_0) ).
fof(c_0_27,axiom,
! [X6,X50,X7,X4] : hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X7)),X6) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X50,tc_Lambda_OdB,tc_Lambda_OdB),
file('<stdin>',cls_Abs__App__neq__Var__apps_0) ).
fof(c_0_28,axiom,
! [X50,X7,X23] :
( c_Lambda_OdB_OAbs(X23) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X50,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(X23) = X7 ),
file('<stdin>',cls_Abs__eq__apps__conv_0) ).
fof(c_0_29,axiom,
! [X50,X7,X5] :
( c_Lambda_OdB_OVar(X5) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X50,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OVar(X5) = X7 ),
file('<stdin>',cls_Var__eq__apps__conv_0) ).
fof(c_0_30,axiom,
! [X50,X7,X23] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X50,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X23)
| X7 = c_Lambda_OdB_OAbs(X23) ),
file('<stdin>',cls_apps__eq__Abs__conv_0) ).
fof(c_0_31,axiom,
! [X6,X7,X8,X9] :
( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X6),X7),X8)),X9) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,X7),X9)),X8)
| ~ c_HOL_Oord__class_Oless(X8,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
file('<stdin>',cls_lift__subst_0) ).
fof(c_0_32,axiom,
! [X50,X7,X5] :
( c_Lambda_OdB_OVar(X5) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X50,tc_Lambda_OdB,tc_Lambda_OdB)
| X50 = c_List_Olist_ONil(tc_Lambda_OdB) ),
file('<stdin>',cls_Var__eq__apps__conv_1) ).
fof(c_0_33,axiom,
! [X50,X7,X23] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X50,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X23)
| X50 = c_List_Olist_ONil(tc_Lambda_OdB) ),
file('<stdin>',cls_apps__eq__Abs__conv_1) ).
fof(c_0_34,axiom,
! [X50,X7,X23] :
( c_Lambda_OdB_OAbs(X23) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X50,tc_Lambda_OdB,tc_Lambda_OdB)
| X50 = c_List_Olist_ONil(tc_Lambda_OdB) ),
file('<stdin>',cls_Abs__eq__apps__conv_1) ).
fof(c_0_35,axiom,
! [X11,X1,X2] : c_Divides_Odiv__class_Omod(X2,c_HOL_Otimes__class_Otimes(X1,X11,tc_nat),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Odiv(X2,X1,tc_nat),X11,tc_nat),tc_nat)),c_Divides_Odiv__class_Omod(X2,X1,tc_nat)),
file('<stdin>',cls_mod__mult2__eq_0) ).
fof(c_0_36,axiom,
! [X23,X18,X11,X1] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X18,X11,tc_nat),tc_nat)),X23),c_HOL_Otimes__class_Otimes(X1,X11,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X23,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat) ),
file('<stdin>',cls_mod__lemma_0) ).
fof(c_0_37,axiom,
! [X11,X1,X2] : c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),X11,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X1,X11,tc_nat),tc_nat)),c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Omod(X1,X11,tc_nat),tc_nat),X11,tc_nat)),
file('<stdin>',cls_div__mult1__eq_0) ).
fof(c_0_38,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)),X3) ),
file('<stdin>',cls_sum__squares__gt__zero__iff_0) ).
fof(c_0_39,axiom,
! [X9,X10,X25,X26,X3] : c_Type_Oshift(c_Type_Oshift(X10,X9,X25,X3),c_HOL_Ozero__class_Ozero(tc_nat),X26,X3) = c_Type_Oshift(c_Type_Oshift(X10,c_HOL_Ozero__class_Ozero(tc_nat),X26,X3),c_Suc(X9),X25,X3),
file('<stdin>',cls_shift__commute_0) ).
fof(c_0_40,axiom,
! [X10,X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Osemiring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X2,X10,X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X1,X10,X3)),X11)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1),X10,X3)),X11) ),
file('<stdin>',cls_combine__common__factor_0) ).
fof(c_0_41,axiom,
! [X12,X13,X8,X9] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X9,X12,tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X8,X12,tc_nat)),X13)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X8),X12,tc_nat)),X13),
file('<stdin>',cls_left__add__mult__distrib_0) ).
fof(c_0_42,axiom,
! [X7,X23] : hAPP(hAPP(c_Lambda_OdB_OApp,X23),X7) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X23),X7),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
file('<stdin>',cls_App__eq__foldl__conv_4) ).
fof(c_0_43,axiom,
! [X15,X16,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X16,X16,X3)),c_HOL_Otimes__class_Otimes(X15,X15,X3)),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_not__sum__squares__lt__zero_0) ).
fof(c_0_44,axiom,
! [X6,X7,X8,X9] :
( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X6),X7),X8)),X9) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X6),X9)),hAPP(hAPP(c_Lambda_Olift,X7),X9)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),c_HOL_Oone__class_Oone(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X9,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
file('<stdin>',cls_lift__subst__lt_0) ).
fof(c_0_45,axiom,
! [X5] : c_Lambda_OdB_OVar(X5) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
file('<stdin>',cls_Var__eq__apps__conv_2) ).
fof(c_0_46,axiom,
! [X23] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X23),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OAbs(X23),
file('<stdin>',cls_apps__eq__Abs__conv_2) ).
fof(c_0_47,axiom,
! [X23] : c_Lambda_OdB_OAbs(X23) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X23),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
file('<stdin>',cls_Abs__eq__apps__conv_2) ).
fof(c_0_48,axiom,
! [X38,X2,X39,X3] : c_List_Ofoldl(X38,X2,c_List_Olist_ONil(X39),X3,X39) = X2,
file('<stdin>',cls_foldl__Nil_0) ).
fof(c_0_49,axiom,
! [X17,X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X2,X11,X3)),c_HOL_Otimes__class_Otimes(X1,X17,X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X2,X17,X3)),c_HOL_Otimes__class_Otimes(X1,X11,X3))
| X11 = X17
| X2 = X1 ),
file('<stdin>',cls_class__ringb_Onoteq__reduce_0) ).
fof(c_0_50,axiom,
! [X14,X15,X16,X31,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X31,X15,X3)),c_HOL_Otimes__class_Otimes(X16,X14,X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X31,X14,X3)),c_HOL_Otimes__class_Otimes(X16,X15,X3))
| X15 = X14
| X31 = X16 ),
file('<stdin>',cls_class__ringb_Oadd__mul__solve_0) ).
fof(c_0_51,axiom,
! [X12,X6,X9,X24,X25,X26] :
( ~ c_Type_Otyping(X24,X12,X25)
| ~ c_Type_Otyping(c_Type_Oshift(X24,X9,X25,tc_Type_Otype),X6,X26)
| c_Type_Otyping(X24,hAPP(hAPP(hAPP(c_Lambda_Osubst,X6),X12),X9),X26) ),
file('<stdin>',cls_subst__lemma_0) ).
fof(c_0_52,axiom,
! [X4,X5,X13] : c_Divides_Odiv__class_Omod(c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat)),X5)),X4,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X5),X4,tc_nat),
file('<stdin>',cls_mod__mult__self4_0) ).
fof(c_0_53,axiom,
! [X14,X15,X16,X31] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X31,X15,tc_nat)),c_HOL_Otimes__class_Otimes(X16,X14,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X31,X14,tc_nat)),c_HOL_Otimes__class_Otimes(X16,X15,tc_nat))
| X15 = X14
| X31 = X16 ),
file('<stdin>',cls_natgb_Oadd__mul__solve_0) ).
fof(c_0_54,axiom,
! [X17,X11,X1,X2] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X2,X11,tc_nat)),c_HOL_Otimes__class_Otimes(X1,X17,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X2,X17,tc_nat)),c_HOL_Otimes__class_Otimes(X1,X11,tc_nat))
| X11 = X17
| X2 = X1 ),
file('<stdin>',cls_natgb_Onoteq__reduce_0) ).
fof(c_0_55,axiom,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1),X11,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Omod(X2,X11,X3)),c_Divides_Odiv__class_Omod(X1,X11,X3)),X11,X3) ),
file('<stdin>',cls_mod__add__eq_0) ).
fof(c_0_56,axiom,
! [X12,X6,X7,X13] : hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,X6),X12)),X7),X13) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X6),X7),X13)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X12),X7),X13)),
file('<stdin>',cls_subst__App_0) ).
fof(c_0_57,axiom,
! [X15,X16,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X16,X16,X3)),c_HOL_Otimes__class_Otimes(X15,X15,X3)),X3)
| X15 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_sum__squares__gt__zero__iff_2) ).
fof(c_0_58,axiom,
! [X15,X16,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X16,X16,X3)),c_HOL_Otimes__class_Otimes(X15,X15,X3)),X3)
| X16 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_sum__squares__gt__zero__iff_1) ).
fof(c_0_59,axiom,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| X2 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X1,X3)),c_Divides_Odiv__class_Omod(X2,X1,X3)) ),
file('<stdin>',cls_mod__div__decomp_0) ).
fof(c_0_60,axiom,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X1,X3)),c_Divides_Odiv__class_Omod(X2,X1,X3)) = X2 ),
file('<stdin>',cls_mod__div__equality_0) ).
fof(c_0_61,axiom,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X2,X1,X3),X3)),c_Divides_Odiv__class_Omod(X2,X1,X3)) = X2 ),
file('<stdin>',cls_mod__div__equality2_0) ).
fof(c_0_62,axiom,
! [X6,X7,X13] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(X6)),X7),X13) = c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,X6),hAPP(hAPP(c_Lambda_Olift,X7),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)))),
file('<stdin>',cls_subst__Abs_0) ).
fof(c_0_63,axiom,
! [X16,X17,X11,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X16,X11,X3)),c_HOL_Otimes__class_Otimes(X16,X17,X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X16,X17,X3)),c_HOL_Otimes__class_Otimes(X16,X11,X3)) ),
file('<stdin>',cls_class__ringb_Onoteq__reduce_1) ).
fof(c_0_64,axiom,
! [X14,X15,X16,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X16,X15,X3)),c_HOL_Otimes__class_Otimes(X16,X14,X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X16,X14,X3)),c_HOL_Otimes__class_Otimes(X16,X15,X3)) ),
file('<stdin>',cls_class__ringb_Oadd__mul__solve_1) ).
fof(c_0_65,axiom,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,X3),X11,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X11,X3),c_Divides_Odiv__class_Omod(X1,X11,X3),X3),X11,X3) ),
file('<stdin>',cls_mod__mult__eq_0) ).
fof(c_0_66,axiom,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Omod(X2,X11,X3)),X1),X11,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1),X11,X3) ),
file('<stdin>',cls_zmod__simps_I1_J_0) ).
fof(c_0_67,axiom,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1),X11,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Omod(X2,X11,X3)),X1),X11,X3) ),
file('<stdin>',cls_mod__add__left__eq_0) ).
fof(c_0_68,axiom,
! [X17,X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X11)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X17)) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I20_J_0) ).
fof(c_0_69,axiom,
! [X14,X15,X16,X31,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X16,X15,X3),c_Divides_Odiv__class_Odiv(X31,X14,X3),X3) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X16,X31,X3),c_HOL_Otimes__class_Otimes(X15,X14,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X31,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X16,X3) ),
file('<stdin>',cls_div__mult__div__if__dvd_0) ).
fof(c_0_70,axiom,
! [X14,X15,X16] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X16,X15,tc_nat)),c_HOL_Otimes__class_Otimes(X16,X14,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X16,X14,tc_nat)),c_HOL_Otimes__class_Otimes(X16,X15,tc_nat)),
file('<stdin>',cls_natgb_Oadd__mul__solve_1) ).
fof(c_0_71,axiom,
! [X16,X17,X11] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X16,X11,tc_nat)),c_HOL_Otimes__class_Otimes(X16,X17,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X16,X17,tc_nat)),c_HOL_Otimes__class_Otimes(X16,X11,tc_nat)),
file('<stdin>',cls_natgb_Onoteq__reduce_1) ).
fof(c_0_72,axiom,
! [X14,X15,X16,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X15),X14,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Odiv(X16,X14,X3)),c_Divides_Odiv__class_Odiv(X15,X14,X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X15,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X16,X3) ),
file('<stdin>',cls_div__add_0) ).
fof(c_0_73,axiom,
! [X6,X9,X10,X25,X26] :
( c_Type_Otyping(c_Type_Oshift(X10,X9,X25,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X6),X9),X26)
| ~ c_Type_Otyping(X10,X6,X26) ),
file('<stdin>',cls_lift__type_0) ).
fof(c_0_74,axiom,
! [X4,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X4,X3),X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_power__Suc__less_0) ).
fof(c_0_75,axiom,
! [X4,X5] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| c_HOL_Oord__class_Oless(X5,c_HOL_Otimes__class_Otimes(X4,c_Suc(c_Divides_Odiv__class_Odiv(X5,X4,tc_nat)),tc_nat),tc_nat) ),
file('<stdin>',cls_split__div__lemma_2) ).
fof(c_0_76,axiom,
! [X11,X29,X1,X30,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X1,X11,X3) != c_Divides_Odiv__class_Omod(X29,X11,X3)
| c_Divides_Odiv__class_Omod(X2,X11,X3) != c_Divides_Odiv__class_Omod(X30,X11,X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,X3),X11,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X30,X29,X3),X11,X3) ),
file('<stdin>',cls_mod__mult__cong_0) ).
fof(c_0_77,axiom,
! [X11,X29,X1,X30,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X1,X11,X3) != c_Divides_Odiv__class_Omod(X29,X11,X3)
| c_Divides_Odiv__class_Omod(X2,X11,X3) != c_Divides_Odiv__class_Omod(X30,X11,X3)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1),X11,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X30),X29),X11,X3) ),
file('<stdin>',cls_mod__add__cong_0) ).
fof(c_0_78,axiom,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X11,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X1,X2,X3),c_Divides_Odiv__class_Odiv(X11,X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X11,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
file('<stdin>',cls_div__dvd__div_0) ).
fof(c_0_79,axiom,
! [X32,X33,X34,X35,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X35,X34,X3),c_HOL_Otimes__class_Otimes(X33,X32,X3),X3) = c_HOL_Otimes__class_Otimes(X33,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X35,X34,X3),X32,X3),X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I15_J_0) ).
fof(c_0_80,axiom,
! [X32,X33,X34,X35,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X35,X34,X3),c_HOL_Otimes__class_Otimes(X33,X32,X3),X3) = c_HOL_Otimes__class_Otimes(X35,c_HOL_Otimes__class_Otimes(X34,c_HOL_Otimes__class_Otimes(X33,X32,X3),X3),X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I14_J_0) ).
fof(c_0_81,axiom,
! [X4,X5,X13] : c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat)),X5),X4,tc_nat) = c_Divides_Odiv__class_Omod(X5,X4,tc_nat),
file('<stdin>',cls_mod__mult__self3_0) ).
fof(c_0_82,axiom,
! [X8,X9,X10,X26,X3] :
( hAPP(c_Type_Oshift(X10,X9,X26,X3),X8) = hAPP(X10,X8)
| ~ c_HOL_Oord__class_Oless(X8,X9,tc_nat) ),
file('<stdin>',cls_shift__gt_0) ).
fof(c_0_83,axiom,
! [X15,X16,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X16,X16,X3)),c_HOL_Otimes__class_Otimes(X15,X15,X3)) != c_HOL_Ozero__class_Ozero(X3)
| X16 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_sum__squares__eq__zero__iff_0) ).
fof(c_0_84,axiom,
! [X15,X16,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X16,X16,X3)),c_HOL_Otimes__class_Otimes(X15,X15,X3)) != c_HOL_Ozero__class_Ozero(X3)
| X15 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_sum__squares__eq__zero__iff_1) ).
fof(c_0_85,axiom,
! [X6,X13,X9] :
( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X6),X9)),c_Suc(X13)) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X6),X13)),X9)
| ~ c_HOL_Oord__class_Oless(X9,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
file('<stdin>',cls_lift__lift_0) ).
fof(c_0_86,axiom,
! [X44,X45] : c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X45),X44),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X45,tc_Lambda_OdB)),c_Nat_Osize__class_Osize(X44,tc_Lambda_OdB))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
file('<stdin>',cls_dB_Osize_I5_J_0) ).
fof(c_0_87,axiom,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Omod(X2,X1,X3)),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X1,X3)) = X2 ),
file('<stdin>',cls_semiring__div__class_Omod__div__equality_H_0) ).
fof(c_0_88,axiom,
! [X4,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X4,X3),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X4,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X2,X3) ),
file('<stdin>',cls_power__less__power__Suc_0) ).
fof(c_0_89,axiom,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X2,X3),c_HOL_Otimes__class_Otimes(X11,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X11,X3) ),
file('<stdin>',cls_mult__less__cancel__left__pos_0) ).
fof(c_0_90,axiom,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X2,X3),c_HOL_Otimes__class_Otimes(X11,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__less__cancel__left__neg_0) ).
fof(c_0_91,axiom,
! [X4,X5,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X5,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X2,X3) ),
file('<stdin>',cls_power__less__imp__less__exp_0) ).
fof(c_0_92,axiom,
! [X15,X16,X1,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X16,X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X16,X3),c_Power_Opower__class_Opower(X1,X15,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X1,X3) ),
file('<stdin>',cls_power__strict__increasing__iff_0) ).
fof(c_0_93,axiom,
! [X15,X47,X48,X16,X4] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),c_HOL_Otimes__class_Otimes(X4,X48,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Otimes__class_Otimes(X4,X47,tc_nat))
| c_Divides_Odiv__class_Omod(X16,X4,tc_nat) = c_Divides_Odiv__class_Omod(X15,X4,tc_nat) ),
file('<stdin>',cls_nat__mod__eq__iff_1) ).
fof(c_0_94,axiom,
! [X4,X5,X13] :
( c_Ring__and__Field_Odvd__class_Odvd(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat),tc_nat) ),
file('<stdin>',cls_dvd__mult__cancel_0) ).
fof(c_0_95,axiom,
! [X4,X5,X13] :
( c_Ring__and__Field_Odvd__class_Odvd(X5,X4,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat) ),
file('<stdin>',cls_nat__mult__dvd__cancel1_0) ).
fof(c_0_96,axiom,
! [X4,X5,X9] :
( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X9,X5,tc_nat),c_Power_Opower__class_Opower(X9,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X9,tc_nat) ),
file('<stdin>',cls_nat__power__less__imp__less_0) ).
fof(c_0_97,axiom,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat) ),
file('<stdin>',cls_nat__mult__less__cancel1_0) ).
fof(c_0_98,axiom,
! [X4,X2,X21,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X21,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X21,tc_nat) ),
file('<stdin>',cls_power__strict__decreasing_0) ).
fof(c_0_99,axiom,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X11,X3),c_HOL_Otimes__class_Otimes(X1,X11,X3),X3) ),
file('<stdin>',cls_mult__less__cancel__right__disj_0) ).
fof(c_0_100,axiom,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X2,X3),c_HOL_Otimes__class_Otimes(X11,X1,X3),X3) ),
file('<stdin>',cls_mult__less__cancel__left__disj_0) ).
fof(c_0_101,axiom,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X2,X3),c_HOL_Otimes__class_Otimes(X11,X1,X3),X3) ),
file('<stdin>',cls_mult__less__cancel__left__disj_1) ).
fof(c_0_102,axiom,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X2,X3),c_HOL_Otimes__class_Otimes(X11,X1,X3),X3) ),
file('<stdin>',cls_mult__less__cancel__left__disj_2) ).
fof(c_0_103,axiom,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X11,X3),c_HOL_Otimes__class_Otimes(X1,X11,X3),X3) ),
file('<stdin>',cls_mult__less__cancel__right__disj_1) ).
fof(c_0_104,axiom,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X11,X3),c_HOL_Otimes__class_Otimes(X1,X11,X3),X3) ),
file('<stdin>',cls_mult__less__cancel__right__disj_2) ).
fof(c_0_105,axiom,
! [X32,X33,X34,X35,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X35,X34,X3),c_HOL_Otimes__class_Otimes(X33,X32,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X35,X33,X3),c_HOL_Otimes__class_Otimes(X34,X32,X3),X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I13_J_0) ).
fof(c_0_106,axiom,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,X3),X11,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Omod(X1,X11,X3),X3),X11,X3) ),
file('<stdin>',cls_mod__mult__right__eq_0) ).
fof(c_0_107,axiom,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,X3),X11,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X11,X3),X1,X3),X11,X3) ),
file('<stdin>',cls_mod__mult__left__eq_0) ).
fof(c_0_108,axiom,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X11,X3),X1,X3),X11,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,X3),X11,X3) ),
file('<stdin>',cls_zmod__simps_I4_J_0) ).
fof(c_0_109,axiom,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),c_HOL_Otimes__class_Otimes(X11,X1,X3)),X1,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),c_Divides_Odiv__class_Odiv(X2,X1,X3))
| X1 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_div__mult__self1_0) ).
fof(c_0_110,axiom,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),c_HOL_Otimes__class_Otimes(X1,X11,X3)),X1,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),c_Divides_Odiv__class_Odiv(X2,X1,X3))
| X1 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_div__mult__self2_0) ).
fof(c_0_111,axiom,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X11,X3),c_HOL_Otimes__class_Otimes(X1,X11,X3),X3) ),
file('<stdin>',cls_mult__less__cancel__right__disj_3) ).
fof(c_0_112,axiom,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X2,X3),c_HOL_Otimes__class_Otimes(X11,X1,X3),X3) ),
file('<stdin>',cls_mult__less__cancel__left__disj_3) ).
fof(c_0_113,axiom,
! [X14,X15,X16,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X15),X14),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X16,X15,X3)),c_HOL_Otimes__class_Otimes(X16,X14,X3)) ),
file('<stdin>',cls_class__semiring_Omul__d_0) ).
fof(c_0_114,axiom,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring(X3)
| c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1),X11,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X2,X11,X3)),c_HOL_Otimes__class_Otimes(X1,X11,X3)) ),
file('<stdin>',cls_comm__semiring__class_Odistrib_0) ).
fof(c_0_115,axiom,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1),X11,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X2,X11,X3)),c_HOL_Otimes__class_Otimes(X1,X11,X3)) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I8_J_0) ).
fof(c_0_116,axiom,
! [X5,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X2,X5,X3)),c_HOL_Otimes__class_Otimes(X1,X5,X3)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1),X5,X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I1_J_0) ).
fof(c_0_117,axiom,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X1,X2,X3),c_Divides_Odiv__class_Odiv(X11,X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X11,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X11,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
file('<stdin>',cls_div__dvd__div_1) ).
fof(c_0_118,axiom,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),c_Divides_Odiv__class_Omod(X1,X11,X3)),X11,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1),X11,X3) ),
file('<stdin>',cls_zmod__simps_I2_J_0) ).
fof(c_0_119,axiom,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1),X11,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),c_Divides_Odiv__class_Omod(X1,X11,X3)),X11,X3) ),
file('<stdin>',cls_mod__add__right__eq_0) ).
fof(c_0_120,axiom,
! [X15,X16,X4,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(X16,X15,X3),X4,X3) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(X16,X4,X3),c_Power_Opower__class_Opower(X15,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X16,X3) ),
file('<stdin>',cls_div__power_0) ).
fof(c_0_121,axiom,
! [X16,X23,X17,X11,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),c_HOL_Otimes__class_Otimes(X23,X11,X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),c_HOL_Otimes__class_Otimes(X23,X17,X3))
| X11 = X17
| X23 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
fof(c_0_122,axiom,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1)),X11) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X11)),X1) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I23_J_0) ).
fof(c_0_123,axiom,
! [X16,X10,X26,X3] : hAPP(c_Type_Oshift(X10,X16,X26,X3),X16) = X26,
file('<stdin>',cls_shift__eq_0) ).
fof(c_0_124,axiom,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X13),X5,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X13),X4,tc_nat),tc_nat) ),
file('<stdin>',cls_Suc__mult__less__cancel1_0) ).
fof(c_0_125,axiom,
! [X4,X5,X13] : c_HOL_Otimes__class_Otimes(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X13,X5,tc_nat)),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat)),
file('<stdin>',cls_add__mult__distrib2_0) ).
fof(c_0_126,axiom,
! [X4,X5,X13] : c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4),X13,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X5,X13,tc_nat)),c_HOL_Otimes__class_Otimes(X4,X13,tc_nat)),
file('<stdin>',cls_add__mult__distrib_0) ).
fof(c_0_127,axiom,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3)
| X11 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X11,X3),c_HOL_Otimes__class_Otimes(X1,X11,X3),X3) ),
file('<stdin>',cls_dvd__mult__cancel__right_0) ).
fof(c_0_128,axiom,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3)
| X11 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X11,X2,X3),c_HOL_Otimes__class_Otimes(X11,X1,X3),X3) ),
file('<stdin>',cls_dvd__mult__cancel__left_0) ).
fof(c_0_129,axiom,
! [X4,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X4,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X2,X3) ),
file('<stdin>',cls_power__gt1__lemma_0) ).
fof(c_0_130,axiom,
! [X12,X6,X7,X13] : c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,X6),X12),X7,X13) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(X6,X7,X13)),c_Lambda_Osubstn(X12,X7,X13)),
file('<stdin>',cls_substn_Osimps_I2_J_0) ).
fof(c_0_131,axiom,
! [X16,X23,X17,X11] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),c_HOL_Otimes__class_Otimes(X23,X11,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),c_HOL_Otimes__class_Otimes(X23,X17,tc_nat))
| X11 = X17
| X23 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_natgb_Oadd__scale__eq__noteq_0) ).
fof(c_0_132,axiom,
! [X11,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X1),X3) ),
file('<stdin>',cls_add__less__cancel__left_0) ).
fof(c_0_133,axiom,
! [X11,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X11),X3) ),
file('<stdin>',cls_add__less__cancel__right_0) ).
fof(c_0_134,axiom,
! [X4,X5,X13] :
( c_Ring__and__Field_Odvd__class_Odvd(X5,X4,tc_nat)
| X13 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat),tc_nat) ),
file('<stdin>',cls_nat__mult__dvd__cancel__disj_0) ).
fof(c_0_135,axiom,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X13,tc_nat),c_HOL_Otimes__class_Otimes(X4,X13,tc_nat),tc_nat) ),
file('<stdin>',cls_mult__less__cancel2_0) ).
fof(c_0_136,axiom,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat),tc_nat) ),
file('<stdin>',cls_mult__less__cancel1_0) ).
fof(c_0_137,axiom,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X13,tc_nat),c_HOL_Otimes__class_Otimes(X4,X13,tc_nat),tc_nat) ),
file('<stdin>',cls_mult__less__cancel2_1) ).
fof(c_0_138,axiom,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat),tc_nat) ),
file('<stdin>',cls_mult__less__cancel1_1) ).
fof(c_0_139,axiom,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X2,X3),c_HOL_Otimes__class_Otimes(X11,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_mult__strict__left__mono__comm_0) ).
fof(c_0_140,axiom,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X11,X3),c_HOL_Otimes__class_Otimes(X1,X11,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__less__cancel__right__disj_5) ).
fof(c_0_141,axiom,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X11,X3),c_HOL_Otimes__class_Otimes(X1,X11,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X11,X3) ),
file('<stdin>',cls_mult__less__cancel__right__disj_4) ).
fof(c_0_142,axiom,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X11,X3),c_HOL_Otimes__class_Otimes(X1,X11,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_mult__strict__right__mono_0) ).
fof(c_0_143,axiom,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X11,X3),c_HOL_Otimes__class_Otimes(X1,X11,X3),X3)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
file('<stdin>',cls_mult__strict__right__mono__neg_0) ).
fof(c_0_144,axiom,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X2,X3),c_HOL_Otimes__class_Otimes(X11,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__less__cancel__left__disj_5) ).
fof(c_0_145,axiom,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X2,X3),c_HOL_Otimes__class_Otimes(X11,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X11,X3) ),
file('<stdin>',cls_mult__less__cancel__left__disj_4) ).
fof(c_0_146,axiom,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X2,X3),c_HOL_Otimes__class_Otimes(X11,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_mult__strict__left__mono_0) ).
fof(c_0_147,axiom,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X2,X3),c_HOL_Otimes__class_Otimes(X11,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
file('<stdin>',cls_mult__strict__left__mono__neg_0) ).
fof(c_0_148,axiom,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X2,X3),c_HOL_Otimes__class_Otimes(X11,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X11,X3) ),
file('<stdin>',cls_mult__less__cancel__left__pos_1) ).
fof(c_0_149,axiom,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X2,X3),c_HOL_Otimes__class_Otimes(X11,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__less__cancel__left__neg_1) ).
fof(c_0_150,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_sum__squares__eq__zero__iff_2) ).
fof(c_0_151,axiom,
! [X4,X2,X21,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X4,X3),c_Power_Opower__class_Opower(X2,X21,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X21,tc_nat) ),
file('<stdin>',cls_power__strict__increasing_0) ).
fof(c_0_152,axiom,
! [X15,X16,X1,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X16,X3),c_Power_Opower__class_Opower(X1,X15,X3),X3)
| ~ c_HOL_Oord__class_Oless(X16,X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X1,X3) ),
file('<stdin>',cls_power__strict__increasing__iff_1) ).
fof(c_0_153,axiom,
! [X17,X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X11,X3),c_HOL_Otimes__class_Otimes(X1,X17,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X17,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
file('<stdin>',cls_mult__dvd__mono_0) ).
fof(c_0_154,axiom,
! [X5,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X2,X5,X3)),X5) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),c_HOL_Oone__class_Oone(X3)),X5,X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I2_J_0) ).
fof(c_0_155,axiom,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1),X1,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Odiv(X2,X1,X3)),c_HOL_Oone__class_Oone(X3))
| X1 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_div__add__self2_0) ).
fof(c_0_156,axiom,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X2),X1,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Odiv(X2,X1,X3)),c_HOL_Oone__class_Oone(X3))
| X1 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_div__add__self1_0) ).
fof(c_0_157,axiom,
! [X17,X11,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X17),X3)
| ~ c_HOL_Oord__class_Oless(X11,X17,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_add__strict__mono_0) ).
fof(c_0_158,axiom,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X11,X2,X3),c_HOL_Otimes__class_Otimes(X11,X1,X3),X3) = c_HOL_Otimes__class_Otimes(X11,c_Divides_Odiv__class_Omod(X2,X1,X3),X3) ),
file('<stdin>',cls_mod__mult__mult1_0) ).
fof(c_0_159,axiom,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X11,X3),c_HOL_Otimes__class_Otimes(X1,X11,X3),X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X1,X3),X11,X3) ),
file('<stdin>',cls_mod__mult__mult2_0) ).
fof(c_0_160,axiom,
! [X15,X16,X18,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X16,X15,X3),X18,X3) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X16,X18,X3),c_Power_Opower__class_Opower(X15,X18,X3),X3) ),
file('<stdin>',cls_class__semiring_Opwr__mul_0) ).
fof(c_0_161,axiom,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X3)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X2,X1,X3),X4,X3) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X4,X3),c_Power_Opower__class_Opower(X1,X4,X3),X3) ),
file('<stdin>',cls_power__mult__distrib_0) ).
fof(c_0_162,axiom,
! [X4,X5,X13] :
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat) ),
file('<stdin>',cls_nat__mult__dvd__cancel1_1) ).
fof(c_0_163,axiom,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat) ),
file('<stdin>',cls_nat__mult__less__cancel1_1) ).
fof(c_0_164,axiom,
! [X13,X8,X9] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X13,tc_nat),c_HOL_Otimes__class_Otimes(X8,X13,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(X9,X8,tc_nat) ),
file('<stdin>',cls_mult__less__mono1_0) ).
fof(c_0_165,axiom,
! [X13,X8,X9] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X9,tc_nat),c_HOL_Otimes__class_Otimes(X13,X8,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(X9,X8,tc_nat) ),
file('<stdin>',cls_mult__less__mono2_0) ).
fof(c_0_166,axiom,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat) ),
file('<stdin>',cls_mult__less__cancel1_2) ).
fof(c_0_167,axiom,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X13,tc_nat),c_HOL_Otimes__class_Otimes(X4,X13,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat) ),
file('<stdin>',cls_mult__less__cancel2_2) ).
fof(c_0_168,axiom,
! [X6,X7,X13] : hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,X7),X6)),X13) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X7),X13)),hAPP(hAPP(c_Lambda_Olift,X6),X13)),
file('<stdin>',cls_lift_Osimps_I2_J_0) ).
fof(c_0_169,axiom,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),c_HOL_Otimes__class_Otimes(X1,X11,X3)),X1,X3) = c_Divides_Odiv__class_Omod(X2,X1,X3) ),
file('<stdin>',cls_mod__mult__self2_0) ).
fof(c_0_170,axiom,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),c_HOL_Otimes__class_Otimes(X11,X1,X3)),X1,X3) = c_Divides_Odiv__class_Omod(X2,X1,X3) ),
file('<stdin>',cls_mod__mult__self1_0) ).
fof(c_0_171,axiom,
! [X4,X27] :
( ~ hBOOL(hAPP(X27,c_Divides_Odiv__class_Odiv(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
| hBOOL(hAPP(X27,c_HOL_Ozero__class_Ozero(tc_nat))) ),
file('<stdin>',cls_split__div_0) ).
fof(c_0_172,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) ),
file('<stdin>',cls_zero__less__mult__pos_0) ).
fof(c_0_173,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) ),
file('<stdin>',cls_zero__less__mult__pos2_0) ).
fof(c_0_174,axiom,
! [X4,X27] :
( ~ hBOOL(hAPP(X27,c_Divides_Odiv__class_Omod(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
| hBOOL(hAPP(X27,X4)) ),
file('<stdin>',cls_split__mod_0) ).
fof(c_0_175,axiom,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X4),tc_nat) ),
file('<stdin>',cls_nat__add__left__cancel__less_0) ).
fof(c_0_176,axiom,
! [X16,X18,X19,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X16,X19,X3),c_Power_Opower__class_Opower(X16,X18,X3),X3) = c_Power_Opower__class_Opower(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X19),X18),X3) ),
file('<stdin>',cls_class__semiring_Omul__pwr_0) ).
fof(c_0_177,axiom,
! [X4,X5,X2,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_Power_Opower__class_Opower(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4),X3) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X5,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3) ),
file('<stdin>',cls_power__add_0) ).
fof(c_0_178,axiom,
! [X14,X15,X16,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X15),X14)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X15)),X14) ),
file('<stdin>',cls_class__semiring_Oadd__a_0) ).
fof(c_0_179,axiom,
! [X11,X1,X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1)),X11) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X11)) ),
file('<stdin>',cls_comm__monoid__add_Omult__assoc_0) ).
fof(c_0_180,axiom,
! [X11,X1,X2,X3] :
( ~ class_OrderedGroup_Oab__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1)),X11) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X11)) ),
file('<stdin>',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
fof(c_0_181,axiom,
! [X17,X11,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X11)),X17) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I25_J_0) ).
fof(c_0_182,axiom,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1)),X11) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X11)) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I21_J_0) ).
fof(c_0_183,axiom,
! [X4,X5,X13] : c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X5,X4,tc_nat),X13,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X13,tc_nat),c_HOL_Otimes__class_Otimes(X4,X13,tc_nat),tc_nat),
file('<stdin>',cls_mod__mult__distrib_0) ).
fof(c_0_184,axiom,
! [X4,X5,X13] : c_HOL_Otimes__class_Otimes(X13,c_Divides_Odiv__class_Omod(X5,X4,tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat),tc_nat),
file('<stdin>',cls_mod__mult__distrib2_0) ).
fof(c_0_185,axiom,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X2,X3),X11,X3) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X11,X3),X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
file('<stdin>',cls_dvd__div__mult_0) ).
fof(c_0_186,axiom,
! [X4,X5,X13,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X13,X5,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,c_Divides_Odiv__class_Omod(X5,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,X4,X3) ),
file('<stdin>',cls_dvd__mod__iff_0) ).
fof(c_0_187,axiom,
! [X4,X5,X13,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X13,X5,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,c_Divides_Odiv__class_Omod(X5,X4,X3),X3) ),
file('<stdin>',cls_dvd__mod__imp__dvd_0) ).
fof(c_0_188,axiom,
! [X4,X5,X13] :
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat) ),
file('<stdin>',cls_nat__mult__div__cancel1_0) ).
fof(c_0_189,axiom,
! [X28,X13,X8,X9] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X28),tc_nat)
| ~ c_HOL_Oord__class_Oless(X13,X28,tc_nat)
| ~ c_HOL_Oord__class_Oless(X9,X8,tc_nat) ),
file('<stdin>',cls_add__less__mono_0) ).
fof(c_0_190,axiom,
! [X37,X38,X39,X3] :
( c_List_Olist_ONil(X3) != c_List_Omap(X38,X37,X39,X3)
| X37 = c_List_Olist_ONil(X39) ),
file('<stdin>',cls_Nil__is__map__conv_0) ).
fof(c_0_191,axiom,
! [X37,X38,X39,X3] :
( c_List_Omap(X38,X37,X39,X3) != c_List_Olist_ONil(X3)
| X37 = c_List_Olist_ONil(X39) ),
file('<stdin>',cls_map__is__Nil__conv_0) ).
fof(c_0_192,axiom,
! [X44,X45] : c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X45),X44)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X45)),c_Lambda_OdB_OdB__size(X44))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
file('<stdin>',cls_dB_Osize_I2_J_0) ).
fof(c_0_193,axiom,
! [X14,X15,X16,X12,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X15),X14)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X15),X12)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X14) = X12 ),
file('<stdin>',cls_add__cancel__21_0) ).
fof(c_0_194,axiom,
! [X4,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,c_Suc(X4),X3),c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_power__Suc__less__one_0) ).
fof(c_0_195,axiom,
! [X6,X7,X23,X9] :
( c_Lambda_Obeta(hAPP(hAPP(hAPP(c_Lambda_Osubst,X23),X6),X9),hAPP(hAPP(hAPP(c_Lambda_Osubst,X7),X6),X9))
| ~ c_Lambda_Obeta(X23,X7) ),
file('<stdin>',cls_subst__preserves__beta_0) ).
fof(c_0_196,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat) ),
file('<stdin>',cls_one__less__mult_0) ).
fof(c_0_197,axiom,
! [X6,X7,X13] : hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X6),X13)),X7),X13) = X6,
file('<stdin>',cls_subst__lift_0) ).
fof(c_0_198,axiom,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X13),X5,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X13),X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
file('<stdin>',cls_Suc__mult__less__cancel1_1) ).
fof(c_0_199,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__neg__pos_0) ).
fof(c_0_200,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_mult__pos__neg_0) ).
fof(c_0_201,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_mult__pos__neg2_0) ).
fof(c_0_202,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__neg__neg_0) ).
fof(c_0_203,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_mult__pos__pos_0) ).
fof(c_0_204,axiom,
! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_HOL_Otimes__class_Otimes(X5,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X5,X3) ),
file('<stdin>',cls_less__1__mult_0) ).
fof(c_0_205,axiom,
! [X6,X7,X13] : c_Lambda_Osubstn(c_Lambda_OdB_OAbs(X6),X7,X13) = c_Lambda_OdB_OAbs(c_Lambda_Osubstn(X6,X7,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)))),
file('<stdin>',cls_substn_Osimps_I3_J_0) ).
fof(c_0_206,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat) ),
file('<stdin>',cls_n__less__m__mult__n_0) ).
fof(c_0_207,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X4,X5,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat) ),
file('<stdin>',cls_n__less__n__mult__m_0) ).
fof(c_0_208,axiom,
! [X4,X5,X13] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4)),X13) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X13)),
file('<stdin>',cls_nat__add__assoc_0) ).
fof(c_0_209,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_add__pos__pos_0) ).
fof(c_0_210,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_add__neg__neg_0) ).
fof(c_0_211,axiom,
! [X15,X16,X4,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X16,X4,X3),c_Power_Opower__class_Opower(X15,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X15,X3) ),
file('<stdin>',cls_dvd__power__same_0) ).
fof(c_0_212,axiom,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X11,X2,X3),c_HOL_Otimes__class_Otimes(X11,X1,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
file('<stdin>',cls_dvd__mult__cancel__left_2) ).
fof(c_0_213,axiom,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X11,X3),c_HOL_Otimes__class_Otimes(X1,X11,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
file('<stdin>',cls_dvd__mult__cancel__right_2) ).
fof(c_0_214,axiom,
! [X4,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X2,X3) ),
file('<stdin>',cls_one__less__power_0) ).
fof(c_0_215,axiom,
! [X14,X15,X16] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X16,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X14,X15,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X14,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X15,X16,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X15,tc_nat) ),
file('<stdin>',cls_dvd_Oless__trans_1) ).
fof(c_0_216,axiom,
! [X5,X13] :
( c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat)),X13,tc_nat) = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X13,tc_nat) ),
file('<stdin>',cls_Suc__times__mod__eq_0) ).
fof(c_0_217,axiom,
! [X11,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X1),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_add__less__cancel__left_1) ).
fof(c_0_218,axiom,
! [X11,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X1),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_add__strict__left__mono_0) ).
fof(c_0_219,axiom,
! [X11,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X11),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_add__less__cancel__right_1) ).
fof(c_0_220,axiom,
! [X11,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X11),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_add__strict__right__mono_0) ).
fof(c_0_221,axiom,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X11),X3)
| ~ c_HOL_Oord__class_Oless(X1,X11,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_pos__add__strict_0) ).
fof(c_0_222,axiom,
! [X4,X5,X13] :
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X4,tc_nat) ),
file('<stdin>',cls_nat__mult__dvd__cancel__disj_2) ).
fof(c_0_223,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_224,axiom,
! [X4,X5,X13,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X13,c_Divides_Odiv__class_Omod(X5,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,X5,X3) ),
file('<stdin>',cls_dvd__mod_0) ).
fof(c_0_225,axiom,
! [X4,X5,X13,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X13,c_Divides_Odiv__class_Omod(X5,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,X5,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,X4,X3) ),
file('<stdin>',cls_dvd__mod__iff_1) ).
fof(c_0_226,axiom,
! [X4,X5] :
( X4 = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X5,tc_nat),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
file('<stdin>',cls_dvd__mult__cancel2_0) ).
fof(c_0_227,axiom,
! [X4,X5] :
( X4 = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
file('<stdin>',cls_dvd__mult__cancel1_0) ).
fof(c_0_228,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),tc_nat)
| ~ 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) ),
file('<stdin>',cls_nat__0__less__mult__iff_2) ).
fof(c_0_229,axiom,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X11),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X11,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
file('<stdin>',cls_dvd__add_0) ).
fof(c_0_230,axiom,
! [X5,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),c_HOL_Otimes__class_Otimes(X2,X5,X3)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),c_HOL_Oone__class_Oone(X3)),X5,X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I3_J_0) ).
fof(c_0_231,axiom,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X11,X3),c_HOL_Otimes__class_Otimes(X1,X11,X3),X3) = c_Divides_Odiv__class_Odiv(X2,X1,X3)
| X11 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_div__mult__mult2_0) ).
fof(c_0_232,axiom,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X11,X2,X3),c_HOL_Otimes__class_Otimes(X11,X1,X3),X3) = c_Divides_Odiv__class_Odiv(X2,X1,X3)
| X11 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_div__mult__mult1_0) ).
fof(c_0_233,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Odiv(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_Oone__class_Oone(tc_nat),X4,tc_nat) ),
file('<stdin>',cls_div__less__dividend_0) ).
fof(c_0_234,axiom,
! [X14,X15,X16,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X16,c_HOL_Otimes__class_Otimes(X15,X14,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X16,X15,X3),X14,X3) ),
file('<stdin>',cls_class__semiring_Omul__a_0) ).
fof(c_0_235,axiom,
! [X32,X33,X35,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X35,c_HOL_Otimes__class_Otimes(X33,X32,X3),X3) = c_HOL_Otimes__class_Otimes(X33,c_HOL_Otimes__class_Otimes(X35,X32,X3),X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I19_J_0) ).
fof(c_0_236,axiom,
! [X32,X33,X35,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X35,c_HOL_Otimes__class_Otimes(X33,X32,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X35,X33,X3),X32,X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I18_J_0) ).
fof(c_0_237,axiom,
! [X33,X34,X35,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X35,X34,X3),X33,X3) = c_HOL_Otimes__class_Otimes(X35,c_HOL_Otimes__class_Otimes(X34,X33,X3),X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I17_J_0) ).
fof(c_0_238,axiom,
! [X33,X34,X35,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X35,X34,X3),X33,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X35,X33,X3),X34,X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I16_J_0) ).
fof(c_0_239,axiom,
! [X11,X1,X2,X3] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X1,X3),X11,X3) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X1,X11,X3),X3) ),
file('<stdin>',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
fof(c_0_240,axiom,
! [X4,X2,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X4,X3),X2,X3) = c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X4,X3),X3) ),
file('<stdin>',cls_power__commutes_0) ).
fof(c_0_241,axiom,
! [X14,X15,X16] :
( c_Ring__and__Field_Odvd__class_Odvd(X16,X14,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X14,X15,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X14,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X15,X16,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X15,tc_nat) ),
file('<stdin>',cls_dvd_Oless__trans_0) ).
fof(c_0_242,axiom,
! [X4,X5,X2,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_Power_Opower__class_Opower(X2,c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),X3) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X2,X5,X3),X4,X3) ),
file('<stdin>',cls_power__mult_0) ).
fof(c_0_243,axiom,
! [X16,X18,X19,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X16,X19,X3),X18,X3) = c_Power_Opower__class_Opower(X16,c_HOL_Otimes__class_Otimes(X19,X18,tc_nat),X3) ),
file('<stdin>',cls_class__semiring_Opwr__pwr_0) ).
fof(c_0_244,axiom,
! [X4,X5] : c_Divides_Odiv__class_Omod(c_Suc(X5),X4,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(X5,X4,tc_nat)),X4,tc_nat),
file('<stdin>',cls_mod__Suc__eq__Suc__mod_0) ).
fof(c_0_245,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X2),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_even__less__0__iff_0) ).
fof(c_0_246,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X2),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_double__add__less__zero__iff__single__less__zero_0) ).
fof(c_0_247,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X2),X3) ),
file('<stdin>',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
fof(c_0_248,axiom,
! [X7,X13] : hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(X7)),X13) = c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)))),
file('<stdin>',cls_lift_Osimps_I3_J_0) ).
fof(c_0_249,axiom,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
file('<stdin>',cls_nat__add__left__cancel__less_1) ).
fof(c_0_250,axiom,
! [X13,X8,X9] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X13),tc_nat)
| ~ c_HOL_Oord__class_Oless(X9,X8,tc_nat) ),
file('<stdin>',cls_add__less__mono1_0) ).
fof(c_0_251,axiom,
! [X4,X5,X13] :
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(X5,X4,tc_nat)
| X13 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_nat__mult__div__cancel__disj_1) ).
fof(c_0_252,axiom,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X11,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X1,X3),X11,X3) ),
file('<stdin>',cls_dvd__mult__left_0) ).
fof(c_0_253,axiom,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X11,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X1,X3),X11,X3) ),
file('<stdin>',cls_dvd__mult__right_0) ).
fof(c_0_254,axiom,
! [X14,X15,X16,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X15),X14)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X14)) ),
file('<stdin>',cls_add__cancel__21_1) ).
fof(c_0_255,axiom,
! [X11,X1,X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X11)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X11)) ),
file('<stdin>',cls_comm__monoid__add_Omult__left__commute_0) ).
fof(c_0_256,axiom,
! [X17,X11,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X17)) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I22_J_0) ).
fof(c_0_257,axiom,
! [X4,X5,X13] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),X13,tc_nat) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Otimes__class_Otimes(X4,X13,tc_nat),tc_nat),
file('<stdin>',cls_nat__mult__assoc_0) ).
fof(c_0_258,axiom,
! [X11,X1,X2] : c_Divides_Odiv__class_Odiv(X2,c_HOL_Otimes__class_Otimes(X1,X11,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(X2,X1,tc_nat),X11,tc_nat),
file('<stdin>',cls_div__mult2__eq_0) ).
fof(c_0_259,axiom,
! [X16,X4] :
( X4 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X16,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X16,X4,tc_nat),tc_nat) ),
file('<stdin>',cls_nat__zero__less__power__iff_0) ).
fof(c_0_260,axiom,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X2,X1,X3),X11,X3) = c_Divides_Odiv__class_Omod(X2,X11,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X1,X3) ),
file('<stdin>',cls_mod__mod__cancel_0) ).
fof(c_0_261,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),c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),tc_nat) ),
file('<stdin>',cls_nat__0__less__mult__iff_1) ).
fof(c_0_262,axiom,
! [X4,X5] :
( 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),c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),tc_nat) ),
file('<stdin>',cls_nat__0__less__mult__iff_0) ).
fof(c_0_263,axiom,
! [X4,X27] :
( ~ hBOOL(hAPP(X27,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X27,c_Divides_Odiv__class_Odiv(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
file('<stdin>',cls_split__div_5) ).
fof(c_0_264,axiom,
! [X5,X27] :
( hBOOL(hAPP(X27,c_Divides_Odiv__class_Odiv(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
| ~ hBOOL(hAPP(X27,c_HOL_Ozero__class_Ozero(tc_nat))) ),
file('<stdin>',cls_split__div_H_6) ).
fof(c_0_265,axiom,
! [X14,X15,X16] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X16,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X14,X15,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X14,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X15,tc_nat) ),
file('<stdin>',cls_dvd_Ole__less__trans_1) ).
fof(c_0_266,axiom,
! [X14,X15,X16] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X16,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X14,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X15,X16,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X15,tc_nat) ),
file('<stdin>',cls_dvd_Oless__le__trans_1) ).
fof(c_0_267,axiom,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X2,X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X1,X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_div__mult__mult1__if_0) ).
fof(c_0_268,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X2,X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X1,X3),X3) ),
file('<stdin>',cls_dvd__mult__cancel__left_1) ).
fof(c_0_269,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X3),X3),X3) ),
file('<stdin>',cls_dvd__mult__cancel__right_1) ).
fof(c_0_270,axiom,
! [X4,X27] :
( ~ hBOOL(hAPP(X27,X4))
| hBOOL(hAPP(X27,c_Divides_Odiv__class_Omod(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
file('<stdin>',cls_split__mod_5) ).
fof(c_0_271,axiom,
! [X6,X7] : c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X7)),X6),hAPP(hAPP(hAPP(c_Lambda_Osubst,X7),X6),c_HOL_Ozero__class_Ozero(tc_nat))),
file('<stdin>',cls_beta_0) ).
fof(c_0_272,axiom,
! [X4,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_Power_Opower__class_Opower(X2,c_Suc(X4),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X2,X3) ),
file('<stdin>',cls_power__gt1_0) ).
fof(c_0_273,axiom,
! [X4,X5,X28,X13] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X28) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X4)
| ~ c_HOL_Oord__class_Oless(X13,X28,tc_nat)
| c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
file('<stdin>',cls_less__add__eq__less_0) ).
fof(c_0_274,axiom,
! [X4,X13] :
( c_Ring__and__Field_Odvd__class_Odvd(X13,X4,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X13),tc_nat) ),
file('<stdin>',cls_dvd__reduce_0) ).
fof(c_0_275,axiom,
! [X13,X8,X9] :
( c_HOL_Oord__class_Oless(X9,X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X8),X13,tc_nat) ),
file('<stdin>',cls_add__lessD1_0) ).
fof(c_0_276,axiom,
! [X4,X5,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_Power_Opower__class_Opower(X2,X5,X3) != c_Power_Opower__class_Opower(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X2,X3)
| X5 = X4 ),
file('<stdin>',cls_power__inject__exp_0) ).
fof(c_0_277,axiom,
! [X4,X5] :
( c_Divides_Odiv__class_Omod(c_Suc(X5),X4,tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(X5,X4,tc_nat))
| c_Suc(c_Divides_Odiv__class_Omod(X5,X4,tc_nat)) = X4 ),
file('<stdin>',cls_mod__Suc_1) ).
fof(c_0_278,axiom,
! [X4,X5] : c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_nat__mult__div__cancel__disj_0) ).
fof(c_0_279,axiom,
! [X14,X15,X16] :
( c_Ring__and__Field_Odvd__class_Odvd(X16,X14,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X14,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X15,X16,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X15,tc_nat) ),
file('<stdin>',cls_dvd_Oless__le__trans_0) ).
fof(c_0_280,axiom,
! [X14,X15,X16] :
( c_Ring__and__Field_Odvd__class_Odvd(X16,X14,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X14,X15,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X14,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X15,tc_nat) ),
file('<stdin>',cls_dvd_Ole__less__trans_0) ).
fof(c_0_281,axiom,
! [X4,X5] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat),tc_nat),
file('<stdin>',cls_nat__mult__dvd__cancel__disj_1) ).
fof(c_0_282,axiom,
! [X14,X15,X16] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X14)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X14)),
file('<stdin>',cls_nat__add__left__commute_0) ).
fof(c_0_283,axiom,
! [X4,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_zero__less__power_0) ).
fof(c_0_284,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_not__square__less__zero_0) ).
fof(c_0_285,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X2),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_even__less__0__iff_1) ).
fof(c_0_286,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X2),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_double__add__less__zero__iff__single__less__zero_1) ).
fof(c_0_287,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X2),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
fof(c_0_288,axiom,
! [X38,X39,X3] : c_List_Olist_ONil(X3) = c_List_Omap(X38,c_List_Olist_ONil(X39),X39,X3),
file('<stdin>',cls_Nil__is__map__conv_1) ).
fof(c_0_289,axiom,
! [X38,X39,X3] : c_List_Omap(X38,c_List_Olist_ONil(X39),X39,X3) = c_List_Olist_ONil(X3),
file('<stdin>',cls_map__is__Nil__conv_1) ).
fof(c_0_290,axiom,
! [X16,X4,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X16,c_Power_Opower__class_Opower(X16,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
file('<stdin>',cls_dvd__power_0) ).
fof(c_0_291,axiom,
! [X4,X5,X13] :
( c_HOL_Otimes__class_Otimes(X13,X5,tc_nat) != c_HOL_Otimes__class_Otimes(X13,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat)
| X5 = X4 ),
file('<stdin>',cls_nat__mult__eq__cancel1_0) ).
fof(c_0_292,axiom,
! [X4,X5] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
file('<stdin>',cls_nat__dvd__not__less_0) ).
fof(c_0_293,axiom,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X1,X2,X3),X3) = X1
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
file('<stdin>',cls_dvd__mult__div__cancel_0) ).
fof(c_0_294,axiom,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X2,X3),X2,X3) = X1
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
file('<stdin>',cls_dvd__div__mult__self_0) ).
fof(c_0_295,axiom,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X1,X11,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X11,X3) ),
file('<stdin>',cls_dvd__mult_0) ).
fof(c_0_296,axiom,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X1,X11,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
file('<stdin>',cls_dvd__mult2_0) ).
fof(c_0_297,axiom,
! [X5,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),X5) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oone__class_Oone(X3)),c_HOL_Oone__class_Oone(X3)),X5,X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I4_J_0) ).
fof(c_0_298,axiom,
! [X5] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X5,tc_nat),X5,tc_nat) ),
file('<stdin>',cls_dvd__mult__cancel2_1) ).
fof(c_0_299,axiom,
! [X5] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X5,tc_nat) ),
file('<stdin>',cls_dvd__mult__cancel1_1) ).
fof(c_0_300,axiom,
! [X16,X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X16,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X16,tc_nat) ),
file('<stdin>',cls_nat__zero__less__power__iff_1) ).
fof(c_0_301,axiom,
! [X4,X5] :
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X4,X5,tc_nat),X4,tc_nat) = X5
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
file('<stdin>',cls_div__mult__self1__is__m_0) ).
fof(c_0_302,axiom,
! [X4,X5] :
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),X4,tc_nat) = X5
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
file('<stdin>',cls_div__mult__self__is__m_0) ).
fof(c_0_303,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X5,X4,tc_nat),X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
file('<stdin>',cls_mod__less__divisor_0) ).
fof(c_0_304,axiom,
! [X4,X5,X3] :
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Nat_Osemiring__1__class_Oof__nat(X5,X3)),c_Nat_Osemiring__1__class_Oof__nat(X4,X3)) ),
file('<stdin>',cls_of__nat__add_0) ).
fof(c_0_305,axiom,
! [X16,X5] : c_HOL_Oord__class_Oless(X5,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X16)),tc_nat),
file('<stdin>',cls_less__iff__Suc__add_1) ).
fof(c_0_306,axiom,
! [X5,X9] : c_HOL_Oord__class_Oless(X9,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X9)),tc_nat),
file('<stdin>',cls_less__add__Suc2_0) ).
fof(c_0_307,axiom,
! [X5,X9] : c_HOL_Oord__class_Oless(X9,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X5)),tc_nat),
file('<stdin>',cls_less__add__Suc1_0) ).
fof(c_0_308,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_309,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_310,axiom,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X11,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X11,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
file('<stdin>',cls_dvd__trans_0) ).
fof(c_0_311,axiom,
! [X14,X15,X16,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X16,X14,X3)
| ~ c_HOL_Oord__class_Oless(X15,X14,X3)
| ~ c_HOL_Oord__class_Oless(X16,X15,X3) ),
file('<stdin>',cls_order__less__trans_0) ).
fof(c_0_312,axiom,
! [X14,X15,X16,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X14,X16,X3)
| ~ c_HOL_Oord__class_Oless(X14,X15,X3)
| ~ c_HOL_Oord__class_Oless(X15,X16,X3) ),
file('<stdin>',cls_xt1_I10_J_0) ).
fof(c_0_313,axiom,
! [X4,X5] :
( c_Suc(c_Divides_Odiv__class_Omod(X5,X4,tc_nat)) != X4
| c_Divides_Odiv__class_Omod(c_Suc(X5),X4,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_mod__Suc_0) ).
fof(c_0_314,axiom,
! [X4,X5,X3] :
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),X3) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(X5,X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3) ),
file('<stdin>',cls_of__nat__mult_0) ).
fof(c_0_315,axiom,
! [X16,X18,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X16,X18,X3),X16,X3) = c_Power_Opower__class_Opower(X16,c_Suc(X18),X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I28_J_0) ).
fof(c_0_316,axiom,
! [X16,X18,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X16,c_Power_Opower__class_Opower(X16,X18,X3),X3) = c_Power_Opower__class_Opower(X16,c_Suc(X18),X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I27_J_0) ).
fof(c_0_317,axiom,
! [X4,X2,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_Power_Opower__class_Opower(X2,c_Suc(X4),X3) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X4,X3),X2,X3) ),
file('<stdin>',cls_power__Suc2_0) ).
fof(c_0_318,axiom,
! [X4,X2,X3] :
( ~ class_Power_Opower(X3)
| c_Power_Opower__class_Opower(X2,c_Suc(X4),X3) = c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X4,X3),X3) ),
file('<stdin>',cls_power__Suc_0) ).
fof(c_0_319,axiom,
! [X16,X4,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Power_Opower__class_Opower(X16,c_Suc(X4),X3) = c_HOL_Otimes__class_Otimes(X16,c_Power_Opower__class_Opower(X16,X4,X3),X3) ),
file('<stdin>',cls_class__semiring_Opwr__Suc_0) ).
fof(c_0_320,axiom,
! [X16,X18,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Power_Opower__class_Opower(X16,c_Suc(X18),X3) = c_HOL_Otimes__class_Otimes(X16,c_Power_Opower__class_Opower(X16,X18,X3),X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I35_J_0) ).
fof(c_0_321,axiom,
! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X5,X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3) ),
file('<stdin>',cls_of__nat__less__iff_0) ).
fof(c_0_322,axiom,
! [X4,X5] :
( c_Divides_Odiv__class_Odiv(X5,X4,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
file('<stdin>',cls_div__if_0) ).
fof(c_0_323,axiom,
! [X13,X8,X9] :
( c_HOL_Oord__class_Oless(c_Suc(X9),X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(X8,X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(X9,X8,tc_nat) ),
file('<stdin>',cls_less__trans__Suc_0) ).
fof(c_0_324,axiom,
! [X4,X13] :
( c_Ring__and__Field_Odvd__class_Odvd(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X13),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,X4,tc_nat) ),
file('<stdin>',cls_dvd__reduce_1) ).
fof(c_0_325,axiom,
! [X5,X8,X9] :
( c_HOL_Oord__class_Oless(X9,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X8),tc_nat)
| ~ c_HOL_Oord__class_Oless(X9,X8,tc_nat) ),
file('<stdin>',cls_trans__less__add2_0) ).
fof(c_0_326,axiom,
! [X5,X8,X9] :
( c_HOL_Oord__class_Oless(X9,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X5),tc_nat)
| ~ c_HOL_Oord__class_Oless(X9,X8,tc_nat) ),
file('<stdin>',cls_trans__less__add1_0) ).
fof(c_0_327,axiom,
! [X14,X15,X16] :
( c_HOL_Oord__class_Oless(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X14),tc_nat)
| ~ c_HOL_Oord__class_Oless(X16,X14,tc_nat) ),
file('<stdin>',cls_termination__basic__simps_I2_J_0) ).
fof(c_0_328,axiom,
! [X14,X15,X16] :
( c_HOL_Oord__class_Oless(X16,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_termination__basic__simps_I1_J_0) ).
fof(c_0_329,axiom,
! [X8,X9] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X9),X9,tc_nat),
file('<stdin>',cls_not__add__less2_0) ).
fof(c_0_330,axiom,
! [X8,X9] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X8),X9,tc_nat),
file('<stdin>',cls_not__add__less1_0) ).
fof(c_0_331,axiom,
! [X15,X16,X3] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3)
| c_HOL_Otimes__class_Otimes(X16,c_HOL_Otimes__class_Otimes(X16,X15,X3),X3) = c_HOL_Otimes__class_Otimes(X16,X15,X3) ),
file('<stdin>',cls_mult__left__idem_0) ).
fof(c_0_332,axiom,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X2,X1,X3),X1,X3) = c_Divides_Odiv__class_Omod(X2,X1,X3) ),
file('<stdin>',cls_mod__mod__trivial_0) ).
fof(c_0_333,axiom,
! [X14,X15,X16] :
( c_Ring__and__Field_Odvd__class_Odvd(X16,X14,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X14,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X15,tc_nat) ),
file('<stdin>',cls_dvd_Oorder__trans_0) ).
fof(c_0_334,axiom,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X2),X1,X3) = c_Divides_Odiv__class_Omod(X2,X1,X3) ),
file('<stdin>',cls_mod__add__self1_0) ).
fof(c_0_335,axiom,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1),X1,X3) = c_Divides_Odiv__class_Omod(X2,X1,X3) ),
file('<stdin>',cls_mod__add__self2_0) ).
fof(c_0_336,axiom,
! [X6,X9] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X6),X9)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6)) ),
file('<stdin>',cls_lift__IT_0) ).
fof(c_0_337,axiom,
! [X4,X5] : c_HOL_Otimes__class_Otimes(c_Suc(X5),X4,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Otimes__class_Otimes(X5,X4,tc_nat)),
file('<stdin>',cls_mult__Suc_0) ).
fof(c_0_338,axiom,
! [X4,X5] : c_HOL_Otimes__class_Otimes(X5,c_Suc(X4),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),c_HOL_Otimes__class_Otimes(X5,X4,tc_nat)),
file('<stdin>',cls_mult__Suc__right_0) ).
fof(c_0_339,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oone__class_Oone(X3)),c_HOL_Oone__class_Oone(X3)),X3) ),
file('<stdin>',cls_zero__less__two_0) ).
fof(c_0_340,axiom,
! [X4,X5,X3] :
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_Nat_Osemiring__1__class_Oof__nat(c_Power_Opower__class_Opower(X5,X4,tc_nat),X3) = c_Power_Opower__class_Opower(c_Nat_Osemiring__1__class_Oof__nat(X5,X3),X4,X3) ),
file('<stdin>',cls_of__nat__power_0) ).
fof(c_0_341,axiom,
! [X13,X9] :
( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X9)),X13) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),c_HOL_Oone__class_Oone(tc_nat)))
| c_HOL_Oord__class_Oless(X9,X13,tc_nat) ),
file('<stdin>',cls_lift_Osimps_I1_J_1) ).
fof(c_0_342,axiom,
! [X4,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| 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(X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3) ),
file('<stdin>',cls_of__nat__0__less__iff_0) ).
fof(c_0_343,axiom,
! [X12,X8,X9] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X8)),X12),X9) = c_Lambda_OdB_OVar(X8)
| ~ c_HOL_Oord__class_Oless(X8,X9,tc_nat) ),
file('<stdin>',cls_subst__lt_0) ).
fof(c_0_344,axiom,
! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X5,X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
file('<stdin>',cls_of__nat__less__iff_1) ).
fof(c_0_345,axiom,
! [X36,X27] :
( hBOOL(hAPP(X27,X36))
| ~ hBOOL(hAPP(X27,c_Suc(v_sko__Nat__Xnat__Xinducts__1(X27))))
| ~ hBOOL(hAPP(X27,c_HOL_Ozero__class_Ozero(tc_nat))) ),
file('<stdin>',cls_nat_Oinducts_1) ).
fof(c_0_346,axiom,
! [X36,X27] :
( hBOOL(hAPP(X27,X36))
| ~ hBOOL(hAPP(X27,c_Suc(v_sko__Nat__Xnat__Xinduct__1(X27))))
| ~ hBOOL(hAPP(X27,c_HOL_Ozero__class_Ozero(tc_nat))) ),
file('<stdin>',cls_nat_Oinduct_1) ).
fof(c_0_347,axiom,
! [X36,X27] :
( hBOOL(hAPP(X27,X36))
| ~ hBOOL(hAPP(X27,c_Suc(v_sko__List__Xupt__Xinduct__1(X27))))
| ~ hBOOL(hAPP(X27,c_HOL_Ozero__class_Ozero(tc_nat))) ),
file('<stdin>',cls_upt_Oinduct_1) ).
fof(c_0_348,axiom,
! [X36,X27] :
( hBOOL(hAPP(X27,X36))
| ~ hBOOL(hAPP(X27,c_Suc(v_sko__List__Xreplicate__Xinduct__1(X27))))
| ~ hBOOL(hAPP(X27,c_HOL_Ozero__class_Ozero(tc_nat))) ),
file('<stdin>',cls_replicate_Oinduct_1) ).
fof(c_0_349,axiom,
! [X4,X27] :
( hBOOL(hAPP(X27,X4))
| ~ hBOOL(hAPP(X27,c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X27))))
| ~ hBOOL(hAPP(X27,c_HOL_Ozero__class_Ozero(tc_nat))) ),
file('<stdin>',cls_nat__induct_1) ).
fof(c_0_350,axiom,
! [X36,X27] :
( hBOOL(hAPP(X27,X36))
| ~ hBOOL(hAPP(X27,c_Suc(v_sko__List__Xlexn__Xinduct__1(X27))))
| ~ hBOOL(hAPP(X27,c_HOL_Ozero__class_Ozero(tc_nat))) ),
file('<stdin>',cls_lexn_Oinduct_1) ).
fof(c_0_351,axiom,
! [X4,X5,X27] :
( hBOOL(hAPP(hAPP(X27,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_352,axiom,
! [X4,X5,X13] :
( c_HOL_Otimes__class_Otimes(c_Suc(X13),X5,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X13),X4,tc_nat)
| X5 = X4 ),
file('<stdin>',cls_Suc__mult__cancel1_0) ).
fof(c_0_353,axiom,
! [X4,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X3),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X3),X4,X3),X3) ),
file('<stdin>',cls_dvd__power_1) ).
fof(c_0_354,axiom,
! [X4,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3)
| ~ 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_355,axiom,
! [X14,X15,X16,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X15) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X14)
| X15 = X14 ),
file('<stdin>',cls_class__ringb_Oadd__cancel_0) ).
fof(c_0_356,axiom,
! [X12,X6,X7] :
( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X7),X12),hAPP(hAPP(c_Lambda_OdB_OApp,X6),X12))
| ~ c_Lambda_Obeta(X7,X6) ),
file('<stdin>',cls_appL_0) ).
fof(c_0_357,axiom,
! [X12,X6,X7] :
( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X12),X7),hAPP(hAPP(c_Lambda_OdB_OApp,X12),X6))
| ~ c_Lambda_Obeta(X7,X6) ),
file('<stdin>',cls_appR_0) ).
fof(c_0_358,axiom,
! [X7,X23,X9] :
( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_Olift,X23),X9),hAPP(hAPP(c_Lambda_Olift,X7),X9))
| ~ c_Lambda_Obeta(X23,X7) ),
file('<stdin>',cls_lift__preserves__beta_0) ).
fof(c_0_359,axiom,
! [X1,X2,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_order__less__asym_H_0) ).
fof(c_0_360,axiom,
! [X15,X16,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X15,X16,X3)
| ~ c_HOL_Oord__class_Oless(X16,X15,X3) ),
file('<stdin>',cls_order__less__asym_0) ).
fof(c_0_361,axiom,
! [X15,X16,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X16,X15,X3)
| ~ c_HOL_Oord__class_Oless(X15,X16,X3) ),
file('<stdin>',cls_not__less__iff__gr__or__eq_1) ).
fof(c_0_362,axiom,
! [X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
file('<stdin>',cls_xt1_I9_J_0) ).
fof(c_0_363,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_364,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),c_HOL_Oone__class_Oone(X3)),X3) ),
file('<stdin>',cls_less__add__one_0) ).
fof(c_0_365,axiom,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,X3),X1,X3) = X2
| X1 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_div__mult__self1__is__id_0) ).
fof(c_0_366,axiom,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X1,X3),X1,X3) = X2
| X1 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_div__mult__self2__is__id_0) ).
fof(c_0_367,axiom,
! [X11,X1,X2,X3] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X2)
| X1 = X11 ),
file('<stdin>',cls_add__right__cancel_0) ).
fof(c_0_368,axiom,
! [X11,X1,X2,X3] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X11)
| X1 = X11 ),
file('<stdin>',cls_add__left__cancel_0) ).
fof(c_0_369,axiom,
! [X11,X1,X2,X3] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X11)
| X1 = X11 ),
file('<stdin>',cls_add__imp__eq_0) ).
fof(c_0_370,axiom,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X1,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mod__mult__self1__is__0_0) ).
fof(c_0_371,axiom,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,X3),X1,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mod__mult__self2__is__0_0) ).
fof(c_0_372,axiom,
! [X4,X5,X13] :
( c_HOL_Otimes__class_Otimes(X13,X5,tc_nat) != c_HOL_Otimes__class_Otimes(X13,X4,tc_nat)
| X5 = X4
| X13 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_nat__mult__eq__cancel__disj_0) ).
fof(c_0_373,axiom,
! [X4,X5,X13] :
( c_HOL_Otimes__class_Otimes(X13,X5,tc_nat) != c_HOL_Otimes__class_Otimes(X13,X4,tc_nat)
| X13 = c_HOL_Ozero__class_Ozero(tc_nat)
| X5 = X4 ),
file('<stdin>',cls_mult__cancel1_0) ).
fof(c_0_374,axiom,
! [X4,X5,X13] :
( c_HOL_Otimes__class_Otimes(X5,X13,tc_nat) != c_HOL_Otimes__class_Otimes(X4,X13,tc_nat)
| X13 = c_HOL_Ozero__class_Ozero(tc_nat)
| X5 = X4 ),
file('<stdin>',cls_mult__cancel2_0) ).
fof(c_0_375,axiom,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X2,X1,X3),X1,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mod__div__trivial_0) ).
fof(c_0_376,axiom,
! [X7,X13,X9] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X9)),X7),X13) = c_Lambda_OdB_OVar(X9)
| X9 = X13
| c_HOL_Oord__class_Oless(X13,X9,tc_nat) ),
file('<stdin>',cls_subst__Var_2) ).
fof(c_0_377,axiom,
! [X1,X2] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
| X2 = X1 ),
file('<stdin>',cls_dvd_Oneq__le__trans_0) ).
fof(c_0_378,axiom,
! [X1,X2] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| X2 = X1
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
file('<stdin>',cls_dvd_Ole__neq__trans_0) ).
fof(c_0_379,axiom,
! [X15,X16] :
( X16 = X15
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X15,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X16,tc_nat) ),
file('<stdin>',cls_dvd_Oantisym__conv_0) ).
fof(c_0_380,axiom,
! [X4,X5] :
( X5 = X4
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X4,tc_nat) ),
file('<stdin>',cls_dvd__antisym_0) ).
fof(c_0_381,axiom,
! [X15,X16] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X16,tc_nat)
| X16 = X15
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X15,tc_nat) ),
file('<stdin>',cls_dvd_Oless__le_0) ).
fof(c_0_382,axiom,
! [X15,X16] :
( X16 = X15
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X16,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X15,tc_nat) ),
file('<stdin>',cls_dvd_Oantisym_0) ).
fof(c_0_383,axiom,
! [X15,X16] :
( X16 = X15
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X16,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X15,tc_nat) ),
file('<stdin>',cls_dvd_Oeq__iff_2) ).
fof(c_0_384,axiom,
! [X13,X1,X3] :
( ~ class_Ring__and__Field_Odvd(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X13,X3),X3) ),
file('<stdin>',cls_dvdI_0) ).
fof(c_0_385,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) ),
file('<stdin>',cls_dvd__triv__left_0) ).
fof(c_0_386,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) ),
file('<stdin>',cls_dvd__triv__right_0) ).
fof(c_0_387,axiom,
! [X16] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X16,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat),
file('<stdin>',cls_nat__zero__less__power__iff_2) ).
fof(c_0_388,axiom,
! [X16,X7] :
( c_HOL_Oord__class_Oless(X16,X16,tc_nat)
| hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X16)),X7),X16) = X7 ),
file('<stdin>',cls_subst__Var_1) ).
fof(c_0_389,axiom,
! [X49,X6,X10,X26] :
( c_Type_Otyping(X10,X49,X26)
| ~ c_Lambda_Obeta(X6,X49)
| ~ c_Type_Otyping(X10,X6,X26) ),
file('<stdin>',cls_subject__reduction_0) ).
fof(c_0_390,axiom,
! [X16,X17] : c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X17,X16,tc_nat),X17,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_mod__eq__0__iff_1) ).
fof(c_0_391,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_392,axiom,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
file('<stdin>',cls_dvd__eq__mod__eq__0_1) ).
fof(c_0_393,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_394,axiom,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X1,X2,X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
file('<stdin>',cls_dvd__imp__mod__0_0) ).
fof(c_0_395,axiom,
! [X13,X27] :
( hBOOL(hAPP(X27,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X27,c_Suc(c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X27))))
| ~ hBOOL(hAPP(X27,X13)) ),
file('<stdin>',cls_zero__induct_0) ).
fof(c_0_396,axiom,
! [X13,X27] :
( hBOOL(hAPP(X27,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X27,c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X27)))
| ~ hBOOL(hAPP(X27,X13)) ),
file('<stdin>',cls_zero__induct_1) ).
fof(c_0_397,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_398,axiom,
! [X16,X4] :
( c_HOL_Oord__class_Oless(c_Suc(X16),c_Suc(X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(X16,X4,tc_nat) ),
file('<stdin>',cls_less__Suc__eq__0__disj_3) ).
fof(c_0_399,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_400,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_401,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_402,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_403,axiom,
! [X4,X5,X13] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X5) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X4)
| X5 = X4 ),
file('<stdin>',cls_nat__add__left__cancel_0) ).
fof(c_0_404,axiom,
! [X4,X5,X13] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X13) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X13)
| X5 = X4 ),
file('<stdin>',cls_nat__add__right__cancel_0) ).
fof(c_0_405,axiom,
! [X14,X15,X16] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X15) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X14)
| X15 = X14 ),
file('<stdin>',cls_natgb_Oadd__cancel_0) ).
fof(c_0_406,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_407,axiom,
! [X6,X7] : c_Lambda_Osubstn(X6,X7,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,X6),X7),c_HOL_Ozero__class_Ozero(tc_nat)),
file('<stdin>',cls_substn__subst__0_0) ).
fof(c_0_408,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_409,axiom,
! [X5,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_of__nat__less__0__iff_0) ).
fof(c_0_410,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_411,axiom,
! [X4,X5] :
( c_Divides_Odiv__class_Odiv(X5,X4,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
file('<stdin>',cls_div__less_0) ).
fof(c_0_412,axiom,
! [X4,X5] :
( c_Divides_Odiv__class_Omod(X5,X4,tc_nat) = X5
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
file('<stdin>',cls_mod__if_0) ).
fof(c_0_413,axiom,
! [X13,X9] :
( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X9)),X13) = c_Lambda_OdB_OVar(X9)
| ~ c_HOL_Oord__class_Oless(X9,X13,tc_nat) ),
file('<stdin>',cls_lift_Osimps_I1_J_0) ).
fof(c_0_414,axiom,
! [X36,X27] :
( hBOOL(hAPP(X27,X36))
| hBOOL(hAPP(X27,v_sko__List__Xupt__Xinduct__1(X27)))
| ~ hBOOL(hAPP(X27,c_HOL_Ozero__class_Ozero(tc_nat))) ),
file('<stdin>',cls_upt_Oinduct_0) ).
fof(c_0_415,axiom,
! [X36,X27] :
( hBOOL(hAPP(X27,X36))
| hBOOL(hAPP(X27,v_sko__Nat__Xnat__Xinduct__1(X27)))
| ~ hBOOL(hAPP(X27,c_HOL_Ozero__class_Ozero(tc_nat))) ),
file('<stdin>',cls_nat_Oinduct_0) ).
fof(c_0_416,axiom,
! [X36,X27] :
( hBOOL(hAPP(X27,X36))
| hBOOL(hAPP(X27,v_sko__Nat__Xnat__Xinducts__1(X27)))
| ~ hBOOL(hAPP(X27,c_HOL_Ozero__class_Ozero(tc_nat))) ),
file('<stdin>',cls_nat_Oinducts_0) ).
fof(c_0_417,axiom,
! [X36,X27] :
( hBOOL(hAPP(X27,X36))
| hBOOL(hAPP(X27,v_sko__List__Xreplicate__Xinduct__1(X27)))
| ~ hBOOL(hAPP(X27,c_HOL_Ozero__class_Ozero(tc_nat))) ),
file('<stdin>',cls_replicate_Oinduct_0) ).
fof(c_0_418,axiom,
! [X4,X27] :
( hBOOL(hAPP(X27,X4))
| hBOOL(hAPP(X27,c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X27)))
| ~ hBOOL(hAPP(X27,c_HOL_Ozero__class_Ozero(tc_nat))) ),
file('<stdin>',cls_nat__induct_0) ).
fof(c_0_419,axiom,
! [X36,X27] :
( hBOOL(hAPP(X27,X36))
| hBOOL(hAPP(X27,v_sko__List__Xlexn__Xinduct__1(X27)))
| ~ hBOOL(hAPP(X27,c_HOL_Ozero__class_Ozero(tc_nat))) ),
file('<stdin>',cls_lexn_Oinduct_0) ).
fof(c_0_420,axiom,
! [X4,X2,X3] :
( ~ class_Ring__and__Field_Ozero__neq__one(X3)
| ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| ~ class_Ring__and__Field_Omult__zero(X3)
| ~ class_Power_Opower(X3)
| c_Power_Opower__class_Opower(X2,X4,X3) != c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_power__eq__0__iff_0) ).
fof(c_0_421,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ozero__neq__one(X3)
| ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| ~ class_Ring__and__Field_Omult__zero(X3)
| ~ class_Power_Opower(X3)
| c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X3) != c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_power__eq__0__iff_1) ).
fof(c_0_422,axiom,
! [X46] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X46),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X46,tc_Lambda_OdB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
file('<stdin>',cls_dB_Osize_I6_J_0) ).
fof(c_0_423,axiom,
! [X7,X13,X9] :
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X9),X7,X13) = c_Lambda_OdB_OVar(X9)
| X9 = X13
| c_HOL_Oord__class_Oless(X13,X9,tc_nat) ),
file('<stdin>',cls_substn_Osimps_I1_J_2) ).
fof(c_0_424,axiom,
! [X15,X16,X3] :
( ~ class_Orderings_Olinorder(X3)
| X16 = X15
| c_HOL_Oord__class_Oless(X16,X15,X3)
| c_HOL_Oord__class_Oless(X15,X16,X3) ),
file('<stdin>',cls_linorder__antisym__conv3_0) ).
fof(c_0_425,axiom,
! [X15,X16,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X15,X16,X3)
| X16 = X15
| c_HOL_Oord__class_Oless(X16,X15,X3) ),
file('<stdin>',cls_linorder__less__linear_0) ).
fof(c_0_426,axiom,
! [X15,X16,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X15,X16,X3)
| c_HOL_Oord__class_Oless(X16,X15,X3)
| X16 = X15 ),
file('<stdin>',cls_linorder__neqE_0) ).
fof(c_0_427,axiom,
! [X15,X16,X3] :
( ~ class_Orderings_Olinorder(X3)
| X16 = X15
| c_HOL_Oord__class_Oless(X15,X16,X3)
| c_HOL_Oord__class_Oless(X16,X15,X3) ),
file('<stdin>',cls_not__less__iff__gr__or__eq_0) ).
fof(c_0_428,axiom,
! [X15,X16,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X15,X16,X3)
| c_HOL_Oord__class_Oless(X16,X15,X3)
| X16 = X15 ),
file('<stdin>',cls_linorder__neqE__ordered__idom_0) ).
fof(c_0_429,axiom,
! [X54,X44,X55,X45] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X45),X44) != hAPP(hAPP(c_Lambda_OdB_OApp,X55),X54)
| X44 = X54 ),
file('<stdin>',cls_dB_Osimps_I2_J_1) ).
fof(c_0_430,axiom,
! [X54,X44,X55,X45] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X45),X44) != hAPP(hAPP(c_Lambda_OdB_OApp,X55),X54)
| X45 = X55 ),
file('<stdin>',cls_dB_Osimps_I2_J_0) ).
fof(c_0_431,axiom,
! [X5,X3] :
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X5),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oone__class_Oone(X3)),c_Nat_Osemiring__1__class_Oof__nat(X5,X3)) ),
file('<stdin>',cls_of__nat__Suc_0) ).
fof(c_0_432,axiom,
! [X15,X16,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X16,X15,X3) = c_HOL_Otimes__class_Otimes(X15,X16,X3) ),
file('<stdin>',cls_class__semiring_Omul__c_0) ).
fof(c_0_433,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X2,X1,X3) = c_HOL_Otimes__class_Otimes(X1,X2,X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I7_J_0) ).
fof(c_0_434,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_435,axiom,
! [X16] :
( c_HOL_Oord__class_Oless(X16,X16,tc_nat)
| c_HOL_Oord__class_Oless(X16,c_Suc(X16),tc_nat) ),
file('<stdin>',cls_not__less__less__Suc__eq_1) ).
fof(c_0_436,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_not__one__less__zero_0) ).
fof(c_0_437,axiom,
! [X4,X5] : c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat),
file('<stdin>',cls_mult__cancel1_1) ).
fof(c_0_438,axiom,
! [X4,X5] : c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('<stdin>',cls_mult__cancel2_1) ).
fof(c_0_439,axiom,
! [X15,X16,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X15) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X15),X16) ),
file('<stdin>',cls_class__semiring_Oadd__c_0) ).
fof(c_0_440,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X2) ),
file('<stdin>',cls_comm__monoid__add_Omult__commute_0) ).
fof(c_0_441,axiom,
! [X11,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X11) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X2) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I24_J_0) ).
fof(c_0_442,axiom,
! [X5] :
( X5 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
file('<stdin>',cls_dvd__1__iff__1_0) ).
fof(c_0_443,axiom,
! [X12,X13] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X13)),X12),X13) = X12,
file('<stdin>',cls_subst__eq_0) ).
fof(c_0_444,axiom,
! [X9,X10,X26] :
( hAPP(X10,X9) = X26
| ~ c_Type_Otyping(X10,c_Lambda_OdB_OVar(X9),X26) ),
file('<stdin>',cls_typing__elims_I1_J_0) ).
fof(c_0_445,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_446,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| c_HOL_Otimes__class_Otimes(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mult__eq__0__iff_0) ).
fof(c_0_447,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| c_HOL_Otimes__class_Otimes(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_no__zero__divisors_0) ).
fof(c_0_448,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| c_HOL_Otimes__class_Otimes(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3)
| X1 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_no__zero__divirors__neq0_0) ).
fof(c_0_449,axiom,
! [X15,X16] :
( c_HOL_Oord__class_Oless(X15,X16,tc_nat)
| c_HOL_Oord__class_Oless(X16,X15,tc_nat)
| X16 = X15 ),
file('<stdin>',cls_linorder__neqE__nat_0) ).
fof(c_0_450,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_451,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_dvd__0__left_0) ).
fof(c_0_452,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_453,axiom,
! [X16,X5] :
( c_Power_Opower__class_Opower(X16,X5,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X16 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X5 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_nat__power__eq__Suc__0__iff_0) ).
fof(c_0_454,axiom,
! [X4,X5] : c_HOL_Otimes__class_Otimes(X5,X4,tc_nat) = c_HOL_Otimes__class_Otimes(X4,X5,tc_nat),
file('<stdin>',cls_nat__mult__commute_0) ).
fof(c_0_455,axiom,
! [X4,X2,X3] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X3)
| c_Power_Opower__class_Opower(X2,X4,X3) != c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_field__power__not__zero_0) ).
fof(c_0_456,axiom,
! [X16,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| X16 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X2)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_class__ringb_Oadd__r0__iff_0) ).
fof(c_0_457,axiom,
! [X4,X5] :
( c_HOL_Otimes__class_Otimes(X5,X4,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X5 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('<stdin>',cls_mult__eq__1__iff_0) ).
fof(c_0_458,axiom,
! [X4,X5] :
( c_HOL_Otimes__class_Otimes(X5,X4,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('<stdin>',cls_mult__eq__1__iff_1) ).
fof(c_0_459,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X2) != c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_double__eq__0__iff_0) ).
fof(c_0_460,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_461,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_462,axiom,
! [X4,X3] :
( ~ class_Ring__and__Field_Ozero__neq__one(X3)
| ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| ~ class_Ring__and__Field_Omult__zero(X3)
| ~ class_Power_Opower(X3)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X3),X4,X3) = c_HOL_Ozero__class_Ozero(X3)
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_power__eq__0__iff_2) ).
fof(c_0_463,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_464,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_465,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_466,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_467,axiom,
! [X4,X5] :
( c_HOL_Otimes__class_Otimes(X5,X4,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X4 = c_HOL_Ozero__class_Ozero(tc_nat)
| X5 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_mult__is__0_0) ).
fof(c_0_468,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_469,axiom,
! [X16,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X16,X16,X3) ),
file('<stdin>',cls_order__less__irrefl_0) ).
fof(c_0_470,axiom,
! [X16,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X16,X16,X3) ),
file('<stdin>',cls_linorder__neq__iff_1) ).
fof(c_0_471,axiom,
! [X16,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X16,X16,X3) ),
file('<stdin>',cls_order__less__le_1) ).
fof(c_0_472,axiom,
! [X4,X5] :
( X5 != c_HOL_Otimes__class_Otimes(X5,X4,tc_nat)
| X5 = c_HOL_Ozero__class_Ozero(tc_nat)
| X4 = c_HOL_Oone__class_Oone(tc_nat) ),
file('<stdin>',cls_mult__eq__self__implies__10_0) ).
fof(c_0_473,axiom,
! [X5] :
( X5 = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
file('<stdin>',cls_nat__dvd__1__iff__1_0) ).
fof(c_0_474,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_475,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_476,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_477,axiom,
! [X4,X5] :
( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X5,X4,tc_nat)
| X4 = c_HOL_Oone__class_Oone(tc_nat) ),
file('<stdin>',cls_nat__1__eq__mult__iff_1) ).
fof(c_0_478,axiom,
! [X4,X5] :
( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X5,X4,tc_nat)
| X5 = c_HOL_Oone__class_Oone(tc_nat) ),
file('<stdin>',cls_nat__1__eq__mult__iff_0) ).
fof(c_0_479,axiom,
! [X4,X5] :
( c_HOL_Otimes__class_Otimes(X5,X4,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
| X4 = c_HOL_Oone__class_Oone(tc_nat) ),
file('<stdin>',cls_nat__mult__eq__1__iff_1) ).
fof(c_0_480,axiom,
! [X4,X5] :
( c_HOL_Otimes__class_Otimes(X5,X4,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
| X5 = c_HOL_Oone__class_Oone(tc_nat) ),
file('<stdin>',cls_nat__mult__eq__1__iff_0) ).
fof(c_0_481,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_482,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_483,axiom,
! [X61,X62,X3] :
( X62 = X61
| ~ c_fequal(X62,X61,X3) ),
file('<stdin>',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(c_0_484,axiom,
! [X16,X43] : c_Type_Otyping(X43,c_Lambda_OdB_OVar(X16),hAPP(X43,X16)),
file('<stdin>',cls_typing_OVar_0) ).
fof(c_0_485,axiom,
! [X4,X3] :
( ~ class_Ring__and__Field_Osemiring__0(X3)
| ~ class_Power_Opower(X3)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X3),c_Suc(X4),X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_power__0__Suc_0) ).
fof(c_0_486,axiom,
c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
file('<stdin>',cls_mult__eq__1__iff_2) ).
fof(c_0_487,axiom,
! [X4] : ~ c_HOL_Oord__class_Oless(X4,X4,tc_nat),
file('<stdin>',cls_less__not__refl_0) ).
fof(c_0_488,axiom,
! [X16] : ~ c_HOL_Oord__class_Oless(X16,X16,tc_nat),
file('<stdin>',cls_nat__less__le_1) ).
fof(c_0_489,axiom,
! [X4,X3] :
( ~ class_Ring__and__Field_Osemiring__0(X3)
| ~ class_Power_Opower(X3)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X3),X4,X3) = c_HOL_Ozero__class_Ozero(X3)
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_power__0__left_1) ).
fof(c_0_490,axiom,
! [X23] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X23)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X23)) ),
file('<stdin>',cls_Lambda_0) ).
fof(c_0_491,axiom,
! [X3] :
( ~ class_Ring__and__Field_Osemiring__0(X3)
| ~ class_Power_Opower(X3)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(tc_nat),X3) = c_HOL_Oone__class_Oone(X3) ),
file('<stdin>',cls_power__0__left_0) ).
fof(c_0_492,axiom,
! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3)) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_double__eq__0__iff_1) ).
fof(c_0_493,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_494,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_495,axiom,
! [X46] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X46)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X46)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
file('<stdin>',cls_dB_Osize_I3_J_0) ).
fof(c_0_496,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_497,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_498,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_499,axiom,
! [X16,X2] :
( X16 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X2)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_natgb_Oadd__r0__iff_0) ).
fof(c_0_500,axiom,
c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
file('<stdin>',cls_dvd__1__iff__1_1) ).
fof(c_0_501,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oone__class_Oone(X3),X3) ),
file('<stdin>',cls_zero__less__one_0) ).
fof(c_0_502,axiom,
! [X16,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| X16 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),c_HOL_Ozero__class_Ozero(X3)) ),
file('<stdin>',cls_class__ringb_Oadd__r0__iff_1) ).
fof(c_0_503,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X2) = X2 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I5_J_0) ).
fof(c_0_504,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X2) = X2 ),
file('<stdin>',cls_add__0__left_0) ).
fof(c_0_505,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X2) = X2 ),
file('<stdin>',cls_comm__monoid__add_Omult__1_0) ).
fof(c_0_506,axiom,
! [X16,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X16) = X16 ),
file('<stdin>',cls_class__semiring_Oadd__0_0) ).
fof(c_0_507,axiom,
! [X4] : c_Power_Opower__class_Opower(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
file('<stdin>',cls_power__Suc__0_0) ).
fof(c_0_508,axiom,
! [X5] : c_Power_Opower__class_Opower(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X5,tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
file('<stdin>',cls_nat__power__eq__Suc__0__iff_2) ).
fof(c_0_509,axiom,
! [X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mod__0_0) ).
fof(c_0_510,axiom,
! [X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_div__0_0) ).
fof(c_0_511,axiom,
! [X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_div__by__0_0) ).
fof(c_0_512,axiom,
! [X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X2,c_HOL_Oone__class_Oone(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mod__by__1_0) ).
fof(c_0_513,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I9_J_0) ).
fof(c_0_514,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I10_J_0) ).
fof(c_0_515,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mult__eq__0__iff_2) ).
fof(c_0_516,axiom,
! [X1,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X1,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mult__eq__0__iff_1) ).
fof(c_0_517,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Omult__zero(X3)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mult__zero__right_0) ).
fof(c_0_518,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Omult__zero(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mult__zero__left_0) ).
fof(c_0_519,axiom,
! [X16,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X16,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_class__semiring_Omul__0_0) ).
fof(c_0_520,axiom,
! [X4,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X3),X4,X3) = c_HOL_Oone__class_Oone(X3) ),
file('<stdin>',cls_power__one_0) ).
fof(c_0_521,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_522,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_523,axiom,
! [X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(X2,X2,X3) = c_HOL_Oone__class_Oone(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_div__self_0) ).
fof(c_0_524,axiom,
! [X16,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Power_Opower__class_Opower(X16,c_HOL_Ozero__class_Ozero(tc_nat),X3) = c_HOL_Oone__class_Oone(X3) ),
file('<stdin>',cls_class__semiring_Opwr__0_0) ).
fof(c_0_525,axiom,
! [X2,X3] :
( ~ class_Power_Opower(X3)
| c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X3) = c_HOL_Oone__class_Oone(X3) ),
file('<stdin>',cls_power__0_0) ).
fof(c_0_526,axiom,
! [X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(X3),X3) = X2 ),
file('<stdin>',cls_mod__by__0_0) ).
fof(c_0_527,axiom,
! [X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(X2,c_HOL_Oone__class_Oone(X3),X3) = X2 ),
file('<stdin>',cls_div__by__1_0) ).
fof(c_0_528,axiom,
! [X16,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X3),X16,X3) = X16 ),
file('<stdin>',cls_class__semiring_Omul__1_0) ).
fof(c_0_529,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X3),X2,X3) = X2 ),
file('<stdin>',cls_mult__1_0) ).
fof(c_0_530,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X3),X2,X3) = X2 ),
file('<stdin>',cls_mult__1__left_0) ).
fof(c_0_531,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X3),X3) = X2 ),
file('<stdin>',cls_mult__1__right_0) ).
fof(c_0_532,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X3),X3) = X2 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I12_J_0) ).
fof(c_0_533,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X3),X2,X3) = X2 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I11_J_0) ).
fof(c_0_534,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_535,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X3),X2,X3) ),
file('<stdin>',cls_one__dvd_0) ).
fof(c_0_536,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_dvd__0__right_0) ).
fof(c_0_537,axiom,
! [X5] : c_Divides_Odiv__class_Omod(X5,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_mod__1_0) ).
fof(c_0_538,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),c_HOL_Ozero__class_Ozero(X3)) = X2 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(c_0_539,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),c_HOL_Ozero__class_Ozero(X3)) = X2 ),
file('<stdin>',cls_monoid__add__class_Oadd__0__right_0) ).
fof(c_0_540,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),c_HOL_Ozero__class_Ozero(X3)) = X2 ),
file('<stdin>',cls_comm__monoid__add_Omult__1__right_0) ).
fof(c_0_541,axiom,
! [X5] : c_Divides_Odiv__class_Odiv(X5,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = X5,
file('<stdin>',cls_div__1_0) ).
fof(c_0_542,axiom,
! [X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X2,X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mod__self_0) ).
fof(c_0_543,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_Power_Opower__class_Opower(X2,c_HOL_Oone__class_Oone(tc_nat),X3) = X2 ),
file('<stdin>',cls_power__one__right_0) ).
fof(c_0_544,axiom,
! [X16,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Power_Opower__class_Opower(X16,c_HOL_Oone__class_Oone(tc_nat),X3) = X16 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I33_J_0) ).
fof(c_0_545,axiom,
! [X13] : c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X13,tc_nat),
file('<stdin>',cls_dvd__1__left_0) ).
fof(c_0_546,axiom,
! [X36,X54,X55] : hAPP(hAPP(c_Lambda_OdB_OApp,X55),X54) != c_Lambda_OdB_OVar(X36),
file('<stdin>',cls_dB_Osimps_I5_J_0) ).
fof(c_0_547,axiom,
! [X36,X54,X55] : c_Lambda_OdB_OVar(X36) != hAPP(hAPP(c_Lambda_OdB_OApp,X55),X54),
file('<stdin>',cls_dB_Osimps_I4_J_0) ).
fof(c_0_548,axiom,
! [X52,X44,X45] : c_Lambda_OdB_OAbs(X52) != hAPP(hAPP(c_Lambda_OdB_OApp,X45),X44),
file('<stdin>',cls_dB_Osimps_I9_J_0) ).
fof(c_0_549,axiom,
! [X52,X44,X45] : hAPP(hAPP(c_Lambda_OdB_OApp,X45),X44) != c_Lambda_OdB_OAbs(X52),
file('<stdin>',cls_dB_Osimps_I8_J_0) ).
fof(c_0_550,axiom,
! [X16] : c_Power_Opower__class_Opower(X16,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
file('<stdin>',cls_nat__power__eq__Suc__0__iff_1) ).
fof(c_0_551,axiom,
! [X16,X3] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3)
| c_HOL_Otimes__class_Otimes(X16,X16,X3) = X16 ),
file('<stdin>',cls_mult__idem_0) ).
fof(c_0_552,axiom,
! [X16] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X16),tc_nat),
file('<stdin>',cls_gr0__conv__Suc_1) ).
fof(c_0_553,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_554,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X2,X3) ),
file('<stdin>',cls_dvd__refl_0) ).
fof(c_0_555,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat),
file('<stdin>',cls_nat__mult__eq__1__iff_2) ).
fof(c_0_556,axiom,
c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
file('<stdin>',cls_nat__1__eq__mult__iff_2) ).
fof(c_0_557,axiom,
! [X20,X3] : c_List_Olistsp(X20,c_List_Olist_ONil(X3),X3),
file('<stdin>',cls_listsp_ONil_0) ).
fof(c_0_558,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_559,axiom,
! [X4] : c_HOL_Oord__class_Oless(X4,c_Suc(X4),tc_nat),
file('<stdin>',cls_lessI_0) ).
fof(c_0_560,axiom,
! [X16] : c_HOL_Oord__class_Oless(X16,c_Suc(X16),tc_nat),
file('<stdin>',cls_less__Suc__eq_2) ).
fof(c_0_561,axiom,
c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
file('<stdin>',cls_nat__dvd__1__iff__1_1) ).
fof(c_0_562,axiom,
! [X19] : c_Power_Opower__class_Opower(X19,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat),
file('<stdin>',cls_power__eq__if_0) ).
fof(c_0_563,axiom,
! [X4] : c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_mult__is__0_1) ).
fof(c_0_564,axiom,
! [X5] : c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_mult__is__0_2) ).
fof(c_0_565,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_566,axiom,
! [X4] : c_HOL_Otimes__class_Otimes(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X4,
file('<stdin>',cls_nat__mult__1__right_0) ).
fof(c_0_567,axiom,
! [X4] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X4,tc_nat) = X4,
file('<stdin>',cls_nat__mult__1_0) ).
fof(c_0_568,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_569,axiom,
! [X16,X3] : c_fequal(X16,X16,X3),
file('<stdin>',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
fof(c_0_570,axiom,
! [X4,X5,X3] :
( ~ class_Nat_Osemiring__char__0(X3)
| c_Nat_Osemiring__1__class_Oof__nat(X5,X3) != c_Nat_Osemiring__1__class_Oof__nat(X4,X3)
| X5 = X4 ),
file('<stdin>',cls_of__nat__eq__iff_0) ).
fof(c_0_571,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_572,axiom,
! [X16] : c_Ring__and__Field_Odvd__class_Odvd(X16,X16,tc_nat),
file('<stdin>',cls_dvd_Oeq__iff_0) ).
fof(c_0_573,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_574,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_575,axiom,
! [X16] : X16 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),c_HOL_Ozero__class_Ozero(tc_nat)),
file('<stdin>',cls_natgb_Oadd__r0__iff_1) ).
fof(c_0_576,axiom,
! [X6,X7] :
( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X7),c_Lambda_OdB_OAbs(X6))
| ~ c_Lambda_Obeta(X7,X6) ),
file('<stdin>',cls_abs_0) ).
fof(c_0_577,axiom,
! [X59,X60] :
( class_Orderings_Oorder(tc_fun(X59,X60))
| ~ class_Orderings_Oorder(X60) ),
file('<stdin>',clsarity_fun__Orderings_Oorder) ).
fof(c_0_578,axiom,
! [X59,X60] :
( class_Orderings_Opreorder(tc_fun(X59,X60))
| ~ class_Orderings_Opreorder(X60) ),
file('<stdin>',clsarity_fun__Orderings_Opreorder) ).
fof(c_0_579,axiom,
! [X6,X9] : ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X9),X6),
file('<stdin>',cls_beta__cases_I1_J_0) ).
fof(c_0_580,axiom,
! [X3] :
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_of__nat__0_0) ).
fof(c_0_581,axiom,
! [X3] :
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X3) = c_HOL_Oone__class_Oone(X3) ),
file('<stdin>',cls_of__nat__1_0) ).
fof(c_0_582,axiom,
! [X36] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(X36),tc_Lambda_OdB) = c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_dB_Osize_I4_J_0) ).
fof(c_0_583,axiom,
! [X3] :
( ~ class_Ring__and__Field_Ozero__neq__one(X3)
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Oone__class_Oone(X3) ),
file('<stdin>',cls_zero__neq__one_0) ).
fof(c_0_584,axiom,
! [X3] :
( ~ class_Ring__and__Field_Ozero__neq__one(X3)
| c_HOL_Oone__class_Oone(X3) != c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_one__neq__zero_0) ).
fof(c_0_585,axiom,
! [X15,X16] :
( c_Suc(X16) != c_Suc(X15)
| X16 = X15 ),
file('<stdin>',cls_Suc__inject_0) ).
fof(c_0_586,axiom,
! [X53,X36] :
( c_Suc(X36) != c_Suc(X53)
| X36 = X53 ),
file('<stdin>',cls_nat_Oinject_0) ).
fof(c_0_587,axiom,
! [X52,X46] :
( c_Lambda_OdB_OAbs(X46) != c_Lambda_OdB_OAbs(X52)
| X46 = X52 ),
file('<stdin>',cls_dB_Osimps_I3_J_0) ).
fof(c_0_588,axiom,
! [X53,X36] :
( c_Lambda_OdB_OVar(X36) != c_Lambda_OdB_OVar(X53)
| X36 = X53 ),
file('<stdin>',cls_dB_Osimps_I1_J_0) ).
fof(c_0_589,axiom,
! [X4] :
( X4 = c_Suc(c_ATP__Linkup_Osko__Nat__Xnot0__implies__Suc__1__1(X4))
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_not0__implies__Suc_0) ).
fof(c_0_590,axiom,
! [X22] :
( X22 = c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__Xnchotomy__1__1(X22))
| X22 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_nat_Onchotomy_0) ).
fof(c_0_591,axiom,
! [X15] :
( X15 = c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__Xexhaust__1__1(X15))
| X15 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_nat_Oexhaust_0) ).
fof(c_0_592,axiom,
! [X36,X52] : c_Lambda_OdB_OVar(X36) != c_Lambda_OdB_OAbs(X52),
file('<stdin>',cls_dB_Osimps_I6_J_0) ).
fof(c_0_593,axiom,
! [X36,X52] : c_Lambda_OdB_OAbs(X52) != c_Lambda_OdB_OVar(X36),
file('<stdin>',cls_dB_Osimps_I7_J_0) ).
fof(c_0_594,axiom,
! [X36] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(X36)) = c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_dB_Osize_I1_J_0) ).
fof(c_0_595,axiom,
! [X53] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X53),
file('<stdin>',cls_nat_Osimps_I2_J_0) ).
fof(c_0_596,axiom,
! [X5] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X5),
file('<stdin>',cls_Zero__neq__Suc_0) ).
fof(c_0_597,axiom,
! [X53] : c_Suc(X53) != c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_nat_Osimps_I3_J_0) ).
fof(c_0_598,axiom,
! [X5] : c_Suc(X5) != c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_Suc__neq__Zero_0) ).
fof(c_0_599,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_600,axiom,
! [X4] : c_Suc(X4) != X4,
file('<stdin>',cls_Suc__n__not__n_0) ).
fof(c_0_601,axiom,
! [X4] : X4 != c_Suc(X4),
file('<stdin>',cls_n__not__Suc__n_0) ).
fof(c_0_602,axiom,
class_Power_Opower(tc_nat),
file('<stdin>',clsarity_nat__Power_Opower) ).
fof(c_0_603,axiom,
class_Orderings_Oorder(tc_nat),
file('<stdin>',clsarity_nat__Orderings_Oorder) ).
fof(c_0_604,axiom,
class_Orderings_Olinorder(tc_nat),
file('<stdin>',clsarity_nat__Orderings_Olinorder) ).
fof(c_0_605,axiom,
class_Orderings_Opreorder(tc_nat),
file('<stdin>',clsarity_nat__Orderings_Opreorder) ).
fof(c_0_606,axiom,
class_Ring__and__Field_Odvd(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Odvd) ).
fof(c_0_607,axiom,
class_Nat_Osemiring__char__0(tc_nat),
file('<stdin>',clsarity_nat__Nat_Osemiring__char__0) ).
fof(c_0_608,axiom,
class_Divides_Osemiring__div(tc_nat),
file('<stdin>',clsarity_nat__Divides_Osemiring__div) ).
fof(c_0_609,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Omonoid__add) ).
fof(c_0_610,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Osemiring) ).
fof(c_0_611,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Omonoid__mult) ).
fof(c_0_612,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Omult__zero) ).
fof(c_0_613,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Osemiring__0) ).
fof(c_0_614,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Osemiring__1) ).
fof(c_0_615,axiom,
class_OrderedGroup_Osemigroup__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Osemigroup__add) ).
fof(c_0_616,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
fof(c_0_617,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
fof(c_0_618,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
fof(c_0_619,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
fof(c_0_620,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
fof(c_0_621,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
fof(c_0_622,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
fof(c_0_623,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(c_0_624,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
fof(c_0_625,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(c_0_626,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(c_0_627,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
fof(c_0_628,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).
fof(c_0_629,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(c_0_630,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_631,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(c_0_632,axiom,
! [X12,X41,X6,X9] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,X6,X41,tc_Lambda_OdB,tc_Lambda_OdB)),X12),X9) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X6),X12),X9),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X12,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X9,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X41,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
c_0_0 ).
fof(c_0_633,plain,
! [X12,X41,X9,X10,X42,X26] :
( c_Type_Otypings(X10,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X12,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X9,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X41,tc_Lambda_OdB,tc_Lambda_OdB),X42)
| ~ c_Type_Otypings(c_Type_Oshift(X10,X9,X26,tc_Type_Otype),X41,X42)
| ~ c_Type_Otyping(X10,X12,X26) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_634,plain,
! [X50,X7,X23] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X23)),X7),X50,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X7))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X23),X7),c_HOL_Ozero__class_Ozero(tc_nat)),X50,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_635,axiom,
! [X41,X6,X9] : hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,X6,X41,tc_Lambda_OdB,tc_Lambda_OdB)),X9) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X6),X9),c_List_Omap(c_COMBC(c_Lambda_Olift,X9,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X41,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
c_0_3 ).
fof(c_0_636,plain,
! [X41,X9,X10,X25,X26] :
( X26 = X25
| ~ c_Type_Otyping(X10,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X9),X41,tc_Lambda_OdB,tc_Lambda_OdB),X25)
| ~ c_Type_Otyping(X10,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X9),X41,tc_Lambda_OdB,tc_Lambda_OdB),X26) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_637,axiom,
! [X56,X57,X27,X58,X39,X3] : c_COMBB(X27,X57,X56,X39,X3,X58) = hAPP(X27,hAPP(X57,X56)),
c_0_5 ).
fof(c_0_638,plain,
! [X41,X9,X10,X25,X42] :
( c_Type_Otypings(c_Type_Oshift(X10,X9,X25,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,X9,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X41,tc_Lambda_OdB,tc_Lambda_OdB),X42)
| ~ c_Type_Otypings(X10,X41,X42) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_639,plain,
! [X41] :
( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X41,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_List_Olistsp(c_InductTermi_OIT,X41,tc_Lambda_OdB) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_640,plain,
! [X51,X4] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X51,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_List_Olistsp(c_InductTermi_OIT,X51,tc_Lambda_OdB) ),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_641,plain,
! [X50,X7,X23] :
( c_Lambda_Obeta(c_List_Ofoldl(c_Lambda_OdB_OApp,X23,X50,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X50,tc_Lambda_OdB,tc_Lambda_OdB))
| ~ c_Lambda_Obeta(X23,X7) ),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_642,axiom,
! [X50,X7,X51,X23] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X23),X51,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X7),X50,tc_Lambda_OdB,tc_Lambda_OdB)
| X51 = X50 ),
c_0_10 ).
fof(c_0_643,axiom,
! [X50,X7,X51,X23] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X23),X51,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X7),X50,tc_Lambda_OdB,tc_Lambda_OdB)
| X23 = X7 ),
c_0_11 ).
fof(c_0_644,axiom,
! [X50,X51,X4,X5] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X51,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X50,tc_Lambda_OdB,tc_Lambda_OdB)
| X51 = X50 ),
c_0_12 ).
fof(c_0_645,axiom,
! [X50,X51,X4,X5] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X51,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X50,tc_Lambda_OdB,tc_Lambda_OdB)
| X5 = X4 ),
c_0_13 ).
fof(c_0_646,plain,
! [X40,X15,X16,X3] :
( ~ class_OrderedGroup_Osemigroup__add(X3)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X15),X40,X3,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X15,X40,X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_647,axiom,
! [X41,X50,X23,X4] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X41,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X23),X50,tc_Lambda_OdB,tc_Lambda_OdB),
c_0_15 ).
fof(c_0_648,axiom,
! [X41,X7,X23] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X23,X41,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X41,tc_Lambda_OdB,tc_Lambda_OdB)
| X23 = X7 ),
c_0_16 ).
fof(c_0_649,plain,
! [X40,X16,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3),X40,X3,X3)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X16,X40,X3,X3) ),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_650,plain,
! [X13,X8,X9,X27] :
( ~ c_HOL_Oord__class_Oless(X8,X13,tc_nat)
| X13 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ hBOOL(hAPP(X27,c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X13,X9,tc_nat)),X8),X13,tc_nat)))
| hBOOL(hAPP(X27,X9)) ),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_651,plain,
! [X13,X8,X9,X27] :
( ~ c_HOL_Oord__class_Oless(X8,X13,tc_nat)
| X13 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ hBOOL(hAPP(X27,c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X13,X9,tc_nat)),X8),X13,tc_nat)))
| hBOOL(hAPP(X27,X8)) ),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_652,plain,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X1,X3)),c_Divides_Odiv__class_Omod(X2,X1,X3))),X11) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X11) ),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
fof(c_0_653,plain,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X2,X1,X3),X3)),c_Divides_Odiv__class_Omod(X2,X1,X3))),X11) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X11) ),
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_654,plain,
! [X22,X12,X6,X8,X9] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X6),hAPP(hAPP(c_Lambda_Olift,X22),X9)),c_Suc(X8))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X12),X22),X8)),X9) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X6),X12),X9)),X22),X8)
| ~ c_HOL_Oord__class_Oless(X9,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_655,axiom,
! [X11,X1,X2] : c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),X11,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(X2,X11,tc_nat)),c_Divides_Odiv__class_Odiv(X1,X11,tc_nat))),c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(X2,X11,tc_nat)),c_Divides_Odiv__class_Omod(X1,X11,tc_nat)),X11,tc_nat)),
c_0_23 ).
fof(c_0_656,axiom,
! [X56,X57,X27,X58,X39,X3] : hAPP(c_COMBC(X27,X57,X39,X58,X3),X56) = hAPP(hAPP(X27,X56),X57),
c_0_24 ).
fof(c_0_657,axiom,
! [X56,X57,X27,X58,X39,X3] : hAPP(c_COMBC(X27,X57,X39,X58,X3),X56) = hAPP(hAPP(X27,X56),X57),
c_0_25 ).
fof(c_0_658,axiom,
! [X6,X7,X23] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X23),X7) != c_List_Ofoldl(c_Lambda_OdB_OApp,X6,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,X23),X7) = X6 ),
c_0_26 ).
fof(c_0_659,axiom,
! [X6,X50,X7,X4] : hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X7)),X6) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X50,tc_Lambda_OdB,tc_Lambda_OdB),
c_0_27 ).
fof(c_0_660,axiom,
! [X50,X7,X23] :
( c_Lambda_OdB_OAbs(X23) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X50,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(X23) = X7 ),
c_0_28 ).
fof(c_0_661,axiom,
! [X50,X7,X5] :
( c_Lambda_OdB_OVar(X5) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X50,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OVar(X5) = X7 ),
c_0_29 ).
fof(c_0_662,axiom,
! [X50,X7,X23] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X50,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X23)
| X7 = c_Lambda_OdB_OAbs(X23) ),
c_0_30 ).
fof(c_0_663,plain,
! [X6,X7,X8,X9] :
( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X6),X7),X8)),X9) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,X7),X9)),X8)
| ~ c_HOL_Oord__class_Oless(X8,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_664,axiom,
! [X50,X7,X5] :
( c_Lambda_OdB_OVar(X5) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X50,tc_Lambda_OdB,tc_Lambda_OdB)
| X50 = c_List_Olist_ONil(tc_Lambda_OdB) ),
c_0_32 ).
fof(c_0_665,axiom,
! [X50,X7,X23] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X50,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X23)
| X50 = c_List_Olist_ONil(tc_Lambda_OdB) ),
c_0_33 ).
fof(c_0_666,axiom,
! [X50,X7,X23] :
( c_Lambda_OdB_OAbs(X23) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X50,tc_Lambda_OdB,tc_Lambda_OdB)
| X50 = c_List_Olist_ONil(tc_Lambda_OdB) ),
c_0_34 ).
fof(c_0_667,axiom,
! [X11,X1,X2] : c_Divides_Odiv__class_Omod(X2,c_HOL_Otimes__class_Otimes(X1,X11,tc_nat),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Odiv(X2,X1,tc_nat),X11,tc_nat),tc_nat)),c_Divides_Odiv__class_Omod(X2,X1,tc_nat)),
c_0_35 ).
fof(c_0_668,plain,
! [X23,X18,X11,X1] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X18,X11,tc_nat),tc_nat)),X23),c_HOL_Otimes__class_Otimes(X1,X11,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X23,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_36]) ).
fof(c_0_669,axiom,
! [X11,X1,X2] : c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),X11,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X1,X11,tc_nat),tc_nat)),c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Omod(X1,X11,tc_nat),tc_nat),X11,tc_nat)),
c_0_37 ).
fof(c_0_670,plain,
! [X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_38]) ).
fof(c_0_671,axiom,
! [X9,X10,X25,X26,X3] : c_Type_Oshift(c_Type_Oshift(X10,X9,X25,X3),c_HOL_Ozero__class_Ozero(tc_nat),X26,X3) = c_Type_Oshift(c_Type_Oshift(X10,c_HOL_Ozero__class_Ozero(tc_nat),X26,X3),c_Suc(X9),X25,X3),
c_0_39 ).
fof(c_0_672,plain,
! [X10,X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Osemiring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X2,X10,X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X1,X10,X3)),X11)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1),X10,X3)),X11) ),
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_673,axiom,
! [X12,X13,X8,X9] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X9,X12,tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X8,X12,tc_nat)),X13)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X8),X12,tc_nat)),X13),
c_0_41 ).
fof(c_0_674,axiom,
! [X7,X23] : hAPP(hAPP(c_Lambda_OdB_OApp,X23),X7) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X23),X7),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
c_0_42 ).
fof(c_0_675,plain,
! [X15,X16,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X16,X16,X3)),c_HOL_Otimes__class_Otimes(X15,X15,X3)),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_43]) ).
fof(c_0_676,plain,
! [X6,X7,X8,X9] :
( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X6),X7),X8)),X9) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X6),X9)),hAPP(hAPP(c_Lambda_Olift,X7),X9)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),c_HOL_Oone__class_Oone(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X9,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_44]) ).
fof(c_0_677,axiom,
! [X5] : c_Lambda_OdB_OVar(X5) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
c_0_45 ).
fof(c_0_678,axiom,
! [X23] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X23),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OAbs(X23),
c_0_46 ).
fof(c_0_679,axiom,
! [X23] : c_Lambda_OdB_OAbs(X23) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X23),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
c_0_47 ).
fof(c_0_680,axiom,
! [X38,X2,X39,X3] : c_List_Ofoldl(X38,X2,c_List_Olist_ONil(X39),X3,X39) = X2,
c_0_48 ).
fof(c_0_681,plain,
! [X17,X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X2,X11,X3)),c_HOL_Otimes__class_Otimes(X1,X17,X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X2,X17,X3)),c_HOL_Otimes__class_Otimes(X1,X11,X3))
| X11 = X17
| X2 = X1 ),
inference(fof_simplification,[status(thm)],[c_0_49]) ).
fof(c_0_682,plain,
! [X14,X15,X16,X31,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X31,X15,X3)),c_HOL_Otimes__class_Otimes(X16,X14,X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X31,X14,X3)),c_HOL_Otimes__class_Otimes(X16,X15,X3))
| X15 = X14
| X31 = X16 ),
inference(fof_simplification,[status(thm)],[c_0_50]) ).
fof(c_0_683,plain,
! [X12,X6,X9,X24,X25,X26] :
( ~ c_Type_Otyping(X24,X12,X25)
| ~ c_Type_Otyping(c_Type_Oshift(X24,X9,X25,tc_Type_Otype),X6,X26)
| c_Type_Otyping(X24,hAPP(hAPP(hAPP(c_Lambda_Osubst,X6),X12),X9),X26) ),
inference(fof_simplification,[status(thm)],[c_0_51]) ).
fof(c_0_684,axiom,
! [X4,X5,X13] : c_Divides_Odiv__class_Omod(c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat)),X5)),X4,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X5),X4,tc_nat),
c_0_52 ).
fof(c_0_685,axiom,
! [X14,X15,X16,X31] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X31,X15,tc_nat)),c_HOL_Otimes__class_Otimes(X16,X14,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X31,X14,tc_nat)),c_HOL_Otimes__class_Otimes(X16,X15,tc_nat))
| X15 = X14
| X31 = X16 ),
c_0_53 ).
fof(c_0_686,axiom,
! [X17,X11,X1,X2] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X2,X11,tc_nat)),c_HOL_Otimes__class_Otimes(X1,X17,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X2,X17,tc_nat)),c_HOL_Otimes__class_Otimes(X1,X11,tc_nat))
| X11 = X17
| X2 = X1 ),
c_0_54 ).
fof(c_0_687,plain,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1),X11,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Omod(X2,X11,X3)),c_Divides_Odiv__class_Omod(X1,X11,X3)),X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_55]) ).
fof(c_0_688,axiom,
! [X12,X6,X7,X13] : hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,X6),X12)),X7),X13) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X6),X7),X13)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X12),X7),X13)),
c_0_56 ).
fof(c_0_689,plain,
! [X15,X16,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X16,X16,X3)),c_HOL_Otimes__class_Otimes(X15,X15,X3)),X3)
| X15 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_57]) ).
fof(c_0_690,plain,
! [X15,X16,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X16,X16,X3)),c_HOL_Otimes__class_Otimes(X15,X15,X3)),X3)
| X16 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_58]) ).
fof(c_0_691,plain,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| X2 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X1,X3)),c_Divides_Odiv__class_Omod(X2,X1,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_59]) ).
fof(c_0_692,plain,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X1,X3)),c_Divides_Odiv__class_Omod(X2,X1,X3)) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_60]) ).
fof(c_0_693,plain,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X2,X1,X3),X3)),c_Divides_Odiv__class_Omod(X2,X1,X3)) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_61]) ).
fof(c_0_694,axiom,
! [X6,X7,X13] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(X6)),X7),X13) = c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,X6),hAPP(hAPP(c_Lambda_Olift,X7),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)))),
c_0_62 ).
fof(c_0_695,plain,
! [X16,X17,X11,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X16,X11,X3)),c_HOL_Otimes__class_Otimes(X16,X17,X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X16,X17,X3)),c_HOL_Otimes__class_Otimes(X16,X11,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_63]) ).
fof(c_0_696,plain,
! [X14,X15,X16,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X16,X15,X3)),c_HOL_Otimes__class_Otimes(X16,X14,X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X16,X14,X3)),c_HOL_Otimes__class_Otimes(X16,X15,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_64]) ).
fof(c_0_697,plain,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,X3),X11,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X11,X3),c_Divides_Odiv__class_Omod(X1,X11,X3),X3),X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_65]) ).
fof(c_0_698,plain,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Omod(X2,X11,X3)),X1),X11,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1),X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_66]) ).
fof(c_0_699,plain,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1),X11,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Omod(X2,X11,X3)),X1),X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_67]) ).
fof(c_0_700,plain,
! [X17,X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X11)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X17)) ),
inference(fof_simplification,[status(thm)],[c_0_68]) ).
fof(c_0_701,plain,
! [X14,X15,X16,X31,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X16,X15,X3),c_Divides_Odiv__class_Odiv(X31,X14,X3),X3) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X16,X31,X3),c_HOL_Otimes__class_Otimes(X15,X14,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X31,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_69]) ).
fof(c_0_702,axiom,
! [X14,X15,X16] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X16,X15,tc_nat)),c_HOL_Otimes__class_Otimes(X16,X14,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X16,X14,tc_nat)),c_HOL_Otimes__class_Otimes(X16,X15,tc_nat)),
c_0_70 ).
fof(c_0_703,axiom,
! [X16,X17,X11] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X16,X11,tc_nat)),c_HOL_Otimes__class_Otimes(X16,X17,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X16,X17,tc_nat)),c_HOL_Otimes__class_Otimes(X16,X11,tc_nat)),
c_0_71 ).
fof(c_0_704,plain,
! [X14,X15,X16,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X15),X14,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Odiv(X16,X14,X3)),c_Divides_Odiv__class_Odiv(X15,X14,X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X15,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_72]) ).
fof(c_0_705,plain,
! [X6,X9,X10,X25,X26] :
( c_Type_Otyping(c_Type_Oshift(X10,X9,X25,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X6),X9),X26)
| ~ c_Type_Otyping(X10,X6,X26) ),
inference(fof_simplification,[status(thm)],[c_0_73]) ).
fof(c_0_706,plain,
! [X4,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X4,X3),X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_74]) ).
fof(c_0_707,plain,
! [X4,X5] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| c_HOL_Oord__class_Oless(X5,c_HOL_Otimes__class_Otimes(X4,c_Suc(c_Divides_Odiv__class_Odiv(X5,X4,tc_nat)),tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_75]) ).
fof(c_0_708,plain,
! [X11,X29,X1,X30,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X1,X11,X3) != c_Divides_Odiv__class_Omod(X29,X11,X3)
| c_Divides_Odiv__class_Omod(X2,X11,X3) != c_Divides_Odiv__class_Omod(X30,X11,X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,X3),X11,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X30,X29,X3),X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_76]) ).
fof(c_0_709,plain,
! [X11,X29,X1,X30,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X1,X11,X3) != c_Divides_Odiv__class_Omod(X29,X11,X3)
| c_Divides_Odiv__class_Omod(X2,X11,X3) != c_Divides_Odiv__class_Omod(X30,X11,X3)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1),X11,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X30),X29),X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_77]) ).
fof(c_0_710,plain,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X11,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X1,X2,X3),c_Divides_Odiv__class_Odiv(X11,X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X11,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_78]) ).
fof(c_0_711,plain,
! [X32,X33,X34,X35,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X35,X34,X3),c_HOL_Otimes__class_Otimes(X33,X32,X3),X3) = c_HOL_Otimes__class_Otimes(X33,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X35,X34,X3),X32,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_79]) ).
fof(c_0_712,plain,
! [X32,X33,X34,X35,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X35,X34,X3),c_HOL_Otimes__class_Otimes(X33,X32,X3),X3) = c_HOL_Otimes__class_Otimes(X35,c_HOL_Otimes__class_Otimes(X34,c_HOL_Otimes__class_Otimes(X33,X32,X3),X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_80]) ).
fof(c_0_713,axiom,
! [X4,X5,X13] : c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat)),X5),X4,tc_nat) = c_Divides_Odiv__class_Omod(X5,X4,tc_nat),
c_0_81 ).
fof(c_0_714,plain,
! [X8,X9,X10,X26,X3] :
( hAPP(c_Type_Oshift(X10,X9,X26,X3),X8) = hAPP(X10,X8)
| ~ c_HOL_Oord__class_Oless(X8,X9,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_82]) ).
fof(c_0_715,plain,
! [X15,X16,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X16,X16,X3)),c_HOL_Otimes__class_Otimes(X15,X15,X3)) != c_HOL_Ozero__class_Ozero(X3)
| X16 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_83]) ).
fof(c_0_716,plain,
! [X15,X16,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X16,X16,X3)),c_HOL_Otimes__class_Otimes(X15,X15,X3)) != c_HOL_Ozero__class_Ozero(X3)
| X15 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_84]) ).
fof(c_0_717,plain,
! [X6,X13,X9] :
( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X6),X9)),c_Suc(X13)) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X6),X13)),X9)
| ~ c_HOL_Oord__class_Oless(X9,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_85]) ).
fof(c_0_718,axiom,
! [X44,X45] : c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X45),X44),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X45,tc_Lambda_OdB)),c_Nat_Osize__class_Osize(X44,tc_Lambda_OdB))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
c_0_86 ).
fof(c_0_719,plain,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Omod(X2,X1,X3)),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X1,X3)) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_87]) ).
fof(c_0_720,plain,
! [X4,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X4,X3),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X4,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_88]) ).
fof(c_0_721,plain,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X2,X3),c_HOL_Otimes__class_Otimes(X11,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_89]) ).
fof(c_0_722,plain,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X2,X3),c_HOL_Otimes__class_Otimes(X11,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_90]) ).
fof(c_0_723,plain,
! [X4,X5,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X5,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_91]) ).
fof(c_0_724,plain,
! [X15,X16,X1,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X16,X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X16,X3),c_Power_Opower__class_Opower(X1,X15,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_92]) ).
fof(c_0_725,axiom,
! [X15,X47,X48,X16,X4] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),c_HOL_Otimes__class_Otimes(X4,X48,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Otimes__class_Otimes(X4,X47,tc_nat))
| c_Divides_Odiv__class_Omod(X16,X4,tc_nat) = c_Divides_Odiv__class_Omod(X15,X4,tc_nat) ),
c_0_93 ).
fof(c_0_726,plain,
! [X4,X5,X13] :
( c_Ring__and__Field_Odvd__class_Odvd(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_94]) ).
fof(c_0_727,plain,
! [X4,X5,X13] :
( c_Ring__and__Field_Odvd__class_Odvd(X5,X4,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_95]) ).
fof(c_0_728,plain,
! [X4,X5,X9] :
( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X9,X5,tc_nat),c_Power_Opower__class_Opower(X9,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X9,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_96]) ).
fof(c_0_729,plain,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_97]) ).
fof(c_0_730,plain,
! [X4,X2,X21,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X21,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X21,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_98]) ).
fof(c_0_731,plain,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X11,X3),c_HOL_Otimes__class_Otimes(X1,X11,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_99]) ).
fof(c_0_732,plain,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X2,X3),c_HOL_Otimes__class_Otimes(X11,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_100]) ).
fof(c_0_733,plain,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X2,X3),c_HOL_Otimes__class_Otimes(X11,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_101]) ).
fof(c_0_734,plain,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X2,X3),c_HOL_Otimes__class_Otimes(X11,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_102]) ).
fof(c_0_735,plain,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X11,X3),c_HOL_Otimes__class_Otimes(X1,X11,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_103]) ).
fof(c_0_736,plain,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X11,X3),c_HOL_Otimes__class_Otimes(X1,X11,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_104]) ).
fof(c_0_737,plain,
! [X32,X33,X34,X35,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X35,X34,X3),c_HOL_Otimes__class_Otimes(X33,X32,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X35,X33,X3),c_HOL_Otimes__class_Otimes(X34,X32,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_105]) ).
fof(c_0_738,plain,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,X3),X11,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Omod(X1,X11,X3),X3),X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_106]) ).
fof(c_0_739,plain,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,X3),X11,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X11,X3),X1,X3),X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_107]) ).
fof(c_0_740,plain,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X11,X3),X1,X3),X11,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,X3),X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_108]) ).
fof(c_0_741,plain,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),c_HOL_Otimes__class_Otimes(X11,X1,X3)),X1,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),c_Divides_Odiv__class_Odiv(X2,X1,X3))
| X1 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_109]) ).
fof(c_0_742,plain,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),c_HOL_Otimes__class_Otimes(X1,X11,X3)),X1,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),c_Divides_Odiv__class_Odiv(X2,X1,X3))
| X1 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_110]) ).
fof(c_0_743,plain,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X11,X3),c_HOL_Otimes__class_Otimes(X1,X11,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_111]) ).
fof(c_0_744,plain,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X2,X3),c_HOL_Otimes__class_Otimes(X11,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_112]) ).
fof(c_0_745,plain,
! [X14,X15,X16,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X15),X14),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X16,X15,X3)),c_HOL_Otimes__class_Otimes(X16,X14,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_113]) ).
fof(c_0_746,plain,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring(X3)
| c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1),X11,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X2,X11,X3)),c_HOL_Otimes__class_Otimes(X1,X11,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_114]) ).
fof(c_0_747,plain,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1),X11,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X2,X11,X3)),c_HOL_Otimes__class_Otimes(X1,X11,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_115]) ).
fof(c_0_748,plain,
! [X5,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X2,X5,X3)),c_HOL_Otimes__class_Otimes(X1,X5,X3)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1),X5,X3) ),
inference(fof_simplification,[status(thm)],[c_0_116]) ).
fof(c_0_749,plain,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X1,X2,X3),c_Divides_Odiv__class_Odiv(X11,X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X11,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X11,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_117]) ).
fof(c_0_750,plain,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),c_Divides_Odiv__class_Omod(X1,X11,X3)),X11,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1),X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_118]) ).
fof(c_0_751,plain,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1),X11,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),c_Divides_Odiv__class_Omod(X1,X11,X3)),X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_119]) ).
fof(c_0_752,plain,
! [X15,X16,X4,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(X16,X15,X3),X4,X3) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(X16,X4,X3),c_Power_Opower__class_Opower(X15,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_120]) ).
fof(c_0_753,plain,
! [X16,X23,X17,X11,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),c_HOL_Otimes__class_Otimes(X23,X11,X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),c_HOL_Otimes__class_Otimes(X23,X17,X3))
| X11 = X17
| X23 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_121]) ).
fof(c_0_754,plain,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1)),X11) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X11)),X1) ),
inference(fof_simplification,[status(thm)],[c_0_122]) ).
fof(c_0_755,axiom,
! [X16,X10,X26,X3] : hAPP(c_Type_Oshift(X10,X16,X26,X3),X16) = X26,
c_0_123 ).
fof(c_0_756,plain,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X13),X5,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X13),X4,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_124]) ).
fof(c_0_757,axiom,
! [X4,X5,X13] : c_HOL_Otimes__class_Otimes(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X13,X5,tc_nat)),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat)),
c_0_125 ).
fof(c_0_758,axiom,
! [X4,X5,X13] : c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4),X13,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X5,X13,tc_nat)),c_HOL_Otimes__class_Otimes(X4,X13,tc_nat)),
c_0_126 ).
fof(c_0_759,plain,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3)
| X11 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X11,X3),c_HOL_Otimes__class_Otimes(X1,X11,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_127]) ).
fof(c_0_760,plain,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3)
| X11 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X11,X2,X3),c_HOL_Otimes__class_Otimes(X11,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_128]) ).
fof(c_0_761,plain,
! [X4,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X4,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_129]) ).
fof(c_0_762,axiom,
! [X12,X6,X7,X13] : c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,X6),X12),X7,X13) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(X6,X7,X13)),c_Lambda_Osubstn(X12,X7,X13)),
c_0_130 ).
fof(c_0_763,axiom,
! [X16,X23,X17,X11] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),c_HOL_Otimes__class_Otimes(X23,X11,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),c_HOL_Otimes__class_Otimes(X23,X17,tc_nat))
| X11 = X17
| X23 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_131 ).
fof(c_0_764,plain,
! [X11,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X1),X3) ),
inference(fof_simplification,[status(thm)],[c_0_132]) ).
fof(c_0_765,plain,
! [X11,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X11),X3) ),
inference(fof_simplification,[status(thm)],[c_0_133]) ).
fof(c_0_766,plain,
! [X4,X5,X13] :
( c_Ring__and__Field_Odvd__class_Odvd(X5,X4,tc_nat)
| X13 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_134]) ).
fof(c_0_767,plain,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X13,tc_nat),c_HOL_Otimes__class_Otimes(X4,X13,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_135]) ).
fof(c_0_768,plain,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_136]) ).
fof(c_0_769,plain,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X13,tc_nat),c_HOL_Otimes__class_Otimes(X4,X13,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_137]) ).
fof(c_0_770,plain,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_138]) ).
fof(c_0_771,plain,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X2,X3),c_HOL_Otimes__class_Otimes(X11,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_139]) ).
fof(c_0_772,plain,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X11,X3),c_HOL_Otimes__class_Otimes(X1,X11,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_140]) ).
fof(c_0_773,plain,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X11,X3),c_HOL_Otimes__class_Otimes(X1,X11,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_141]) ).
fof(c_0_774,plain,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X11,X3),c_HOL_Otimes__class_Otimes(X1,X11,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_142]) ).
fof(c_0_775,plain,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X11,X3),c_HOL_Otimes__class_Otimes(X1,X11,X3),X3)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_143]) ).
fof(c_0_776,plain,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X2,X3),c_HOL_Otimes__class_Otimes(X11,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_144]) ).
fof(c_0_777,plain,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X2,X3),c_HOL_Otimes__class_Otimes(X11,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_145]) ).
fof(c_0_778,plain,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X2,X3),c_HOL_Otimes__class_Otimes(X11,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X11,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_146]) ).
fof(c_0_779,plain,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X2,X3),c_HOL_Otimes__class_Otimes(X11,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_147]) ).
fof(c_0_780,plain,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X2,X3),c_HOL_Otimes__class_Otimes(X11,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_148]) ).
fof(c_0_781,plain,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X2,X3),c_HOL_Otimes__class_Otimes(X11,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_149]) ).
fof(c_0_782,plain,
! [X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_150]) ).
fof(c_0_783,plain,
! [X4,X2,X21,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X4,X3),c_Power_Opower__class_Opower(X2,X21,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X21,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_151]) ).
fof(c_0_784,plain,
! [X15,X16,X1,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X16,X3),c_Power_Opower__class_Opower(X1,X15,X3),X3)
| ~ c_HOL_Oord__class_Oless(X16,X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_152]) ).
fof(c_0_785,plain,
! [X17,X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X11,X3),c_HOL_Otimes__class_Otimes(X1,X17,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X17,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_153]) ).
fof(c_0_786,plain,
! [X5,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X2,X5,X3)),X5) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),c_HOL_Oone__class_Oone(X3)),X5,X3) ),
inference(fof_simplification,[status(thm)],[c_0_154]) ).
fof(c_0_787,plain,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1),X1,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Odiv(X2,X1,X3)),c_HOL_Oone__class_Oone(X3))
| X1 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_155]) ).
fof(c_0_788,plain,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X2),X1,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Odiv(X2,X1,X3)),c_HOL_Oone__class_Oone(X3))
| X1 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_156]) ).
fof(c_0_789,plain,
! [X17,X11,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X17),X3)
| ~ c_HOL_Oord__class_Oless(X11,X17,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_157]) ).
fof(c_0_790,plain,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X11,X2,X3),c_HOL_Otimes__class_Otimes(X11,X1,X3),X3) = c_HOL_Otimes__class_Otimes(X11,c_Divides_Odiv__class_Omod(X2,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_158]) ).
fof(c_0_791,plain,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X11,X3),c_HOL_Otimes__class_Otimes(X1,X11,X3),X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X1,X3),X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_159]) ).
fof(c_0_792,plain,
! [X15,X16,X18,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X16,X15,X3),X18,X3) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X16,X18,X3),c_Power_Opower__class_Opower(X15,X18,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_160]) ).
fof(c_0_793,plain,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X3)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X2,X1,X3),X4,X3) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X4,X3),c_Power_Opower__class_Opower(X1,X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_161]) ).
fof(c_0_794,plain,
! [X4,X5,X13] :
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_162]) ).
fof(c_0_795,plain,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_163]) ).
fof(c_0_796,plain,
! [X13,X8,X9] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X13,tc_nat),c_HOL_Otimes__class_Otimes(X8,X13,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(X9,X8,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_164]) ).
fof(c_0_797,plain,
! [X13,X8,X9] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X9,tc_nat),c_HOL_Otimes__class_Otimes(X13,X8,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(X9,X8,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_165]) ).
fof(c_0_798,plain,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_166]) ).
fof(c_0_799,plain,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X13,tc_nat),c_HOL_Otimes__class_Otimes(X4,X13,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_167]) ).
fof(c_0_800,axiom,
! [X6,X7,X13] : hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,X7),X6)),X13) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X7),X13)),hAPP(hAPP(c_Lambda_Olift,X6),X13)),
c_0_168 ).
fof(c_0_801,plain,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),c_HOL_Otimes__class_Otimes(X1,X11,X3)),X1,X3) = c_Divides_Odiv__class_Omod(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_169]) ).
fof(c_0_802,plain,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),c_HOL_Otimes__class_Otimes(X11,X1,X3)),X1,X3) = c_Divides_Odiv__class_Omod(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_170]) ).
fof(c_0_803,plain,
! [X4,X27] :
( ~ hBOOL(hAPP(X27,c_Divides_Odiv__class_Odiv(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
| hBOOL(hAPP(X27,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(fof_simplification,[status(thm)],[c_0_171]) ).
fof(c_0_804,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_172]) ).
fof(c_0_805,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_173]) ).
fof(c_0_806,plain,
! [X4,X27] :
( ~ hBOOL(hAPP(X27,c_Divides_Odiv__class_Omod(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
| hBOOL(hAPP(X27,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_174]) ).
fof(c_0_807,plain,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X4),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_175]) ).
fof(c_0_808,plain,
! [X16,X18,X19,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X16,X19,X3),c_Power_Opower__class_Opower(X16,X18,X3),X3) = c_Power_Opower__class_Opower(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X19),X18),X3) ),
inference(fof_simplification,[status(thm)],[c_0_176]) ).
fof(c_0_809,plain,
! [X4,X5,X2,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_Power_Opower__class_Opower(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4),X3) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X5,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_177]) ).
fof(c_0_810,plain,
! [X14,X15,X16,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X15),X14)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X15)),X14) ),
inference(fof_simplification,[status(thm)],[c_0_178]) ).
fof(c_0_811,plain,
! [X11,X1,X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1)),X11) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X11)) ),
inference(fof_simplification,[status(thm)],[c_0_179]) ).
fof(c_0_812,plain,
! [X11,X1,X2,X3] :
( ~ class_OrderedGroup_Oab__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1)),X11) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X11)) ),
inference(fof_simplification,[status(thm)],[c_0_180]) ).
fof(c_0_813,plain,
! [X17,X11,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X11)),X17) ),
inference(fof_simplification,[status(thm)],[c_0_181]) ).
fof(c_0_814,plain,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1)),X11) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X11)) ),
inference(fof_simplification,[status(thm)],[c_0_182]) ).
fof(c_0_815,axiom,
! [X4,X5,X13] : c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X5,X4,tc_nat),X13,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X13,tc_nat),c_HOL_Otimes__class_Otimes(X4,X13,tc_nat),tc_nat),
c_0_183 ).
fof(c_0_816,axiom,
! [X4,X5,X13] : c_HOL_Otimes__class_Otimes(X13,c_Divides_Odiv__class_Omod(X5,X4,tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat),tc_nat),
c_0_184 ).
fof(c_0_817,plain,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X2,X3),X11,X3) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X11,X3),X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_185]) ).
fof(c_0_818,plain,
! [X4,X5,X13,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X13,X5,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,c_Divides_Odiv__class_Omod(X5,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_186]) ).
fof(c_0_819,plain,
! [X4,X5,X13,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X13,X5,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,c_Divides_Odiv__class_Omod(X5,X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_187]) ).
fof(c_0_820,plain,
! [X4,X5,X13] :
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_188]) ).
fof(c_0_821,plain,
! [X28,X13,X8,X9] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X28),tc_nat)
| ~ c_HOL_Oord__class_Oless(X13,X28,tc_nat)
| ~ c_HOL_Oord__class_Oless(X9,X8,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_189]) ).
fof(c_0_822,axiom,
! [X37,X38,X39,X3] :
( c_List_Olist_ONil(X3) != c_List_Omap(X38,X37,X39,X3)
| X37 = c_List_Olist_ONil(X39) ),
c_0_190 ).
fof(c_0_823,axiom,
! [X37,X38,X39,X3] :
( c_List_Omap(X38,X37,X39,X3) != c_List_Olist_ONil(X3)
| X37 = c_List_Olist_ONil(X39) ),
c_0_191 ).
fof(c_0_824,axiom,
! [X44,X45] : c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X45),X44)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X45)),c_Lambda_OdB_OdB__size(X44))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
c_0_192 ).
fof(c_0_825,plain,
! [X14,X15,X16,X12,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X15),X14)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X15),X12)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X14) = X12 ),
inference(fof_simplification,[status(thm)],[c_0_193]) ).
fof(c_0_826,plain,
! [X4,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,c_Suc(X4),X3),c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_194]) ).
fof(c_0_827,plain,
! [X6,X7,X23,X9] :
( c_Lambda_Obeta(hAPP(hAPP(hAPP(c_Lambda_Osubst,X23),X6),X9),hAPP(hAPP(hAPP(c_Lambda_Osubst,X7),X6),X9))
| ~ c_Lambda_Obeta(X23,X7) ),
inference(fof_simplification,[status(thm)],[c_0_195]) ).
fof(c_0_828,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_196]) ).
fof(c_0_829,axiom,
! [X6,X7,X13] : hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X6),X13)),X7),X13) = X6,
c_0_197 ).
fof(c_0_830,plain,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X13),X5,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X13),X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_198]) ).
fof(c_0_831,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_199]) ).
fof(c_0_832,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_200]) ).
fof(c_0_833,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_201]) ).
fof(c_0_834,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_202]) ).
fof(c_0_835,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_203]) ).
fof(c_0_836,plain,
! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_HOL_Otimes__class_Otimes(X5,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X5,X3) ),
inference(fof_simplification,[status(thm)],[c_0_204]) ).
fof(c_0_837,axiom,
! [X6,X7,X13] : c_Lambda_Osubstn(c_Lambda_OdB_OAbs(X6),X7,X13) = c_Lambda_OdB_OAbs(c_Lambda_Osubstn(X6,X7,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)))),
c_0_205 ).
fof(c_0_838,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_206]) ).
fof(c_0_839,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X4,X5,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_207]) ).
fof(c_0_840,axiom,
! [X4,X5,X13] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4)),X13) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X13)),
c_0_208 ).
fof(c_0_841,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_209]) ).
fof(c_0_842,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_210]) ).
fof(c_0_843,plain,
! [X15,X16,X4,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X16,X4,X3),c_Power_Opower__class_Opower(X15,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X15,X3) ),
inference(fof_simplification,[status(thm)],[c_0_211]) ).
fof(c_0_844,plain,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X11,X2,X3),c_HOL_Otimes__class_Otimes(X11,X1,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_212]) ).
fof(c_0_845,plain,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X11,X3),c_HOL_Otimes__class_Otimes(X1,X11,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_213]) ).
fof(c_0_846,plain,
! [X4,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_214]) ).
fof(c_0_847,plain,
! [X14,X15,X16] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X16,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X14,X15,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X14,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X15,X16,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X15,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_215]) ).
fof(c_0_848,plain,
! [X5,X13] :
( c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat)),X13,tc_nat) = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X13,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_216]) ).
fof(c_0_849,plain,
! [X11,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X1),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_217]) ).
fof(c_0_850,plain,
! [X11,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X1),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_218]) ).
fof(c_0_851,plain,
! [X11,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X11),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_219]) ).
fof(c_0_852,plain,
! [X11,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X11),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_220]) ).
fof(c_0_853,plain,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X11),X3)
| ~ c_HOL_Oord__class_Oless(X1,X11,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_221]) ).
fof(c_0_854,plain,
! [X4,X5,X13] :
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_222]) ).
fof(c_0_855,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_223]) ).
fof(c_0_856,plain,
! [X4,X5,X13,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X13,c_Divides_Odiv__class_Omod(X5,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,X5,X3) ),
inference(fof_simplification,[status(thm)],[c_0_224]) ).
fof(c_0_857,plain,
! [X4,X5,X13,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X13,c_Divides_Odiv__class_Omod(X5,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,X5,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_225]) ).
fof(c_0_858,plain,
! [X4,X5] :
( X4 = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X5,tc_nat),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_226]) ).
fof(c_0_859,plain,
! [X4,X5] :
( X4 = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_227]) ).
fof(c_0_860,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),tc_nat)
| ~ 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) ),
inference(fof_simplification,[status(thm)],[c_0_228]) ).
fof(c_0_861,plain,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X11),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X11,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_229]) ).
fof(c_0_862,plain,
! [X5,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),c_HOL_Otimes__class_Otimes(X2,X5,X3)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),c_HOL_Oone__class_Oone(X3)),X5,X3) ),
inference(fof_simplification,[status(thm)],[c_0_230]) ).
fof(c_0_863,plain,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X11,X3),c_HOL_Otimes__class_Otimes(X1,X11,X3),X3) = c_Divides_Odiv__class_Odiv(X2,X1,X3)
| X11 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_231]) ).
fof(c_0_864,plain,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X11,X2,X3),c_HOL_Otimes__class_Otimes(X11,X1,X3),X3) = c_Divides_Odiv__class_Odiv(X2,X1,X3)
| X11 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_232]) ).
fof(c_0_865,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Odiv(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_Oone__class_Oone(tc_nat),X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_233]) ).
fof(c_0_866,plain,
! [X14,X15,X16,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X16,c_HOL_Otimes__class_Otimes(X15,X14,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X16,X15,X3),X14,X3) ),
inference(fof_simplification,[status(thm)],[c_0_234]) ).
fof(c_0_867,plain,
! [X32,X33,X35,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X35,c_HOL_Otimes__class_Otimes(X33,X32,X3),X3) = c_HOL_Otimes__class_Otimes(X33,c_HOL_Otimes__class_Otimes(X35,X32,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_235]) ).
fof(c_0_868,plain,
! [X32,X33,X35,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X35,c_HOL_Otimes__class_Otimes(X33,X32,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X35,X33,X3),X32,X3) ),
inference(fof_simplification,[status(thm)],[c_0_236]) ).
fof(c_0_869,plain,
! [X33,X34,X35,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X35,X34,X3),X33,X3) = c_HOL_Otimes__class_Otimes(X35,c_HOL_Otimes__class_Otimes(X34,X33,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_237]) ).
fof(c_0_870,plain,
! [X33,X34,X35,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X35,X34,X3),X33,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X35,X33,X3),X34,X3) ),
inference(fof_simplification,[status(thm)],[c_0_238]) ).
fof(c_0_871,plain,
! [X11,X1,X2,X3] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X1,X3),X11,X3) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X1,X11,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_239]) ).
fof(c_0_872,plain,
! [X4,X2,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X4,X3),X2,X3) = c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_240]) ).
fof(c_0_873,plain,
! [X14,X15,X16] :
( c_Ring__and__Field_Odvd__class_Odvd(X16,X14,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X14,X15,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X14,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X15,X16,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X15,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_241]) ).
fof(c_0_874,plain,
! [X4,X5,X2,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_Power_Opower__class_Opower(X2,c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),X3) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X2,X5,X3),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_242]) ).
fof(c_0_875,plain,
! [X16,X18,X19,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X16,X19,X3),X18,X3) = c_Power_Opower__class_Opower(X16,c_HOL_Otimes__class_Otimes(X19,X18,tc_nat),X3) ),
inference(fof_simplification,[status(thm)],[c_0_243]) ).
fof(c_0_876,axiom,
! [X4,X5] : c_Divides_Odiv__class_Omod(c_Suc(X5),X4,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(X5,X4,tc_nat)),X4,tc_nat),
c_0_244 ).
fof(c_0_877,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X2),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_245]) ).
fof(c_0_878,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X2),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_246]) ).
fof(c_0_879,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X2),X3) ),
inference(fof_simplification,[status(thm)],[c_0_247]) ).
fof(c_0_880,axiom,
! [X7,X13] : hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(X7)),X13) = c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)))),
c_0_248 ).
fof(c_0_881,plain,
! [X4,X5,X13] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_249]) ).
fof(c_0_882,plain,
! [X13,X8,X9] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X13),tc_nat)
| ~ c_HOL_Oord__class_Oless(X9,X8,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_250]) ).
fof(c_0_883,axiom,
! [X4,X5,X13] :
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X13,X5,tc_nat),c_HOL_Otimes__class_Otimes(X13,X4,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(X5,X4,tc_nat)
| X13 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_251 ).
fof(c_0_884,plain,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X11,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X1,X3),X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_252]) ).
fof(c_0_885,plain,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X11,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X1,X3),X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_253]) ).
fof(c_0_886,plain,
! [X14,X15,X16,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X15),X14)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_254]) ).
fof(c_0_887,plain,
! [X11,X1,X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X11)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X11)) ),
inference(fof_simplification,[status(thm)],[c_0_255]) ).
fof(c_0_888,plain,
! [X17,X11,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X17)) ),
inference(fof_simplification,[status(thm)],[c_0_256]) ).
fof(c_0_889,axiom,
! [X4,X5,X13] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),X13,tc_nat) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Otimes__class_Otimes(X4,X13,tc_nat),tc_nat),
c_0_257 ).
fof(c_0_890,axiom,
! [X11,X1,X2] : c_Divides_Odiv__class_Odiv(X2,c_HOL_Otimes__class_Otimes(X1,X11,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(X2,X1,tc_nat),X11,tc_nat),
c_0_258 ).
fof(c_0_891,plain,
! [X16,X4] :
( X4 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X16,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X16,X4,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_259]) ).
fof(c_0_892,plain,
! [X11,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X2,X1,X3),X11,X3) = c_Divides_Odiv__class_Omod(X2,X11,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_260]) ).
fof(c_0_893,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),c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_261]) ).
fof(c_0_894,plain,
! [X4,X5] :
( 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),c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_262]) ).
fof(c_0_895,plain,
! [X4,X27] :
( ~ hBOOL(hAPP(X27,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X27,c_Divides_Odiv__class_Odiv(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
inference(fof_simplification,[status(thm)],[c_0_263]) ).
fof(c_0_896,plain,
! [X5,X27] :
( hBOOL(hAPP(X27,c_Divides_Odiv__class_Odiv(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
| ~ hBOOL(hAPP(X27,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(fof_simplification,[status(thm)],[c_0_264]) ).
fof(c_0_897,plain,
! [X14,X15,X16] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X16,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X14,X15,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X14,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X15,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_265]) ).
fof(c_0_898,plain,
! [X14,X15,X16] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X16,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X14,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X15,X16,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X15,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_266]) ).
fof(c_0_899,plain,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X2,X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X1,X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_267]) ).
fof(c_0_900,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X2,X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_268]) ).
fof(c_0_901,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X3),X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_269]) ).
fof(c_0_902,plain,
! [X4,X27] :
( ~ hBOOL(hAPP(X27,X4))
| hBOOL(hAPP(X27,c_Divides_Odiv__class_Omod(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
inference(fof_simplification,[status(thm)],[c_0_270]) ).
fof(c_0_903,axiom,
! [X6,X7] : c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X7)),X6),hAPP(hAPP(hAPP(c_Lambda_Osubst,X7),X6),c_HOL_Ozero__class_Ozero(tc_nat))),
c_0_271 ).
fof(c_0_904,plain,
! [X4,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_Power_Opower__class_Opower(X2,c_Suc(X4),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_272]) ).
fof(c_0_905,plain,
! [X4,X5,X28,X13] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X28) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X4)
| ~ c_HOL_Oord__class_Oless(X13,X28,tc_nat)
| c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_273]) ).
fof(c_0_906,plain,
! [X4,X13] :
( c_Ring__and__Field_Odvd__class_Odvd(X13,X4,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X13),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_274]) ).
fof(c_0_907,plain,
! [X13,X8,X9] :
( c_HOL_Oord__class_Oless(X9,X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X8),X13,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_275]) ).
fof(c_0_908,plain,
! [X4,X5,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_Power_Opower__class_Opower(X2,X5,X3) != c_Power_Opower__class_Opower(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X2,X3)
| X5 = X4 ),
inference(fof_simplification,[status(thm)],[c_0_276]) ).
fof(c_0_909,axiom,
! [X4,X5] :
( c_Divides_Odiv__class_Omod(c_Suc(X5),X4,tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(X5,X4,tc_nat))
| c_Suc(c_Divides_Odiv__class_Omod(X5,X4,tc_nat)) = X4 ),
c_0_277 ).
fof(c_0_910,axiom,
! [X4,X5] : c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_278 ).
fof(c_0_911,plain,
! [X14,X15,X16] :
( c_Ring__and__Field_Odvd__class_Odvd(X16,X14,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X14,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X15,X16,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X15,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_279]) ).
fof(c_0_912,plain,
! [X14,X15,X16] :
( c_Ring__and__Field_Odvd__class_Odvd(X16,X14,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X14,X15,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X14,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X15,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_280]) ).
fof(c_0_913,axiom,
! [X4,X5] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat),tc_nat),
c_0_281 ).
fof(c_0_914,axiom,
! [X14,X15,X16] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X14)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X14)),
c_0_282 ).
fof(c_0_915,plain,
! [X4,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_283]) ).
fof(c_0_916,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_284]) ).
fof(c_0_917,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X2),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_285]) ).
fof(c_0_918,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X2),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_286]) ).
fof(c_0_919,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X2),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_287]) ).
fof(c_0_920,axiom,
! [X38,X39,X3] : c_List_Olist_ONil(X3) = c_List_Omap(X38,c_List_Olist_ONil(X39),X39,X3),
c_0_288 ).
fof(c_0_921,axiom,
! [X38,X39,X3] : c_List_Omap(X38,c_List_Olist_ONil(X39),X39,X3) = c_List_Olist_ONil(X3),
c_0_289 ).
fof(c_0_922,plain,
! [X16,X4,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X16,c_Power_Opower__class_Opower(X16,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_290]) ).
fof(c_0_923,plain,
! [X4,X5,X13] :
( c_HOL_Otimes__class_Otimes(X13,X5,tc_nat) != c_HOL_Otimes__class_Otimes(X13,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat)
| X5 = X4 ),
inference(fof_simplification,[status(thm)],[c_0_291]) ).
fof(c_0_924,plain,
! [X4,X5] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(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_292]) ).
fof(c_0_925,plain,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X1,X2,X3),X3) = X1
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_293]) ).
fof(c_0_926,plain,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X2,X3),X2,X3) = X1
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_294]) ).
fof(c_0_927,plain,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X1,X11,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_295]) ).
fof(c_0_928,plain,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X1,X11,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_296]) ).
fof(c_0_929,plain,
! [X5,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),X5) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oone__class_Oone(X3)),c_HOL_Oone__class_Oone(X3)),X5,X3) ),
inference(fof_simplification,[status(thm)],[c_0_297]) ).
fof(c_0_930,plain,
! [X5] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X5,tc_nat),X5,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_298]) ).
fof(c_0_931,plain,
! [X5] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X5,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_299]) ).
fof(c_0_932,plain,
! [X16,X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X16,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X16,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_300]) ).
fof(c_0_933,plain,
! [X4,X5] :
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X4,X5,tc_nat),X4,tc_nat) = X5
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_301]) ).
fof(c_0_934,plain,
! [X4,X5] :
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),X4,tc_nat) = X5
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_302]) ).
fof(c_0_935,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X5,X4,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_303]) ).
fof(c_0_936,plain,
! [X4,X5,X3] :
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Nat_Osemiring__1__class_Oof__nat(X5,X3)),c_Nat_Osemiring__1__class_Oof__nat(X4,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_304]) ).
fof(c_0_937,axiom,
! [X16,X5] : c_HOL_Oord__class_Oless(X5,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X16)),tc_nat),
c_0_305 ).
fof(c_0_938,axiom,
! [X5,X9] : c_HOL_Oord__class_Oless(X9,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X9)),tc_nat),
c_0_306 ).
fof(c_0_939,axiom,
! [X5,X9] : c_HOL_Oord__class_Oless(X9,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X5)),tc_nat),
c_0_307 ).
fof(c_0_940,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_308]) ).
fof(c_0_941,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_309]) ).
fof(c_0_942,plain,
! [X11,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X11,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X11,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_310]) ).
fof(c_0_943,plain,
! [X14,X15,X16,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X16,X14,X3)
| ~ c_HOL_Oord__class_Oless(X15,X14,X3)
| ~ c_HOL_Oord__class_Oless(X16,X15,X3) ),
inference(fof_simplification,[status(thm)],[c_0_311]) ).
fof(c_0_944,plain,
! [X14,X15,X16,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X14,X16,X3)
| ~ c_HOL_Oord__class_Oless(X14,X15,X3)
| ~ c_HOL_Oord__class_Oless(X15,X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_312]) ).
fof(c_0_945,axiom,
! [X4,X5] :
( c_Suc(c_Divides_Odiv__class_Omod(X5,X4,tc_nat)) != X4
| c_Divides_Odiv__class_Omod(c_Suc(X5),X4,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_313 ).
fof(c_0_946,plain,
! [X4,X5,X3] :
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),X3) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(X5,X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_314]) ).
fof(c_0_947,plain,
! [X16,X18,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X16,X18,X3),X16,X3) = c_Power_Opower__class_Opower(X16,c_Suc(X18),X3) ),
inference(fof_simplification,[status(thm)],[c_0_315]) ).
fof(c_0_948,plain,
! [X16,X18,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X16,c_Power_Opower__class_Opower(X16,X18,X3),X3) = c_Power_Opower__class_Opower(X16,c_Suc(X18),X3) ),
inference(fof_simplification,[status(thm)],[c_0_316]) ).
fof(c_0_949,plain,
! [X4,X2,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_Power_Opower__class_Opower(X2,c_Suc(X4),X3) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X4,X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_317]) ).
fof(c_0_950,plain,
! [X4,X2,X3] :
( ~ class_Power_Opower(X3)
| c_Power_Opower__class_Opower(X2,c_Suc(X4),X3) = c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_318]) ).
fof(c_0_951,plain,
! [X16,X4,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Power_Opower__class_Opower(X16,c_Suc(X4),X3) = c_HOL_Otimes__class_Otimes(X16,c_Power_Opower__class_Opower(X16,X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_319]) ).
fof(c_0_952,plain,
! [X16,X18,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Power_Opower__class_Opower(X16,c_Suc(X18),X3) = c_HOL_Otimes__class_Otimes(X16,c_Power_Opower__class_Opower(X16,X18,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_320]) ).
fof(c_0_953,plain,
! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X5,X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_321]) ).
fof(c_0_954,plain,
! [X4,X5] :
( c_Divides_Odiv__class_Odiv(X5,X4,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(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_322]) ).
fof(c_0_955,plain,
! [X13,X8,X9] :
( c_HOL_Oord__class_Oless(c_Suc(X9),X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(X8,X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(X9,X8,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_323]) ).
fof(c_0_956,plain,
! [X4,X13] :
( c_Ring__and__Field_Odvd__class_Odvd(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X13),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_324]) ).
fof(c_0_957,plain,
! [X5,X8,X9] :
( c_HOL_Oord__class_Oless(X9,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X8),tc_nat)
| ~ c_HOL_Oord__class_Oless(X9,X8,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_325]) ).
fof(c_0_958,plain,
! [X5,X8,X9] :
( c_HOL_Oord__class_Oless(X9,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X5),tc_nat)
| ~ c_HOL_Oord__class_Oless(X9,X8,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_326]) ).
fof(c_0_959,plain,
! [X14,X15,X16] :
( c_HOL_Oord__class_Oless(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X14),tc_nat)
| ~ c_HOL_Oord__class_Oless(X16,X14,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_327]) ).
fof(c_0_960,plain,
! [X14,X15,X16] :
( c_HOL_Oord__class_Oless(X16,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_328]) ).
fof(c_0_961,plain,
! [X8,X9] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X9),X9,tc_nat),
inference(fof_simplification,[status(thm)],[c_0_329]) ).
fof(c_0_962,plain,
! [X8,X9] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X8),X9,tc_nat),
inference(fof_simplification,[status(thm)],[c_0_330]) ).
fof(c_0_963,plain,
! [X15,X16,X3] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3)
| c_HOL_Otimes__class_Otimes(X16,c_HOL_Otimes__class_Otimes(X16,X15,X3),X3) = c_HOL_Otimes__class_Otimes(X16,X15,X3) ),
inference(fof_simplification,[status(thm)],[c_0_331]) ).
fof(c_0_964,plain,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X2,X1,X3),X1,X3) = c_Divides_Odiv__class_Omod(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_332]) ).
fof(c_0_965,plain,
! [X14,X15,X16] :
( c_Ring__and__Field_Odvd__class_Odvd(X16,X14,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X14,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X15,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_333]) ).
fof(c_0_966,plain,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X2),X1,X3) = c_Divides_Odiv__class_Omod(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_334]) ).
fof(c_0_967,plain,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1),X1,X3) = c_Divides_Odiv__class_Omod(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_335]) ).
fof(c_0_968,plain,
! [X6,X9] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X6),X9)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_336]) ).
fof(c_0_969,axiom,
! [X4,X5] : c_HOL_Otimes__class_Otimes(c_Suc(X5),X4,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Otimes__class_Otimes(X5,X4,tc_nat)),
c_0_337 ).
fof(c_0_970,axiom,
! [X4,X5] : c_HOL_Otimes__class_Otimes(X5,c_Suc(X4),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),c_HOL_Otimes__class_Otimes(X5,X4,tc_nat)),
c_0_338 ).
fof(c_0_971,plain,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oone__class_Oone(X3)),c_HOL_Oone__class_Oone(X3)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_339]) ).
fof(c_0_972,plain,
! [X4,X5,X3] :
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_Nat_Osemiring__1__class_Oof__nat(c_Power_Opower__class_Opower(X5,X4,tc_nat),X3) = c_Power_Opower__class_Opower(c_Nat_Osemiring__1__class_Oof__nat(X5,X3),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_340]) ).
fof(c_0_973,axiom,
! [X13,X9] :
( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X9)),X13) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),c_HOL_Oone__class_Oone(tc_nat)))
| c_HOL_Oord__class_Oless(X9,X13,tc_nat) ),
c_0_341 ).
fof(c_0_974,plain,
! [X4,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| 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(X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_342]) ).
fof(c_0_975,plain,
! [X12,X8,X9] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X8)),X12),X9) = c_Lambda_OdB_OVar(X8)
| ~ c_HOL_Oord__class_Oless(X8,X9,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_343]) ).
fof(c_0_976,plain,
! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X5,X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_344]) ).
fof(c_0_977,plain,
! [X36,X27] :
( hBOOL(hAPP(X27,X36))
| ~ hBOOL(hAPP(X27,c_Suc(v_sko__Nat__Xnat__Xinducts__1(X27))))
| ~ hBOOL(hAPP(X27,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(fof_simplification,[status(thm)],[c_0_345]) ).
fof(c_0_978,plain,
! [X36,X27] :
( hBOOL(hAPP(X27,X36))
| ~ hBOOL(hAPP(X27,c_Suc(v_sko__Nat__Xnat__Xinduct__1(X27))))
| ~ hBOOL(hAPP(X27,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(fof_simplification,[status(thm)],[c_0_346]) ).
fof(c_0_979,plain,
! [X36,X27] :
( hBOOL(hAPP(X27,X36))
| ~ hBOOL(hAPP(X27,c_Suc(v_sko__List__Xupt__Xinduct__1(X27))))
| ~ hBOOL(hAPP(X27,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(fof_simplification,[status(thm)],[c_0_347]) ).
fof(c_0_980,plain,
! [X36,X27] :
( hBOOL(hAPP(X27,X36))
| ~ hBOOL(hAPP(X27,c_Suc(v_sko__List__Xreplicate__Xinduct__1(X27))))
| ~ hBOOL(hAPP(X27,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(fof_simplification,[status(thm)],[c_0_348]) ).
fof(c_0_981,plain,
! [X4,X27] :
( hBOOL(hAPP(X27,X4))
| ~ hBOOL(hAPP(X27,c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X27))))
| ~ hBOOL(hAPP(X27,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(fof_simplification,[status(thm)],[c_0_349]) ).
fof(c_0_982,plain,
! [X36,X27] :
( hBOOL(hAPP(X27,X36))
| ~ hBOOL(hAPP(X27,c_Suc(v_sko__List__Xlexn__Xinduct__1(X27))))
| ~ hBOOL(hAPP(X27,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(fof_simplification,[status(thm)],[c_0_350]) ).
fof(c_0_983,axiom,
! [X4,X5,X27] :
( hBOOL(hAPP(hAPP(X27,X4),X5))
| c_HOL_Oord__class_Oless(X4,X5,tc_nat)
| X5 = X4
| c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
c_0_351 ).
fof(c_0_984,axiom,
! [X4,X5,X13] :
( c_HOL_Otimes__class_Otimes(c_Suc(X13),X5,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X13),X4,tc_nat)
| X5 = X4 ),
c_0_352 ).
fof(c_0_985,plain,
! [X4,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X3),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X3),X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_353]) ).
fof(c_0_986,plain,
! [X4,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_354]) ).
fof(c_0_987,plain,
! [X14,X15,X16,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X15) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X14)
| X15 = X14 ),
inference(fof_simplification,[status(thm)],[c_0_355]) ).
fof(c_0_988,plain,
! [X12,X6,X7] :
( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X7),X12),hAPP(hAPP(c_Lambda_OdB_OApp,X6),X12))
| ~ c_Lambda_Obeta(X7,X6) ),
inference(fof_simplification,[status(thm)],[c_0_356]) ).
fof(c_0_989,plain,
! [X12,X6,X7] :
( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X12),X7),hAPP(hAPP(c_Lambda_OdB_OApp,X12),X6))
| ~ c_Lambda_Obeta(X7,X6) ),
inference(fof_simplification,[status(thm)],[c_0_357]) ).
fof(c_0_990,plain,
! [X7,X23,X9] :
( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_Olift,X23),X9),hAPP(hAPP(c_Lambda_Olift,X7),X9))
| ~ c_Lambda_Obeta(X23,X7) ),
inference(fof_simplification,[status(thm)],[c_0_358]) ).
fof(c_0_991,plain,
! [X1,X2,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_359]) ).
fof(c_0_992,plain,
! [X15,X16,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X15,X16,X3)
| ~ c_HOL_Oord__class_Oless(X16,X15,X3) ),
inference(fof_simplification,[status(thm)],[c_0_360]) ).
fof(c_0_993,plain,
! [X15,X16,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X16,X15,X3)
| ~ c_HOL_Oord__class_Oless(X15,X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_361]) ).
fof(c_0_994,plain,
! [X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_362]) ).
fof(c_0_995,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_363]) ).
fof(c_0_996,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),c_HOL_Oone__class_Oone(X3)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_364]) ).
fof(c_0_997,plain,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,X3),X1,X3) = X2
| X1 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_365]) ).
fof(c_0_998,plain,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X1,X3),X1,X3) = X2
| X1 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_366]) ).
fof(c_0_999,plain,
! [X11,X1,X2,X3] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X2)
| X1 = X11 ),
inference(fof_simplification,[status(thm)],[c_0_367]) ).
fof(c_0_1000,plain,
! [X11,X1,X2,X3] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X11)
| X1 = X11 ),
inference(fof_simplification,[status(thm)],[c_0_368]) ).
fof(c_0_1001,plain,
! [X11,X1,X2,X3] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X11)
| X1 = X11 ),
inference(fof_simplification,[status(thm)],[c_0_369]) ).
fof(c_0_1002,plain,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X1,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_370]) ).
fof(c_0_1003,plain,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,X3),X1,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_371]) ).
fof(c_0_1004,axiom,
! [X4,X5,X13] :
( c_HOL_Otimes__class_Otimes(X13,X5,tc_nat) != c_HOL_Otimes__class_Otimes(X13,X4,tc_nat)
| X5 = X4
| X13 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_372 ).
fof(c_0_1005,axiom,
! [X4,X5,X13] :
( c_HOL_Otimes__class_Otimes(X13,X5,tc_nat) != c_HOL_Otimes__class_Otimes(X13,X4,tc_nat)
| X13 = c_HOL_Ozero__class_Ozero(tc_nat)
| X5 = X4 ),
c_0_373 ).
fof(c_0_1006,axiom,
! [X4,X5,X13] :
( c_HOL_Otimes__class_Otimes(X5,X13,tc_nat) != c_HOL_Otimes__class_Otimes(X4,X13,tc_nat)
| X13 = c_HOL_Ozero__class_Ozero(tc_nat)
| X5 = X4 ),
c_0_374 ).
fof(c_0_1007,plain,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X2,X1,X3),X1,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_375]) ).
fof(c_0_1008,axiom,
! [X7,X13,X9] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X9)),X7),X13) = c_Lambda_OdB_OVar(X9)
| X9 = X13
| c_HOL_Oord__class_Oless(X13,X9,tc_nat) ),
c_0_376 ).
fof(c_0_1009,plain,
! [X1,X2] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
| X2 = X1 ),
inference(fof_simplification,[status(thm)],[c_0_377]) ).
fof(c_0_1010,plain,
! [X1,X2] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| X2 = X1
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_378]) ).
fof(c_0_1011,plain,
! [X15,X16] :
( X16 = X15
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X15,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X16,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_379]) ).
fof(c_0_1012,plain,
! [X4,X5] :
( X5 = X4
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_380]) ).
fof(c_0_1013,plain,
! [X15,X16] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X16,tc_nat)
| X16 = X15
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X15,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_381]) ).
fof(c_0_1014,plain,
! [X15,X16] :
( X16 = X15
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X16,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X15,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_382]) ).
fof(c_0_1015,plain,
! [X15,X16] :
( X16 = X15
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X16,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X15,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_383]) ).
fof(c_0_1016,plain,
! [X13,X1,X3] :
( ~ class_Ring__and__Field_Odvd(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X13,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_384]) ).
fof(c_0_1017,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_385]) ).
fof(c_0_1018,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_386]) ).
fof(c_0_1019,axiom,
! [X16] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X16,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat),
c_0_387 ).
fof(c_0_1020,axiom,
! [X16,X7] :
( c_HOL_Oord__class_Oless(X16,X16,tc_nat)
| hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X16)),X7),X16) = X7 ),
c_0_388 ).
fof(c_0_1021,plain,
! [X49,X6,X10,X26] :
( c_Type_Otyping(X10,X49,X26)
| ~ c_Lambda_Obeta(X6,X49)
| ~ c_Type_Otyping(X10,X6,X26) ),
inference(fof_simplification,[status(thm)],[c_0_389]) ).
fof(c_0_1022,axiom,
! [X16,X17] : c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X17,X16,tc_nat),X17,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_390 ).
fof(c_0_1023,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_391]) ).
fof(c_0_1024,plain,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_392]) ).
fof(c_0_1025,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_393 ).
fof(c_0_1026,plain,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X1,X2,X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_394]) ).
fof(c_0_1027,plain,
! [X13,X27] :
( hBOOL(hAPP(X27,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X27,c_Suc(c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X27))))
| ~ hBOOL(hAPP(X27,X13)) ),
inference(fof_simplification,[status(thm)],[c_0_395]) ).
fof(c_0_1028,plain,
! [X13,X27] :
( hBOOL(hAPP(X27,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X27,c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X27)))
| ~ hBOOL(hAPP(X27,X13)) ),
inference(fof_simplification,[status(thm)],[c_0_396]) ).
fof(c_0_1029,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_397]) ).
fof(c_0_1030,plain,
! [X16,X4] :
( c_HOL_Oord__class_Oless(c_Suc(X16),c_Suc(X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(X16,X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_398]) ).
fof(c_0_1031,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_399]) ).
fof(c_0_1032,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_400]) ).
fof(c_0_1033,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_401]) ).
fof(c_0_1034,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_402]) ).
fof(c_0_1035,axiom,
! [X4,X5,X13] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X5) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X4)
| X5 = X4 ),
c_0_403 ).
fof(c_0_1036,axiom,
! [X4,X5,X13] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X13) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X13)
| X5 = X4 ),
c_0_404 ).
fof(c_0_1037,axiom,
! [X14,X15,X16] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X15) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X14)
| X15 = X14 ),
c_0_405 ).
fof(c_0_1038,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_406]) ).
fof(c_0_1039,axiom,
! [X6,X7] : c_Lambda_Osubstn(X6,X7,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,X6),X7),c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_407 ).
fof(c_0_1040,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_408 ).
fof(c_0_1041,plain,
! [X5,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_409]) ).
fof(c_0_1042,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_410]) ).
fof(c_0_1043,plain,
! [X4,X5] :
( c_Divides_Odiv__class_Odiv(X5,X4,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_411]) ).
fof(c_0_1044,plain,
! [X4,X5] :
( c_Divides_Odiv__class_Omod(X5,X4,tc_nat) = X5
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_412]) ).
fof(c_0_1045,plain,
! [X13,X9] :
( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X9)),X13) = c_Lambda_OdB_OVar(X9)
| ~ c_HOL_Oord__class_Oless(X9,X13,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_413]) ).
fof(c_0_1046,plain,
! [X36,X27] :
( hBOOL(hAPP(X27,X36))
| hBOOL(hAPP(X27,v_sko__List__Xupt__Xinduct__1(X27)))
| ~ hBOOL(hAPP(X27,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(fof_simplification,[status(thm)],[c_0_414]) ).
fof(c_0_1047,plain,
! [X36,X27] :
( hBOOL(hAPP(X27,X36))
| hBOOL(hAPP(X27,v_sko__Nat__Xnat__Xinduct__1(X27)))
| ~ hBOOL(hAPP(X27,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(fof_simplification,[status(thm)],[c_0_415]) ).
fof(c_0_1048,plain,
! [X36,X27] :
( hBOOL(hAPP(X27,X36))
| hBOOL(hAPP(X27,v_sko__Nat__Xnat__Xinducts__1(X27)))
| ~ hBOOL(hAPP(X27,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(fof_simplification,[status(thm)],[c_0_416]) ).
fof(c_0_1049,plain,
! [X36,X27] :
( hBOOL(hAPP(X27,X36))
| hBOOL(hAPP(X27,v_sko__List__Xreplicate__Xinduct__1(X27)))
| ~ hBOOL(hAPP(X27,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(fof_simplification,[status(thm)],[c_0_417]) ).
fof(c_0_1050,plain,
! [X4,X27] :
( hBOOL(hAPP(X27,X4))
| hBOOL(hAPP(X27,c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X27)))
| ~ hBOOL(hAPP(X27,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(fof_simplification,[status(thm)],[c_0_418]) ).
fof(c_0_1051,plain,
! [X36,X27] :
( hBOOL(hAPP(X27,X36))
| hBOOL(hAPP(X27,v_sko__List__Xlexn__Xinduct__1(X27)))
| ~ hBOOL(hAPP(X27,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(fof_simplification,[status(thm)],[c_0_419]) ).
fof(c_0_1052,plain,
! [X4,X2,X3] :
( ~ class_Ring__and__Field_Ozero__neq__one(X3)
| ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| ~ class_Ring__and__Field_Omult__zero(X3)
| ~ class_Power_Opower(X3)
| c_Power_Opower__class_Opower(X2,X4,X3) != c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_420]) ).
fof(c_0_1053,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Ozero__neq__one(X3)
| ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| ~ class_Ring__and__Field_Omult__zero(X3)
| ~ class_Power_Opower(X3)
| c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X3) != c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_421]) ).
fof(c_0_1054,axiom,
! [X46] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X46),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X46,tc_Lambda_OdB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
c_0_422 ).
fof(c_0_1055,axiom,
! [X7,X13,X9] :
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X9),X7,X13) = c_Lambda_OdB_OVar(X9)
| X9 = X13
| c_HOL_Oord__class_Oless(X13,X9,tc_nat) ),
c_0_423 ).
fof(c_0_1056,plain,
! [X15,X16,X3] :
( ~ class_Orderings_Olinorder(X3)
| X16 = X15
| c_HOL_Oord__class_Oless(X16,X15,X3)
| c_HOL_Oord__class_Oless(X15,X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_424]) ).
fof(c_0_1057,plain,
! [X15,X16,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X15,X16,X3)
| X16 = X15
| c_HOL_Oord__class_Oless(X16,X15,X3) ),
inference(fof_simplification,[status(thm)],[c_0_425]) ).
fof(c_0_1058,plain,
! [X15,X16,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X15,X16,X3)
| c_HOL_Oord__class_Oless(X16,X15,X3)
| X16 = X15 ),
inference(fof_simplification,[status(thm)],[c_0_426]) ).
fof(c_0_1059,plain,
! [X15,X16,X3] :
( ~ class_Orderings_Olinorder(X3)
| X16 = X15
| c_HOL_Oord__class_Oless(X15,X16,X3)
| c_HOL_Oord__class_Oless(X16,X15,X3) ),
inference(fof_simplification,[status(thm)],[c_0_427]) ).
fof(c_0_1060,plain,
! [X15,X16,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X15,X16,X3)
| c_HOL_Oord__class_Oless(X16,X15,X3)
| X16 = X15 ),
inference(fof_simplification,[status(thm)],[c_0_428]) ).
fof(c_0_1061,axiom,
! [X54,X44,X55,X45] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X45),X44) != hAPP(hAPP(c_Lambda_OdB_OApp,X55),X54)
| X44 = X54 ),
c_0_429 ).
fof(c_0_1062,axiom,
! [X54,X44,X55,X45] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X45),X44) != hAPP(hAPP(c_Lambda_OdB_OApp,X55),X54)
| X45 = X55 ),
c_0_430 ).
fof(c_0_1063,plain,
! [X5,X3] :
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X5),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oone__class_Oone(X3)),c_Nat_Osemiring__1__class_Oof__nat(X5,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_431]) ).
fof(c_0_1064,plain,
! [X15,X16,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X16,X15,X3) = c_HOL_Otimes__class_Otimes(X15,X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_432]) ).
fof(c_0_1065,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X2,X1,X3) = c_HOL_Otimes__class_Otimes(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_433]) ).
fof(c_0_1066,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_434 ).
fof(c_0_1067,axiom,
! [X16] :
( c_HOL_Oord__class_Oless(X16,X16,tc_nat)
| c_HOL_Oord__class_Oless(X16,c_Suc(X16),tc_nat) ),
c_0_435 ).
fof(c_0_1068,plain,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_436]) ).
fof(c_0_1069,axiom,
! [X4,X5] : c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat),
c_0_437 ).
fof(c_0_1070,axiom,
! [X4,X5] : c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_438 ).
fof(c_0_1071,plain,
! [X15,X16,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X15) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X15),X16) ),
inference(fof_simplification,[status(thm)],[c_0_439]) ).
fof(c_0_1072,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X2) ),
inference(fof_simplification,[status(thm)],[c_0_440]) ).
fof(c_0_1073,plain,
! [X11,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X11) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X11),X2) ),
inference(fof_simplification,[status(thm)],[c_0_441]) ).
fof(c_0_1074,plain,
! [X5] :
( X5 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_442]) ).
fof(c_0_1075,axiom,
! [X12,X13] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X13)),X12),X13) = X12,
c_0_443 ).
fof(c_0_1076,plain,
! [X9,X10,X26] :
( hAPP(X10,X9) = X26
| ~ c_Type_Otyping(X10,c_Lambda_OdB_OVar(X9),X26) ),
inference(fof_simplification,[status(thm)],[c_0_444]) ).
fof(c_0_1077,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_445 ).
fof(c_0_1078,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| c_HOL_Otimes__class_Otimes(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_446]) ).
fof(c_0_1079,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| c_HOL_Otimes__class_Otimes(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_447]) ).
fof(c_0_1080,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| c_HOL_Otimes__class_Otimes(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3)
| X1 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_448]) ).
fof(c_0_1081,axiom,
! [X15,X16] :
( c_HOL_Oord__class_Oless(X15,X16,tc_nat)
| c_HOL_Oord__class_Oless(X16,X15,tc_nat)
| X16 = X15 ),
c_0_449 ).
fof(c_0_1082,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_450 ).
fof(c_0_1083,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_451]) ).
fof(c_0_1084,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_452]) ).
fof(c_0_1085,axiom,
! [X16,X5] :
( c_Power_Opower__class_Opower(X16,X5,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X16 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X5 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_453 ).
fof(c_0_1086,axiom,
! [X4,X5] : c_HOL_Otimes__class_Otimes(X5,X4,tc_nat) = c_HOL_Otimes__class_Otimes(X4,X5,tc_nat),
c_0_454 ).
fof(c_0_1087,plain,
! [X4,X2,X3] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X3)
| c_Power_Opower__class_Opower(X2,X4,X3) != c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_455]) ).
fof(c_0_1088,plain,
! [X16,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| X16 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),X2)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_456]) ).
fof(c_0_1089,axiom,
! [X4,X5] :
( c_HOL_Otimes__class_Otimes(X5,X4,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X5 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_457 ).
fof(c_0_1090,axiom,
! [X4,X5] :
( c_HOL_Otimes__class_Otimes(X5,X4,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_458 ).
fof(c_0_1091,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X2) != c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_459]) ).
fof(c_0_1092,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_460 ).
fof(c_0_1093,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_461 ).
fof(c_0_1094,plain,
! [X4,X3] :
( ~ class_Ring__and__Field_Ozero__neq__one(X3)
| ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| ~ class_Ring__and__Field_Omult__zero(X3)
| ~ class_Power_Opower(X3)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X3),X4,X3) = c_HOL_Ozero__class_Ozero(X3)
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_462]) ).
fof(c_0_1095,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_463 ).
fof(c_0_1096,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_464 ).
fof(c_0_1097,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_465 ).
fof(c_0_1098,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_466 ).
fof(c_0_1099,axiom,
! [X4,X5] :
( c_HOL_Otimes__class_Otimes(X5,X4,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X4 = c_HOL_Ozero__class_Ozero(tc_nat)
| X5 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_467 ).
fof(c_0_1100,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_468]) ).
fof(c_0_1101,plain,
! [X16,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X16,X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_469]) ).
fof(c_0_1102,plain,
! [X16,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X16,X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_470]) ).
fof(c_0_1103,plain,
! [X16,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X16,X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_471]) ).
fof(c_0_1104,axiom,
! [X4,X5] :
( X5 != c_HOL_Otimes__class_Otimes(X5,X4,tc_nat)
| X5 = c_HOL_Ozero__class_Ozero(tc_nat)
| X4 = c_HOL_Oone__class_Oone(tc_nat) ),
c_0_472 ).
fof(c_0_1105,plain,
! [X5] :
( X5 = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_473]) ).
fof(c_0_1106,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_474 ).
fof(c_0_1107,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_475 ).
fof(c_0_1108,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_476 ).
fof(c_0_1109,axiom,
! [X4,X5] :
( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X5,X4,tc_nat)
| X4 = c_HOL_Oone__class_Oone(tc_nat) ),
c_0_477 ).
fof(c_0_1110,axiom,
! [X4,X5] :
( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X5,X4,tc_nat)
| X5 = c_HOL_Oone__class_Oone(tc_nat) ),
c_0_478 ).
fof(c_0_1111,axiom,
! [X4,X5] :
( c_HOL_Otimes__class_Otimes(X5,X4,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
| X4 = c_HOL_Oone__class_Oone(tc_nat) ),
c_0_479 ).
fof(c_0_1112,axiom,
! [X4,X5] :
( c_HOL_Otimes__class_Otimes(X5,X4,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
| X5 = c_HOL_Oone__class_Oone(tc_nat) ),
c_0_480 ).
fof(c_0_1113,plain,
! [X4] : ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(fof_simplification,[status(thm)],[c_0_481]) ).
fof(c_0_1114,plain,
! [X5] : ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(fof_simplification,[status(thm)],[c_0_482]) ).
fof(c_0_1115,plain,
! [X61,X62,X3] :
( X62 = X61
| ~ c_fequal(X62,X61,X3) ),
inference(fof_simplification,[status(thm)],[c_0_483]) ).
fof(c_0_1116,axiom,
! [X16,X43] : c_Type_Otyping(X43,c_Lambda_OdB_OVar(X16),hAPP(X43,X16)),
c_0_484 ).
fof(c_0_1117,plain,
! [X4,X3] :
( ~ class_Ring__and__Field_Osemiring__0(X3)
| ~ class_Power_Opower(X3)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X3),c_Suc(X4),X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_485]) ).
fof(c_0_1118,axiom,
c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_486 ).
fof(c_0_1119,plain,
! [X4] : ~ c_HOL_Oord__class_Oless(X4,X4,tc_nat),
inference(fof_simplification,[status(thm)],[c_0_487]) ).
fof(c_0_1120,plain,
! [X16] : ~ c_HOL_Oord__class_Oless(X16,X16,tc_nat),
inference(fof_simplification,[status(thm)],[c_0_488]) ).
fof(c_0_1121,plain,
! [X4,X3] :
( ~ class_Ring__and__Field_Osemiring__0(X3)
| ~ class_Power_Opower(X3)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X3),X4,X3) = c_HOL_Ozero__class_Ozero(X3)
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_489]) ).
fof(c_0_1122,plain,
! [X23] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X23)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X23)) ),
inference(fof_simplification,[status(thm)],[c_0_490]) ).
fof(c_0_1123,plain,
! [X3] :
( ~ class_Ring__and__Field_Osemiring__0(X3)
| ~ class_Power_Opower(X3)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(tc_nat),X3) = c_HOL_Oone__class_Oone(X3) ),
inference(fof_simplification,[status(thm)],[c_0_491]) ).
fof(c_0_1124,plain,
! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3)) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_492]) ).
fof(c_0_1125,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_493 ).
fof(c_0_1126,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_494 ).
fof(c_0_1127,axiom,
! [X46] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X46)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X46)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
c_0_495 ).
fof(c_0_1128,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_496 ).
fof(c_0_1129,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_497 ).
fof(c_0_1130,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_498 ).
fof(c_0_1131,axiom,
! [X16,X2] :
( X16 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X2)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_499 ).
fof(c_0_1132,axiom,
c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
c_0_500 ).
fof(c_0_1133,plain,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oone__class_Oone(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_501]) ).
fof(c_0_1134,plain,
! [X16,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| X16 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X16),c_HOL_Ozero__class_Ozero(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_502]) ).
fof(c_0_1135,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X2) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_503]) ).
fof(c_0_1136,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X2) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_504]) ).
fof(c_0_1137,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X2) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_505]) ).
fof(c_0_1138,plain,
! [X16,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X16) = X16 ),
inference(fof_simplification,[status(thm)],[c_0_506]) ).
fof(c_0_1139,axiom,
! [X4] : c_Power_Opower__class_Opower(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_507 ).
fof(c_0_1140,axiom,
! [X5] : c_Power_Opower__class_Opower(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X5,tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_508 ).
fof(c_0_1141,plain,
! [X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_509]) ).
fof(c_0_1142,plain,
! [X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_510]) ).
fof(c_0_1143,plain,
! [X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_511]) ).
fof(c_0_1144,plain,
! [X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X2,c_HOL_Oone__class_Oone(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_512]) ).
fof(c_0_1145,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_513]) ).
fof(c_0_1146,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_514]) ).
fof(c_0_1147,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_515]) ).
fof(c_0_1148,plain,
! [X1,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X1,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_516]) ).
fof(c_0_1149,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Omult__zero(X3)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_517]) ).
fof(c_0_1150,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Omult__zero(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_518]) ).
fof(c_0_1151,plain,
! [X16,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X16,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_519]) ).
fof(c_0_1152,plain,
! [X4,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X3),X4,X3) = c_HOL_Oone__class_Oone(X3) ),
inference(fof_simplification,[status(thm)],[c_0_520]) ).
fof(c_0_1153,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_521 ).
fof(c_0_1154,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_522 ).
fof(c_0_1155,plain,
! [X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(X2,X2,X3) = c_HOL_Oone__class_Oone(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_523]) ).
fof(c_0_1156,plain,
! [X16,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Power_Opower__class_Opower(X16,c_HOL_Ozero__class_Ozero(tc_nat),X3) = c_HOL_Oone__class_Oone(X3) ),
inference(fof_simplification,[status(thm)],[c_0_524]) ).
fof(c_0_1157,plain,
! [X2,X3] :
( ~ class_Power_Opower(X3)
| c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X3) = c_HOL_Oone__class_Oone(X3) ),
inference(fof_simplification,[status(thm)],[c_0_525]) ).
fof(c_0_1158,plain,
! [X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(X3),X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_526]) ).
fof(c_0_1159,plain,
! [X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(X2,c_HOL_Oone__class_Oone(X3),X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_527]) ).
fof(c_0_1160,plain,
! [X16,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X3),X16,X3) = X16 ),
inference(fof_simplification,[status(thm)],[c_0_528]) ).
fof(c_0_1161,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X3),X2,X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_529]) ).
fof(c_0_1162,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X3),X2,X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_530]) ).
fof(c_0_1163,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X3),X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_531]) ).
fof(c_0_1164,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X3),X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_532]) ).
fof(c_0_1165,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X3),X2,X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_533]) ).
fof(c_0_1166,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_534 ).
fof(c_0_1167,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_535]) ).
fof(c_0_1168,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_536]) ).
fof(c_0_1169,axiom,
! [X5] : c_Divides_Odiv__class_Omod(X5,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_537 ).
fof(c_0_1170,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),c_HOL_Ozero__class_Ozero(X3)) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_538]) ).
fof(c_0_1171,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),c_HOL_Ozero__class_Ozero(X3)) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_539]) ).
fof(c_0_1172,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),c_HOL_Ozero__class_Ozero(X3)) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_540]) ).
fof(c_0_1173,axiom,
! [X5] : c_Divides_Odiv__class_Odiv(X5,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = X5,
c_0_541 ).
fof(c_0_1174,plain,
! [X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X2,X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_542]) ).
fof(c_0_1175,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_Power_Opower__class_Opower(X2,c_HOL_Oone__class_Oone(tc_nat),X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_543]) ).
fof(c_0_1176,plain,
! [X16,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Power_Opower__class_Opower(X16,c_HOL_Oone__class_Oone(tc_nat),X3) = X16 ),
inference(fof_simplification,[status(thm)],[c_0_544]) ).
fof(c_0_1177,axiom,
! [X13] : c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X13,tc_nat),
c_0_545 ).
fof(c_0_1178,axiom,
! [X36,X54,X55] : hAPP(hAPP(c_Lambda_OdB_OApp,X55),X54) != c_Lambda_OdB_OVar(X36),
c_0_546 ).
fof(c_0_1179,axiom,
! [X36,X54,X55] : c_Lambda_OdB_OVar(X36) != hAPP(hAPP(c_Lambda_OdB_OApp,X55),X54),
c_0_547 ).
fof(c_0_1180,axiom,
! [X52,X44,X45] : c_Lambda_OdB_OAbs(X52) != hAPP(hAPP(c_Lambda_OdB_OApp,X45),X44),
c_0_548 ).
fof(c_0_1181,axiom,
! [X52,X44,X45] : hAPP(hAPP(c_Lambda_OdB_OApp,X45),X44) != c_Lambda_OdB_OAbs(X52),
c_0_549 ).
fof(c_0_1182,axiom,
! [X16] : c_Power_Opower__class_Opower(X16,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_550 ).
fof(c_0_1183,plain,
! [X16,X3] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3)
| c_HOL_Otimes__class_Otimes(X16,X16,X3) = X16 ),
inference(fof_simplification,[status(thm)],[c_0_551]) ).
fof(c_0_1184,axiom,
! [X16] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X16),tc_nat),
c_0_552 ).
fof(c_0_1185,axiom,
! [X4] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X4),tc_nat),
c_0_553 ).
fof(c_0_1186,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_554]) ).
fof(c_0_1187,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat),
c_0_555 ).
fof(c_0_1188,axiom,
c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
c_0_556 ).
fof(c_0_1189,axiom,
! [X20,X3] : c_List_Olistsp(X20,c_List_Olist_ONil(X3),X3),
c_0_557 ).
fof(c_0_1190,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_558 ).
fof(c_0_1191,axiom,
! [X4] : c_HOL_Oord__class_Oless(X4,c_Suc(X4),tc_nat),
c_0_559 ).
fof(c_0_1192,axiom,
! [X16] : c_HOL_Oord__class_Oless(X16,c_Suc(X16),tc_nat),
c_0_560 ).
fof(c_0_1193,axiom,
c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
c_0_561 ).
fof(c_0_1194,axiom,
! [X19] : c_Power_Opower__class_Opower(X19,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat),
c_0_562 ).
fof(c_0_1195,axiom,
! [X4] : c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_563 ).
fof(c_0_1196,axiom,
! [X5] : c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_564 ).
fof(c_0_1197,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_565 ).
fof(c_0_1198,axiom,
! [X4] : c_HOL_Otimes__class_Otimes(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X4,
c_0_566 ).
fof(c_0_1199,axiom,
! [X4] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X4,tc_nat) = X4,
c_0_567 ).
fof(c_0_1200,axiom,
! [X4] : c_Suc(X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X4),
c_0_568 ).
fof(c_0_1201,axiom,
! [X16,X3] : c_fequal(X16,X16,X3),
c_0_569 ).
fof(c_0_1202,plain,
! [X4,X5,X3] :
( ~ class_Nat_Osemiring__char__0(X3)
| c_Nat_Osemiring__1__class_Oof__nat(X5,X3) != c_Nat_Osemiring__1__class_Oof__nat(X4,X3)
| X5 = X4 ),
inference(fof_simplification,[status(thm)],[c_0_570]) ).
fof(c_0_1203,axiom,
! [X4] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X4) = X4,
c_0_571 ).
fof(c_0_1204,axiom,
! [X16] : c_Ring__and__Field_Odvd__class_Odvd(X16,X16,tc_nat),
c_0_572 ).
fof(c_0_1205,axiom,
! [X4] : c_Suc(X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),
c_0_573 ).
fof(c_0_1206,axiom,
! [X5] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),c_HOL_Ozero__class_Ozero(tc_nat)) = X5,
c_0_574 ).
fof(c_0_1207,axiom,
! [X16] : X16 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_575 ).
fof(c_0_1208,plain,
! [X6,X7] :
( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X7),c_Lambda_OdB_OAbs(X6))
| ~ c_Lambda_Obeta(X7,X6) ),
inference(fof_simplification,[status(thm)],[c_0_576]) ).
fof(c_0_1209,plain,
! [X59,X60] :
( class_Orderings_Oorder(tc_fun(X59,X60))
| ~ class_Orderings_Oorder(X60) ),
inference(fof_simplification,[status(thm)],[c_0_577]) ).
fof(c_0_1210,plain,
! [X59,X60] :
( class_Orderings_Opreorder(tc_fun(X59,X60))
| ~ class_Orderings_Opreorder(X60) ),
inference(fof_simplification,[status(thm)],[c_0_578]) ).
fof(c_0_1211,plain,
! [X6,X9] : ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X9),X6),
inference(fof_simplification,[status(thm)],[c_0_579]) ).
fof(c_0_1212,plain,
! [X3] :
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_580]) ).
fof(c_0_1213,plain,
! [X3] :
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X3) = c_HOL_Oone__class_Oone(X3) ),
inference(fof_simplification,[status(thm)],[c_0_581]) ).
fof(c_0_1214,axiom,
! [X36] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(X36),tc_Lambda_OdB) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_582 ).
fof(c_0_1215,plain,
! [X3] :
( ~ class_Ring__and__Field_Ozero__neq__one(X3)
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Oone__class_Oone(X3) ),
inference(fof_simplification,[status(thm)],[c_0_583]) ).
fof(c_0_1216,plain,
! [X3] :
( ~ class_Ring__and__Field_Ozero__neq__one(X3)
| c_HOL_Oone__class_Oone(X3) != c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_584]) ).
fof(c_0_1217,axiom,
! [X15,X16] :
( c_Suc(X16) != c_Suc(X15)
| X16 = X15 ),
c_0_585 ).
fof(c_0_1218,axiom,
! [X53,X36] :
( c_Suc(X36) != c_Suc(X53)
| X36 = X53 ),
c_0_586 ).
fof(c_0_1219,axiom,
! [X52,X46] :
( c_Lambda_OdB_OAbs(X46) != c_Lambda_OdB_OAbs(X52)
| X46 = X52 ),
c_0_587 ).
fof(c_0_1220,axiom,
! [X53,X36] :
( c_Lambda_OdB_OVar(X36) != c_Lambda_OdB_OVar(X53)
| X36 = X53 ),
c_0_588 ).
fof(c_0_1221,axiom,
! [X4] :
( X4 = c_Suc(c_ATP__Linkup_Osko__Nat__Xnot0__implies__Suc__1__1(X4))
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_589 ).
fof(c_0_1222,axiom,
! [X22] :
( X22 = c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__Xnchotomy__1__1(X22))
| X22 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_590 ).
fof(c_0_1223,axiom,
! [X15] :
( X15 = c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__Xexhaust__1__1(X15))
| X15 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_591 ).
fof(c_0_1224,axiom,
! [X36,X52] : c_Lambda_OdB_OVar(X36) != c_Lambda_OdB_OAbs(X52),
c_0_592 ).
fof(c_0_1225,axiom,
! [X36,X52] : c_Lambda_OdB_OAbs(X52) != c_Lambda_OdB_OVar(X36),
c_0_593 ).
fof(c_0_1226,axiom,
! [X36] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(X36)) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_594 ).
fof(c_0_1227,axiom,
! [X53] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X53),
c_0_595 ).
fof(c_0_1228,axiom,
! [X5] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X5),
c_0_596 ).
fof(c_0_1229,axiom,
! [X53] : c_Suc(X53) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_597 ).
fof(c_0_1230,axiom,
! [X5] : c_Suc(X5) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_598 ).
fof(c_0_1231,axiom,
c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_599 ).
fof(c_0_1232,axiom,
! [X4] : c_Suc(X4) != X4,
c_0_600 ).
fof(c_0_1233,axiom,
! [X4] : X4 != c_Suc(X4),
c_0_601 ).
fof(c_0_1234,axiom,
class_Power_Opower(tc_nat),
c_0_602 ).
fof(c_0_1235,axiom,
class_Orderings_Oorder(tc_nat),
c_0_603 ).
fof(c_0_1236,axiom,
class_Orderings_Olinorder(tc_nat),
c_0_604 ).
fof(c_0_1237,axiom,
class_Orderings_Opreorder(tc_nat),
c_0_605 ).
fof(c_0_1238,axiom,
class_Ring__and__Field_Odvd(tc_nat),
c_0_606 ).
fof(c_0_1239,axiom,
class_Nat_Osemiring__char__0(tc_nat),
c_0_607 ).
fof(c_0_1240,axiom,
class_Divides_Osemiring__div(tc_nat),
c_0_608 ).
fof(c_0_1241,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
c_0_609 ).
fof(c_0_1242,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
c_0_610 ).
fof(c_0_1243,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
c_0_611 ).
fof(c_0_1244,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
c_0_612 ).
fof(c_0_1245,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
c_0_613 ).
fof(c_0_1246,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
c_0_614 ).
fof(c_0_1247,axiom,
class_OrderedGroup_Osemigroup__add(tc_nat),
c_0_615 ).
fof(c_0_1248,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
c_0_616 ).
fof(c_0_1249,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
c_0_617 ).
fof(c_0_1250,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
c_0_618 ).
fof(c_0_1251,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
c_0_619 ).
fof(c_0_1252,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
c_0_620 ).
fof(c_0_1253,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
c_0_621 ).
fof(c_0_1254,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
c_0_622 ).
fof(c_0_1255,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
c_0_623 ).
fof(c_0_1256,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
c_0_624 ).
fof(c_0_1257,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
c_0_625 ).
fof(c_0_1258,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
c_0_626 ).
fof(c_0_1259,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
c_0_627 ).
fof(c_0_1260,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
c_0_628 ).
fof(c_0_1261,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
c_0_629 ).
fof(c_0_1262,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
c_0_630 ).
fof(c_0_1263,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
c_0_631 ).
fof(c_0_1264,plain,
! [X42,X43,X44,X45] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,X44,X43,tc_Lambda_OdB,tc_Lambda_OdB)),X42),X45) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X44),X42),X45),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X42,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X45,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X43,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(variable_rename,[status(thm)],[c_0_632]) ).
fof(c_0_1265,plain,
! [X43,X44,X45,X46,X47,X48] :
( c_Type_Otypings(X46,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X43,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X45,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X44,tc_Lambda_OdB,tc_Lambda_OdB),X47)
| ~ c_Type_Otypings(c_Type_Oshift(X46,X45,X48,tc_Type_Otype),X44,X47)
| ~ c_Type_Otyping(X46,X43,X48) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_633])])]) ).
fof(c_0_1266,plain,
! [X51,X52,X53] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X53)),X52),X51,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X52))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X53),X52),c_HOL_Ozero__class_Ozero(tc_nat)),X51,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(variable_rename,[status(thm)],[c_0_634]) ).
fof(c_0_1267,plain,
! [X42,X43,X44] : hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,X43,X42,tc_Lambda_OdB,tc_Lambda_OdB)),X44) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X43),X44),c_List_Omap(c_COMBC(c_Lambda_Olift,X44,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X42,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(variable_rename,[status(thm)],[c_0_635]) ).
fof(c_0_1268,plain,
! [X42,X43,X44,X45,X46] :
( X46 = X45
| ~ c_Type_Otyping(X44,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X43),X42,tc_Lambda_OdB,tc_Lambda_OdB),X45)
| ~ c_Type_Otyping(X44,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X43),X42,tc_Lambda_OdB,tc_Lambda_OdB),X46) ),
inference(variable_rename,[status(thm)],[c_0_636]) ).
fof(c_0_1269,plain,
! [X59,X60,X61,X62,X63,X64] : c_COMBB(X61,X60,X59,X63,X64,X62) = hAPP(X61,hAPP(X60,X59)),
inference(variable_rename,[status(thm)],[c_0_637]) ).
fof(c_0_1270,plain,
! [X43,X44,X45,X46,X47] :
( c_Type_Otypings(c_Type_Oshift(X45,X44,X46,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,X44,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X43,tc_Lambda_OdB,tc_Lambda_OdB),X47)
| ~ c_Type_Otypings(X45,X43,X47) ),
inference(variable_rename,[status(thm)],[c_0_638]) ).
fof(c_0_1271,plain,
! [X42] :
( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X42,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_List_Olistsp(c_InductTermi_OIT,X42,tc_Lambda_OdB) ),
inference(variable_rename,[status(thm)],[c_0_639]) ).
fof(c_0_1272,plain,
! [X52,X53] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X53),X52,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_List_Olistsp(c_InductTermi_OIT,X52,tc_Lambda_OdB) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_640])])]) ).
fof(c_0_1273,plain,
! [X51,X52,X53] :
( c_Lambda_Obeta(c_List_Ofoldl(c_Lambda_OdB_OApp,X53,X51,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X52,X51,tc_Lambda_OdB,tc_Lambda_OdB))
| ~ c_Lambda_Obeta(X53,X52) ),
inference(variable_rename,[status(thm)],[c_0_641]) ).
fof(c_0_1274,plain,
! [X52,X53,X54,X55] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X55),X54,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X53),X52,tc_Lambda_OdB,tc_Lambda_OdB)
| X54 = X52 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_642])])]) ).
fof(c_0_1275,plain,
! [X52,X53,X54,X55] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X55),X54,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X53),X52,tc_Lambda_OdB,tc_Lambda_OdB)
| X55 = X53 ),
inference(variable_rename,[status(thm)],[c_0_643]) ).
fof(c_0_1276,plain,
! [X52,X53,X54,X55] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X55),X53,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X54),X52,tc_Lambda_OdB,tc_Lambda_OdB)
| X53 = X52 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_644])])]) ).
fof(c_0_1277,plain,
! [X52,X53,X54,X55] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X55),X53,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X54),X52,tc_Lambda_OdB,tc_Lambda_OdB)
| X55 = X54 ),
inference(variable_rename,[status(thm)],[c_0_645]) ).
fof(c_0_1278,plain,
! [X41,X42,X43,X44] :
( ~ class_OrderedGroup_Osemigroup__add(X44)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X44),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X44),X43),X42),X41,X44,X44) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X44),X43),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X44),X42,X41,X44,X44)) ),
inference(variable_rename,[status(thm)],[c_0_646]) ).
fof(c_0_1279,plain,
! [X51,X52,X53,X54] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X54),X51,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X53),X52,tc_Lambda_OdB,tc_Lambda_OdB),
inference(variable_rename,[status(thm)],[c_0_647]) ).
fof(c_0_1280,plain,
! [X42,X43,X44] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X44,X42,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X43,X42,tc_Lambda_OdB,tc_Lambda_OdB)
| X44 = X43 ),
inference(variable_rename,[status(thm)],[c_0_648]) ).
fof(c_0_1281,plain,
! [X41,X42,X43] :
( ~ class_OrderedGroup_Omonoid__add(X43)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X43),X42),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X43),c_HOL_Ozero__class_Ozero(X43),X41,X43,X43)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X43),X42,X41,X43,X43) ),
inference(variable_rename,[status(thm)],[c_0_649]) ).
fof(c_0_1282,plain,
! [X28,X29,X30,X31] :
( ~ c_HOL_Oord__class_Oless(X29,X28,tc_nat)
| X28 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ hBOOL(hAPP(X31,c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X28,X30,tc_nat)),X29),X28,tc_nat)))
| hBOOL(hAPP(X31,X30)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_650])])]) ).
fof(c_0_1283,plain,
! [X28,X29,X30,X31] :
( ~ c_HOL_Oord__class_Oless(X29,X28,tc_nat)
| X28 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ hBOOL(hAPP(X31,c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X28,X30,tc_nat)),X29),X28,tc_nat)))
| hBOOL(hAPP(X31,X29)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_651])])]) ).
fof(c_0_1284,plain,
! [X12,X13,X14,X15] :
( ~ class_Divides_Osemiring__div(X15)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X14,X13,X15),X13,X15)),c_Divides_Odiv__class_Omod(X14,X13,X15))),X12) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X12) ),
inference(variable_rename,[status(thm)],[c_0_652]) ).
fof(c_0_1285,plain,
! [X12,X13,X14,X15] :
( ~ class_Divides_Osemiring__div(X15)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),c_HOL_Otimes__class_Otimes(X13,c_Divides_Odiv__class_Odiv(X14,X13,X15),X15)),c_Divides_Odiv__class_Omod(X14,X13,X15))),X12) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X12) ),
inference(variable_rename,[status(thm)],[c_0_653]) ).
fof(c_0_1286,plain,
! [X23,X24,X25,X26,X27] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X25),hAPP(hAPP(c_Lambda_Olift,X23),X27)),c_Suc(X26))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X24),X23),X26)),X27) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X25),X24),X27)),X23),X26)
| ~ c_HOL_Oord__class_Oless(X27,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X26),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_654]) ).
fof(c_0_1287,plain,
! [X12,X13,X14] : c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X13),X12,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(X14,X12,tc_nat)),c_Divides_Odiv__class_Odiv(X13,X12,tc_nat))),c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(X14,X12,tc_nat)),c_Divides_Odiv__class_Omod(X13,X12,tc_nat)),X12,tc_nat)),
inference(variable_rename,[status(thm)],[c_0_655]) ).
fof(c_0_1288,plain,
! [X59,X60,X61,X62,X63,X64] : hAPP(c_COMBC(X61,X60,X63,X62,X64),X59) = hAPP(hAPP(X61,X59),X60),
inference(variable_rename,[status(thm)],[c_0_656]) ).
fof(c_0_1289,plain,
! [X59,X60,X61,X62,X63,X64] : hAPP(c_COMBC(X61,X60,X63,X62,X64),X59) = hAPP(hAPP(X61,X59),X60),
inference(variable_rename,[status(thm)],[c_0_657]) ).
fof(c_0_1290,plain,
! [X24,X25,X26] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X26),X25) != c_List_Ofoldl(c_Lambda_OdB_OApp,X24,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,X26),X25) = X24 ),
inference(variable_rename,[status(thm)],[c_0_658]) ).
fof(c_0_1291,plain,
! [X51,X52,X53,X54] : hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X53)),X51) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X54),X52,tc_Lambda_OdB,tc_Lambda_OdB),
inference(variable_rename,[status(thm)],[c_0_659]) ).
fof(c_0_1292,plain,
! [X51,X52,X53] :
( c_Lambda_OdB_OAbs(X53) != c_List_Ofoldl(c_Lambda_OdB_OApp,X52,X51,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(X53) = X52 ),
inference(variable_rename,[status(thm)],[c_0_660]) ).
fof(c_0_1293,plain,
! [X51,X52,X53] :
( c_Lambda_OdB_OVar(X53) != c_List_Ofoldl(c_Lambda_OdB_OApp,X52,X51,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OVar(X53) = X52 ),
inference(variable_rename,[status(thm)],[c_0_661]) ).
fof(c_0_1294,plain,
! [X51,X52,X53] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X52,X51,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X53)
| X52 = c_Lambda_OdB_OAbs(X53) ),
inference(variable_rename,[status(thm)],[c_0_662]) ).
fof(c_0_1295,plain,
! [X10,X11,X12,X13] :
( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X10),X11),X12)),X13) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X10),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,X11),X13)),X12)
| ~ c_HOL_Oord__class_Oless(X12,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_663]) ).
fof(c_0_1296,plain,
! [X51,X52,X53] :
( c_Lambda_OdB_OVar(X53) != c_List_Ofoldl(c_Lambda_OdB_OApp,X52,X51,tc_Lambda_OdB,tc_Lambda_OdB)
| X51 = c_List_Olist_ONil(tc_Lambda_OdB) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_664])])]) ).
fof(c_0_1297,plain,
! [X51,X52,X53] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X52,X51,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X53)
| X51 = c_List_Olist_ONil(tc_Lambda_OdB) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_665])])]) ).
fof(c_0_1298,plain,
! [X51,X52,X53] :
( c_Lambda_OdB_OAbs(X53) != c_List_Ofoldl(c_Lambda_OdB_OApp,X52,X51,tc_Lambda_OdB,tc_Lambda_OdB)
| X51 = c_List_Olist_ONil(tc_Lambda_OdB) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_666])])]) ).
fof(c_0_1299,plain,
! [X12,X13,X14] : c_Divides_Odiv__class_Omod(X14,c_HOL_Otimes__class_Otimes(X13,X12,tc_nat),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X13,c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Odiv(X14,X13,tc_nat),X12,tc_nat),tc_nat)),c_Divides_Odiv__class_Omod(X14,X13,tc_nat)),
inference(variable_rename,[status(thm)],[c_0_667]) ).
fof(c_0_1300,plain,
! [X24,X25,X26,X27] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X27,c_Divides_Odiv__class_Omod(X25,X26,tc_nat),tc_nat)),X24),c_HOL_Otimes__class_Otimes(X27,X26,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X24,X27,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X26,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_668]) ).
fof(c_0_1301,plain,
! [X12,X13,X14] : c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X14,X13,tc_nat),X12,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X14,c_Divides_Odiv__class_Odiv(X13,X12,tc_nat),tc_nat)),c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X14,c_Divides_Odiv__class_Omod(X13,X12,tc_nat),tc_nat),X12,tc_nat)),
inference(variable_rename,[status(thm)],[c_0_669]) ).
fof(c_0_1302,plain,
! [X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4)),X4) ),
inference(variable_rename,[status(thm)],[c_0_670]) ).
fof(c_0_1303,plain,
! [X27,X28,X29,X30,X31] : c_Type_Oshift(c_Type_Oshift(X28,X27,X29,X31),c_HOL_Ozero__class_Ozero(tc_nat),X30,X31) = c_Type_Oshift(c_Type_Oshift(X28,c_HOL_Ozero__class_Ozero(tc_nat),X30,X31),c_Suc(X27),X29,X31),
inference(variable_rename,[status(thm)],[c_0_671]) ).
fof(c_0_1304,plain,
! [X12,X13,X14,X15,X16] :
( ~ class_Ring__and__Field_Osemiring(X16)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X16),c_HOL_Otimes__class_Otimes(X15,X12,X16)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X16),c_HOL_Otimes__class_Otimes(X14,X12,X16)),X13)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X16),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X16),X15),X14),X12,X16)),X13) ),
inference(variable_rename,[status(thm)],[c_0_672]) ).
fof(c_0_1305,plain,
! [X14,X15,X16,X17] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X17,X14,tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X16,X14,tc_nat)),X15)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X16),X14,tc_nat)),X15),
inference(variable_rename,[status(thm)],[c_0_673]) ).
fof(c_0_1306,plain,
! [X24,X25] : hAPP(hAPP(c_Lambda_OdB_OApp,X25),X24) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X25),X24),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(variable_rename,[status(thm)],[c_0_674]) ).
fof(c_0_1307,plain,
! [X17,X18,X19] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X19)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X19),c_HOL_Otimes__class_Otimes(X18,X18,X19)),c_HOL_Otimes__class_Otimes(X17,X17,X19)),c_HOL_Ozero__class_Ozero(X19),X19) ),
inference(variable_rename,[status(thm)],[c_0_675]) ).
fof(c_0_1308,plain,
! [X10,X11,X12,X13] :
( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X10),X11),X12)),X13) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X10),X13)),hAPP(hAPP(c_Lambda_Olift,X11),X13)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),c_HOL_Oone__class_Oone(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_676]) ).
fof(c_0_1309,plain,
! [X6] : c_Lambda_OdB_OVar(X6) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X6),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(variable_rename,[status(thm)],[c_0_677]) ).
fof(c_0_1310,plain,
! [X24] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X24),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OAbs(X24),
inference(variable_rename,[status(thm)],[c_0_678]) ).
fof(c_0_1311,plain,
! [X24] : c_Lambda_OdB_OAbs(X24) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X24),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(variable_rename,[status(thm)],[c_0_679]) ).
fof(c_0_1312,plain,
! [X40,X41,X42,X43] : c_List_Ofoldl(X40,X41,c_List_Olist_ONil(X42),X43,X42) = X41,
inference(variable_rename,[status(thm)],[c_0_680]) ).
fof(c_0_1313,plain,
! [X18,X19,X20,X21,X22] :
( ~ class_Ring__and__Field_Oidom(X22)
| ~ class_Int_Onumber__ring(X22)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),c_HOL_Otimes__class_Otimes(X21,X19,X22)),c_HOL_Otimes__class_Otimes(X20,X18,X22)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),c_HOL_Otimes__class_Otimes(X21,X18,X22)),c_HOL_Otimes__class_Otimes(X20,X19,X22))
| X19 = X18
| X21 = X20 ),
inference(variable_rename,[status(thm)],[c_0_681]) ).
fof(c_0_1314,plain,
! [X32,X33,X34,X35,X36] :
( ~ class_Ring__and__Field_Oidom(X36)
| ~ class_Int_Onumber__ring(X36)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),c_HOL_Otimes__class_Otimes(X35,X33,X36)),c_HOL_Otimes__class_Otimes(X34,X32,X36)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),c_HOL_Otimes__class_Otimes(X35,X32,X36)),c_HOL_Otimes__class_Otimes(X34,X33,X36))
| X33 = X32
| X35 = X34 ),
inference(variable_rename,[status(thm)],[c_0_682]) ).
fof(c_0_1315,plain,
! [X27,X28,X29,X30,X31,X32] :
( ~ c_Type_Otyping(X30,X27,X31)
| ~ c_Type_Otyping(c_Type_Oshift(X30,X29,X31,tc_Type_Otype),X28,X32)
| c_Type_Otyping(X30,hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X27),X29),X32) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_683])])]) ).
fof(c_0_1316,plain,
! [X14,X15,X16] : c_Divides_Odiv__class_Omod(c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X16,X14,tc_nat)),X15)),X14,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X15),X14,tc_nat),
inference(variable_rename,[status(thm)],[c_0_684]) ).
fof(c_0_1317,plain,
! [X32,X33,X34,X35] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X35,X33,tc_nat)),c_HOL_Otimes__class_Otimes(X34,X32,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X35,X32,tc_nat)),c_HOL_Otimes__class_Otimes(X34,X33,tc_nat))
| X33 = X32
| X35 = X34 ),
inference(variable_rename,[status(thm)],[c_0_685]) ).
fof(c_0_1318,plain,
! [X18,X19,X20,X21] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X21,X19,tc_nat)),c_HOL_Otimes__class_Otimes(X20,X18,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X21,X18,tc_nat)),c_HOL_Otimes__class_Otimes(X20,X19,tc_nat))
| X19 = X18
| X21 = X20 ),
inference(variable_rename,[status(thm)],[c_0_686]) ).
fof(c_0_1319,plain,
! [X12,X13,X14,X15] :
( ~ class_Divides_Osemiring__div(X15)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X13),X12,X15) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),c_Divides_Odiv__class_Omod(X14,X12,X15)),c_Divides_Odiv__class_Omod(X13,X12,X15)),X12,X15) ),
inference(variable_rename,[status(thm)],[c_0_687]) ).
fof(c_0_1320,plain,
! [X14,X15,X16,X17] : hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,X15),X14)),X16),X17) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X15),X16),X17)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X14),X16),X17)),
inference(variable_rename,[status(thm)],[c_0_688]) ).
fof(c_0_1321,plain,
! [X17,X18,X19] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X19)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X19),c_HOL_Otimes__class_Otimes(X18,X18,X19)),c_HOL_Otimes__class_Otimes(X17,X17,X19)),X19)
| X17 = c_HOL_Ozero__class_Ozero(X19) ),
inference(variable_rename,[status(thm)],[c_0_689]) ).
fof(c_0_1322,plain,
! [X17,X18,X19] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X19)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X19),c_HOL_Otimes__class_Otimes(X18,X18,X19)),c_HOL_Otimes__class_Otimes(X17,X17,X19)),X19)
| X18 = c_HOL_Ozero__class_Ozero(X19) ),
inference(variable_rename,[status(thm)],[c_0_690]) ).
fof(c_0_1323,plain,
! [X4,X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| X5 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X5,X4,X6),X4,X6)),c_Divides_Odiv__class_Omod(X5,X4,X6)) ),
inference(variable_rename,[status(thm)],[c_0_691]) ).
fof(c_0_1324,plain,
! [X4,X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X5,X4,X6),X4,X6)),c_Divides_Odiv__class_Omod(X5,X4,X6)) = X5 ),
inference(variable_rename,[status(thm)],[c_0_692]) ).
fof(c_0_1325,plain,
! [X4,X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),c_HOL_Otimes__class_Otimes(X4,c_Divides_Odiv__class_Odiv(X5,X4,X6),X6)),c_Divides_Odiv__class_Omod(X5,X4,X6)) = X5 ),
inference(variable_rename,[status(thm)],[c_0_693]) ).
fof(c_0_1326,plain,
! [X14,X15,X16] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(X14)),X15),X16) = c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,X14),hAPP(hAPP(c_Lambda_Olift,X15),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),c_HOL_Oone__class_Oone(tc_nat)))),
inference(variable_rename,[status(thm)],[c_0_694]) ).
fof(c_0_1327,plain,
! [X18,X19,X20,X21] :
( ~ class_Ring__and__Field_Oidom(X21)
| ~ class_Int_Onumber__ring(X21)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X21),c_HOL_Otimes__class_Otimes(X18,X20,X21)),c_HOL_Otimes__class_Otimes(X18,X19,X21)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X21),c_HOL_Otimes__class_Otimes(X18,X19,X21)),c_HOL_Otimes__class_Otimes(X18,X20,X21)) ),
inference(variable_rename,[status(thm)],[c_0_695]) ).
fof(c_0_1328,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Oidom(X20)
| ~ class_Int_Onumber__ring(X20)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),c_HOL_Otimes__class_Otimes(X19,X18,X20)),c_HOL_Otimes__class_Otimes(X19,X17,X20)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),c_HOL_Otimes__class_Otimes(X19,X17,X20)),c_HOL_Otimes__class_Otimes(X19,X18,X20)) ),
inference(variable_rename,[status(thm)],[c_0_696]) ).
fof(c_0_1329,plain,
! [X12,X13,X14,X15] :
( ~ class_Divides_Osemiring__div(X15)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X14,X13,X15),X12,X15) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X14,X12,X15),c_Divides_Odiv__class_Omod(X13,X12,X15),X15),X12,X15) ),
inference(variable_rename,[status(thm)],[c_0_697]) ).
fof(c_0_1330,plain,
! [X12,X13,X14,X15] :
( ~ class_Divides_Osemiring__div(X15)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),c_Divides_Odiv__class_Omod(X14,X12,X15)),X13),X12,X15) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X13),X12,X15) ),
inference(variable_rename,[status(thm)],[c_0_698]) ).
fof(c_0_1331,plain,
! [X12,X13,X14,X15] :
( ~ class_Divides_Osemiring__div(X15)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X13),X12,X15) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),c_Divides_Odiv__class_Omod(X14,X12,X15)),X13),X12,X15) ),
inference(variable_rename,[status(thm)],[c_0_699]) ).
fof(c_0_1332,plain,
! [X18,X19,X20,X21,X22] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X22)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),X21),X20)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),X19),X18)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),X21),X19)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),X20),X18)) ),
inference(variable_rename,[status(thm)],[c_0_700]) ).
fof(c_0_1333,plain,
! [X32,X33,X34,X35,X36] :
( ~ class_Divides_Osemiring__div(X36)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X34,X33,X36),c_Divides_Odiv__class_Odiv(X35,X32,X36),X36) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X34,X35,X36),c_HOL_Otimes__class_Otimes(X33,X32,X36),X36)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X32,X35,X36)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X33,X34,X36) ),
inference(variable_rename,[status(thm)],[c_0_701]) ).
fof(c_0_1334,plain,
! [X17,X18,X19] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X19,X18,tc_nat)),c_HOL_Otimes__class_Otimes(X19,X17,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X19,X17,tc_nat)),c_HOL_Otimes__class_Otimes(X19,X18,tc_nat)),
inference(variable_rename,[status(thm)],[c_0_702]) ).
fof(c_0_1335,plain,
! [X18,X19,X20] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X18,X20,tc_nat)),c_HOL_Otimes__class_Otimes(X18,X19,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X18,X19,tc_nat)),c_HOL_Otimes__class_Otimes(X18,X20,tc_nat)),
inference(variable_rename,[status(thm)],[c_0_703]) ).
fof(c_0_1336,plain,
! [X17,X18,X19,X20] :
( ~ class_Divides_Osemiring__div(X20)
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X19),X18),X17,X20) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),c_Divides_Odiv__class_Odiv(X19,X17,X20)),c_Divides_Odiv__class_Odiv(X18,X17,X20))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X18,X20)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X19,X20) ),
inference(variable_rename,[status(thm)],[c_0_704]) ).
fof(c_0_1337,plain,
! [X27,X28,X29,X30,X31] :
( c_Type_Otyping(c_Type_Oshift(X29,X28,X30,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X27),X28),X31)
| ~ c_Type_Otyping(X29,X27,X31) ),
inference(variable_rename,[status(thm)],[c_0_705]) ).
fof(c_0_1338,plain,
! [X5,X6,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X7)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X6,c_Power_Opower__class_Opower(X6,X5,X7),X7),c_Power_Opower__class_Opower(X6,X5,X7),X7)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Oone__class_Oone(X7),X7)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X7),X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_706]) ).
fof(c_0_1339,plain,
! [X6,X7] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
| c_HOL_Oord__class_Oless(X7,c_HOL_Otimes__class_Otimes(X6,c_Suc(c_Divides_Odiv__class_Odiv(X7,X6,tc_nat)),tc_nat),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_707])])]) ).
fof(c_0_1340,plain,
! [X31,X32,X33,X34,X35,X36] :
( ~ class_Divides_Osemiring__div(X36)
| c_Divides_Odiv__class_Omod(X33,X31,X36) != c_Divides_Odiv__class_Omod(X32,X31,X36)
| c_Divides_Odiv__class_Omod(X35,X31,X36) != c_Divides_Odiv__class_Omod(X34,X31,X36)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X35,X33,X36),X31,X36) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X34,X32,X36),X31,X36) ),
inference(variable_rename,[status(thm)],[c_0_708]) ).
fof(c_0_1341,plain,
! [X31,X32,X33,X34,X35,X36] :
( ~ class_Divides_Osemiring__div(X36)
| c_Divides_Odiv__class_Omod(X33,X31,X36) != c_Divides_Odiv__class_Omod(X32,X31,X36)
| c_Divides_Odiv__class_Omod(X35,X31,X36) != c_Divides_Odiv__class_Omod(X34,X31,X36)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X35),X33),X31,X36) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X34),X32),X31,X36) ),
inference(variable_rename,[status(thm)],[c_0_709]) ).
fof(c_0_1342,plain,
! [X12,X13,X14,X15] :
( ~ class_Divides_Osemiring__div(X15)
| c_Ring__and__Field_Odvd__class_Odvd(X13,X12,X15)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X13,X14,X15),c_Divides_Odiv__class_Odiv(X12,X14,X15),X15)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X12,X15)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_710]) ).
fof(c_0_1343,plain,
! [X36,X37,X38,X39,X40] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X39,X38,X40),c_HOL_Otimes__class_Otimes(X37,X36,X40),X40) = c_HOL_Otimes__class_Otimes(X37,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X39,X38,X40),X36,X40),X40) ),
inference(variable_rename,[status(thm)],[c_0_711]) ).
fof(c_0_1344,plain,
! [X36,X37,X38,X39,X40] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X39,X38,X40),c_HOL_Otimes__class_Otimes(X37,X36,X40),X40) = c_HOL_Otimes__class_Otimes(X39,c_HOL_Otimes__class_Otimes(X38,c_HOL_Otimes__class_Otimes(X37,X36,X40),X40),X40) ),
inference(variable_rename,[status(thm)],[c_0_712]) ).
fof(c_0_1345,plain,
! [X14,X15,X16] : c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X16,X14,tc_nat)),X15),X14,tc_nat) = c_Divides_Odiv__class_Omod(X15,X14,tc_nat),
inference(variable_rename,[status(thm)],[c_0_713]) ).
fof(c_0_1346,plain,
! [X27,X28,X29,X30,X31] :
( hAPP(c_Type_Oshift(X29,X28,X30,X31),X27) = hAPP(X29,X27)
| ~ c_HOL_Oord__class_Oless(X27,X28,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_714])])]) ).
fof(c_0_1347,plain,
! [X17,X18,X19] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X19)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X19),c_HOL_Otimes__class_Otimes(X18,X18,X19)),c_HOL_Otimes__class_Otimes(X17,X17,X19)) != c_HOL_Ozero__class_Ozero(X19)
| X18 = c_HOL_Ozero__class_Ozero(X19) ),
inference(variable_rename,[status(thm)],[c_0_715]) ).
fof(c_0_1348,plain,
! [X17,X18,X19] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X19)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X19),c_HOL_Otimes__class_Otimes(X18,X18,X19)),c_HOL_Otimes__class_Otimes(X17,X17,X19)) != c_HOL_Ozero__class_Ozero(X19)
| X17 = c_HOL_Ozero__class_Ozero(X19) ),
inference(variable_rename,[status(thm)],[c_0_716]) ).
fof(c_0_1349,plain,
! [X14,X15,X16] :
( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X14),X16)),c_Suc(X15)) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X14),X15)),X16)
| ~ 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(variable_rename,[status(thm)],[c_0_717]) ).
fof(c_0_1350,plain,
! [X46,X47] : c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X47),X46),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X47,tc_Lambda_OdB)),c_Nat_Osize__class_Osize(X46,tc_Lambda_OdB))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
inference(variable_rename,[status(thm)],[c_0_718]) ).
fof(c_0_1351,plain,
! [X4,X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),c_Divides_Odiv__class_Omod(X5,X4,X6)),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X5,X4,X6),X4,X6)) = X5 ),
inference(variable_rename,[status(thm)],[c_0_719]) ).
fof(c_0_1352,plain,
! [X5,X6,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X7)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X6,X5,X7),c_HOL_Otimes__class_Otimes(X6,c_Power_Opower__class_Opower(X6,X5,X7),X7),X7)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X7),X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_720]) ).
fof(c_0_1353,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X15)
| c_HOL_Oord__class_Oless(X14,X13,X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X12,X14,X15),c_HOL_Otimes__class_Otimes(X12,X13,X15),X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X15),X12,X15) ),
inference(variable_rename,[status(thm)],[c_0_721]) ).
fof(c_0_1354,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X15)
| c_HOL_Oord__class_Oless(X13,X14,X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X12,X14,X15),c_HOL_Otimes__class_Otimes(X12,X13,X15),X15)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_722]) ).
fof(c_0_1355,plain,
! [X6,X7,X8,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X9)
| c_HOL_Oord__class_Oless(X7,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X8,X7,X9),c_Power_Opower__class_Opower(X8,X6,X9),X9)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X9),X8,X9) ),
inference(variable_rename,[status(thm)],[c_0_723]) ).
fof(c_0_1356,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Oordered__semidom(X20)
| c_HOL_Oord__class_Oless(X18,X17,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X19,X18,X20),c_Power_Opower__class_Opower(X19,X17,X20),X20)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X20),X19,X20) ),
inference(variable_rename,[status(thm)],[c_0_724]) ).
fof(c_0_1357,plain,
! [X49,X50,X51,X52,X53] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X52),c_HOL_Otimes__class_Otimes(X53,X51,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X49),c_HOL_Otimes__class_Otimes(X53,X50,tc_nat))
| c_Divides_Odiv__class_Omod(X52,X53,tc_nat) = c_Divides_Odiv__class_Omod(X49,X53,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_725]) ).
fof(c_0_1358,plain,
! [X14,X15,X16] :
( c_Ring__and__Field_Odvd__class_Odvd(X15,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X16,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X16,X15,tc_nat),c_HOL_Otimes__class_Otimes(X16,X14,tc_nat),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_726])])]) ).
fof(c_0_1359,plain,
! [X14,X15,X16] :
( c_Ring__and__Field_Odvd__class_Odvd(X15,X14,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X16,X15,tc_nat),c_HOL_Otimes__class_Otimes(X16,X14,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X16,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_727])])]) ).
fof(c_0_1360,plain,
! [X10,X11,X12] :
( c_HOL_Oord__class_Oless(X11,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X12,X11,tc_nat),c_Power_Opower__class_Opower(X12,X10,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X12,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_728])])]) ).
fof(c_0_1361,plain,
! [X14,X15,X16] :
( c_HOL_Oord__class_Oless(X15,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X16,X15,tc_nat),c_HOL_Otimes__class_Otimes(X16,X14,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X16,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_729])])]) ).
fof(c_0_1362,plain,
! [X22,X23,X24,X25] :
( ~ class_Ring__and__Field_Oordered__semidom(X25)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X23,X24,X25),c_Power_Opower__class_Opower(X23,X22,X25),X25)
| ~ c_HOL_Oord__class_Oless(X23,c_HOL_Oone__class_Oone(X25),X25)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X25),X23,X25)
| ~ c_HOL_Oord__class_Oless(X22,X24,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_730]) ).
fof(c_0_1363,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X15)
| c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X15),X15)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X15),X12,X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X14,X12,X15),c_HOL_Otimes__class_Otimes(X13,X12,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_731]) ).
fof(c_0_1364,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X15)
| c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X15),X15)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X15),X12,X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X12,X14,X15),c_HOL_Otimes__class_Otimes(X12,X13,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_732]) ).
fof(c_0_1365,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X15)
| c_HOL_Oord__class_Oless(X13,X14,X15)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X15),X12,X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X12,X14,X15),c_HOL_Otimes__class_Otimes(X12,X13,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_733]) ).
fof(c_0_1366,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X15)
| c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X15),X15)
| c_HOL_Oord__class_Oless(X14,X13,X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X12,X14,X15),c_HOL_Otimes__class_Otimes(X12,X13,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_734]) ).
fof(c_0_1367,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X15)
| c_HOL_Oord__class_Oless(X13,X14,X15)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X15),X12,X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X14,X12,X15),c_HOL_Otimes__class_Otimes(X13,X12,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_735]) ).
fof(c_0_1368,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X15)
| c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X15),X15)
| c_HOL_Oord__class_Oless(X14,X13,X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X14,X12,X15),c_HOL_Otimes__class_Otimes(X13,X12,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_736]) ).
fof(c_0_1369,plain,
! [X36,X37,X38,X39,X40] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X39,X38,X40),c_HOL_Otimes__class_Otimes(X37,X36,X40),X40) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X39,X37,X40),c_HOL_Otimes__class_Otimes(X38,X36,X40),X40) ),
inference(variable_rename,[status(thm)],[c_0_737]) ).
fof(c_0_1370,plain,
! [X12,X13,X14,X15] :
( ~ class_Divides_Osemiring__div(X15)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X14,X13,X15),X12,X15) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X14,c_Divides_Odiv__class_Omod(X13,X12,X15),X15),X12,X15) ),
inference(variable_rename,[status(thm)],[c_0_738]) ).
fof(c_0_1371,plain,
! [X12,X13,X14,X15] :
( ~ class_Divides_Osemiring__div(X15)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X14,X13,X15),X12,X15) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X14,X12,X15),X13,X15),X12,X15) ),
inference(variable_rename,[status(thm)],[c_0_739]) ).
fof(c_0_1372,plain,
! [X12,X13,X14,X15] :
( ~ class_Divides_Osemiring__div(X15)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X14,X12,X15),X13,X15),X12,X15) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X14,X13,X15),X12,X15) ),
inference(variable_rename,[status(thm)],[c_0_740]) ).
fof(c_0_1373,plain,
! [X12,X13,X14,X15] :
( ~ class_Divides_Osemiring__div(X15)
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),c_HOL_Otimes__class_Otimes(X12,X13,X15)),X13,X15) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X12),c_Divides_Odiv__class_Odiv(X14,X13,X15))
| X13 = c_HOL_Ozero__class_Ozero(X15) ),
inference(variable_rename,[status(thm)],[c_0_741]) ).
fof(c_0_1374,plain,
! [X12,X13,X14,X15] :
( ~ class_Divides_Osemiring__div(X15)
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),c_HOL_Otimes__class_Otimes(X13,X12,X15)),X13,X15) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X12),c_Divides_Odiv__class_Odiv(X14,X13,X15))
| X13 = c_HOL_Ozero__class_Ozero(X15) ),
inference(variable_rename,[status(thm)],[c_0_742]) ).
fof(c_0_1375,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X15)
| c_HOL_Oord__class_Oless(X13,X14,X15)
| c_HOL_Oord__class_Oless(X14,X13,X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X14,X12,X15),c_HOL_Otimes__class_Otimes(X13,X12,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_743]) ).
fof(c_0_1376,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X15)
| c_HOL_Oord__class_Oless(X13,X14,X15)
| c_HOL_Oord__class_Oless(X14,X13,X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X12,X14,X15),c_HOL_Otimes__class_Otimes(X12,X13,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_744]) ).
fof(c_0_1377,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X20)
| c_HOL_Otimes__class_Otimes(X19,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X18),X17),X20) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),c_HOL_Otimes__class_Otimes(X19,X18,X20)),c_HOL_Otimes__class_Otimes(X19,X17,X20)) ),
inference(variable_rename,[status(thm)],[c_0_745]) ).
fof(c_0_1378,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring(X15)
| c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X13),X12,X15) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),c_HOL_Otimes__class_Otimes(X14,X12,X15)),c_HOL_Otimes__class_Otimes(X13,X12,X15)) ),
inference(variable_rename,[status(thm)],[c_0_746]) ).
fof(c_0_1379,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X15)
| c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X13),X12,X15) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),c_HOL_Otimes__class_Otimes(X14,X12,X15)),c_HOL_Otimes__class_Otimes(X13,X12,X15)) ),
inference(variable_rename,[status(thm)],[c_0_747]) ).
fof(c_0_1380,plain,
! [X6,X7,X8,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),c_HOL_Otimes__class_Otimes(X8,X6,X9)),c_HOL_Otimes__class_Otimes(X7,X6,X9)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X8),X7),X6,X9) ),
inference(variable_rename,[status(thm)],[c_0_748]) ).
fof(c_0_1381,plain,
! [X12,X13,X14,X15] :
( ~ class_Divides_Osemiring__div(X15)
| c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X13,X14,X15),c_Divides_Odiv__class_Odiv(X12,X14,X15),X15)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,X12,X15)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X12,X15)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_749]) ).
fof(c_0_1382,plain,
! [X12,X13,X14,X15] :
( ~ class_Divides_Osemiring__div(X15)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),c_Divides_Odiv__class_Omod(X13,X12,X15)),X12,X15) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X13),X12,X15) ),
inference(variable_rename,[status(thm)],[c_0_750]) ).
fof(c_0_1383,plain,
! [X12,X13,X14,X15] :
( ~ class_Divides_Osemiring__div(X15)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X13),X12,X15) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),c_Divides_Odiv__class_Omod(X13,X12,X15)),X12,X15) ),
inference(variable_rename,[status(thm)],[c_0_751]) ).
fof(c_0_1384,plain,
! [X17,X18,X19,X20] :
( ~ class_Divides_Osemiring__div(X20)
| c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(X18,X17,X20),X19,X20) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(X18,X19,X20),c_Power_Opower__class_Opower(X17,X19,X20),X20)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X18,X20) ),
inference(variable_rename,[status(thm)],[c_0_752]) ).
fof(c_0_1385,plain,
! [X24,X25,X26,X27,X28] :
( ~ class_Ring__and__Field_Oidom(X28)
| ~ class_Int_Onumber__ring(X28)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X24),c_HOL_Otimes__class_Otimes(X25,X27,X28)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X24),c_HOL_Otimes__class_Otimes(X25,X26,X28))
| X27 = X26
| X25 = c_HOL_Ozero__class_Ozero(X28) ),
inference(variable_rename,[status(thm)],[c_0_753]) ).
fof(c_0_1386,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X15)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X13)),X12) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X12)),X13) ),
inference(variable_rename,[status(thm)],[c_0_754]) ).
fof(c_0_1387,plain,
! [X27,X28,X29,X30] : hAPP(c_Type_Oshift(X28,X27,X29,X30),X27) = X29,
inference(variable_rename,[status(thm)],[c_0_755]) ).
fof(c_0_1388,plain,
! [X14,X15,X16] :
( c_HOL_Oord__class_Oless(X15,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X16),X15,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X16),X14,tc_nat),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_756])])]) ).
fof(c_0_1389,plain,
! [X14,X15,X16] : c_HOL_Otimes__class_Otimes(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X14),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X16,X15,tc_nat)),c_HOL_Otimes__class_Otimes(X16,X14,tc_nat)),
inference(variable_rename,[status(thm)],[c_0_757]) ).
fof(c_0_1390,plain,
! [X14,X15,X16] : c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X14),X16,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X15,X16,tc_nat)),c_HOL_Otimes__class_Otimes(X14,X16,tc_nat)),
inference(variable_rename,[status(thm)],[c_0_758]) ).
fof(c_0_1391,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oidom(X15)
| c_Ring__and__Field_Odvd__class_Odvd(X14,X13,X15)
| X12 = c_HOL_Ozero__class_Ozero(X15)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X14,X12,X15),c_HOL_Otimes__class_Otimes(X13,X12,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_759]) ).
fof(c_0_1392,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oidom(X15)
| c_Ring__and__Field_Odvd__class_Odvd(X14,X13,X15)
| X12 = c_HOL_Ozero__class_Ozero(X15)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X12,X14,X15),c_HOL_Otimes__class_Otimes(X12,X13,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_760]) ).
fof(c_0_1393,plain,
! [X5,X6,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X7)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X7),c_HOL_Otimes__class_Otimes(X6,c_Power_Opower__class_Opower(X6,X5,X7),X7),X7)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X7),X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_761]) ).
fof(c_0_1394,plain,
! [X14,X15,X16,X17] : c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,X15),X14),X16,X17) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(X15,X16,X17)),c_Lambda_Osubstn(X14,X16,X17)),
inference(variable_rename,[status(thm)],[c_0_762]) ).
fof(c_0_1395,plain,
! [X24,X25,X26,X27] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),c_HOL_Otimes__class_Otimes(X25,X27,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),c_HOL_Otimes__class_Otimes(X25,X26,tc_nat))
| X27 = X26
| X25 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_763]) ).
fof(c_0_1396,plain,
! [X12,X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X15)
| c_HOL_Oord__class_Oless(X14,X13,X15)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X12),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X12),X13),X15) ),
inference(variable_rename,[status(thm)],[c_0_764]) ).
fof(c_0_1397,plain,
! [X12,X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X15)
| c_HOL_Oord__class_Oless(X14,X13,X15)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X13),X12),X15) ),
inference(variable_rename,[status(thm)],[c_0_765]) ).
fof(c_0_1398,plain,
! [X14,X15,X16] :
( c_Ring__and__Field_Odvd__class_Odvd(X15,X14,tc_nat)
| X16 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X16,X15,tc_nat),c_HOL_Otimes__class_Otimes(X16,X14,tc_nat),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_766])])]) ).
fof(c_0_1399,plain,
! [X14,X15,X16] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X16,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X16,tc_nat),c_HOL_Otimes__class_Otimes(X14,X16,tc_nat),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_767]) ).
fof(c_0_1400,plain,
! [X14,X15,X16] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X16,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X16,X15,tc_nat),c_HOL_Otimes__class_Otimes(X16,X14,tc_nat),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_768]) ).
fof(c_0_1401,plain,
! [X14,X15,X16] :
( c_HOL_Oord__class_Oless(X15,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X16,tc_nat),c_HOL_Otimes__class_Otimes(X14,X16,tc_nat),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_769])])]) ).
fof(c_0_1402,plain,
! [X14,X15,X16] :
( c_HOL_Oord__class_Oless(X15,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X16,X15,tc_nat),c_HOL_Otimes__class_Otimes(X16,X14,tc_nat),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_770])])]) ).
fof(c_0_1403,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X15)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X12,X14,X15),c_HOL_Otimes__class_Otimes(X12,X13,X15),X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X15),X12,X15)
| ~ c_HOL_Oord__class_Oless(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_771]) ).
fof(c_0_1404,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X15)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X14,X12,X15),c_HOL_Otimes__class_Otimes(X13,X12,X15),X15)
| ~ c_HOL_Oord__class_Oless(X13,X14,X15)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_772]) ).
fof(c_0_1405,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X15)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X14,X12,X15),c_HOL_Otimes__class_Otimes(X13,X12,X15),X15)
| ~ c_HOL_Oord__class_Oless(X14,X13,X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X15),X12,X15) ),
inference(variable_rename,[status(thm)],[c_0_773]) ).
fof(c_0_1406,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X15)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X14,X12,X15),c_HOL_Otimes__class_Otimes(X13,X12,X15),X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X15),X12,X15)
| ~ c_HOL_Oord__class_Oless(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_774]) ).
fof(c_0_1407,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X15)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X14,X12,X15),c_HOL_Otimes__class_Otimes(X13,X12,X15),X15)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X15),X15)
| ~ c_HOL_Oord__class_Oless(X13,X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_775]) ).
fof(c_0_1408,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X15)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X12,X14,X15),c_HOL_Otimes__class_Otimes(X12,X13,X15),X15)
| ~ c_HOL_Oord__class_Oless(X13,X14,X15)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_776]) ).
fof(c_0_1409,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X15)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X12,X14,X15),c_HOL_Otimes__class_Otimes(X12,X13,X15),X15)
| ~ c_HOL_Oord__class_Oless(X14,X13,X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X15),X12,X15) ),
inference(variable_rename,[status(thm)],[c_0_777]) ).
fof(c_0_1410,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X15)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X12,X14,X15),c_HOL_Otimes__class_Otimes(X12,X13,X15),X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X15),X12,X15)
| ~ c_HOL_Oord__class_Oless(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_778]) ).
fof(c_0_1411,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X15)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X12,X14,X15),c_HOL_Otimes__class_Otimes(X12,X13,X15),X15)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X15),X15)
| ~ c_HOL_Oord__class_Oless(X13,X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_779]) ).
fof(c_0_1412,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X15)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X12,X14,X15),c_HOL_Otimes__class_Otimes(X12,X13,X15),X15)
| ~ c_HOL_Oord__class_Oless(X14,X13,X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X15),X12,X15) ),
inference(variable_rename,[status(thm)],[c_0_780]) ).
fof(c_0_1413,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X15)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X12,X14,X15),c_HOL_Otimes__class_Otimes(X12,X13,X15),X15)
| ~ c_HOL_Oord__class_Oless(X13,X14,X15)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_781]) ).
fof(c_0_1414,plain,
! [X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4)) = c_HOL_Ozero__class_Ozero(X4) ),
inference(variable_rename,[status(thm)],[c_0_782]) ).
fof(c_0_1415,plain,
! [X22,X23,X24,X25] :
( ~ class_Ring__and__Field_Oordered__semidom(X25)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X23,X22,X25),c_Power_Opower__class_Opower(X23,X24,X25),X25)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X25),X23,X25)
| ~ c_HOL_Oord__class_Oless(X22,X24,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_783]) ).
fof(c_0_1416,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Oordered__semidom(X20)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X19,X18,X20),c_Power_Opower__class_Opower(X19,X17,X20),X20)
| ~ c_HOL_Oord__class_Oless(X18,X17,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X20),X19,X20) ),
inference(variable_rename,[status(thm)],[c_0_784]) ).
fof(c_0_1417,plain,
! [X18,X19,X20,X21,X22] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X22)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X21,X19,X22),c_HOL_Otimes__class_Otimes(X20,X18,X22),X22)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X19,X18,X22)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X21,X20,X22) ),
inference(variable_rename,[status(thm)],[c_0_785]) ).
fof(c_0_1418,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X8)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),c_HOL_Otimes__class_Otimes(X7,X6,X8)),X6) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X7),c_HOL_Oone__class_Oone(X8)),X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_786]) ).
fof(c_0_1419,plain,
! [X4,X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X5),X4),X4,X6) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),c_Divides_Odiv__class_Odiv(X5,X4,X6)),c_HOL_Oone__class_Oone(X6))
| X4 = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_787]) ).
fof(c_0_1420,plain,
! [X4,X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X5),X4,X6) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),c_Divides_Odiv__class_Odiv(X5,X4,X6)),c_HOL_Oone__class_Oone(X6))
| X4 = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_788]) ).
fof(c_0_1421,plain,
! [X18,X19,X20,X21,X22] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X22)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),X21),X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),X20),X18),X22)
| ~ c_HOL_Oord__class_Oless(X19,X18,X22)
| ~ c_HOL_Oord__class_Oless(X21,X20,X22) ),
inference(variable_rename,[status(thm)],[c_0_789]) ).
fof(c_0_1422,plain,
! [X12,X13,X14,X15] :
( ~ class_Divides_Osemiring__div(X15)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X12,X14,X15),c_HOL_Otimes__class_Otimes(X12,X13,X15),X15) = c_HOL_Otimes__class_Otimes(X12,c_Divides_Odiv__class_Omod(X14,X13,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_790]) ).
fof(c_0_1423,plain,
! [X12,X13,X14,X15] :
( ~ class_Divides_Osemiring__div(X15)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X14,X12,X15),c_HOL_Otimes__class_Otimes(X13,X12,X15),X15) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X14,X13,X15),X12,X15) ),
inference(variable_rename,[status(thm)],[c_0_791]) ).
fof(c_0_1424,plain,
! [X19,X20,X21,X22] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X22)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X20,X19,X22),X21,X22) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X20,X21,X22),c_Power_Opower__class_Opower(X19,X21,X22),X22) ),
inference(variable_rename,[status(thm)],[c_0_792]) ).
fof(c_0_1425,plain,
! [X5,X6,X7,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X8)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X7,X6,X8),X5,X8) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X7,X5,X8),c_Power_Opower__class_Opower(X6,X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_793]) ).
fof(c_0_1426,plain,
! [X14,X15,X16] :
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X16,X15,tc_nat),c_HOL_Otimes__class_Otimes(X16,X14,tc_nat),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X16,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_794]) ).
fof(c_0_1427,plain,
! [X14,X15,X16] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X16,X15,tc_nat),c_HOL_Otimes__class_Otimes(X16,X14,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X15,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X16,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_795]) ).
fof(c_0_1428,plain,
! [X14,X15,X16] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X16,X14,tc_nat),c_HOL_Otimes__class_Otimes(X15,X14,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(X16,X15,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_796]) ).
fof(c_0_1429,plain,
! [X14,X15,X16] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X14,X16,tc_nat),c_HOL_Otimes__class_Otimes(X14,X15,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(X16,X15,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_797]) ).
fof(c_0_1430,plain,
! [X14,X15,X16] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X16,X15,tc_nat),c_HOL_Otimes__class_Otimes(X16,X14,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X15,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X16,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_798]) ).
fof(c_0_1431,plain,
! [X14,X15,X16] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X16,tc_nat),c_HOL_Otimes__class_Otimes(X14,X16,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X15,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X16,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_799]) ).
fof(c_0_1432,plain,
! [X14,X15,X16] : hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,X15),X14)),X16) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X15),X16)),hAPP(hAPP(c_Lambda_Olift,X14),X16)),
inference(variable_rename,[status(thm)],[c_0_800]) ).
fof(c_0_1433,plain,
! [X12,X13,X14,X15] :
( ~ class_Divides_Osemiring__div(X15)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),c_HOL_Otimes__class_Otimes(X13,X12,X15)),X13,X15) = c_Divides_Odiv__class_Omod(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_801]) ).
fof(c_0_1434,plain,
! [X12,X13,X14,X15] :
( ~ class_Divides_Osemiring__div(X15)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),c_HOL_Otimes__class_Otimes(X12,X13,X15)),X13,X15) = c_Divides_Odiv__class_Omod(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_802]) ).
fof(c_0_1435,plain,
! [X28,X29] :
( ~ hBOOL(hAPP(X29,c_Divides_Odiv__class_Odiv(X28,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
| hBOOL(hAPP(X29,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(variable_rename,[status(thm)],[c_0_803]) ).
fof(c_0_1436,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X6)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X4,X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X5,X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_HOL_Otimes__class_Otimes(X5,X4,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_804]) ).
fof(c_0_1437,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X6)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X4,X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X5,X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_HOL_Otimes__class_Otimes(X4,X5,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_805]) ).
fof(c_0_1438,plain,
! [X28,X29] :
( ~ hBOOL(hAPP(X29,c_Divides_Odiv__class_Omod(X28,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
| hBOOL(hAPP(X29,X28)) ),
inference(variable_rename,[status(thm)],[c_0_806]) ).
fof(c_0_1439,plain,
! [X14,X15,X16] :
( c_HOL_Oord__class_Oless(X15,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X14),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_807])])]) ).
fof(c_0_1440,plain,
! [X20,X21,X22,X23] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X23)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X20,X22,X23),c_Power_Opower__class_Opower(X20,X21,X23),X23) = c_Power_Opower__class_Opower(X20,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X21),X23) ),
inference(variable_rename,[status(thm)],[c_0_808]) ).
fof(c_0_1441,plain,
! [X6,X7,X8,X9] :
( ~ class_OrderedGroup_Omonoid__mult(X9)
| c_Power_Opower__class_Opower(X8,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X6),X9) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X8,X7,X9),c_Power_Opower__class_Opower(X8,X6,X9),X9) ),
inference(variable_rename,[status(thm)],[c_0_809]) ).
fof(c_0_1442,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X20)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X18),X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X19),X18)),X17) ),
inference(variable_rename,[status(thm)],[c_0_810]) ).
fof(c_0_1443,plain,
! [X12,X13,X14,X15] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X15)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X13)),X12) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X13),X12)) ),
inference(variable_rename,[status(thm)],[c_0_811]) ).
fof(c_0_1444,plain,
! [X12,X13,X14,X15] :
( ~ class_OrderedGroup_Oab__semigroup__add(X15)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X13)),X12) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X13),X12)) ),
inference(variable_rename,[status(thm)],[c_0_812]) ).
fof(c_0_1445,plain,
! [X18,X19,X20,X21] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X21)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X21),X20),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X21),X19),X18)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X21),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X21),X20),X19)),X18) ),
inference(variable_rename,[status(thm)],[c_0_813]) ).
fof(c_0_1446,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X15)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X13)),X12) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X13),X12)) ),
inference(variable_rename,[status(thm)],[c_0_814]) ).
fof(c_0_1447,plain,
! [X14,X15,X16] : c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X15,X14,tc_nat),X16,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X15,X16,tc_nat),c_HOL_Otimes__class_Otimes(X14,X16,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_815]) ).
fof(c_0_1448,plain,
! [X14,X15,X16] : c_HOL_Otimes__class_Otimes(X16,c_Divides_Odiv__class_Omod(X15,X14,tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X16,X15,tc_nat),c_HOL_Otimes__class_Otimes(X16,X14,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_816]) ).
fof(c_0_1449,plain,
! [X12,X13,X14,X15] :
( ~ class_Divides_Osemiring__div(X15)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X13,X14,X15),X12,X15) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X13,X12,X15),X14,X15)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_817]) ).
fof(c_0_1450,plain,
! [X14,X15,X16,X17] :
( ~ class_Divides_Osemiring__div(X17)
| c_Ring__and__Field_Odvd__class_Odvd(X16,X15,X17)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,c_Divides_Odiv__class_Omod(X15,X14,X17),X17)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X14,X17) ),
inference(variable_rename,[status(thm)],[c_0_818]) ).
fof(c_0_1451,plain,
! [X14,X15,X16,X17] :
( ~ class_Divides_Osemiring__div(X17)
| c_Ring__and__Field_Odvd__class_Odvd(X16,X15,X17)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X14,X17)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,c_Divides_Odiv__class_Omod(X15,X14,X17),X17) ),
inference(variable_rename,[status(thm)],[c_0_819]) ).
fof(c_0_1452,plain,
! [X14,X15,X16] :
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X16,X15,tc_nat),c_HOL_Otimes__class_Otimes(X16,X14,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(X15,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X16,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_820]) ).
fof(c_0_1453,plain,
! [X29,X30,X31,X32] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X32),X30),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X31),X29),tc_nat)
| ~ c_HOL_Oord__class_Oless(X30,X29,tc_nat)
| ~ c_HOL_Oord__class_Oless(X32,X31,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_821]) ).
fof(c_0_1454,plain,
! [X40,X41,X42,X43] :
( c_List_Olist_ONil(X43) != c_List_Omap(X41,X40,X42,X43)
| X40 = c_List_Olist_ONil(X42) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_822])])]) ).
fof(c_0_1455,plain,
! [X40,X41,X42,X43] :
( c_List_Omap(X41,X40,X42,X43) != c_List_Olist_ONil(X43)
| X40 = c_List_Olist_ONil(X42) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_823])])]) ).
fof(c_0_1456,plain,
! [X46,X47] : c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X47),X46)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X47)),c_Lambda_OdB_OdB__size(X46))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
inference(variable_rename,[status(thm)],[c_0_824]) ).
fof(c_0_1457,plain,
! [X17,X18,X19,X20,X21] :
( ~ class_OrderedGroup_Oab__group__add(X21)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X21),X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X21),X18),X17)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X21),X18),X20)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X21),X19),X17) = X20 ),
inference(variable_rename,[status(thm)],[c_0_825]) ).
fof(c_0_1458,plain,
! [X5,X6,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X7)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X6,c_Suc(X5),X7),c_HOL_Oone__class_Oone(X7),X7)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Oone__class_Oone(X7),X7)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X7),X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_826]) ).
fof(c_0_1459,plain,
! [X24,X25,X26,X27] :
( c_Lambda_Obeta(hAPP(hAPP(hAPP(c_Lambda_Osubst,X26),X24),X27),hAPP(hAPP(hAPP(c_Lambda_Osubst,X25),X24),X27))
| ~ c_Lambda_Obeta(X26,X25) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_827])])]) ).
fof(c_0_1460,plain,
! [X6,X7] :
( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X6,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_828]) ).
fof(c_0_1461,plain,
! [X14,X15,X16] : hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X14),X16)),X15),X16) = X14,
inference(variable_rename,[status(thm)],[c_0_829]) ).
fof(c_0_1462,plain,
! [X14,X15,X16] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X16),X15,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X16),X14,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X15,X14,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_830])])]) ).
fof(c_0_1463,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X6)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X4,X6)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_831]) ).
fof(c_0_1464,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X6)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_832]) ).
fof(c_0_1465,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X6)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X5,X6),c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_833]) ).
fof(c_0_1466,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X6)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_HOL_Otimes__class_Otimes(X5,X4,X6),X6)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_834]) ).
fof(c_0_1467,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X6)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_HOL_Otimes__class_Otimes(X5,X4,X6),X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X4,X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_835]) ).
fof(c_0_1468,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X8)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X8),c_HOL_Otimes__class_Otimes(X7,X6,X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X8),X6,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X8),X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_836]) ).
fof(c_0_1469,plain,
! [X14,X15,X16] : c_Lambda_Osubstn(c_Lambda_OdB_OAbs(X14),X15,X16) = c_Lambda_OdB_OAbs(c_Lambda_Osubstn(X14,X15,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),c_HOL_Oone__class_Oone(tc_nat)))),
inference(variable_rename,[status(thm)],[c_0_837]) ).
fof(c_0_1470,plain,
! [X6,X7] :
( c_HOL_Oord__class_Oless(X6,c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X6,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_838]) ).
fof(c_0_1471,plain,
! [X6,X7] :
( c_HOL_Oord__class_Oless(X6,c_HOL_Otimes__class_Otimes(X6,X7,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X6,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_839]) ).
fof(c_0_1472,plain,
! [X14,X15,X16] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X14)),X16) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X16)),
inference(variable_rename,[status(thm)],[c_0_840]) ).
fof(c_0_1473,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X6)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X5),X4),X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X4,X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_841]) ).
fof(c_0_1474,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X6)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X5),X4),c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_842]) ).
fof(c_0_1475,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X20)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X18,X19,X20),c_Power_Opower__class_Opower(X17,X19,X20),X20)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X17,X20) ),
inference(variable_rename,[status(thm)],[c_0_843]) ).
fof(c_0_1476,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oidom(X15)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X12,X14,X15),c_HOL_Otimes__class_Otimes(X12,X13,X15),X15)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_844]) ).
fof(c_0_1477,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oidom(X15)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X14,X12,X15),c_HOL_Otimes__class_Otimes(X13,X12,X15),X15)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_845]) ).
fof(c_0_1478,plain,
! [X5,X6,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X7)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X7),c_Power_Opower__class_Opower(X6,X5,X7),X7)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X7),X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_846]) ).
fof(c_0_1479,plain,
! [X17,X18,X19] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X19,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X17,X18,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X17,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X18,X19,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X19,X18,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_847]) ).
fof(c_0_1480,plain,
! [X14,X15] :
( c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Otimes__class_Otimes(X15,X14,tc_nat)),X15,tc_nat) = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X15,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_848]) ).
fof(c_0_1481,plain,
! [X12,X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X15)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X12),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X12),X13),X15)
| ~ c_HOL_Oord__class_Oless(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_849]) ).
fof(c_0_1482,plain,
! [X12,X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X15)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X12),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X12),X13),X15)
| ~ c_HOL_Oord__class_Oless(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_850]) ).
fof(c_0_1483,plain,
! [X12,X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X15)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X13),X12),X15)
| ~ c_HOL_Oord__class_Oless(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_851]) ).
fof(c_0_1484,plain,
! [X12,X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X15)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X13),X12),X15)
| ~ c_HOL_Oord__class_Oless(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_852]) ).
fof(c_0_1485,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X15)
| c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X12),X15)
| ~ c_HOL_Oord__class_Oless(X13,X12,X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X15),X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_853]) ).
fof(c_0_1486,plain,
! [X14,X15,X16] :
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X16,X15,tc_nat),c_HOL_Otimes__class_Otimes(X16,X14,tc_nat),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X14,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_854])])]) ).
fof(c_0_1487,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_855])])]) ).
fof(c_0_1488,plain,
! [X14,X15,X16,X17] :
( ~ class_Divides_Osemiring__div(X17)
| c_Ring__and__Field_Odvd__class_Odvd(X16,c_Divides_Odiv__class_Omod(X15,X14,X17),X17)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X14,X17)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X15,X17) ),
inference(variable_rename,[status(thm)],[c_0_856]) ).
fof(c_0_1489,plain,
! [X14,X15,X16,X17] :
( ~ class_Divides_Osemiring__div(X17)
| c_Ring__and__Field_Odvd__class_Odvd(X16,c_Divides_Odiv__class_Omod(X15,X14,X17),X17)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X15,X17)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X14,X17) ),
inference(variable_rename,[status(thm)],[c_0_857]) ).
fof(c_0_1490,plain,
! [X6,X7] :
( X6 = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X6,X7,tc_nat),X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_858])])]) ).
fof(c_0_1491,plain,
! [X6,X7] :
( X6 = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_859])])]) ).
fof(c_0_1492,plain,
! [X6,X7] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat)
| ~ 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) ),
inference(variable_rename,[status(thm)],[c_0_860]) ).
fof(c_0_1493,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X15)
| c_Ring__and__Field_Odvd__class_Odvd(X14,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X13),X12),X15)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X12,X15)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_861]) ).
fof(c_0_1494,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X8)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),c_HOL_Otimes__class_Otimes(X7,X6,X8)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X7),c_HOL_Oone__class_Oone(X8)),X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_862]) ).
fof(c_0_1495,plain,
! [X12,X13,X14,X15] :
( ~ class_Divides_Osemiring__div(X15)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X14,X12,X15),c_HOL_Otimes__class_Otimes(X13,X12,X15),X15) = c_Divides_Odiv__class_Odiv(X14,X13,X15)
| X12 = c_HOL_Ozero__class_Ozero(X15) ),
inference(variable_rename,[status(thm)],[c_0_863]) ).
fof(c_0_1496,plain,
! [X12,X13,X14,X15] :
( ~ class_Divides_Osemiring__div(X15)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X12,X14,X15),c_HOL_Otimes__class_Otimes(X12,X13,X15),X15) = c_Divides_Odiv__class_Odiv(X14,X13,X15)
| X12 = c_HOL_Ozero__class_Ozero(X15) ),
inference(variable_rename,[status(thm)],[c_0_864]) ).
fof(c_0_1497,plain,
! [X6,X7] :
( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Odiv(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_Oone__class_Oone(tc_nat),X6,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_865]) ).
fof(c_0_1498,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X20)
| c_HOL_Otimes__class_Otimes(X19,c_HOL_Otimes__class_Otimes(X18,X17,X20),X20) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X19,X18,X20),X17,X20) ),
inference(variable_rename,[status(thm)],[c_0_866]) ).
fof(c_0_1499,plain,
! [X36,X37,X38,X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| c_HOL_Otimes__class_Otimes(X38,c_HOL_Otimes__class_Otimes(X37,X36,X39),X39) = c_HOL_Otimes__class_Otimes(X37,c_HOL_Otimes__class_Otimes(X38,X36,X39),X39) ),
inference(variable_rename,[status(thm)],[c_0_867]) ).
fof(c_0_1500,plain,
! [X36,X37,X38,X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| c_HOL_Otimes__class_Otimes(X38,c_HOL_Otimes__class_Otimes(X37,X36,X39),X39) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X38,X37,X39),X36,X39) ),
inference(variable_rename,[status(thm)],[c_0_868]) ).
fof(c_0_1501,plain,
! [X36,X37,X38,X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X38,X37,X39),X36,X39) = c_HOL_Otimes__class_Otimes(X38,c_HOL_Otimes__class_Otimes(X37,X36,X39),X39) ),
inference(variable_rename,[status(thm)],[c_0_869]) ).
fof(c_0_1502,plain,
! [X36,X37,X38,X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X38,X37,X39),X36,X39) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X38,X36,X39),X37,X39) ),
inference(variable_rename,[status(thm)],[c_0_870]) ).
fof(c_0_1503,plain,
! [X12,X13,X14,X15] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X15)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X14,X13,X15),X12,X15) = c_HOL_Otimes__class_Otimes(X14,c_HOL_Otimes__class_Otimes(X13,X12,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_871]) ).
fof(c_0_1504,plain,
! [X5,X6,X7] :
( ~ class_OrderedGroup_Omonoid__mult(X7)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X6,X5,X7),X6,X7) = c_HOL_Otimes__class_Otimes(X6,c_Power_Opower__class_Opower(X6,X5,X7),X7) ),
inference(variable_rename,[status(thm)],[c_0_872]) ).
fof(c_0_1505,plain,
! [X17,X18,X19] :
( c_Ring__and__Field_Odvd__class_Odvd(X19,X17,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X17,X18,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X17,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X18,X19,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X19,X18,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_873]) ).
fof(c_0_1506,plain,
! [X6,X7,X8,X9] :
( ~ class_OrderedGroup_Omonoid__mult(X9)
| c_Power_Opower__class_Opower(X8,c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),X9) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X8,X7,X9),X6,X9) ),
inference(variable_rename,[status(thm)],[c_0_874]) ).
fof(c_0_1507,plain,
! [X20,X21,X22,X23] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X23)
| c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X20,X22,X23),X21,X23) = c_Power_Opower__class_Opower(X20,c_HOL_Otimes__class_Otimes(X22,X21,tc_nat),X23) ),
inference(variable_rename,[status(thm)],[c_0_875]) ).
fof(c_0_1508,plain,
! [X6,X7] : c_Divides_Odiv__class_Omod(c_Suc(X7),X6,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(X7,X6,tc_nat)),X6,tc_nat),
inference(variable_rename,[status(thm)],[c_0_876]) ).
fof(c_0_1509,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X5),X5)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X4),X4),c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_877]) ).
fof(c_0_1510,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X5),X5)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X4),X4),c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_878]) ).
fof(c_0_1511,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X4,X5)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X4),X4),X5) ),
inference(variable_rename,[status(thm)],[c_0_879]) ).
fof(c_0_1512,plain,
! [X14,X15] : hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(X14)),X15) = c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)))),
inference(variable_rename,[status(thm)],[c_0_880]) ).
fof(c_0_1513,plain,
! [X14,X15,X16] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X14),tc_nat)
| ~ c_HOL_Oord__class_Oless(X15,X14,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_881])])]) ).
fof(c_0_1514,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(variable_rename,[status(thm)],[c_0_882]) ).
fof(c_0_1515,plain,
! [X14,X15,X16] :
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X16,X15,tc_nat),c_HOL_Otimes__class_Otimes(X16,X14,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(X15,X14,tc_nat)
| X16 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_883]) ).
fof(c_0_1516,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X15)
| c_Ring__and__Field_Odvd__class_Odvd(X14,X12,X15)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X14,X13,X15),X12,X15) ),
inference(variable_rename,[status(thm)],[c_0_884]) ).
fof(c_0_1517,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X15)
| c_Ring__and__Field_Odvd__class_Odvd(X13,X12,X15)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X14,X13,X15),X12,X15) ),
inference(variable_rename,[status(thm)],[c_0_885]) ).
fof(c_0_1518,plain,
! [X17,X18,X19,X20] :
( ~ class_OrderedGroup_Oab__group__add(X20)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X18),X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X18),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X19),X17)) ),
inference(variable_rename,[status(thm)],[c_0_886]) ).
fof(c_0_1519,plain,
! [X12,X13,X14,X15] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X15)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X13),X12)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X12)) ),
inference(variable_rename,[status(thm)],[c_0_887]) ).
fof(c_0_1520,plain,
! [X18,X19,X20,X21] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X21)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X21),X20),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X21),X19),X18)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X21),X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X21),X20),X18)) ),
inference(variable_rename,[status(thm)],[c_0_888]) ).
fof(c_0_1521,plain,
! [X14,X15,X16] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X15,X14,tc_nat),X16,tc_nat) = c_HOL_Otimes__class_Otimes(X15,c_HOL_Otimes__class_Otimes(X14,X16,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_889]) ).
fof(c_0_1522,plain,
! [X12,X13,X14] : c_Divides_Odiv__class_Odiv(X14,c_HOL_Otimes__class_Otimes(X13,X12,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(X14,X13,tc_nat),X12,tc_nat),
inference(variable_rename,[status(thm)],[c_0_890]) ).
fof(c_0_1523,plain,
! [X17,X18] :
( X18 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X17,X18,tc_nat),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_891]) ).
fof(c_0_1524,plain,
! [X12,X13,X14,X15] :
( ~ class_Divides_Osemiring__div(X15)
| c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X14,X13,X15),X12,X15) = c_Divides_Odiv__class_Omod(X14,X12,X15)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X12,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_892]) ).
fof(c_0_1525,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),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_893])])]) ).
fof(c_0_1526,plain,
! [X6,X7] :
( 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),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_894]) ).
fof(c_0_1527,plain,
! [X28,X29] :
( ~ hBOOL(hAPP(X29,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X29,c_Divides_Odiv__class_Odiv(X28,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
inference(variable_rename,[status(thm)],[c_0_895]) ).
fof(c_0_1528,plain,
! [X28,X29] :
( hBOOL(hAPP(X29,c_Divides_Odiv__class_Odiv(X28,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
| ~ hBOOL(hAPP(X29,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(variable_rename,[status(thm)],[c_0_896]) ).
fof(c_0_1529,plain,
! [X17,X18,X19] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X19,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X17,X18,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X17,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X19,X18,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_897]) ).
fof(c_0_1530,plain,
! [X17,X18,X19] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X19,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X17,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X18,X19,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X19,X18,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_898]) ).
fof(c_0_1531,plain,
! [X4,X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X6),X5,X6),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X6),X4,X6),X6) = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_899]) ).
fof(c_0_1532,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oidom(X6)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X6),X5,X6),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X6),X4,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_900]) ).
fof(c_0_1533,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oidom(X6)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X6),X6),c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X6),X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_901]) ).
fof(c_0_1534,plain,
! [X28,X29] :
( ~ hBOOL(hAPP(X29,X28))
| hBOOL(hAPP(X29,c_Divides_Odiv__class_Omod(X28,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
inference(variable_rename,[status(thm)],[c_0_902]) ).
fof(c_0_1535,plain,
! [X8,X9] : c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X9)),X8),hAPP(hAPP(hAPP(c_Lambda_Osubst,X9),X8),c_HOL_Ozero__class_Ozero(tc_nat))),
inference(variable_rename,[status(thm)],[c_0_903]) ).
fof(c_0_1536,plain,
! [X5,X6,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X7)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X7),c_Power_Opower__class_Opower(X6,c_Suc(X5),X7),X7)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X7),X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_904]) ).
fof(c_0_1537,plain,
! [X29,X30,X31,X32] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X30),X31) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X32),X29)
| ~ c_HOL_Oord__class_Oless(X32,X31,tc_nat)
| c_HOL_Oord__class_Oless(X30,X29,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_905]) ).
fof(c_0_1538,plain,
! [X14,X15] :
( c_Ring__and__Field_Odvd__class_Odvd(X15,X14,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X15),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_906]) ).
fof(c_0_1539,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(variable_rename,[status(thm)],[c_0_907]) ).
fof(c_0_1540,plain,
! [X6,X7,X8,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X9)
| c_Power_Opower__class_Opower(X8,X7,X9) != c_Power_Opower__class_Opower(X8,X6,X9)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X9),X8,X9)
| X7 = X6 ),
inference(variable_rename,[status(thm)],[c_0_908]) ).
fof(c_0_1541,plain,
! [X6,X7] :
( c_Divides_Odiv__class_Omod(c_Suc(X7),X6,tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(X7,X6,tc_nat))
| c_Suc(c_Divides_Odiv__class_Omod(X7,X6,tc_nat)) = X6 ),
inference(variable_rename,[status(thm)],[c_0_909]) ).
fof(c_0_1542,plain,
! [X6,X7] : c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_910]) ).
fof(c_0_1543,plain,
! [X17,X18,X19] :
( c_Ring__and__Field_Odvd__class_Odvd(X19,X17,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X17,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X18,X19,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X19,X18,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_911]) ).
fof(c_0_1544,plain,
! [X17,X18,X19] :
( c_Ring__and__Field_Odvd__class_Odvd(X19,X17,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X17,X18,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X17,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X19,X18,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_912]) ).
fof(c_0_1545,plain,
! [X6,X7] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_913]) ).
fof(c_0_1546,plain,
! [X17,X18,X19] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X19),X17)),
inference(variable_rename,[status(thm)],[c_0_914]) ).
fof(c_0_1547,plain,
! [X5,X6,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X7)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X7),c_Power_Opower__class_Opower(X6,X5,X7),X7)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X7),X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_915]) ).
fof(c_0_1548,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X4,X5),c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_916]) ).
fof(c_0_1549,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X4),X4),c_HOL_Ozero__class_Ozero(X5),X5)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_917]) ).
fof(c_0_1550,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X4),X4),c_HOL_Ozero__class_Ozero(X5),X5)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_918]) ).
fof(c_0_1551,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X4),X4),X5)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_919]) ).
fof(c_0_1552,plain,
! [X40,X41,X42] : c_List_Olist_ONil(X42) = c_List_Omap(X40,c_List_Olist_ONil(X41),X41,X42),
inference(variable_rename,[status(thm)],[c_0_920]) ).
fof(c_0_1553,plain,
! [X40,X41,X42] : c_List_Omap(X40,c_List_Olist_ONil(X41),X41,X42) = c_List_Olist_ONil(X42),
inference(variable_rename,[status(thm)],[c_0_921]) ).
fof(c_0_1554,plain,
! [X17,X18,X19] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X19)
| c_Ring__and__Field_Odvd__class_Odvd(X17,c_Power_Opower__class_Opower(X17,X18,X19),X19)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_922]) ).
fof(c_0_1555,plain,
! [X14,X15,X16] :
( c_HOL_Otimes__class_Otimes(X16,X15,tc_nat) != c_HOL_Otimes__class_Otimes(X16,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X16,tc_nat)
| X15 = X14 ),
inference(variable_rename,[status(thm)],[c_0_923]) ).
fof(c_0_1556,plain,
! [X6,X7] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(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_924]) ).
fof(c_0_1557,plain,
! [X4,X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| c_HOL_Otimes__class_Otimes(X5,c_Divides_Odiv__class_Odiv(X4,X5,X6),X6) = X4
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_925]) ).
fof(c_0_1558,plain,
! [X4,X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X4,X5,X6),X5,X6) = X4
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_926]) ).
fof(c_0_1559,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X15)
| c_Ring__and__Field_Odvd__class_Odvd(X14,c_HOL_Otimes__class_Otimes(X13,X12,X15),X15)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X12,X15) ),
inference(variable_rename,[status(thm)],[c_0_927]) ).
fof(c_0_1560,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X15)
| c_Ring__and__Field_Odvd__class_Odvd(X14,c_HOL_Otimes__class_Otimes(X13,X12,X15),X15)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_928]) ).
fof(c_0_1561,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X6),X6) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),c_HOL_Oone__class_Oone(X7)),c_HOL_Oone__class_Oone(X7)),X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_929]) ).
fof(c_0_1562,plain,
! [X6] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X6,tc_nat),X6,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_930]) ).
fof(c_0_1563,plain,
! [X6] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X6,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X6,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_931]) ).
fof(c_0_1564,plain,
! [X17,X18] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X17,X18,tc_nat),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_932])])]) ).
fof(c_0_1565,plain,
! [X6,X7] :
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X6,X7,tc_nat),X6,tc_nat) = X7
| ~ 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_933])])]) ).
fof(c_0_1566,plain,
! [X6,X7] :
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),X6,tc_nat) = X7
| ~ 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_934])])]) ).
fof(c_0_1567,plain,
! [X6,X7] :
( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X7,X6,tc_nat),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_935])])]) ).
fof(c_0_1568,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Osemiring__1(X8)
| c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X6),X8) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),c_Nat_Osemiring__1__class_Oof__nat(X7,X8)),c_Nat_Osemiring__1__class_Oof__nat(X6,X8)) ),
inference(variable_rename,[status(thm)],[c_0_936]) ).
fof(c_0_1569,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_937]) ).
fof(c_0_1570,plain,
! [X10,X11] : c_HOL_Oord__class_Oless(X11,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X11)),tc_nat),
inference(variable_rename,[status(thm)],[c_0_938]) ).
fof(c_0_1571,plain,
! [X10,X11] : c_HOL_Oord__class_Oless(X11,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X10)),tc_nat),
inference(variable_rename,[status(thm)],[c_0_939]) ).
fof(c_0_1572,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_940]) ).
fof(c_0_1573,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_941])])]) ).
fof(c_0_1574,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X15)
| c_Ring__and__Field_Odvd__class_Odvd(X14,X12,X15)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,X12,X15)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_942]) ).
fof(c_0_1575,plain,
! [X17,X18,X19,X20] :
( ~ class_Orderings_Opreorder(X20)
| c_HOL_Oord__class_Oless(X19,X17,X20)
| ~ c_HOL_Oord__class_Oless(X18,X17,X20)
| ~ c_HOL_Oord__class_Oless(X19,X18,X20) ),
inference(variable_rename,[status(thm)],[c_0_943]) ).
fof(c_0_1576,plain,
! [X17,X18,X19,X20] :
( ~ class_Orderings_Oorder(X20)
| c_HOL_Oord__class_Oless(X17,X19,X20)
| ~ c_HOL_Oord__class_Oless(X17,X18,X20)
| ~ c_HOL_Oord__class_Oless(X18,X19,X20) ),
inference(variable_rename,[status(thm)],[c_0_944]) ).
fof(c_0_1577,plain,
! [X6,X7] :
( c_Suc(c_Divides_Odiv__class_Omod(X7,X6,tc_nat)) != X6
| c_Divides_Odiv__class_Omod(c_Suc(X7),X6,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_945]) ).
fof(c_0_1578,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Osemiring__1(X8)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),X8) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(X7,X8),c_Nat_Osemiring__1__class_Oof__nat(X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_946]) ).
fof(c_0_1579,plain,
! [X19,X20,X21] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X21)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X19,X20,X21),X19,X21) = c_Power_Opower__class_Opower(X19,c_Suc(X20),X21) ),
inference(variable_rename,[status(thm)],[c_0_947]) ).
fof(c_0_1580,plain,
! [X19,X20,X21] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X21)
| c_HOL_Otimes__class_Otimes(X19,c_Power_Opower__class_Opower(X19,X20,X21),X21) = c_Power_Opower__class_Opower(X19,c_Suc(X20),X21) ),
inference(variable_rename,[status(thm)],[c_0_948]) ).
fof(c_0_1581,plain,
! [X5,X6,X7] :
( ~ class_OrderedGroup_Omonoid__mult(X7)
| c_Power_Opower__class_Opower(X6,c_Suc(X5),X7) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X6,X5,X7),X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_949]) ).
fof(c_0_1582,plain,
! [X5,X6,X7] :
( ~ class_Power_Opower(X7)
| c_Power_Opower__class_Opower(X6,c_Suc(X5),X7) = c_HOL_Otimes__class_Otimes(X6,c_Power_Opower__class_Opower(X6,X5,X7),X7) ),
inference(variable_rename,[status(thm)],[c_0_950]) ).
fof(c_0_1583,plain,
! [X17,X18,X19] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X19)
| c_Power_Opower__class_Opower(X17,c_Suc(X18),X19) = c_HOL_Otimes__class_Otimes(X17,c_Power_Opower__class_Opower(X17,X18,X19),X19) ),
inference(variable_rename,[status(thm)],[c_0_951]) ).
fof(c_0_1584,plain,
! [X19,X20,X21] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X21)
| c_Power_Opower__class_Opower(X19,c_Suc(X20),X21) = c_HOL_Otimes__class_Otimes(X19,c_Power_Opower__class_Opower(X19,X20,X21),X21) ),
inference(variable_rename,[status(thm)],[c_0_952]) ).
fof(c_0_1585,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X8)
| c_HOL_Oord__class_Oless(X7,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X7,X8),c_Nat_Osemiring__1__class_Oof__nat(X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_953]) ).
fof(c_0_1586,plain,
! [X6,X7] :
( c_Divides_Odiv__class_Odiv(X7,X6,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_954]) ).
fof(c_0_1587,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(variable_rename,[status(thm)],[c_0_955]) ).
fof(c_0_1588,plain,
! [X14,X15] :
( c_Ring__and__Field_Odvd__class_Odvd(X15,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X15),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X14,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_956]) ).
fof(c_0_1589,plain,
! [X10,X11,X12] :
( c_HOL_Oord__class_Oless(X12,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X11),tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X11,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_957]) ).
fof(c_0_1590,plain,
! [X10,X11,X12] :
( c_HOL_Oord__class_Oless(X12,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X10),tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X11,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_958]) ).
fof(c_0_1591,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,X17,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_959]) ).
fof(c_0_1592,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_960]) ).
fof(c_0_1593,plain,
! [X10,X11] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X11),X11,tc_nat),
inference(variable_rename,[status(thm)],[c_0_961]) ).
fof(c_0_1594,plain,
! [X10,X11] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X10),X11,tc_nat),
inference(variable_rename,[status(thm)],[c_0_962]) ).
fof(c_0_1595,plain,
! [X17,X18,X19] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X19)
| c_HOL_Otimes__class_Otimes(X18,c_HOL_Otimes__class_Otimes(X18,X17,X19),X19) = c_HOL_Otimes__class_Otimes(X18,X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_963]) ).
fof(c_0_1596,plain,
! [X4,X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X5,X4,X6),X4,X6) = c_Divides_Odiv__class_Omod(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_964]) ).
fof(c_0_1597,plain,
! [X17,X18,X19] :
( c_Ring__and__Field_Odvd__class_Odvd(X19,X17,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X17,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X19,X18,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_965]) ).
fof(c_0_1598,plain,
! [X4,X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X5),X4,X6) = c_Divides_Odiv__class_Omod(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_966]) ).
fof(c_0_1599,plain,
! [X4,X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X5),X4),X4,X6) = c_Divides_Odiv__class_Omod(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_967]) ).
fof(c_0_1600,plain,
! [X10,X11] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X10),X11)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X10)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_968])])]) ).
fof(c_0_1601,plain,
! [X6,X7] : c_HOL_Otimes__class_Otimes(c_Suc(X7),X6,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat)),
inference(variable_rename,[status(thm)],[c_0_969]) ).
fof(c_0_1602,plain,
! [X6,X7] : c_HOL_Otimes__class_Otimes(X7,c_Suc(X6),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat)),
inference(variable_rename,[status(thm)],[c_0_970]) ).
fof(c_0_1603,plain,
! [X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_HOL_Oone__class_Oone(X4)),c_HOL_Oone__class_Oone(X4)),X4) ),
inference(variable_rename,[status(thm)],[c_0_971]) ).
fof(c_0_1604,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Osemiring__1(X8)
| c_Nat_Osemiring__1__class_Oof__nat(c_Power_Opower__class_Opower(X7,X6,tc_nat),X8) = c_Power_Opower__class_Opower(c_Nat_Osemiring__1__class_Oof__nat(X7,X8),X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_972]) ).
fof(c_0_1605,plain,
! [X14,X15] :
( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X15)),X14) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)))
| c_HOL_Oord__class_Oless(X15,X14,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_973]) ).
fof(c_0_1606,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Oordered__semidom(X6)
| 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(X6),c_Nat_Osemiring__1__class_Oof__nat(X5,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_974]) ).
fof(c_0_1607,plain,
! [X13,X14,X15] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X14)),X13),X15) = c_Lambda_OdB_OVar(X14)
| ~ c_HOL_Oord__class_Oless(X14,X15,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_975]) ).
fof(c_0_1608,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X8)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X7,X8),c_Nat_Osemiring__1__class_Oof__nat(X6,X8),X8)
| ~ c_HOL_Oord__class_Oless(X7,X6,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_976]) ).
fof(c_0_1609,plain,
! [X37,X38] :
( hBOOL(hAPP(X38,X37))
| ~ hBOOL(hAPP(X38,c_Suc(v_sko__Nat__Xnat__Xinducts__1(X38))))
| ~ hBOOL(hAPP(X38,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(variable_rename,[status(thm)],[c_0_977]) ).
fof(c_0_1610,plain,
! [X37,X38] :
( hBOOL(hAPP(X38,X37))
| ~ hBOOL(hAPP(X38,c_Suc(v_sko__Nat__Xnat__Xinduct__1(X38))))
| ~ hBOOL(hAPP(X38,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(variable_rename,[status(thm)],[c_0_978]) ).
fof(c_0_1611,plain,
! [X37,X38] :
( hBOOL(hAPP(X38,X37))
| ~ hBOOL(hAPP(X38,c_Suc(v_sko__List__Xupt__Xinduct__1(X38))))
| ~ hBOOL(hAPP(X38,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(variable_rename,[status(thm)],[c_0_979]) ).
fof(c_0_1612,plain,
! [X37,X38] :
( hBOOL(hAPP(X38,X37))
| ~ hBOOL(hAPP(X38,c_Suc(v_sko__List__Xreplicate__Xinduct__1(X38))))
| ~ hBOOL(hAPP(X38,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(variable_rename,[status(thm)],[c_0_980]) ).
fof(c_0_1613,plain,
! [X28,X29] :
( hBOOL(hAPP(X29,X28))
| ~ hBOOL(hAPP(X29,c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X29))))
| ~ hBOOL(hAPP(X29,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(variable_rename,[status(thm)],[c_0_981]) ).
fof(c_0_1614,plain,
! [X37,X38] :
( hBOOL(hAPP(X38,X37))
| ~ hBOOL(hAPP(X38,c_Suc(v_sko__List__Xlexn__Xinduct__1(X38))))
| ~ hBOOL(hAPP(X38,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(variable_rename,[status(thm)],[c_0_982]) ).
fof(c_0_1615,plain,
! [X28,X29,X30] :
( hBOOL(hAPP(hAPP(X30,X28),X29))
| c_HOL_Oord__class_Oless(X28,X29,tc_nat)
| X29 = X28
| c_HOL_Oord__class_Oless(X29,X28,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_983])])]) ).
fof(c_0_1616,plain,
! [X14,X15,X16] :
( c_HOL_Otimes__class_Otimes(c_Suc(X16),X15,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X16),X14,tc_nat)
| X15 = X14 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_984])])]) ).
fof(c_0_1617,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X6)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X6),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X6),X5,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_985]) ).
fof(c_0_1618,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Oordered__semidom(X6)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_Nat_Osemiring__1__class_Oof__nat(X5,X6),X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_986]) ).
fof(c_0_1619,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Oidom(X20)
| ~ class_Int_Onumber__ring(X20)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X19),X18) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X19),X17)
| X18 = X17 ),
inference(variable_rename,[status(thm)],[c_0_987]) ).
fof(c_0_1620,plain,
! [X13,X14,X15] :
( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X15),X13),hAPP(hAPP(c_Lambda_OdB_OApp,X14),X13))
| ~ c_Lambda_Obeta(X15,X14) ),
inference(variable_rename,[status(thm)],[c_0_988]) ).
fof(c_0_1621,plain,
! [X13,X14,X15] :
( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X13),X15),hAPP(hAPP(c_Lambda_OdB_OApp,X13),X14))
| ~ c_Lambda_Obeta(X15,X14) ),
inference(variable_rename,[status(thm)],[c_0_989]) ).
fof(c_0_1622,plain,
! [X24,X25,X26] :
( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_Olift,X25),X26),hAPP(hAPP(c_Lambda_Olift,X24),X26))
| ~ c_Lambda_Obeta(X25,X24) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_990])])]) ).
fof(c_0_1623,plain,
! [X4,X5,X6] :
( ~ class_Orderings_Opreorder(X6)
| ~ c_HOL_Oord__class_Oless(X4,X5,X6)
| ~ c_HOL_Oord__class_Oless(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_991]) ).
fof(c_0_1624,plain,
! [X17,X18,X19] :
( ~ class_Orderings_Opreorder(X19)
| ~ c_HOL_Oord__class_Oless(X17,X18,X19)
| ~ c_HOL_Oord__class_Oless(X18,X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_992]) ).
fof(c_0_1625,plain,
! [X17,X18,X19] :
( ~ class_Orderings_Olinorder(X19)
| ~ c_HOL_Oord__class_Oless(X18,X17,X19)
| ~ c_HOL_Oord__class_Oless(X17,X18,X19) ),
inference(variable_rename,[status(thm)],[c_0_993]) ).
fof(c_0_1626,plain,
! [X4,X5,X6] :
( ~ class_Orderings_Oorder(X6)
| ~ c_HOL_Oord__class_Oless(X5,X4,X6)
| ~ c_HOL_Oord__class_Oless(X4,X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_994]) ).
fof(c_0_1627,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_995]) ).
fof(c_0_1628,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_HOL_Oord__class_Oless(X4,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X4),c_HOL_Oone__class_Oone(X5)),X5) ),
inference(variable_rename,[status(thm)],[c_0_996]) ).
fof(c_0_1629,plain,
! [X4,X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X4,X5,X6),X4,X6) = X5
| X4 = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_997]) ).
fof(c_0_1630,plain,
! [X4,X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X5,X4,X6),X4,X6) = X5
| X4 = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_998]) ).
fof(c_0_1631,plain,
! [X12,X13,X14,X15] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X15)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X13),X14) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X12),X14)
| X13 = X12 ),
inference(variable_rename,[status(thm)],[c_0_999]) ).
fof(c_0_1632,plain,
! [X12,X13,X14,X15] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X15)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X13) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X12)
| X13 = X12 ),
inference(variable_rename,[status(thm)],[c_0_1000]) ).
fof(c_0_1633,plain,
! [X12,X13,X14,X15] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X15)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X13) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X12)
| X13 = X12 ),
inference(variable_rename,[status(thm)],[c_0_1001]) ).
fof(c_0_1634,plain,
! [X4,X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X4,X5,X6),X4,X6) = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_1002]) ).
fof(c_0_1635,plain,
! [X4,X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X4,X6),X4,X6) = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_1003]) ).
fof(c_0_1636,plain,
! [X14,X15,X16] :
( c_HOL_Otimes__class_Otimes(X16,X15,tc_nat) != c_HOL_Otimes__class_Otimes(X16,X14,tc_nat)
| X15 = X14
| X16 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1004]) ).
fof(c_0_1637,plain,
! [X14,X15,X16] :
( c_HOL_Otimes__class_Otimes(X16,X15,tc_nat) != c_HOL_Otimes__class_Otimes(X16,X14,tc_nat)
| X16 = c_HOL_Ozero__class_Ozero(tc_nat)
| X15 = X14 ),
inference(variable_rename,[status(thm)],[c_0_1005]) ).
fof(c_0_1638,plain,
! [X14,X15,X16] :
( c_HOL_Otimes__class_Otimes(X15,X16,tc_nat) != c_HOL_Otimes__class_Otimes(X14,X16,tc_nat)
| X16 = c_HOL_Ozero__class_Ozero(tc_nat)
| X15 = X14 ),
inference(variable_rename,[status(thm)],[c_0_1006]) ).
fof(c_0_1639,plain,
! [X4,X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X5,X4,X6),X4,X6) = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_1007]) ).
fof(c_0_1640,plain,
! [X14,X15,X16] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X16)),X14),X15) = c_Lambda_OdB_OVar(X16)
| X16 = X15
| c_HOL_Oord__class_Oless(X15,X16,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1008]) ).
fof(c_0_1641,plain,
! [X3,X4] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,tc_nat)
| X4 = X3 ),
inference(variable_rename,[status(thm)],[c_0_1009]) ).
fof(c_0_1642,plain,
! [X3,X4] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,tc_nat)
| X4 = X3
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1010]) ).
fof(c_0_1643,plain,
! [X17,X18] :
( X18 = X17
| ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X17,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X18,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1011]) ).
fof(c_0_1644,plain,
! [X6,X7] :
( X7 = X6
| ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X7,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1012]) ).
fof(c_0_1645,plain,
! [X17,X18] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X18,tc_nat)
| X18 = X17
| ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X17,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1013]) ).
fof(c_0_1646,plain,
! [X17,X18] :
( X18 = X17
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X18,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X17,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1014]) ).
fof(c_0_1647,plain,
! [X17,X18] :
( X18 = X17
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X18,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X17,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1015]) ).
fof(c_0_1648,plain,
! [X14,X15,X16] :
( ~ class_Ring__and__Field_Odvd(X16)
| c_Ring__and__Field_Odvd__class_Odvd(X15,c_HOL_Otimes__class_Otimes(X15,X14,X16),X16) ),
inference(variable_rename,[status(thm)],[c_0_1016]) ).
fof(c_0_1649,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X6)
| c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Otimes__class_Otimes(X5,X4,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1017]) ).
fof(c_0_1650,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X6)
| c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Otimes__class_Otimes(X4,X5,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1018]) ).
fof(c_0_1651,plain,
! [X17] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X17,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1019]) ).
fof(c_0_1652,plain,
! [X17,X18] :
( c_HOL_Oord__class_Oless(X17,X17,tc_nat)
| hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X17)),X18),X17) = X18 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1020])])]) ).
fof(c_0_1653,plain,
! [X50,X51,X52,X53] :
( c_Type_Otyping(X52,X50,X53)
| ~ c_Lambda_Obeta(X51,X50)
| ~ c_Type_Otyping(X52,X51,X53) ),
inference(variable_rename,[status(thm)],[c_0_1021]) ).
fof(c_0_1654,plain,
! [X18,X19] : c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X19,X18,tc_nat),X19,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_1022]) ).
fof(c_0_1655,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_1023]) ).
fof(c_0_1656,plain,
! [X4,X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| c_Divides_Odiv__class_Omod(X4,X5,X6) != c_HOL_Ozero__class_Ozero(X6)
| c_Ring__and__Field_Odvd__class_Odvd(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_1024]) ).
fof(c_0_1657,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_1025]) ).
fof(c_0_1658,plain,
! [X4,X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| c_Divides_Odiv__class_Omod(X4,X5,X6) = c_HOL_Ozero__class_Ozero(X6)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_1026]) ).
fof(c_0_1659,plain,
! [X28,X29] :
( hBOOL(hAPP(X29,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X29,c_Suc(c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X29))))
| ~ hBOOL(hAPP(X29,X28)) ),
inference(variable_rename,[status(thm)],[c_0_1027]) ).
fof(c_0_1660,plain,
! [X28,X29] :
( hBOOL(hAPP(X29,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X29,c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X29)))
| ~ hBOOL(hAPP(X29,X28)) ),
inference(variable_rename,[status(thm)],[c_0_1028]) ).
fof(c_0_1661,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_1029]) ).
fof(c_0_1662,plain,
! [X17,X18] :
( c_HOL_Oord__class_Oless(c_Suc(X17),c_Suc(X18),tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,X18,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1030]) ).
fof(c_0_1663,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_1031]) ).
fof(c_0_1664,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_1032]) ).
fof(c_0_1665,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_1033]) ).
fof(c_0_1666,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_1034]) ).
fof(c_0_1667,plain,
! [X14,X15,X16] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X15) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X14)
| X15 = X14 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1035])])]) ).
fof(c_0_1668,plain,
! [X14,X15,X16] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X16) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X16)
| X15 = X14 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1036])])]) ).
fof(c_0_1669,plain,
! [X17,X18,X19] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X19),X18) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X19),X17)
| X18 = X17 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1037])])]) ).
fof(c_0_1670,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_1038]) ).
fof(c_0_1671,plain,
! [X8,X9] : c_Lambda_Osubstn(X8,X9,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,X8),X9),c_HOL_Ozero__class_Ozero(tc_nat)),
inference(variable_rename,[status(thm)],[c_0_1039]) ).
fof(c_0_1672,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_1040]) ).
fof(c_0_1673,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X7)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X6,X7),c_HOL_Ozero__class_Ozero(X7),X7) ),
inference(variable_rename,[status(thm)],[c_0_1041]) ).
fof(c_0_1674,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_1042]) ).
fof(c_0_1675,plain,
! [X6,X7] :
( c_Divides_Odiv__class_Odiv(X7,X6,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,X6,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1043]) ).
fof(c_0_1676,plain,
! [X6,X7] :
( c_Divides_Odiv__class_Omod(X7,X6,tc_nat) = X7
| ~ c_HOL_Oord__class_Oless(X7,X6,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1044]) ).
fof(c_0_1677,plain,
! [X14,X15] :
( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X15)),X14) = c_Lambda_OdB_OVar(X15)
| ~ c_HOL_Oord__class_Oless(X15,X14,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1045]) ).
fof(c_0_1678,plain,
! [X37,X38] :
( hBOOL(hAPP(X38,X37))
| hBOOL(hAPP(X38,v_sko__List__Xupt__Xinduct__1(X38)))
| ~ hBOOL(hAPP(X38,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(variable_rename,[status(thm)],[c_0_1046]) ).
fof(c_0_1679,plain,
! [X37,X38] :
( hBOOL(hAPP(X38,X37))
| hBOOL(hAPP(X38,v_sko__Nat__Xnat__Xinduct__1(X38)))
| ~ hBOOL(hAPP(X38,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(variable_rename,[status(thm)],[c_0_1047]) ).
fof(c_0_1680,plain,
! [X37,X38] :
( hBOOL(hAPP(X38,X37))
| hBOOL(hAPP(X38,v_sko__Nat__Xnat__Xinducts__1(X38)))
| ~ hBOOL(hAPP(X38,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(variable_rename,[status(thm)],[c_0_1048]) ).
fof(c_0_1681,plain,
! [X37,X38] :
( hBOOL(hAPP(X38,X37))
| hBOOL(hAPP(X38,v_sko__List__Xreplicate__Xinduct__1(X38)))
| ~ hBOOL(hAPP(X38,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(variable_rename,[status(thm)],[c_0_1049]) ).
fof(c_0_1682,plain,
! [X28,X29] :
( hBOOL(hAPP(X29,X28))
| hBOOL(hAPP(X29,c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X29)))
| ~ hBOOL(hAPP(X29,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(variable_rename,[status(thm)],[c_0_1050]) ).
fof(c_0_1683,plain,
! [X37,X38] :
( hBOOL(hAPP(X38,X37))
| hBOOL(hAPP(X38,v_sko__List__Xlexn__Xinduct__1(X38)))
| ~ hBOOL(hAPP(X38,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(variable_rename,[status(thm)],[c_0_1051]) ).
fof(c_0_1684,plain,
! [X5,X6,X7] :
( ~ class_Ring__and__Field_Ozero__neq__one(X7)
| ~ class_Ring__and__Field_Ono__zero__divisors(X7)
| ~ class_Ring__and__Field_Omult__zero(X7)
| ~ class_Power_Opower(X7)
| c_Power_Opower__class_Opower(X6,X5,X7) != c_HOL_Ozero__class_Ozero(X7)
| X6 = c_HOL_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[c_0_1052]) ).
fof(c_0_1685,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ozero__neq__one(X5)
| ~ class_Ring__and__Field_Ono__zero__divisors(X5)
| ~ class_Ring__and__Field_Omult__zero(X5)
| ~ class_Power_Opower(X5)
| c_Power_Opower__class_Opower(X4,c_HOL_Ozero__class_Ozero(tc_nat),X5) != c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1053]) ).
fof(c_0_1686,plain,
! [X47] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X47),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X47,tc_Lambda_OdB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
inference(variable_rename,[status(thm)],[c_0_1054]) ).
fof(c_0_1687,plain,
! [X14,X15,X16] :
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X16),X14,X15) = c_Lambda_OdB_OVar(X16)
| X16 = X15
| c_HOL_Oord__class_Oless(X15,X16,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1055]) ).
fof(c_0_1688,plain,
! [X17,X18,X19] :
( ~ class_Orderings_Olinorder(X19)
| X18 = X17
| c_HOL_Oord__class_Oless(X18,X17,X19)
| c_HOL_Oord__class_Oless(X17,X18,X19) ),
inference(variable_rename,[status(thm)],[c_0_1056]) ).
fof(c_0_1689,plain,
! [X17,X18,X19] :
( ~ class_Orderings_Olinorder(X19)
| c_HOL_Oord__class_Oless(X17,X18,X19)
| X18 = X17
| c_HOL_Oord__class_Oless(X18,X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_1057]) ).
fof(c_0_1690,plain,
! [X17,X18,X19] :
( ~ class_Orderings_Olinorder(X19)
| c_HOL_Oord__class_Oless(X17,X18,X19)
| c_HOL_Oord__class_Oless(X18,X17,X19)
| X18 = X17 ),
inference(variable_rename,[status(thm)],[c_0_1058]) ).
fof(c_0_1691,plain,
! [X17,X18,X19] :
( ~ class_Orderings_Olinorder(X19)
| X18 = X17
| c_HOL_Oord__class_Oless(X17,X18,X19)
| c_HOL_Oord__class_Oless(X18,X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_1059]) ).
fof(c_0_1692,plain,
! [X17,X18,X19] :
( ~ class_Ring__and__Field_Oordered__idom(X19)
| c_HOL_Oord__class_Oless(X17,X18,X19)
| c_HOL_Oord__class_Oless(X18,X17,X19)
| X18 = X17 ),
inference(variable_rename,[status(thm)],[c_0_1060]) ).
fof(c_0_1693,plain,
! [X56,X57,X58,X59] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X59),X57) != hAPP(hAPP(c_Lambda_OdB_OApp,X58),X56)
| X57 = X56 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1061])])]) ).
fof(c_0_1694,plain,
! [X56,X57,X58,X59] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X59),X57) != hAPP(hAPP(c_Lambda_OdB_OApp,X58),X56)
| X59 = X58 ),
inference(variable_rename,[status(thm)],[c_0_1062]) ).
fof(c_0_1695,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Osemiring__1(X7)
| c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X6),X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),c_HOL_Oone__class_Oone(X7)),c_Nat_Osemiring__1__class_Oof__nat(X6,X7)) ),
inference(variable_rename,[status(thm)],[c_0_1063]) ).
fof(c_0_1696,plain,
! [X17,X18,X19] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X19)
| c_HOL_Otimes__class_Otimes(X18,X17,X19) = c_HOL_Otimes__class_Otimes(X17,X18,X19) ),
inference(variable_rename,[status(thm)],[c_0_1064]) ).
fof(c_0_1697,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X6)
| c_HOL_Otimes__class_Otimes(X5,X4,X6) = c_HOL_Otimes__class_Otimes(X4,X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_1065]) ).
fof(c_0_1698,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_1066]) ).
fof(c_0_1699,plain,
! [X17] :
( c_HOL_Oord__class_Oless(X17,X17,tc_nat)
| c_HOL_Oord__class_Oless(X17,c_Suc(X17),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1067]) ).
fof(c_0_1700,plain,
! [X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(variable_rename,[status(thm)],[c_0_1068]) ).
fof(c_0_1701,plain,
! [X6,X7] : c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat),
inference(variable_rename,[status(thm)],[c_0_1069]) ).
fof(c_0_1702,plain,
! [X6,X7] : c_HOL_Otimes__class_Otimes(X7,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X6,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1070]) ).
fof(c_0_1703,plain,
! [X17,X18,X19] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X19)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X19),X18),X17) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X19),X17),X18) ),
inference(variable_rename,[status(thm)],[c_0_1071]) ).
fof(c_0_1704,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X6)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X5),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X5) ),
inference(variable_rename,[status(thm)],[c_0_1072]) ).
fof(c_0_1705,plain,
! [X12,X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X14)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X14),X13),X12) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X14),X12),X13) ),
inference(variable_rename,[status(thm)],[c_0_1073]) ).
fof(c_0_1706,plain,
! [X6] :
( X6 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X6,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1074]) ).
fof(c_0_1707,plain,
! [X14,X15] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X15)),X14),X15) = X14,
inference(variable_rename,[status(thm)],[c_0_1075]) ).
fof(c_0_1708,plain,
! [X27,X28,X29] :
( hAPP(X28,X27) = X29
| ~ c_Type_Otyping(X28,c_Lambda_OdB_OVar(X27),X29) ),
inference(variable_rename,[status(thm)],[c_0_1076]) ).
fof(c_0_1709,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_1077]) ).
fof(c_0_1710,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X6)
| c_HOL_Otimes__class_Otimes(X5,X4,X6) != c_HOL_Ozero__class_Ozero(X6)
| X4 = c_HOL_Ozero__class_Ozero(X6)
| X5 = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_1078]) ).
fof(c_0_1711,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X6)
| c_HOL_Otimes__class_Otimes(X5,X4,X6) != c_HOL_Ozero__class_Ozero(X6)
| X4 = c_HOL_Ozero__class_Ozero(X6)
| X5 = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_1079]) ).
fof(c_0_1712,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X6)
| c_HOL_Otimes__class_Otimes(X5,X4,X6) != c_HOL_Ozero__class_Ozero(X6)
| X5 = c_HOL_Ozero__class_Ozero(X6)
| X4 = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_1080]) ).
fof(c_0_1713,plain,
! [X17,X18] :
( c_HOL_Oord__class_Oless(X17,X18,tc_nat)
| c_HOL_Oord__class_Oless(X18,X17,tc_nat)
| X18 = X17 ),
inference(variable_rename,[status(thm)],[c_0_1081]) ).
fof(c_0_1714,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_1082]) ).
fof(c_0_1715,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| X4 = c_HOL_Ozero__class_Ozero(X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X5),X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_1083]) ).
fof(c_0_1716,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_1084]) ).
fof(c_0_1717,plain,
! [X17,X18] :
( c_Power_Opower__class_Opower(X17,X18,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X17 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X18 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1085]) ).
fof(c_0_1718,plain,
! [X6,X7] : c_HOL_Otimes__class_Otimes(X7,X6,tc_nat) = c_HOL_Otimes__class_Otimes(X6,X7,tc_nat),
inference(variable_rename,[status(thm)],[c_0_1086]) ).
fof(c_0_1719,plain,
! [X5,X6,X7] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X7)
| c_Power_Opower__class_Opower(X6,X5,X7) != c_HOL_Ozero__class_Ozero(X7)
| X6 = c_HOL_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[c_0_1087]) ).
fof(c_0_1720,plain,
! [X17,X18,X19] :
( ~ class_Ring__and__Field_Oidom(X19)
| ~ class_Int_Onumber__ring(X19)
| X17 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X19),X17),X18)
| X18 = c_HOL_Ozero__class_Ozero(X19) ),
inference(variable_rename,[status(thm)],[c_0_1088]) ).
fof(c_0_1721,plain,
! [X6,X7] :
( c_HOL_Otimes__class_Otimes(X7,X6,tc_nat) != 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_1089]) ).
fof(c_0_1722,plain,
! [X6,X7] :
( c_HOL_Otimes__class_Otimes(X7,X6,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X6 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1090])])]) ).
fof(c_0_1723,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X4),X4) != c_HOL_Ozero__class_Ozero(X5)
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1091]) ).
fof(c_0_1724,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_1092]) ).
fof(c_0_1725,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_1093]) ).
fof(c_0_1726,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Ozero__neq__one(X6)
| ~ class_Ring__and__Field_Ono__zero__divisors(X6)
| ~ class_Ring__and__Field_Omult__zero(X6)
| ~ class_Power_Opower(X6)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X6),X5,X6) = c_HOL_Ozero__class_Ozero(X6)
| X5 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1094]) ).
fof(c_0_1727,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_1095]) ).
fof(c_0_1728,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_1096])])]) ).
fof(c_0_1729,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_1097]) ).
fof(c_0_1730,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_1098])])]) ).
fof(c_0_1731,plain,
! [X6,X7] :
( c_HOL_Otimes__class_Otimes(X7,X6,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X6 = c_HOL_Ozero__class_Ozero(tc_nat)
| X7 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1099]) ).
fof(c_0_1732,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_1100 ).
fof(c_0_1733,plain,
! [X17,X18] :
( ~ class_Orderings_Opreorder(X18)
| ~ c_HOL_Oord__class_Oless(X17,X17,X18) ),
inference(variable_rename,[status(thm)],[c_0_1101]) ).
fof(c_0_1734,plain,
! [X17,X18] :
( ~ class_Orderings_Olinorder(X18)
| ~ c_HOL_Oord__class_Oless(X17,X17,X18) ),
inference(variable_rename,[status(thm)],[c_0_1102]) ).
fof(c_0_1735,plain,
! [X17,X18] :
( ~ class_Orderings_Oorder(X18)
| ~ c_HOL_Oord__class_Oless(X17,X17,X18) ),
inference(variable_rename,[status(thm)],[c_0_1103]) ).
fof(c_0_1736,plain,
! [X6,X7] :
( X7 != c_HOL_Otimes__class_Otimes(X7,X6,tc_nat)
| X7 = c_HOL_Ozero__class_Ozero(tc_nat)
| X6 = c_HOL_Oone__class_Oone(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1104]) ).
fof(c_0_1737,plain,
! [X6] :
( X6 = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X6,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1105]) ).
fof(c_0_1738,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_1106]) ).
fof(c_0_1739,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_1107]) ).
fof(c_0_1740,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_1108]) ).
fof(c_0_1741,plain,
! [X6,X7] :
( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X7,X6,tc_nat)
| X6 = c_HOL_Oone__class_Oone(tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1109])])]) ).
fof(c_0_1742,plain,
! [X6,X7] :
( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X7,X6,tc_nat)
| X7 = c_HOL_Oone__class_Oone(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1110]) ).
fof(c_0_1743,plain,
! [X6,X7] :
( c_HOL_Otimes__class_Otimes(X7,X6,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
| X6 = c_HOL_Oone__class_Oone(tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1111])])]) ).
fof(c_0_1744,plain,
! [X6,X7] :
( c_HOL_Otimes__class_Otimes(X7,X6,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
| X7 = c_HOL_Oone__class_Oone(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1112]) ).
fof(c_0_1745,plain,
! [X5] : ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1113]) ).
fof(c_0_1746,plain,
! [X6] : ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1114]) ).
fof(c_0_1747,plain,
! [X63,X64,X65] :
( X64 = X63
| ~ c_fequal(X64,X63,X65) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1115])])]) ).
fof(c_0_1748,plain,
! [X44,X45] : c_Type_Otyping(X45,c_Lambda_OdB_OVar(X44),hAPP(X45,X44)),
inference(variable_rename,[status(thm)],[c_0_1116]) ).
fof(c_0_1749,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Osemiring__0(X6)
| ~ class_Power_Opower(X6)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X6),c_Suc(X5),X6) = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_1117]) ).
fof(c_0_1750,axiom,
c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_1118 ).
fof(c_0_1751,plain,
! [X5] : ~ c_HOL_Oord__class_Oless(X5,X5,tc_nat),
inference(variable_rename,[status(thm)],[c_0_1119]) ).
fof(c_0_1752,plain,
! [X17] : ~ c_HOL_Oord__class_Oless(X17,X17,tc_nat),
inference(variable_rename,[status(thm)],[c_0_1120]) ).
fof(c_0_1753,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Osemiring__0(X6)
| ~ class_Power_Opower(X6)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X6),X5,X6) = c_HOL_Ozero__class_Ozero(X6)
| X5 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1121]) ).
fof(c_0_1754,plain,
! [X24] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X24)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X24)) ),
inference(variable_rename,[status(thm)],[c_0_1122]) ).
fof(c_0_1755,plain,
! [X4] :
( ~ class_Ring__and__Field_Osemiring__0(X4)
| ~ class_Power_Opower(X4)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(tc_nat),X4) = c_HOL_Oone__class_Oone(X4) ),
inference(variable_rename,[status(thm)],[c_0_1123]) ).
fof(c_0_1756,plain,
! [X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_HOL_Ozero__class_Ozero(X4)),c_HOL_Ozero__class_Ozero(X4)) = c_HOL_Ozero__class_Ozero(X4) ),
inference(variable_rename,[status(thm)],[c_0_1124]) ).
fof(c_0_1757,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_1125 ).
fof(c_0_1758,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_1126 ).
fof(c_0_1759,plain,
! [X47] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X47)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X47)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
inference(variable_rename,[status(thm)],[c_0_1127]) ).
fof(c_0_1760,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_1128]) ).
fof(c_0_1761,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_1129])])]) ).
fof(c_0_1762,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_1130])])]) ).
fof(c_0_1763,plain,
! [X17,X18] :
( X17 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X18)
| X18 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1131]) ).
fof(c_0_1764,axiom,
c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
c_0_1132 ).
fof(c_0_1765,plain,
! [X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oone__class_Oone(X4),X4) ),
inference(variable_rename,[status(thm)],[c_0_1133]) ).
fof(c_0_1766,plain,
! [X17,X18] :
( ~ class_Ring__and__Field_Oidom(X18)
| ~ class_Int_Onumber__ring(X18)
| X17 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X18),X17),c_HOL_Ozero__class_Ozero(X18)) ),
inference(variable_rename,[status(thm)],[c_0_1134]) ).
fof(c_0_1767,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Ozero__class_Ozero(X5)),X4) = X4 ),
inference(variable_rename,[status(thm)],[c_0_1135]) ).
fof(c_0_1768,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Omonoid__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Ozero__class_Ozero(X5)),X4) = X4 ),
inference(variable_rename,[status(thm)],[c_0_1136]) ).
fof(c_0_1769,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Ozero__class_Ozero(X5)),X4) = X4 ),
inference(variable_rename,[status(thm)],[c_0_1137]) ).
fof(c_0_1770,plain,
! [X17,X18] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X18),c_HOL_Ozero__class_Ozero(X18)),X17) = X17 ),
inference(variable_rename,[status(thm)],[c_0_1138]) ).
fof(c_0_1771,plain,
! [X5] : c_Power_Opower__class_Opower(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X5,tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(variable_rename,[status(thm)],[c_0_1139]) ).
fof(c_0_1772,plain,
! [X6] : c_Power_Opower__class_Opower(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X6,tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(variable_rename,[status(thm)],[c_0_1140]) ).
fof(c_0_1773,plain,
! [X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X5),X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1141]) ).
fof(c_0_1774,plain,
! [X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X5),X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1142]) ).
fof(c_0_1775,plain,
! [X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Odiv(X4,c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1143]) ).
fof(c_0_1776,plain,
! [X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(X4,c_HOL_Oone__class_Oone(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1144]) ).
fof(c_0_1777,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1145]) ).
fof(c_0_1778,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1146]) ).
fof(c_0_1779,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X5)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1147]) ).
fof(c_0_1780,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1148]) ).
fof(c_0_1781,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Omult__zero(X5)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1149]) ).
fof(c_0_1782,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Omult__zero(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1150]) ).
fof(c_0_1783,plain,
! [X17,X18] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X18),X17,X18) = c_HOL_Ozero__class_Ozero(X18) ),
inference(variable_rename,[status(thm)],[c_0_1151]) ).
fof(c_0_1784,plain,
! [X5,X6] :
( ~ class_OrderedGroup_Omonoid__mult(X6)
| c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X6),X5,X6) = c_HOL_Oone__class_Oone(X6) ),
inference(variable_rename,[status(thm)],[c_0_1152]) ).
fof(c_0_1785,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_1153 ).
fof(c_0_1786,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_1154 ).
fof(c_0_1787,plain,
! [X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Odiv(X4,X4,X5) = c_HOL_Oone__class_Oone(X5)
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1155]) ).
fof(c_0_1788,plain,
! [X17,X18] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
| c_Power_Opower__class_Opower(X17,c_HOL_Ozero__class_Ozero(tc_nat),X18) = c_HOL_Oone__class_Oone(X18) ),
inference(variable_rename,[status(thm)],[c_0_1156]) ).
fof(c_0_1789,plain,
! [X4,X5] :
( ~ class_Power_Opower(X5)
| c_Power_Opower__class_Opower(X4,c_HOL_Ozero__class_Ozero(tc_nat),X5) = c_HOL_Oone__class_Oone(X5) ),
inference(variable_rename,[status(thm)],[c_0_1157]) ).
fof(c_0_1790,plain,
! [X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(X4,c_HOL_Ozero__class_Ozero(X5),X5) = X4 ),
inference(variable_rename,[status(thm)],[c_0_1158]) ).
fof(c_0_1791,plain,
! [X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Odiv(X4,c_HOL_Oone__class_Oone(X5),X5) = X4 ),
inference(variable_rename,[status(thm)],[c_0_1159]) ).
fof(c_0_1792,plain,
! [X17,X18] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X18),X17,X18) = X17 ),
inference(variable_rename,[status(thm)],[c_0_1160]) ).
fof(c_0_1793,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X5),X4,X5) = X4 ),
inference(variable_rename,[status(thm)],[c_0_1161]) ).
fof(c_0_1794,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X5),X4,X5) = X4 ),
inference(variable_rename,[status(thm)],[c_0_1162]) ).
fof(c_0_1795,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Oone__class_Oone(X5),X5) = X4 ),
inference(variable_rename,[status(thm)],[c_0_1163]) ).
fof(c_0_1796,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Oone__class_Oone(X5),X5) = X4 ),
inference(variable_rename,[status(thm)],[c_0_1164]) ).
fof(c_0_1797,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X5),X4,X5) = X4 ),
inference(variable_rename,[status(thm)],[c_0_1165]) ).
fof(c_0_1798,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_1166 ).
fof(c_0_1799,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X5),X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_1167]) ).
fof(c_0_1800,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1168]) ).
fof(c_0_1801,plain,
! [X6] : c_Divides_Odiv__class_Omod(X6,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_1169]) ).
fof(c_0_1802,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X4),c_HOL_Ozero__class_Ozero(X5)) = X4 ),
inference(variable_rename,[status(thm)],[c_0_1170]) ).
fof(c_0_1803,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Omonoid__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X4),c_HOL_Ozero__class_Ozero(X5)) = X4 ),
inference(variable_rename,[status(thm)],[c_0_1171]) ).
fof(c_0_1804,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X4),c_HOL_Ozero__class_Ozero(X5)) = X4 ),
inference(variable_rename,[status(thm)],[c_0_1172]) ).
fof(c_0_1805,plain,
! [X6] : c_Divides_Odiv__class_Odiv(X6,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = X6,
inference(variable_rename,[status(thm)],[c_0_1173]) ).
fof(c_0_1806,plain,
! [X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(X4,X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1174]) ).
fof(c_0_1807,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| c_Power_Opower__class_Opower(X4,c_HOL_Oone__class_Oone(tc_nat),X5) = X4 ),
inference(variable_rename,[status(thm)],[c_0_1175]) ).
fof(c_0_1808,plain,
! [X17,X18] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
| c_Power_Opower__class_Opower(X17,c_HOL_Oone__class_Oone(tc_nat),X18) = X17 ),
inference(variable_rename,[status(thm)],[c_0_1176]) ).
fof(c_0_1809,plain,
! [X14] : c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X14,tc_nat),
inference(variable_rename,[status(thm)],[c_0_1177]) ).
fof(c_0_1810,plain,
! [X56,X57,X58] : hAPP(hAPP(c_Lambda_OdB_OApp,X58),X57) != c_Lambda_OdB_OVar(X56),
inference(variable_rename,[status(thm)],[c_0_1178]) ).
fof(c_0_1811,plain,
! [X56,X57,X58] : c_Lambda_OdB_OVar(X56) != hAPP(hAPP(c_Lambda_OdB_OApp,X58),X57),
inference(variable_rename,[status(thm)],[c_0_1179]) ).
fof(c_0_1812,plain,
! [X53,X54,X55] : c_Lambda_OdB_OAbs(X53) != hAPP(hAPP(c_Lambda_OdB_OApp,X55),X54),
inference(variable_rename,[status(thm)],[c_0_1180]) ).
fof(c_0_1813,plain,
! [X53,X54,X55] : hAPP(hAPP(c_Lambda_OdB_OApp,X55),X54) != c_Lambda_OdB_OAbs(X53),
inference(variable_rename,[status(thm)],[c_0_1181]) ).
fof(c_0_1814,plain,
! [X17] : c_Power_Opower__class_Opower(X17,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(variable_rename,[status(thm)],[c_0_1182]) ).
fof(c_0_1815,plain,
! [X17,X18] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X18)
| c_HOL_Otimes__class_Otimes(X17,X17,X18) = X17 ),
inference(variable_rename,[status(thm)],[c_0_1183]) ).
fof(c_0_1816,plain,
! [X17] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X17),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1184]) ).
fof(c_0_1817,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_1185]) ).
fof(c_0_1818,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X4,X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_1186]) ).
fof(c_0_1819,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat),
c_0_1187 ).
fof(c_0_1820,axiom,
c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
c_0_1188 ).
fof(c_0_1821,plain,
! [X21,X22] : c_List_Olistsp(X21,c_List_Olist_ONil(X22),X22),
inference(variable_rename,[status(thm)],[c_0_1189]) ).
fof(c_0_1822,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_1190]) ).
fof(c_0_1823,plain,
! [X5] : c_HOL_Oord__class_Oless(X5,c_Suc(X5),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1191]) ).
fof(c_0_1824,plain,
! [X17] : c_HOL_Oord__class_Oless(X17,c_Suc(X17),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1192]) ).
fof(c_0_1825,axiom,
c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
c_0_1193 ).
fof(c_0_1826,plain,
! [X20] : c_Power_Opower__class_Opower(X20,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat),
inference(variable_rename,[status(thm)],[c_0_1194]) ).
fof(c_0_1827,plain,
! [X5] : c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_1195]) ).
fof(c_0_1828,plain,
! [X6] : c_HOL_Otimes__class_Otimes(X6,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_1196]) ).
fof(c_0_1829,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_1197 ).
fof(c_0_1830,plain,
! [X5] : c_HOL_Otimes__class_Otimes(X5,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X5,
inference(variable_rename,[status(thm)],[c_0_1198]) ).
fof(c_0_1831,plain,
! [X5] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X5,tc_nat) = X5,
inference(variable_rename,[status(thm)],[c_0_1199]) ).
fof(c_0_1832,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_1200]) ).
fof(c_0_1833,plain,
! [X17,X18] : c_fequal(X17,X17,X18),
inference(variable_rename,[status(thm)],[c_0_1201]) ).
fof(c_0_1834,plain,
! [X6,X7,X8] :
( ~ class_Nat_Osemiring__char__0(X8)
| c_Nat_Osemiring__1__class_Oof__nat(X7,X8) != c_Nat_Osemiring__1__class_Oof__nat(X6,X8)
| X7 = X6 ),
inference(variable_rename,[status(thm)],[c_0_1202]) ).
fof(c_0_1835,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_1203]) ).
fof(c_0_1836,plain,
! [X17] : c_Ring__and__Field_Odvd__class_Odvd(X17,X17,tc_nat),
inference(variable_rename,[status(thm)],[c_0_1204]) ).
fof(c_0_1837,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_1205]) ).
fof(c_0_1838,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_1206]) ).
fof(c_0_1839,plain,
! [X17] : X17 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),c_HOL_Ozero__class_Ozero(tc_nat)),
inference(variable_rename,[status(thm)],[c_0_1207]) ).
fof(c_0_1840,plain,
! [X8,X9] :
( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X9),c_Lambda_OdB_OAbs(X8))
| ~ c_Lambda_Obeta(X9,X8) ),
inference(variable_rename,[status(thm)],[c_0_1208]) ).
fof(c_0_1841,plain,
! [X61,X62] :
( class_Orderings_Oorder(tc_fun(X61,X62))
| ~ class_Orderings_Oorder(X62) ),
inference(variable_rename,[status(thm)],[c_0_1209]) ).
fof(c_0_1842,plain,
! [X61,X62] :
( class_Orderings_Opreorder(tc_fun(X61,X62))
| ~ class_Orderings_Opreorder(X62) ),
inference(variable_rename,[status(thm)],[c_0_1210]) ).
fof(c_0_1843,plain,
! [X10,X11] : ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X11),X10),
inference(variable_rename,[status(thm)],[c_0_1211]) ).
fof(c_0_1844,plain,
! [X4] :
( ~ class_Ring__and__Field_Osemiring__1(X4)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(variable_rename,[status(thm)],[c_0_1212]) ).
fof(c_0_1845,plain,
! [X4] :
( ~ class_Ring__and__Field_Osemiring__1(X4)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X4) = c_HOL_Oone__class_Oone(X4) ),
inference(variable_rename,[status(thm)],[c_0_1213]) ).
fof(c_0_1846,plain,
! [X37] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(X37),tc_Lambda_OdB) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_1214]) ).
fof(c_0_1847,plain,
! [X4] :
( ~ class_Ring__and__Field_Ozero__neq__one(X4)
| c_HOL_Ozero__class_Ozero(X4) != c_HOL_Oone__class_Oone(X4) ),
inference(variable_rename,[status(thm)],[c_0_1215]) ).
fof(c_0_1848,plain,
! [X4] :
( ~ class_Ring__and__Field_Ozero__neq__one(X4)
| c_HOL_Oone__class_Oone(X4) != c_HOL_Ozero__class_Ozero(X4) ),
inference(variable_rename,[status(thm)],[c_0_1216]) ).
fof(c_0_1849,plain,
! [X17,X18] :
( c_Suc(X18) != c_Suc(X17)
| X18 = X17 ),
inference(variable_rename,[status(thm)],[c_0_1217]) ).
fof(c_0_1850,plain,
! [X54,X55] :
( c_Suc(X55) != c_Suc(X54)
| X55 = X54 ),
inference(variable_rename,[status(thm)],[c_0_1218]) ).
fof(c_0_1851,plain,
! [X53,X54] :
( c_Lambda_OdB_OAbs(X54) != c_Lambda_OdB_OAbs(X53)
| X54 = X53 ),
inference(variable_rename,[status(thm)],[c_0_1219]) ).
fof(c_0_1852,plain,
! [X54,X55] :
( c_Lambda_OdB_OVar(X55) != c_Lambda_OdB_OVar(X54)
| X55 = X54 ),
inference(variable_rename,[status(thm)],[c_0_1220]) ).
fof(c_0_1853,plain,
! [X5] :
( X5 = c_Suc(c_ATP__Linkup_Osko__Nat__Xnot0__implies__Suc__1__1(X5))
| X5 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1221]) ).
fof(c_0_1854,plain,
! [X23] :
( X23 = c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__Xnchotomy__1__1(X23))
| X23 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1222]) ).
fof(c_0_1855,plain,
! [X16] :
( X16 = c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__Xexhaust__1__1(X16))
| X16 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1223]) ).
fof(c_0_1856,plain,
! [X53,X54] : c_Lambda_OdB_OVar(X53) != c_Lambda_OdB_OAbs(X54),
inference(variable_rename,[status(thm)],[c_0_1224]) ).
fof(c_0_1857,plain,
! [X53,X54] : c_Lambda_OdB_OAbs(X54) != c_Lambda_OdB_OVar(X53),
inference(variable_rename,[status(thm)],[c_0_1225]) ).
fof(c_0_1858,plain,
! [X37] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(X37)) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_1226]) ).
fof(c_0_1859,plain,
! [X54] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X54),
inference(variable_rename,[status(thm)],[c_0_1227]) ).
fof(c_0_1860,plain,
! [X6] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X6),
inference(variable_rename,[status(thm)],[c_0_1228]) ).
fof(c_0_1861,plain,
! [X54] : c_Suc(X54) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_1229]) ).
fof(c_0_1862,plain,
! [X6] : c_Suc(X6) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_1230]) ).
fof(c_0_1863,axiom,
c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_1231 ).
fof(c_0_1864,plain,
! [X5] : c_Suc(X5) != X5,
inference(variable_rename,[status(thm)],[c_0_1232]) ).
fof(c_0_1865,plain,
! [X5] : X5 != c_Suc(X5),
inference(variable_rename,[status(thm)],[c_0_1233]) ).
fof(c_0_1866,axiom,
class_Power_Opower(tc_nat),
c_0_1234 ).
fof(c_0_1867,axiom,
class_Orderings_Oorder(tc_nat),
c_0_1235 ).
fof(c_0_1868,axiom,
class_Orderings_Olinorder(tc_nat),
c_0_1236 ).
fof(c_0_1869,axiom,
class_Orderings_Opreorder(tc_nat),
c_0_1237 ).
fof(c_0_1870,axiom,
class_Ring__and__Field_Odvd(tc_nat),
c_0_1238 ).
fof(c_0_1871,axiom,
class_Nat_Osemiring__char__0(tc_nat),
c_0_1239 ).
fof(c_0_1872,axiom,
class_Divides_Osemiring__div(tc_nat),
c_0_1240 ).
fof(c_0_1873,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
c_0_1241 ).
fof(c_0_1874,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
c_0_1242 ).
fof(c_0_1875,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
c_0_1243 ).
fof(c_0_1876,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
c_0_1244 ).
fof(c_0_1877,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
c_0_1245 ).
fof(c_0_1878,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
c_0_1246 ).
fof(c_0_1879,axiom,
class_OrderedGroup_Osemigroup__add(tc_nat),
c_0_1247 ).
fof(c_0_1880,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
c_0_1248 ).
fof(c_0_1881,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
c_0_1249 ).
fof(c_0_1882,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
c_0_1250 ).
fof(c_0_1883,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
c_0_1251 ).
fof(c_0_1884,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
c_0_1252 ).
fof(c_0_1885,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
c_0_1253 ).
fof(c_0_1886,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
c_0_1254 ).
fof(c_0_1887,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
c_0_1255 ).
fof(c_0_1888,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
c_0_1256 ).
fof(c_0_1889,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
c_0_1257 ).
fof(c_0_1890,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
c_0_1258 ).
fof(c_0_1891,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
c_0_1259 ).
fof(c_0_1892,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
c_0_1260 ).
fof(c_0_1893,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
c_0_1261 ).
fof(c_0_1894,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
c_0_1262 ).
fof(c_0_1895,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
c_0_1263 ).
cnf(c_0_1896,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(c_COMBC(c_COMBC(c_Lambda_Osubst,X3,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(split_conjunct,[status(thm)],[c_0_1264]) ).
cnf(c_0_1897,plain,
( c_Type_Otypings(X1,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X2,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X5,tc_Lambda_OdB,tc_Lambda_OdB),X6)
| ~ c_Type_Otyping(X1,X2,X3)
| ~ c_Type_Otypings(c_Type_Oshift(X1,X4,X3,tc_Type_Otype),X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1265]) ).
cnf(c_0_1898,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_1266]) ).
cnf(c_0_1899,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(c_COMBC(c_Lambda_Olift,X3,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(split_conjunct,[status(thm)],[c_0_1267]) ).
cnf(c_0_1900,plain,
( X4 = X5
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X5) ),
inference(split_conjunct,[status(thm)],[c_0_1268]) ).
cnf(c_0_1901,plain,
c_COMBB(X1,X2,X3,X4,X5,X6) = hAPP(X1,hAPP(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_1269]) ).
cnf(c_0_1902,plain,
( c_Type_Otypings(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3)
| ~ c_Type_Otypings(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1270]) ).
cnf(c_0_1903,plain,
( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_1271]) ).
cnf(c_0_1904,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_1272]) ).
cnf(c_0_1905,plain,
( 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))
| ~ c_Lambda_Obeta(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1273]) ).
cnf(c_0_1906,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_1274]) ).
cnf(c_0_1907,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_1275]) ).
cnf(c_0_1908,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_1276]) ).
cnf(c_0_1909,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_1277]) ).
cnf(c_0_1910,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_1278]) ).
cnf(c_0_1911,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_1279]) ).
cnf(c_0_1912,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_1280]) ).
cnf(c_0_1913,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_1281]) ).
cnf(c_0_1914,plain,
( hBOOL(hAPP(X1,X2))
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat)),X4),X3,tc_nat)))
| ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1282]) ).
cnf(c_0_1915,plain,
( hBOOL(hAPP(X1,X2))
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat)),X2),X3,tc_nat)))
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1283]) ).
cnf(c_0_1916,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1)),c_Divides_Odiv__class_Omod(X2,X3,X1))),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1284]) ).
cnf(c_0_1917,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X3,X2,X1),X1)),c_Divides_Odiv__class_Omod(X3,X2,X1))),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1285]) ).
cnf(c_0_1918,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_1286]) ).
cnf(c_0_1919,plain,
c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(X1,X3,tc_nat)),c_Divides_Odiv__class_Odiv(X2,X3,tc_nat))),c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(X1,X3,tc_nat)),c_Divides_Odiv__class_Omod(X2,X3,tc_nat)),X3,tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_1287]) ).
cnf(c_0_1920,plain,
hAPP(c_COMBC(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X1,X6),X2),
inference(split_conjunct,[status(thm)],[c_0_1288]) ).
cnf(c_0_1921,plain,
hAPP(c_COMBC(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X1,X6),X2),
inference(split_conjunct,[status(thm)],[c_0_1289]) ).
cnf(c_0_1922,plain,
( hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) = X3
| hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_1290]) ).
cnf(c_0_1923,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_1291]) ).
cnf(c_0_1924,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_1292]) ).
cnf(c_0_1925,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_1293]) ).
cnf(c_0_1926,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_1294]) ).
cnf(c_0_1927,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_1295]) ).
cnf(c_0_1928,plain,
( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| c_Lambda_OdB_OVar(X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_1296]) ).
cnf(c_0_1929,plain,
( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1297]) ).
cnf(c_0_1930,plain,
( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_1298]) ).
cnf(c_0_1931,plain,
c_Divides_Odiv__class_Omod(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Odiv(X1,X2,tc_nat),X3,tc_nat),tc_nat)),c_Divides_Odiv__class_Omod(X1,X2,tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_1299]) ).
cnf(c_0_1932,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(X4,X1,tc_nat),tc_nat)),X2),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1300]) ).
cnf(c_0_1933,plain,
c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X2,X3,tc_nat),tc_nat)),c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X3,tc_nat),tc_nat),X3,tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_1301]) ).
cnf(c_0_1934,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1302]) ).
cnf(c_0_1935,plain,
c_Type_Oshift(c_Type_Oshift(X1,X2,X3,X4),c_HOL_Ozero__class_Ozero(tc_nat),X5,X4) = c_Type_Oshift(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),X5,X4),c_Suc(X2),X3,X4),
inference(split_conjunct,[status(thm)],[c_0_1303]) ).
cnf(c_0_1936,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X4,X3,X1)),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X3,X1)),X5)
| ~ class_Ring__and__Field_Osemiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1304]) ).
cnf(c_0_1937,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat)),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),X2,tc_nat)),X4),
inference(split_conjunct,[status(thm)],[c_0_1305]) ).
cnf(c_0_1938,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(split_conjunct,[status(thm)],[c_0_1306]) ).
cnf(c_0_1939,plain,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X2,X1)),c_HOL_Otimes__class_Otimes(X3,X3,X1)),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1307]) ).
cnf(c_0_1940,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_1308]) ).
cnf(c_0_1941,plain,
c_Lambda_OdB_OVar(X1) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(split_conjunct,[status(thm)],[c_0_1309]) ).
cnf(c_0_1942,plain,
c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OAbs(X1),
inference(split_conjunct,[status(thm)],[c_0_1310]) ).
cnf(c_0_1943,plain,
c_Lambda_OdB_OAbs(X1) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(split_conjunct,[status(thm)],[c_0_1311]) ).
cnf(c_0_1944,plain,
c_List_Ofoldl(X1,X2,c_List_Olist_ONil(X3),X4,X3) = X2,
inference(split_conjunct,[status(thm)],[c_0_1312]) ).
cnf(c_0_1945,plain,
( X1 = X2
| X3 = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X3,X5)),c_HOL_Otimes__class_Otimes(X2,X4,X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X4,X5)),c_HOL_Otimes__class_Otimes(X2,X3,X5))
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(split_conjunct,[status(thm)],[c_0_1313]) ).
cnf(c_0_1946,plain,
( X1 = X2
| X3 = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X3,X5)),c_HOL_Otimes__class_Otimes(X2,X4,X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X4,X5)),c_HOL_Otimes__class_Otimes(X2,X3,X5))
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(split_conjunct,[status(thm)],[c_0_1314]) ).
cnf(c_0_1947,plain,
( c_Type_Otyping(X1,hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4),X5)
| ~ c_Type_Otyping(c_Type_Oshift(X1,X4,X6,tc_Type_Otype),X2,X5)
| ~ c_Type_Otyping(X1,X3,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1315]) ).
cnf(c_0_1948,plain,
c_Divides_Odiv__class_Omod(c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),X3)),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X3),X2,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1316]) ).
cnf(c_0_1949,plain,
( X1 = X2
| X3 = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X4,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_1317]) ).
cnf(c_0_1950,plain,
( X1 = X2
| X3 = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X4,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_1318]) ).
cnf(c_0_1951,plain,
( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X4,X1)),c_Divides_Odiv__class_Omod(X3,X4,X1)),X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1319]) ).
cnf(c_0_1952,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_1320]) ).
cnf(c_0_1953,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X3,X3,X2)),c_HOL_Otimes__class_Otimes(X1,X1,X2)),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1321]) ).
cnf(c_0_1954,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X1,X1,X2)),c_HOL_Otimes__class_Otimes(X3,X3,X2)),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1322]) ).
cnf(c_0_1955,plain,
( X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X3,X2),X3,X2)),c_Divides_Odiv__class_Omod(X1,X3,X2))
| ~ class_Divides_Osemiring__div(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1323]) ).
cnf(c_0_1956,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1)),c_Divides_Odiv__class_Omod(X2,X3,X1)) = X2
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1324]) ).
cnf(c_0_1957,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X3,X2,X1),X1)),c_Divides_Odiv__class_Omod(X3,X2,X1)) = X3
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1325]) ).
cnf(c_0_1958,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_1326]) ).
cnf(c_0_1959,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),c_HOL_Otimes__class_Otimes(X2,X4,X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X2,X3,X1))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1327]) ).
cnf(c_0_1960,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),c_HOL_Otimes__class_Otimes(X2,X4,X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X2,X3,X1))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1328]) ).
cnf(c_0_1961,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X4,X3),c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1329]) ).
cnf(c_0_1962,plain,
( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X3,X1)),X4),X3,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X3,X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1330]) ).
cnf(c_0_1963,plain,
( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X4,X1)),X3),X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1331]) ).
cnf(c_0_1964,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_1332]) ).
cnf(c_0_1965,plain,
( c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X5,X4,X3),X3) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X5,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1333]) ).
cnf(c_0_1966,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_1334]) ).
cnf(c_0_1967,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_1335]) ).
cnf(c_0_1968,plain,
( c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X1,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Odiv(X2,X1,X3)),c_Divides_Odiv__class_Odiv(X4,X1,X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1336]) ).
cnf(c_0_1969,plain,
( c_Type_Otyping(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X2),X4),X3)
| ~ c_Type_Otyping(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1337]) ).
cnf(c_0_1970,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1338]) ).
cnf(c_0_1971,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Suc(c_Divides_Odiv__class_Odiv(X1,X2,tc_nat)),tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1339]) ).
cnf(c_0_1972,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X6,X3),X4,X3)
| c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X5,X4,X3)
| c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X6,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1340]) ).
cnf(c_0_1973,plain,
( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X6),X4,X1)
| c_Divides_Odiv__class_Omod(X2,X4,X1) != c_Divides_Odiv__class_Omod(X5,X4,X1)
| c_Divides_Odiv__class_Omod(X3,X4,X1) != c_Divides_Odiv__class_Omod(X6,X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1341]) ).
cnf(c_0_1974,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1342]) ).
cnf(c_0_1975,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1343]) ).
cnf(c_0_1976,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X4,X5,X3),X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1344]) ).
cnf(c_0_1977,plain,
c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),X3),X2,tc_nat) = c_Divides_Odiv__class_Omod(X3,X2,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1345]) ).
cnf(c_0_1978,plain,
( hAPP(c_Type_Oshift(X3,X2,X4,X5),X1) = hAPP(X3,X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1346]) ).
cnf(c_0_1979,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X1,X1,X2)),c_HOL_Otimes__class_Otimes(X3,X3,X2)) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1347]) ).
cnf(c_0_1980,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X3,X3,X2)),c_HOL_Otimes__class_Otimes(X1,X1,X2)) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1348]) ).
cnf(c_0_1981,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_1349]) ).
cnf(c_0_1982,plain,
c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),tc_Lambda_OdB) = 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_Lambda_OdB)),c_Nat_Osize__class_Osize(X2,tc_Lambda_OdB))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
inference(split_conjunct,[status(thm)],[c_0_1350]) ).
cnf(c_0_1983,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X3,X1)),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1)) = X2
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1351]) ).
cnf(c_0_1984,plain,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1352]) ).
cnf(c_0_1985,plain,
( c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1353]) ).
cnf(c_0_1986,plain,
( c_HOL_Oord__class_Oless(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1354]) ).
cnf(c_0_1987,plain,
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1355]) ).
cnf(c_0_1988,plain,
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1356]) ).
cnf(c_0_1989,plain,
( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(X3,X2,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Otimes__class_Otimes(X2,X5,tc_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_1357]) ).
cnf(c_0_1990,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,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_1358]) ).
cnf(c_0_1991,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1359]) ).
cnf(c_0_1992,plain,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,tc_nat),c_Power_Opower__class_Opower(X1,X3,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1360]) ).
cnf(c_0_1993,plain,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1361]) ).
cnf(c_0_1994,plain,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X2,X3),c_Power_Opower__class_Opower(X4,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(X3),X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1362]) ).
cnf(c_0_1995,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1363]) ).
cnf(c_0_1996,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1364]) ).
cnf(c_0_1997,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1365]) ).
cnf(c_0_1998,plain,
( c_HOL_Oord__class_Oless(X2,X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1366]) ).
cnf(c_0_1999,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1367]) ).
cnf(c_0_2000,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1368]) ).
cnf(c_0_2001,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1369]) ).
cnf(c_0_2002,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1370]) ).
cnf(c_0_2003,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1371]) ).
cnf(c_0_2004,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X2,X3),X4,X3),X2,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X4,X3),X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1372]) ).
cnf(c_0_2005,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),c_HOL_Otimes__class_Otimes(X4,X1,X2)),X1,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X4),c_Divides_Odiv__class_Odiv(X3,X1,X2))
| ~ class_Divides_Osemiring__div(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1373]) ).
cnf(c_0_2006,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),c_HOL_Otimes__class_Otimes(X1,X4,X2)),X1,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X4),c_Divides_Odiv__class_Odiv(X3,X1,X2))
| ~ class_Divides_Osemiring__div(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1374]) ).
cnf(c_0_2007,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1375]) ).
cnf(c_0_2008,plain,
( c_HOL_Oord__class_Oless(X2,X4,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1376]) ).
cnf(c_0_2009,plain,
( c_HOL_Otimes__class_Otimes(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X4),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2)),c_HOL_Otimes__class_Otimes(X1,X4,X2))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1377]) ).
cnf(c_0_2010,plain,
( c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X3,X4,X1))
| ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1378]) ).
cnf(c_0_2011,plain,
( c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X3,X4,X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1379]) ).
cnf(c_0_2012,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),c_HOL_Otimes__class_Otimes(X4,X3,X1)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1380]) ).
cnf(c_0_2013,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1381]) ).
cnf(c_0_2014,plain,
( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_Divides_Odiv__class_Omod(X3,X4,X1)),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1382]) ).
cnf(c_0_2015,plain,
( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_Divides_Odiv__class_Omod(X3,X4,X1)),X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1383]) ).
cnf(c_0_2016,plain,
( c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(X2,X1,X3),X4,X3) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(X2,X4,X3),c_Power_Opower__class_Opower(X1,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1384]) ).
cnf(c_0_2017,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),c_HOL_Otimes__class_Otimes(X1,X3,X2)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),c_HOL_Otimes__class_Otimes(X1,X4,X2))
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1385]) ).
cnf(c_0_2018,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_1386]) ).
cnf(c_0_2019,plain,
hAPP(c_Type_Oshift(X1,X2,X3,X4),X2) = X3,
inference(split_conjunct,[status(thm)],[c_0_1387]) ).
cnf(c_0_2020,plain,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X1),X3,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1388]) ).
cnf(c_0_2021,plain,
c_HOL_Otimes__class_Otimes(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_1389]) ).
cnf(c_0_2022,plain,
c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_1390]) ).
cnf(c_0_2023,plain,
( X2 = c_HOL_Ozero__class_Ozero(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1391]) ).
cnf(c_0_2024,plain,
( X1 = c_HOL_Ozero__class_Ozero(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1392]) ).
cnf(c_0_2025,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1393]) ).
cnf(c_0_2026,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_1394]) ).
cnf(c_0_2027,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_1395]) ).
cnf(c_0_2028,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_1396]) ).
cnf(c_0_2029,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_1397]) ).
cnf(c_0_2030,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1398]) ).
cnf(c_0_2031,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1399]) ).
cnf(c_0_2032,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1400]) ).
cnf(c_0_2033,plain,
( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1401]) ).
cnf(c_0_2034,plain,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1402]) ).
cnf(c_0_2035,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1403]) ).
cnf(c_0_2036,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1404]) ).
cnf(c_0_2037,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1405]) ).
cnf(c_0_2038,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1406]) ).
cnf(c_0_2039,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1407]) ).
cnf(c_0_2040,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1408]) ).
cnf(c_0_2041,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1409]) ).
cnf(c_0_2042,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1410]) ).
cnf(c_0_2043,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1411]) ).
cnf(c_0_2044,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1412]) ).
cnf(c_0_2045,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1413]) ).
cnf(c_0_2046,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1414]) ).
cnf(c_0_2047,plain,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X1,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1415]) ).
cnf(c_0_2048,plain,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1416]) ).
cnf(c_0_2049,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1417]) ).
cnf(c_0_2050,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),X3) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Oone__class_Oone(X1)),X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1418]) ).
cnf(c_0_2051,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1),X1,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_Divides_Odiv__class_Odiv(X3,X1,X2)),c_HOL_Oone__class_Oone(X2))
| ~ class_Divides_Osemiring__div(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1419]) ).
cnf(c_0_2052,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),X1,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_Divides_Odiv__class_Odiv(X3,X1,X2)),c_HOL_Oone__class_Oone(X2))
| ~ class_Divides_Osemiring__div(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1420]) ).
cnf(c_0_2053,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_1421]) ).
cnf(c_0_2054,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1422]) ).
cnf(c_0_2055,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1423]) ).
cnf(c_0_2056,plain,
( c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1424]) ).
cnf(c_0_2057,plain,
( c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1425]) ).
cnf(c_0_2058,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1426]) ).
cnf(c_0_2059,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1427]) ).
cnf(c_0_2060,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1428]) ).
cnf(c_0_2061,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1429]) ).
cnf(c_0_2062,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1430]) ).
cnf(c_0_2063,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1431]) ).
cnf(c_0_2064,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_1432]) ).
cnf(c_0_2065,plain,
( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Otimes__class_Otimes(X3,X4,X1)),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1433]) ).
cnf(c_0_2066,plain,
( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Otimes__class_Otimes(X3,X4,X1)),X4,X1) = c_Divides_Odiv__class_Omod(X2,X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1434]) ).
cnf(c_0_2067,plain,
( hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
inference(split_conjunct,[status(thm)],[c_0_1435]) ).
cnf(c_0_2068,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1436]) ).
cnf(c_0_2069,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),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1437]) ).
cnf(c_0_2070,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
inference(split_conjunct,[status(thm)],[c_0_1438]) ).
cnf(c_0_2071,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_1439]) ).
cnf(c_0_2072,plain,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X3),X3) = c_Power_Opower__class_Opower(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X4),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1440]) ).
cnf(c_0_2073,plain,
( c_Power_Opower__class_Opower(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X4) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X4),c_Power_Opower__class_Opower(X1,X3,X4),X4)
| ~ class_OrderedGroup_Omonoid__mult(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1441]) ).
cnf(c_0_2074,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_1442]) ).
cnf(c_0_2075,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_1443]) ).
cnf(c_0_2076,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_1444]) ).
cnf(c_0_2077,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_1445]) ).
cnf(c_0_2078,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_1446]) ).
cnf(c_0_2079,plain,
c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X3,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1447]) ).
cnf(c_0_2080,plain,
c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X3,tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1448]) ).
cnf(c_0_2081,plain,
( c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X4,X3) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1449]) ).
cnf(c_0_2082,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1450]) ).
cnf(c_0_2083,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X3,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X4)
| ~ class_Divides_Osemiring__div(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1451]) ).
cnf(c_0_2084,plain,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1452]) ).
cnf(c_0_2085,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_1453]) ).
cnf(c_0_2086,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Olist_ONil(X3) != c_List_Omap(X4,X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1454]) ).
cnf(c_0_2087,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Omap(X3,X1,X2,X4) != c_List_Olist_ONil(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1455]) ).
cnf(c_0_2088,plain,
c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X1)),c_Lambda_OdB_OdB__size(X2))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
inference(split_conjunct,[status(thm)],[c_0_1456]) ).
cnf(c_0_2089,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_1457]) ).
cnf(c_0_2090,plain,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,c_Suc(X3),X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1458]) ).
cnf(c_0_2091,plain,
( c_Lambda_Obeta(hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4))
| ~ c_Lambda_Obeta(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1459]) ).
cnf(c_0_2092,plain,
( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1460]) ).
cnf(c_0_2093,plain,
hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X1),X2)),X3),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_1461]) ).
cnf(c_0_2094,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1462]) ).
cnf(c_0_2095,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1463]) ).
cnf(c_0_2096,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1464]) ).
cnf(c_0_2097,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1465]) ).
cnf(c_0_2098,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,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_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1466]) ).
cnf(c_0_2099,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1467]) ).
cnf(c_0_2100,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1468]) ).
cnf(c_0_2101,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_1469]) ).
cnf(c_0_2102,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1470]) ).
cnf(c_0_2103,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1471]) ).
cnf(c_0_2104,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_1472]) ).
cnf(c_0_2105,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_1473]) ).
cnf(c_0_2106,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_1474]) ).
cnf(c_0_2107,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1475]) ).
cnf(c_0_2108,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1476]) ).
cnf(c_0_2109,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1477]) ).
cnf(c_0_2110,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1478]) ).
cnf(c_0_2111,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1479]) ).
cnf(c_0_2112,plain,
( c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),X1,tc_nat) = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1480]) ).
cnf(c_0_2113,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_1481]) ).
cnf(c_0_2114,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_1482]) ).
cnf(c_0_2115,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_1483]) ).
cnf(c_0_2116,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_1484]) ).
cnf(c_0_2117,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_1485]) ).
cnf(c_0_2118,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1486]) ).
cnf(c_0_2119,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_1487]) ).
cnf(c_0_2120,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1488]) ).
cnf(c_0_2121,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1489]) ).
cnf(c_0_2122,plain,
( X2 = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1490]) ).
cnf(c_0_2123,plain,
( X2 = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1491]) ).
cnf(c_0_2124,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),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_1492]) ).
cnf(c_0_2125,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1493]) ).
cnf(c_0_2126,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Otimes__class_Otimes(X3,X2,X1)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),c_HOL_Oone__class_Oone(X1)),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1494]) ).
cnf(c_0_2127,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X4,X1,X2),X2) = c_Divides_Odiv__class_Odiv(X3,X4,X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1495]) ).
cnf(c_0_2128,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2) = c_Divides_Odiv__class_Odiv(X3,X4,X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1496]) ).
cnf(c_0_2129,plain,
( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Odiv(X2,X1,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(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_1497]) ).
cnf(c_0_2130,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X4),X3,X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1498]) ).
cnf(c_0_2131,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X1,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1499]) ).
cnf(c_0_2132,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X4),X3,X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1500]) ).
cnf(c_0_2133,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1501]) ).
cnf(c_0_2134,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X4,X3),X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1502]) ).
cnf(c_0_2135,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ class_OrderedGroup_Oab__semigroup__mult(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1503]) ).
cnf(c_0_2136,plain,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),X1,X3) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3)
| ~ class_OrderedGroup_Omonoid__mult(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1504]) ).
cnf(c_0_2137,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1505]) ).
cnf(c_0_2138,plain,
( c_Power_Opower__class_Opower(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X1,X2,X4),X3,X4)
| ~ class_OrderedGroup_Omonoid__mult(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1506]) ).
cnf(c_0_2139,plain,
( c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X1,X2,X3),X4,X3) = c_Power_Opower__class_Opower(X1,c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1507]) ).
cnf(c_0_2140,plain,
c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)),X2,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1508]) ).
cnf(c_0_2141,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_1509]) ).
cnf(c_0_2142,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_1510]) ).
cnf(c_0_2143,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_1511]) ).
cnf(c_0_2144,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_1512]) ).
cnf(c_0_2145,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_1513]) ).
cnf(c_0_2146,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_1514]) ).
cnf(c_0_2147,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1515]) ).
cnf(c_0_2148,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1516]) ).
cnf(c_0_2149,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1517]) ).
cnf(c_0_2150,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_1518]) ).
cnf(c_0_2151,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_1519]) ).
cnf(c_0_2152,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_1520]) ).
cnf(c_0_2153,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1521]) ).
cnf(c_0_2154,plain,
c_Divides_Odiv__class_Odiv(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(X1,X2,tc_nat),X3,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1522]) ).
cnf(c_0_2155,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X1,X2,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1523]) ).
cnf(c_0_2156,plain,
( c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X4,X2,X3),X1,X3) = c_Divides_Odiv__class_Omod(X4,X1,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1524]) ).
cnf(c_0_2157,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(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1525]) ).
cnf(c_0_2158,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),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1526]) ).
cnf(c_0_2159,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(split_conjunct,[status(thm)],[c_0_1527]) ).
cnf(c_0_2160,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(split_conjunct,[status(thm)],[c_0_1528]) ).
cnf(c_0_2161,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1529]) ).
cnf(c_0_2162,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1530]) ).
cnf(c_0_2163,plain,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X3,X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1531]) ).
cnf(c_0_2164,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X3,X1),X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1532]) ).
cnf(c_0_2165,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2),c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X2),X2),X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1533]) ).
cnf(c_0_2166,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1534]) ).
cnf(c_0_2167,plain,
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_1535]) ).
cnf(c_0_2168,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,c_Suc(X3),X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1536]) ).
cnf(c_0_2169,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_1537]) ).
cnf(c_0_2170,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1538]) ).
cnf(c_0_2171,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_1539]) ).
cnf(c_0_2172,plain,
( X1 = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| c_Power_Opower__class_Opower(X4,X1,X3) != c_Power_Opower__class_Opower(X4,X2,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1540]) ).
cnf(c_0_2173,plain,
( c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) = X2
| c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_1541]) ).
cnf(c_0_2174,plain,
c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1542]) ).
cnf(c_0_2175,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1543]) ).
cnf(c_0_2176,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1544]) ).
cnf(c_0_2177,plain,
c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1545]) ).
cnf(c_0_2178,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_1546]) ).
cnf(c_0_2179,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1547]) ).
cnf(c_0_2180,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1548]) ).
cnf(c_0_2181,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_1549]) ).
cnf(c_0_2182,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_1550]) ).
cnf(c_0_2183,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_1551]) ).
cnf(c_0_2184,plain,
c_List_Olist_ONil(X1) = c_List_Omap(X2,c_List_Olist_ONil(X3),X3,X1),
inference(split_conjunct,[status(thm)],[c_0_1552]) ).
cnf(c_0_2185,plain,
c_List_Omap(X1,c_List_Olist_ONil(X2),X2,X3) = c_List_Olist_ONil(X3),
inference(split_conjunct,[status(thm)],[c_0_1553]) ).
cnf(c_0_2186,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_Power_Opower__class_Opower(X2,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1554]) ).
cnf(c_0_2187,plain,
( X1 = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| c_HOL_Otimes__class_Otimes(X3,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1555]) ).
cnf(c_0_2188,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1556]) ).
cnf(c_0_2189,plain,
( c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X2,X1,X3),X3) = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1557]) ).
cnf(c_0_2190,plain,
( c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X1,X3) = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1558]) ).
cnf(c_0_2191,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1559]) ).
cnf(c_0_2192,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1560]) ).
cnf(c_0_2193,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1)),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1561]) ).
cnf(c_0_2194,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X1,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_1562]) ).
cnf(c_0_2195,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(tc_nat),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_1563]) ).
cnf(c_0_2196,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X1,X2,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_1564]) ).
cnf(c_0_2197,plain,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X1,tc_nat) = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1565]) ).
cnf(c_0_2198,plain,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),X1,tc_nat) = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1566]) ).
cnf(c_0_2199,plain,
( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X2,X1,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_1567]) ).
cnf(c_0_2200,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_1568]) ).
cnf(c_0_2201,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_1569]) ).
cnf(c_0_2202,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_1570]) ).
cnf(c_0_2203,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_1571]) ).
cnf(c_0_2204,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_1572]) ).
cnf(c_0_2205,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_1573]) ).
cnf(c_0_2206,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1574]) ).
cnf(c_0_2207,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_1575]) ).
cnf(c_0_2208,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_1576]) ).
cnf(c_0_2209,plain,
( c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1577]) ).
cnf(c_0_2210,plain,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
| ~ class_Ring__and__Field_Osemiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1578]) ).
cnf(c_0_2211,plain,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),X1,X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1579]) ).
cnf(c_0_2212,plain,
( c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1580]) ).
cnf(c_0_2213,plain,
( c_Power_Opower__class_Opower(X1,c_Suc(X2),X3) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),X1,X3)
| ~ class_OrderedGroup_Omonoid__mult(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1581]) ).
cnf(c_0_2214,plain,
( c_Power_Opower__class_Opower(X1,c_Suc(X2),X3) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3)
| ~ class_Power_Opower(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1582]) ).
cnf(c_0_2215,plain,
( c_Power_Opower__class_Opower(X1,c_Suc(X2),X3) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1583]) ).
cnf(c_0_2216,plain,
( c_Power_Opower__class_Opower(X1,c_Suc(X2),X3) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1584]) ).
cnf(c_0_2217,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_1585]) ).
cnf(c_0_2218,plain,
( c_Divides_Odiv__class_Odiv(X2,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1586]) ).
cnf(c_0_2219,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_1587]) ).
cnf(c_0_2220,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1588]) ).
cnf(c_0_2221,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_1589]) ).
cnf(c_0_2222,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_1590]) ).
cnf(c_0_2223,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_1591]) ).
cnf(c_0_2224,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_1592]) ).
cnf(c_0_2225,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_1593]) ).
cnf(c_0_2226,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_1594]) ).
cnf(c_0_2227,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) = c_HOL_Otimes__class_Otimes(X1,X2,X3)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1595]) ).
cnf(c_0_2228,plain,
( c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X1,X2,X3),X2,X3) = c_Divides_Odiv__class_Omod(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1596]) ).
cnf(c_0_2229,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1597]) ).
cnf(c_0_2230,plain,
( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X2,X1) = c_Divides_Odiv__class_Omod(X3,X2,X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1598]) ).
cnf(c_0_2231,plain,
( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1599]) ).
cnf(c_0_2232,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_1600]) ).
cnf(c_0_2233,plain,
c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_1601]) ).
cnf(c_0_2234,plain,
c_HOL_Otimes__class_Otimes(X1,c_Suc(X2),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_1602]) ).
cnf(c_0_2235,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_1603]) ).
cnf(c_0_2236,plain,
( c_Nat_Osemiring__1__class_Oof__nat(c_Power_Opower__class_Opower(X1,X2,tc_nat),X3) = c_Power_Opower__class_Opower(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),X2,X3)
| ~ class_Ring__and__Field_Osemiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1604]) ).
cnf(c_0_2237,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_1605]) ).
cnf(c_0_2238,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_1606]) ).
cnf(c_0_2239,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_1607]) ).
cnf(c_0_2240,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_1608]) ).
cnf(c_0_2241,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X1,c_Suc(v_sko__Nat__Xnat__Xinducts__1(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_1609]) ).
cnf(c_0_2242,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X1,c_Suc(v_sko__Nat__Xnat__Xinduct__1(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_1610]) ).
cnf(c_0_2243,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X1,c_Suc(v_sko__List__Xupt__Xinduct__1(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_1611]) ).
cnf(c_0_2244,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X1,c_Suc(v_sko__List__Xreplicate__Xinduct__1(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_1612]) ).
cnf(c_0_2245,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X1,c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_1613]) ).
cnf(c_0_2246,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X1,c_Suc(v_sko__List__Xlexn__Xinduct__1(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_1614]) ).
cnf(c_0_2247,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_1615]) ).
cnf(c_0_2248,plain,
( X1 = X2
| c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1616]) ).
cnf(c_0_2249,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1617]) ).
cnf(c_0_2250,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_1618]) ).
cnf(c_0_2251,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_1619]) ).
cnf(c_0_2252,plain,
( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3))
| ~ c_Lambda_Obeta(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1620]) ).
cnf(c_0_2253,plain,
( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2))
| ~ c_Lambda_Obeta(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1621]) ).
cnf(c_0_2254,plain,
( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_Olift,X1),X3),hAPP(hAPP(c_Lambda_Olift,X2),X3))
| ~ c_Lambda_Obeta(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1622]) ).
cnf(c_0_2255,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_1623]) ).
cnf(c_0_2256,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_1624]) ).
cnf(c_0_2257,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_1625]) ).
cnf(c_0_2258,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_1626]) ).
cnf(c_0_2259,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_1627]) ).
cnf(c_0_2260,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_1628]) ).
cnf(c_0_2261,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X3,X2),X1,X2) = X3
| ~ class_Divides_Osemiring__div(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1629]) ).
cnf(c_0_2262,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X1,X2),X1,X2) = X3
| ~ class_Divides_Osemiring__div(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1630]) ).
cnf(c_0_2263,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_1631]) ).
cnf(c_0_2264,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_1632]) ).
cnf(c_0_2265,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_1633]) ).
cnf(c_0_2266,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X1,X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1634]) ).
cnf(c_0_2267,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1635]) ).
cnf(c_0_2268,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = X3
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1636]) ).
cnf(c_0_2269,plain,
( X1 = X2
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(X3,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1637]) ).
cnf(c_0_2270,plain,
( X1 = X2
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) != c_HOL_Otimes__class_Otimes(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1638]) ).
cnf(c_0_2271,plain,
( c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X1,X2,X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1639]) ).
cnf(c_0_2272,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_1640]) ).
cnf(c_0_2273,plain,
( X1 = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1641]) ).
cnf(c_0_2274,plain,
( X1 = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1642]) ).
cnf(c_0_2275,plain,
( X2 = X1
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1643]) ).
cnf(c_0_2276,plain,
( X1 = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1644]) ).
cnf(c_0_2277,plain,
( X1 = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1645]) ).
cnf(c_0_2278,plain,
( X1 = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1646]) ).
cnf(c_0_2279,plain,
( X1 = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1647]) ).
cnf(c_0_2280,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1648]) ).
cnf(c_0_2281,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1649]) ).
cnf(c_0_2282,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1650]) ).
cnf(c_0_2283,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1651]) ).
cnf(c_0_2284,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_1652]) ).
cnf(c_0_2285,plain,
( c_Type_Otyping(X1,X4,X3)
| ~ c_Type_Otyping(X1,X2,X3)
| ~ c_Lambda_Obeta(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1653]) ).
cnf(c_0_2286,plain,
c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1654]) ).
cnf(c_0_2287,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_1655]) ).
cnf(c_0_2288,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Divides_Odiv__class_Omod(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1656]) ).
cnf(c_0_2289,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_1657]) ).
cnf(c_0_2290,plain,
( c_Divides_Odiv__class_Omod(X2,X1,X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1658]) ).
cnf(c_0_2291,plain,
( hBOOL(hAPP(X1,c_Suc(c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X1))))
| hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1659]) ).
cnf(c_0_2292,plain,
( hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1660]) ).
cnf(c_0_2293,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_1661]) ).
cnf(c_0_2294,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_1662]) ).
cnf(c_0_2295,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_1663]) ).
cnf(c_0_2296,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_1664]) ).
cnf(c_0_2297,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_1665]) ).
cnf(c_0_2298,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_1666]) ).
cnf(c_0_2299,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_1667]) ).
cnf(c_0_2300,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_1668]) ).
cnf(c_0_2301,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_1669]) ).
cnf(c_0_2302,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_1670]) ).
cnf(c_0_2303,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_1671]) ).
cnf(c_0_2304,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_1672]) ).
cnf(c_0_2305,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_1673]) ).
cnf(c_0_2306,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_1674]) ).
cnf(c_0_2307,plain,
( c_Divides_Odiv__class_Odiv(X1,X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1675]) ).
cnf(c_0_2308,plain,
( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = X1
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1676]) ).
cnf(c_0_2309,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_1677]) ).
cnf(c_0_2310,plain,
( hBOOL(hAPP(X1,v_sko__List__Xupt__Xinduct__1(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(split_conjunct,[status(thm)],[c_0_1678]) ).
cnf(c_0_2311,plain,
( hBOOL(hAPP(X1,v_sko__Nat__Xnat__Xinduct__1(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(split_conjunct,[status(thm)],[c_0_1679]) ).
cnf(c_0_2312,plain,
( hBOOL(hAPP(X1,v_sko__Nat__Xnat__Xinducts__1(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(split_conjunct,[status(thm)],[c_0_1680]) ).
cnf(c_0_2313,plain,
( hBOOL(hAPP(X1,v_sko__List__Xreplicate__Xinduct__1(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(split_conjunct,[status(thm)],[c_0_1681]) ).
cnf(c_0_2314,plain,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(split_conjunct,[status(thm)],[c_0_1682]) ).
cnf(c_0_2315,plain,
( hBOOL(hAPP(X1,v_sko__List__Xlexn__Xinduct__1(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(split_conjunct,[status(thm)],[c_0_1683]) ).
cnf(c_0_2316,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1684]) ).
cnf(c_0_2317,plain,
( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1685]) ).
cnf(c_0_2318,plain,
c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X1),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X1,tc_Lambda_OdB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
inference(split_conjunct,[status(thm)],[c_0_1686]) ).
cnf(c_0_2319,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_1687]) ).
cnf(c_0_2320,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_1688]) ).
cnf(c_0_2321,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_1689]) ).
cnf(c_0_2322,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_1690]) ).
cnf(c_0_2323,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_1691]) ).
cnf(c_0_2324,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_1692]) ).
cnf(c_0_2325,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_1693]) ).
cnf(c_0_2326,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_1694]) ).
cnf(c_0_2327,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_1695]) ).
cnf(c_0_2328,plain,
( c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X2,X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1696]) ).
cnf(c_0_2329,plain,
( c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X2,X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1697]) ).
cnf(c_0_2330,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_1698]) ).
cnf(c_0_2331,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_1699]) ).
cnf(c_0_2332,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_1700]) ).
cnf(c_0_2333,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1701]) ).
cnf(c_0_2334,plain,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1702]) ).
cnf(c_0_2335,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_1703]) ).
cnf(c_0_2336,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_1704]) ).
cnf(c_0_2337,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_1705]) ).
cnf(c_0_2338,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1706]) ).
cnf(c_0_2339,plain,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1) = X2,
inference(split_conjunct,[status(thm)],[c_0_1707]) ).
cnf(c_0_2340,plain,
( hAPP(X1,X2) = X3
| ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1708]) ).
cnf(c_0_2341,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_1709]) ).
cnf(c_0_2342,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1710]) ).
cnf(c_0_2343,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1711]) ).
cnf(c_0_2344,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1712]) ).
cnf(c_0_2345,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_1713]) ).
cnf(c_0_2346,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_1714]) ).
cnf(c_0_2347,plain,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1715]) ).
cnf(c_0_2348,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_1716]) ).
cnf(c_0_2349,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_Power_Opower__class_Opower(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_1717]) ).
cnf(c_0_2350,plain,
c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) = c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1718]) ).
cnf(c_0_2351,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1719]) ).
cnf(c_0_2352,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_1720]) ).
cnf(c_0_2353,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_1721]) ).
cnf(c_0_2354,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_1722]) ).
cnf(c_0_2355,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_1723]) ).
cnf(c_0_2356,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_1724]) ).
cnf(c_0_2357,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_1725]) ).
cnf(c_0_2358,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1726]) ).
cnf(c_0_2359,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_1727]) ).
cnf(c_0_2360,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_1728]) ).
cnf(c_0_2361,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_1729]) ).
cnf(c_0_2362,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_1730]) ).
cnf(c_0_2363,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1731]) ).
cnf(c_0_2364,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_1732]) ).
cnf(c_0_2365,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1733]) ).
cnf(c_0_2366,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1734]) ).
cnf(c_0_2367,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1735]) ).
cnf(c_0_2368,plain,
( X1 = c_HOL_Oone__class_Oone(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 != c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1736]) ).
cnf(c_0_2369,plain,
( X1 = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1737]) ).
cnf(c_0_2370,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_1738]) ).
cnf(c_0_2371,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_1739]) ).
cnf(c_0_2372,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_1740]) ).
cnf(c_0_2373,plain,
( X1 = c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1741]) ).
cnf(c_0_2374,plain,
( X1 = c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1742]) ).
cnf(c_0_2375,plain,
( X1 = c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1743]) ).
cnf(c_0_2376,plain,
( X1 = c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1744]) ).
cnf(c_0_2377,plain,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1745]) ).
cnf(c_0_2378,plain,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1746]) ).
cnf(c_0_2379,plain,
( X1 = X2
| ~ c_fequal(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1747]) ).
cnf(c_0_2380,plain,
c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),hAPP(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_1748]) ).
cnf(c_0_2381,plain,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Suc(X2),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Power_Opower(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1749]) ).
cnf(c_0_2382,plain,
c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_1750]) ).
cnf(c_0_2383,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1751]) ).
cnf(c_0_2384,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1752]) ).
cnf(c_0_2385,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Osemiring__0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1753]) ).
cnf(c_0_2386,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1754]) ).
cnf(c_0_2387,plain,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Power_Opower(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1755]) ).
cnf(c_0_2388,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_1756]) ).
cnf(c_0_2389,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_1757]) ).
cnf(c_0_2390,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_1758]) ).
cnf(c_0_2391,plain,
c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X1)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
inference(split_conjunct,[status(thm)],[c_0_1759]) ).
cnf(c_0_2392,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_1760]) ).
cnf(c_0_2393,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_1761]) ).
cnf(c_0_2394,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_1762]) ).
cnf(c_0_2395,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_1763]) ).
cnf(c_0_2396,plain,
c_Ring__and__Field_Odvd__class_Odvd(c_Suc(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_1764]) ).
cnf(c_0_2397,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_1765]) ).
cnf(c_0_2398,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_1766]) ).
cnf(c_0_2399,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_1767]) ).
cnf(c_0_2400,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_1768]) ).
cnf(c_0_2401,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_1769]) ).
cnf(c_0_2402,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_1770]) ).
cnf(c_0_2403,plain,
c_Power_Opower__class_Opower(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_1771]) ).
cnf(c_0_2404,plain,
c_Power_Opower__class_Opower(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_1772]) ).
cnf(c_0_2405,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1773]) ).
cnf(c_0_2406,plain,
( c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1774]) ).
cnf(c_0_2407,plain,
( c_Divides_Odiv__class_Odiv(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1775]) ).
cnf(c_0_2408,plain,
( c_Divides_Odiv__class_Omod(X1,c_HOL_Oone__class_Oone(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1776]) ).
cnf(c_0_2409,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1777]) ).
cnf(c_0_2410,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1778]) ).
cnf(c_0_2411,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1779]) ).
cnf(c_0_2412,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1780]) ).
cnf(c_0_2413,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Omult__zero(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1781]) ).
cnf(c_0_2414,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Omult__zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1782]) ).
cnf(c_0_2415,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1783]) ).
cnf(c_0_2416,plain,
( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1784]) ).
cnf(c_0_2417,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_1785]) ).
cnf(c_0_2418,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_1786]) ).
cnf(c_0_2419,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(X1,X1,X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1787]) ).
cnf(c_0_2420,plain,
( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1788]) ).
cnf(c_0_2421,plain,
( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Power_Opower(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1789]) ).
cnf(c_0_2422,plain,
( c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_Divides_Osemiring__div(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1790]) ).
cnf(c_0_2423,plain,
( c_Divides_Odiv__class_Odiv(X1,c_HOL_Oone__class_Oone(X2),X2) = X1
| ~ class_Divides_Osemiring__div(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1791]) ).
cnf(c_0_2424,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1792]) ).
cnf(c_0_2425,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1793]) ).
cnf(c_0_2426,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1794]) ).
cnf(c_0_2427,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X2),X2) = X1
| ~ class_OrderedGroup_Omonoid__mult(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1795]) ).
cnf(c_0_2428,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X2),X2) = X1
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1796]) ).
cnf(c_0_2429,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1797]) ).
cnf(c_0_2430,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_1798]) ).
cnf(c_0_2431,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1799]) ).
cnf(c_0_2432,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1800]) ).
cnf(c_0_2433,plain,
c_Divides_Odiv__class_Omod(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1801]) ).
cnf(c_0_2434,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_1802]) ).
cnf(c_0_2435,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_1803]) ).
cnf(c_0_2436,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_1804]) ).
cnf(c_0_2437,plain,
c_Divides_Odiv__class_Odiv(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = X1,
inference(split_conjunct,[status(thm)],[c_0_1805]) ).
cnf(c_0_2438,plain,
( c_Divides_Odiv__class_Omod(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1806]) ).
cnf(c_0_2439,plain,
( c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X2) = X1
| ~ class_OrderedGroup_Omonoid__mult(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1807]) ).
cnf(c_0_2440,plain,
( c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X2) = X1
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1808]) ).
cnf(c_0_2441,plain,
c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1809]) ).
cnf(c_0_2442,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OVar(X3),
inference(split_conjunct,[status(thm)],[c_0_1810]) ).
cnf(c_0_2443,plain,
c_Lambda_OdB_OVar(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_1811]) ).
cnf(c_0_2444,plain,
c_Lambda_OdB_OAbs(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_1812]) ).
cnf(c_0_2445,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OAbs(X3),
inference(split_conjunct,[status(thm)],[c_0_1813]) ).
cnf(c_0_2446,plain,
c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_1814]) ).
cnf(c_0_2447,plain,
( c_HOL_Otimes__class_Otimes(X1,X1,X2) = X1
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1815]) ).
cnf(c_0_2448,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_1816]) ).
cnf(c_0_2449,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_1817]) ).
cnf(c_0_2450,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X1,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1818]) ).
cnf(c_0_2451,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1819]) ).
cnf(c_0_2452,plain,
c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1820]) ).
cnf(c_0_2453,plain,
c_List_Olistsp(X1,c_List_Olist_ONil(X2),X2),
inference(split_conjunct,[status(thm)],[c_0_1821]) ).
cnf(c_0_2454,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_1822]) ).
cnf(c_0_2455,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1823]) ).
cnf(c_0_2456,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1824]) ).
cnf(c_0_2457,plain,
c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1825]) ).
cnf(c_0_2458,plain,
c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1826]) ).
cnf(c_0_2459,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1827]) ).
cnf(c_0_2460,plain,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1828]) ).
cnf(c_0_2461,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_1829]) ).
cnf(c_0_2462,plain,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1,
inference(split_conjunct,[status(thm)],[c_0_1830]) ).
cnf(c_0_2463,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) = X1,
inference(split_conjunct,[status(thm)],[c_0_1831]) ).
cnf(c_0_2464,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_1832]) ).
cnf(c_0_2465,plain,
c_fequal(X1,X1,X2),
inference(split_conjunct,[status(thm)],[c_0_1833]) ).
cnf(c_0_2466,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_1834]) ).
cnf(c_0_2467,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_1835]) ).
cnf(c_0_2468,plain,
c_Ring__and__Field_Odvd__class_Odvd(X1,X1,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1836]) ).
cnf(c_0_2469,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_1837]) ).
cnf(c_0_2470,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_1838]) ).
cnf(c_0_2471,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_1839]) ).
cnf(c_0_2472,plain,
( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X1),c_Lambda_OdB_OAbs(X2))
| ~ c_Lambda_Obeta(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1840]) ).
cnf(c_0_2473,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1841]) ).
cnf(c_0_2474,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1842]) ).
cnf(c_0_2475,plain,
~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X1),X2),
inference(split_conjunct,[status(thm)],[c_0_1843]) ).
cnf(c_0_2476,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_1844]) ).
cnf(c_0_2477,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_1845]) ).
cnf(c_0_2478,plain,
c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(X1),tc_Lambda_OdB) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1846]) ).
cnf(c_0_2479,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_1847]) ).
cnf(c_0_2480,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_1848]) ).
cnf(c_0_2481,plain,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1849]) ).
cnf(c_0_2482,plain,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1850]) ).
cnf(c_0_2483,plain,
( X1 = X2
| c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1851]) ).
cnf(c_0_2484,plain,
( X1 = X2
| c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1852]) ).
cnf(c_0_2485,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_ATP__Linkup_Osko__Nat__Xnot0__implies__Suc__1__1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1853]) ).
cnf(c_0_2486,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__Xnchotomy__1__1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1854]) ).
cnf(c_0_2487,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__Xexhaust__1__1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1855]) ).
cnf(c_0_2488,plain,
c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OAbs(X2),
inference(split_conjunct,[status(thm)],[c_0_1856]) ).
cnf(c_0_2489,plain,
c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OVar(X2),
inference(split_conjunct,[status(thm)],[c_0_1857]) ).
cnf(c_0_2490,plain,
c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(X1)) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1858]) ).
cnf(c_0_2491,plain,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
inference(split_conjunct,[status(thm)],[c_0_1859]) ).
cnf(c_0_2492,plain,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
inference(split_conjunct,[status(thm)],[c_0_1860]) ).
cnf(c_0_2493,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1861]) ).
cnf(c_0_2494,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1862]) ).
cnf(c_0_2495,plain,
c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_1863]) ).
cnf(c_0_2496,plain,
c_Suc(X1) != X1,
inference(split_conjunct,[status(thm)],[c_0_1864]) ).
cnf(c_0_2497,plain,
X1 != c_Suc(X1),
inference(split_conjunct,[status(thm)],[c_0_1865]) ).
cnf(c_0_2498,plain,
class_Power_Opower(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1866]) ).
cnf(c_0_2499,plain,
class_Orderings_Oorder(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1867]) ).
cnf(c_0_2500,plain,
class_Orderings_Olinorder(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1868]) ).
cnf(c_0_2501,plain,
class_Orderings_Opreorder(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1869]) ).
cnf(c_0_2502,plain,
class_Ring__and__Field_Odvd(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1870]) ).
cnf(c_0_2503,plain,
class_Nat_Osemiring__char__0(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1871]) ).
cnf(c_0_2504,plain,
class_Divides_Osemiring__div(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1872]) ).
cnf(c_0_2505,plain,
class_OrderedGroup_Omonoid__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1873]) ).
cnf(c_0_2506,plain,
class_Ring__and__Field_Osemiring(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1874]) ).
cnf(c_0_2507,plain,
class_OrderedGroup_Omonoid__mult(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1875]) ).
cnf(c_0_2508,plain,
class_Ring__and__Field_Omult__zero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1876]) ).
cnf(c_0_2509,plain,
class_Ring__and__Field_Osemiring__0(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1877]) ).
cnf(c_0_2510,plain,
class_Ring__and__Field_Osemiring__1(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1878]) ).
cnf(c_0_2511,plain,
class_OrderedGroup_Osemigroup__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1879]) ).
cnf(c_0_2512,plain,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1880]) ).
cnf(c_0_2513,plain,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1881]) ).
cnf(c_0_2514,plain,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1882]) ).
cnf(c_0_2515,plain,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1883]) ).
cnf(c_0_2516,plain,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1884]) ).
cnf(c_0_2517,plain,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1885]) ).
cnf(c_0_2518,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1886]) ).
cnf(c_0_2519,plain,
class_Ring__and__Field_Oordered__semidom(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1887]) ).
cnf(c_0_2520,plain,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1888]) ).
cnf(c_0_2521,plain,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1889]) ).
cnf(c_0_2522,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1890]) ).
cnf(c_0_2523,plain,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1891]) ).
cnf(c_0_2524,plain,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1892]) ).
cnf(c_0_2525,plain,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1893]) ).
cnf(c_0_2526,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1894]) ).
cnf(c_0_2527,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1895]) ).
cnf(c_0_2528,plain,
c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X3,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = 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_1896,
[final] ).
cnf(c_0_2529,plain,
( c_Type_Otypings(X1,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X2,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X5,tc_Lambda_OdB,tc_Lambda_OdB),X6)
| ~ c_Type_Otyping(X1,X2,X3)
| ~ c_Type_Otypings(c_Type_Oshift(X1,X4,X3,tc_Type_Otype),X5,X6) ),
c_0_1897,
[final] ).
cnf(c_0_2530,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_1898,
[final] ).
cnf(c_0_2531,plain,
c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X1),X3),c_List_Omap(c_COMBC(c_Lambda_Olift,X3,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),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_1899,
[final] ).
cnf(c_0_2532,plain,
( X4 = X5
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X5) ),
c_0_1900,
[final] ).
cnf(c_0_2533,plain,
c_COMBB(X1,X2,X3,X4,X5,X6) = hAPP(X1,hAPP(X2,X3)),
c_0_1901,
[final] ).
cnf(c_0_2534,plain,
( c_Type_Otypings(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3)
| ~ c_Type_Otypings(X1,X2,X3) ),
c_0_1902,
[final] ).
cnf(c_0_2535,plain,
( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB) ),
c_0_1903,
[final] ).
cnf(c_0_2536,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_1904,
[final] ).
cnf(c_0_2537,plain,
( 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))
| ~ c_Lambda_Obeta(X1,X2) ),
c_0_1905,
[final] ).
cnf(c_0_2538,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_1906,
[final] ).
cnf(c_0_2539,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_1907,
[final] ).
cnf(c_0_2540,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_1908,
[final] ).
cnf(c_0_2541,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_1909,
[final] ).
cnf(c_0_2542,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_1910,
[final] ).
cnf(c_0_2543,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_1911,
[final] ).
cnf(c_0_2544,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_1912,
[final] ).
cnf(c_0_2545,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_1913,
[final] ).
cnf(c_0_2546,plain,
( hBOOL(hAPP(X1,X2))
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat)),X4),X3,tc_nat)))
| ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat) ),
c_0_1914,
[final] ).
cnf(c_0_2547,plain,
( hBOOL(hAPP(X1,X2))
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat)),X2),X3,tc_nat)))
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
c_0_1915,
[final] ).
cnf(c_0_2548,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1)),c_Divides_Odiv__class_Omod(X2,X3,X1))),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)
| ~ class_Divides_Osemiring__div(X1) ),
c_0_1916,
[final] ).
cnf(c_0_2549,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X3,X2,X1),X1)),c_Divides_Odiv__class_Omod(X3,X2,X1))),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)
| ~ class_Divides_Osemiring__div(X1) ),
c_0_1917,
[final] ).
cnf(c_0_2550,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_1918,
[final] ).
cnf(c_0_2551,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(X1,X3,tc_nat)),c_Divides_Odiv__class_Odiv(X2,X3,tc_nat))),c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(X1,X3,tc_nat)),c_Divides_Odiv__class_Omod(X2,X3,tc_nat)),X3,tc_nat)) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat),
c_0_1919,
[final] ).
cnf(c_0_2552,plain,
hAPP(c_COMBC(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X1,X6),X2),
c_0_1920,
[final] ).
cnf(c_0_2553,plain,
hAPP(c_COMBC(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X1,X6),X2),
c_0_1921,
[final] ).
cnf(c_0_2554,plain,
( hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) = X3
| hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
c_0_1922,
[final] ).
cnf(c_0_2555,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_1923,
[final] ).
cnf(c_0_2556,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_1924,
[final] ).
cnf(c_0_2557,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_1925,
[final] ).
cnf(c_0_2558,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_1926,
[final] ).
cnf(c_0_2559,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_1927,
[final] ).
cnf(c_0_2560,plain,
( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| c_Lambda_OdB_OVar(X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
c_0_1928,
[final] ).
cnf(c_0_2561,plain,
( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X3) ),
c_0_1929,
[final] ).
cnf(c_0_2562,plain,
( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
c_0_1930,
[final] ).
cnf(c_0_2563,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Odiv(X1,X2,tc_nat),X3,tc_nat),tc_nat)),c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) = c_Divides_Odiv__class_Omod(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
c_0_1931,
[final] ).
cnf(c_0_2564,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(X4,X1,tc_nat),tc_nat)),X2),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
c_0_1932,
[final] ).
cnf(c_0_2565,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X2,X3,tc_nat),tc_nat)),c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X3,tc_nat),tc_nat),X3,tc_nat)) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat),
c_0_1933,
[final] ).
cnf(c_0_2566,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1934,
[final] ).
cnf(c_0_2567,plain,
c_Type_Oshift(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),X5,X4),c_Suc(X2),X3,X4) = c_Type_Oshift(c_Type_Oshift(X1,X2,X3,X4),c_HOL_Ozero__class_Ozero(tc_nat),X5,X4),
c_0_1935,
[final] ).
cnf(c_0_2568,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X4,X3,X1)),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X3,X1)),X5)
| ~ class_Ring__and__Field_Osemiring(X1) ),
c_0_1936,
[final] ).
cnf(c_0_2569,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat)),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),X2,tc_nat)),X4),
c_0_1937,
[final] ).
cnf(c_0_2570,plain,
c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),
c_0_1938,
[final] ).
cnf(c_0_2571,plain,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X2,X1)),c_HOL_Otimes__class_Otimes(X3,X3,X1)),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1939,
[final] ).
cnf(c_0_2572,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_1940,
[final] ).
cnf(c_0_2573,plain,
c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OVar(X1),
c_0_1941,
[final] ).
cnf(c_0_2574,plain,
c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OAbs(X1),
c_0_1942,
[final] ).
cnf(c_0_2575,plain,
c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OAbs(X1),
c_0_1943,
[final] ).
cnf(c_0_2576,plain,
c_List_Ofoldl(X1,X2,c_List_Olist_ONil(X3),X4,X3) = X2,
c_0_1944,
[final] ).
cnf(c_0_2577,plain,
( X1 = X2
| X3 = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X3,X5)),c_HOL_Otimes__class_Otimes(X2,X4,X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X4,X5)),c_HOL_Otimes__class_Otimes(X2,X3,X5))
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
c_0_1945,
[final] ).
cnf(c_0_2578,plain,
( X1 = X2
| X3 = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X3,X5)),c_HOL_Otimes__class_Otimes(X2,X4,X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X4,X5)),c_HOL_Otimes__class_Otimes(X2,X3,X5))
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
c_0_1946,
[final] ).
cnf(c_0_2579,plain,
( c_Type_Otyping(X1,hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4),X5)
| ~ c_Type_Otyping(c_Type_Oshift(X1,X4,X6,tc_Type_Otype),X2,X5)
| ~ c_Type_Otyping(X1,X3,X6) ),
c_0_1947,
[final] ).
cnf(c_0_2580,plain,
c_Divides_Odiv__class_Omod(c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),X3)),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X3),X2,tc_nat),
c_0_1948,
[final] ).
cnf(c_0_2581,plain,
( X1 = X2
| X3 = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X4,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat)) ),
c_0_1949,
[final] ).
cnf(c_0_2582,plain,
( X1 = X2
| X3 = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X4,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat)) ),
c_0_1950,
[final] ).
cnf(c_0_2583,plain,
( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X4,X1)),c_Divides_Odiv__class_Omod(X3,X4,X1)),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
c_0_1951,
[final] ).
cnf(c_0_2584,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_1952,
[final] ).
cnf(c_0_2585,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X3,X3,X2)),c_HOL_Otimes__class_Otimes(X1,X1,X2)),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_1953,
[final] ).
cnf(c_0_2586,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X1,X1,X2)),c_HOL_Otimes__class_Otimes(X3,X3,X2)),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_1954,
[final] ).
cnf(c_0_2587,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X3,X2),X3,X2)),c_Divides_Odiv__class_Omod(X1,X3,X2)) = X1
| ~ class_Divides_Osemiring__div(X2) ),
c_0_1955,
[final] ).
cnf(c_0_2588,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1)),c_Divides_Odiv__class_Omod(X2,X3,X1)) = X2
| ~ class_Divides_Osemiring__div(X1) ),
c_0_1956,
[final] ).
cnf(c_0_2589,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X3,X2,X1),X1)),c_Divides_Odiv__class_Omod(X3,X2,X1)) = X3
| ~ class_Divides_Osemiring__div(X1) ),
c_0_1957,
[final] ).
cnf(c_0_2590,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_1958,
[final] ).
cnf(c_0_2591,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),c_HOL_Otimes__class_Otimes(X2,X4,X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X2,X3,X1))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
c_0_1959,
[final] ).
cnf(c_0_2592,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),c_HOL_Otimes__class_Otimes(X2,X4,X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X2,X3,X1))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
c_0_1960,
[final] ).
cnf(c_0_2593,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X4,X3),c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1961,
[final] ).
cnf(c_0_2594,plain,
( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X3,X1)),X4),X3,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X3,X1)
| ~ class_Divides_Osemiring__div(X1) ),
c_0_1962,
[final] ).
cnf(c_0_2595,plain,
( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X4,X1)),X3),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
c_0_1963,
[final] ).
cnf(c_0_2596,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_1964,
[final] ).
cnf(c_0_2597,plain,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X5,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X5,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1965,
[final] ).
cnf(c_0_2598,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),
c_0_1966,
[final] ).
cnf(c_0_2599,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),
c_0_1967,
[final] ).
cnf(c_0_2600,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Odiv(X2,X1,X3)),c_Divides_Odiv__class_Odiv(X4,X1,X3)) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X1,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1968,
[final] ).
cnf(c_0_2601,plain,
( c_Type_Otyping(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X2),X4),X3)
| ~ c_Type_Otyping(X1,X2,X3) ),
c_0_1969,
[final] ).
cnf(c_0_2602,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_1970,
[final] ).
cnf(c_0_2603,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Suc(c_Divides_Odiv__class_Odiv(X1,X2,tc_nat)),tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
c_0_1971,
[final] ).
cnf(c_0_2604,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X6,X3),X4,X3)
| c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X5,X4,X3)
| c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X6,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1972,
[final] ).
cnf(c_0_2605,plain,
( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X6),X4,X1)
| c_Divides_Odiv__class_Omod(X2,X4,X1) != c_Divides_Odiv__class_Omod(X5,X4,X1)
| c_Divides_Odiv__class_Omod(X3,X4,X1) != c_Divides_Odiv__class_Omod(X6,X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
c_0_1973,
[final] ).
cnf(c_0_2606,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_1974,
[final] ).
cnf(c_0_2607,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1975,
[final] ).
cnf(c_0_2608,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X4,X5,X3),X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_1976,
[final] ).
cnf(c_0_2609,plain,
c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),X3),X2,tc_nat) = c_Divides_Odiv__class_Omod(X3,X2,tc_nat),
c_0_1977,
[final] ).
cnf(c_0_2610,plain,
( hAPP(c_Type_Oshift(X3,X2,X4,X5),X1) = hAPP(X3,X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1978,
[final] ).
cnf(c_0_2611,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X1,X1,X2)),c_HOL_Otimes__class_Otimes(X3,X3,X2)) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_1979,
[final] ).
cnf(c_0_2612,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X3,X3,X2)),c_HOL_Otimes__class_Otimes(X1,X1,X2)) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_1980,
[final] ).
cnf(c_0_2613,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_1981,
[final] ).
cnf(c_0_2614,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_Lambda_OdB)),c_Nat_Osize__class_Osize(X2,tc_Lambda_OdB))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),tc_Lambda_OdB),
c_0_1982,
[final] ).
cnf(c_0_2615,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X3,X1)),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1)) = X2
| ~ class_Divides_Osemiring__div(X1) ),
c_0_1983,
[final] ).
cnf(c_0_2616,plain,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_1984,
[final] ).
cnf(c_0_2617,plain,
( c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_1985,
[final] ).
cnf(c_0_2618,plain,
( c_HOL_Oord__class_Oless(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_1986,
[final] ).
cnf(c_0_2619,plain,
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_1987,
[final] ).
cnf(c_0_2620,plain,
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_1988,
[final] ).
cnf(c_0_2621,plain,
( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(X3,X2,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Otimes__class_Otimes(X2,X5,tc_nat)) ),
c_0_1989,
[final] ).
cnf(c_0_2622,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
c_0_1990,
[final] ).
cnf(c_0_2623,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
c_0_1991,
[final] ).
cnf(c_0_2624,plain,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,tc_nat),c_Power_Opower__class_Opower(X1,X3,tc_nat),tc_nat) ),
c_0_1992,
[final] ).
cnf(c_0_2625,plain,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
c_0_1993,
[final] ).
cnf(c_0_2626,plain,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X2,X3),c_Power_Opower__class_Opower(X4,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(X3),X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
c_0_1994,
[final] ).
cnf(c_0_2627,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
c_0_1995,
[final] ).
cnf(c_0_2628,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
c_0_1996,
[final] ).
cnf(c_0_2629,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
c_0_1997,
[final] ).
cnf(c_0_2630,plain,
( c_HOL_Oord__class_Oless(X2,X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
c_0_1998,
[final] ).
cnf(c_0_2631,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
c_0_1999,
[final] ).
cnf(c_0_2632,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
c_0_2000,
[final] ).
cnf(c_0_2633,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_2001,
[final] ).
cnf(c_0_2634,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_2002,
[final] ).
cnf(c_0_2635,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_2003,
[final] ).
cnf(c_0_2636,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X2,X3),X4,X3),X2,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X4,X3),X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_2004,
[final] ).
cnf(c_0_2637,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),c_HOL_Otimes__class_Otimes(X4,X1,X2)),X1,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X4),c_Divides_Odiv__class_Odiv(X3,X1,X2))
| ~ class_Divides_Osemiring__div(X2) ),
c_0_2005,
[final] ).
cnf(c_0_2638,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),c_HOL_Otimes__class_Otimes(X1,X4,X2)),X1,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X4),c_Divides_Odiv__class_Odiv(X3,X1,X2))
| ~ class_Divides_Osemiring__div(X2) ),
c_0_2006,
[final] ).
cnf(c_0_2639,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
c_0_2007,
[final] ).
cnf(c_0_2640,plain,
( c_HOL_Oord__class_Oless(X2,X4,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
c_0_2008,
[final] ).
cnf(c_0_2641,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2)),c_HOL_Otimes__class_Otimes(X1,X4,X2)) = c_HOL_Otimes__class_Otimes(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X4),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
c_0_2009,
[final] ).
cnf(c_0_2642,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X3,X4,X1)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
c_0_2010,
[final] ).
cnf(c_0_2643,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X3,X4,X1)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_2011,
[final] ).
cnf(c_0_2644,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),c_HOL_Otimes__class_Otimes(X4,X3,X1)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_2012,
[final] ).
cnf(c_0_2645,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_2013,
[final] ).
cnf(c_0_2646,plain,
( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_Divides_Odiv__class_Omod(X3,X4,X1)),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
c_0_2014,
[final] ).
cnf(c_0_2647,plain,
( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_Divides_Odiv__class_Omod(X3,X4,X1)),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
c_0_2015,
[final] ).
cnf(c_0_2648,plain,
( c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(X2,X4,X3),c_Power_Opower__class_Opower(X1,X4,X3),X3) = c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(X2,X1,X3),X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_2016,
[final] ).
cnf(c_0_2649,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),c_HOL_Otimes__class_Otimes(X1,X3,X2)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),c_HOL_Otimes__class_Otimes(X1,X4,X2))
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_2017,
[final] ).
cnf(c_0_2650,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_2018,
[final] ).
cnf(c_0_2651,plain,
hAPP(c_Type_Oshift(X1,X2,X3,X4),X2) = X3,
c_0_2019,
[final] ).
cnf(c_0_2652,plain,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X1),X3,tc_nat),tc_nat) ),
c_0_2020,
[final] ).
cnf(c_0_2653,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)) = c_HOL_Otimes__class_Otimes(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat),
c_0_2021,
[final] ).
cnf(c_0_2654,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat),
c_0_2022,
[final] ).
cnf(c_0_2655,plain,
( X2 = c_HOL_Ozero__class_Ozero(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
c_0_2023,
[final] ).
cnf(c_0_2656,plain,
( X1 = c_HOL_Ozero__class_Ozero(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
c_0_2024,
[final] ).
cnf(c_0_2657,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_2025,
[final] ).
cnf(c_0_2658,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_2026,
[final] ).
cnf(c_0_2659,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)) ),
c_0_2027,
[final] ).
cnf(c_0_2660,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_2028,
[final] ).
cnf(c_0_2661,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_2029,
[final] ).
cnf(c_0_2662,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
c_0_2030,
[final] ).
cnf(c_0_2663,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
c_0_2031,
[final] ).
cnf(c_0_2664,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
c_0_2032,
[final] ).
cnf(c_0_2665,plain,
( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
c_0_2033,
[final] ).
cnf(c_0_2666,plain,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
c_0_2034,
[final] ).
cnf(c_0_2667,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3) ),
c_0_2035,
[final] ).
cnf(c_0_2668,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_2036,
[final] ).
cnf(c_0_2669,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_2037,
[final] ).
cnf(c_0_2670,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
c_0_2038,
[final] ).
cnf(c_0_2671,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
c_0_2039,
[final] ).
cnf(c_0_2672,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_2040,
[final] ).
cnf(c_0_2673,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_2041,
[final] ).
cnf(c_0_2674,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
c_0_2042,
[final] ).
cnf(c_0_2675,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
c_0_2043,
[final] ).
cnf(c_0_2676,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_2044,
[final] ).
cnf(c_0_2677,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_2045,
[final] ).
cnf(c_0_2678,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_2046,
[final] ).
cnf(c_0_2679,plain,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X1,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
c_0_2047,
[final] ).
cnf(c_0_2680,plain,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_2048,
[final] ).
cnf(c_0_2681,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_2049,
[final] ).
cnf(c_0_2682,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),X3) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Oone__class_Oone(X1)),X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_2050,
[final] ).
cnf(c_0_2683,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1),X1,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_Divides_Odiv__class_Odiv(X3,X1,X2)),c_HOL_Oone__class_Oone(X2))
| ~ class_Divides_Osemiring__div(X2) ),
c_0_2051,
[final] ).
cnf(c_0_2684,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),X1,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_Divides_Odiv__class_Odiv(X3,X1,X2)),c_HOL_Oone__class_Oone(X2))
| ~ class_Divides_Osemiring__div(X2) ),
c_0_2052,
[final] ).
cnf(c_0_2685,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_2053,
[final] ).
cnf(c_0_2686,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_2054,
[final] ).
cnf(c_0_2687,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_2055,
[final] ).
cnf(c_0_2688,plain,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3) = c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_2056,
[final] ).
cnf(c_0_2689,plain,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3) = c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X3) ),
c_0_2057,
[final] ).
cnf(c_0_2690,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
c_0_2058,
[final] ).
cnf(c_0_2691,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
c_0_2059,
[final] ).
cnf(c_0_2692,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
c_0_2060,
[final] ).
cnf(c_0_2693,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
c_0_2061,
[final] ).
cnf(c_0_2694,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
c_0_2062,
[final] ).
cnf(c_0_2695,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
c_0_2063,
[final] ).
cnf(c_0_2696,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_2064,
[final] ).
cnf(c_0_2697,plain,
( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Otimes__class_Otimes(X3,X4,X1)),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1)
| ~ class_Divides_Osemiring__div(X1) ),
c_0_2065,
[final] ).
cnf(c_0_2698,plain,
( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Otimes__class_Otimes(X3,X4,X1)),X4,X1) = c_Divides_Odiv__class_Omod(X2,X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
c_0_2066,
[final] ).
cnf(c_0_2699,plain,
( hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
c_0_2067,
[final] ).
cnf(c_0_2700,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
c_0_2068,
[final] ).
cnf(c_0_2701,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),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
c_0_2069,
[final] ).
cnf(c_0_2702,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
c_0_2070,
[final] ).
cnf(c_0_2703,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_2071,
[final] ).
cnf(c_0_2704,plain,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X3),X3) = c_Power_Opower__class_Opower(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X4),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_2072,
[final] ).
cnf(c_0_2705,plain,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X4),c_Power_Opower__class_Opower(X1,X3,X4),X4) = c_Power_Opower__class_Opower(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X4)
| ~ class_OrderedGroup_Omonoid__mult(X4) ),
c_0_2073,
[final] ).
cnf(c_0_2706,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_2074,
[final] ).
cnf(c_0_2707,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_2075,
[final] ).
cnf(c_0_2708,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_2076,
[final] ).
cnf(c_0_2709,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_2077,
[final] ).
cnf(c_0_2710,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_2078,
[final] ).
cnf(c_0_2711,plain,
c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X3,tc_nat),
c_0_2079,
[final] ).
cnf(c_0_2712,plain,
c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X3,tc_nat),tc_nat),
c_0_2080,
[final] ).
cnf(c_0_2713,plain,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_2081,
[final] ).
cnf(c_0_2714,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_2082,
[final] ).
cnf(c_0_2715,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X3,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X4)
| ~ class_Divides_Osemiring__div(X4) ),
c_0_2083,
[final] ).
cnf(c_0_2716,plain,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
c_0_2084,
[final] ).
cnf(c_0_2717,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_2085,
[final] ).
cnf(c_0_2718,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Omap(X4,X1,X2,X3) != c_List_Olist_ONil(X3) ),
c_0_2086,
[final] ).
cnf(c_0_2719,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Omap(X3,X1,X2,X4) != c_List_Olist_ONil(X4) ),
c_0_2087,
[final] ).
cnf(c_0_2720,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X1)),c_Lambda_OdB_OdB__size(X2))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),
c_0_2088,
[final] ).
cnf(c_0_2721,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_2089,
[final] ).
cnf(c_0_2722,plain,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,c_Suc(X3),X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_2090,
[final] ).
cnf(c_0_2723,plain,
( c_Lambda_Obeta(hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4))
| ~ c_Lambda_Obeta(X1,X2) ),
c_0_2091,
[final] ).
cnf(c_0_2724,plain,
( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
c_0_2092,
[final] ).
cnf(c_0_2725,plain,
hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X1),X2)),X3),X2) = X1,
c_0_2093,
[final] ).
cnf(c_0_2726,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_2094,
[final] ).
cnf(c_0_2727,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2) ),
c_0_2095,
[final] ).
cnf(c_0_2728,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
c_0_2096,
[final] ).
cnf(c_0_2729,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
c_0_2097,
[final] ).
cnf(c_0_2730,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,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_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_2098,
[final] ).
cnf(c_0_2731,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
c_0_2099,
[final] ).
cnf(c_0_2732,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_2100,
[final] ).
cnf(c_0_2733,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_2101,
[final] ).
cnf(c_0_2734,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
c_0_2102,
[final] ).
cnf(c_0_2735,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
c_0_2103,
[final] ).
cnf(c_0_2736,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_2104,
[final] ).
cnf(c_0_2737,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_2105,
[final] ).
cnf(c_0_2738,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_2106,
[final] ).
cnf(c_0_2739,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_2107,
[final] ).
cnf(c_0_2740,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
c_0_2108,
[final] ).
cnf(c_0_2741,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
c_0_2109,
[final] ).
cnf(c_0_2742,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_2110,
[final] ).
cnf(c_0_2743,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
c_0_2111,
[final] ).
cnf(c_0_2744,plain,
( c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),X1,tc_nat) = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) ),
c_0_2112,
[final] ).
cnf(c_0_2745,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_2113,
[final] ).
cnf(c_0_2746,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_2114,
[final] ).
cnf(c_0_2747,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_2115,
[final] ).
cnf(c_0_2748,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_2116,
[final] ).
cnf(c_0_2749,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_2117,
[final] ).
cnf(c_0_2750,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
c_0_2118,
[final] ).
cnf(c_0_2751,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_2119,
[final] ).
cnf(c_0_2752,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_2120,
[final] ).
cnf(c_0_2753,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_2121,
[final] ).
cnf(c_0_2754,plain,
( X2 = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),X1,tc_nat) ),
c_0_2122,
[final] ).
cnf(c_0_2755,plain,
( X2 = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X1,tc_nat) ),
c_0_2123,
[final] ).
cnf(c_0_2756,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),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_2124,
[final] ).
cnf(c_0_2757,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_2125,
[final] ).
cnf(c_0_2758,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Otimes__class_Otimes(X3,X2,X1)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),c_HOL_Oone__class_Oone(X1)),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_2126,
[final] ).
cnf(c_0_2759,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X4,X1,X2),X2) = c_Divides_Odiv__class_Odiv(X3,X4,X2)
| ~ class_Divides_Osemiring__div(X2) ),
c_0_2127,
[final] ).
cnf(c_0_2760,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2) = c_Divides_Odiv__class_Odiv(X3,X4,X2)
| ~ class_Divides_Osemiring__div(X2) ),
c_0_2128,
[final] ).
cnf(c_0_2761,plain,
( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Odiv(X2,X1,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
c_0_2129,
[final] ).
cnf(c_0_2762,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X4),X3,X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
c_0_2130,
[final] ).
cnf(c_0_2763,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X1,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
c_0_2131,
[final] ).
cnf(c_0_2764,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X4),X3,X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
c_0_2132,
[final] ).
cnf(c_0_2765,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_2133,
[final] ).
cnf(c_0_2766,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X4,X3),X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_2134,
[final] ).
cnf(c_0_2767,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ class_OrderedGroup_Oab__semigroup__mult(X3) ),
c_0_2135,
[final] ).
cnf(c_0_2768,plain,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),X1,X3) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3)
| ~ class_OrderedGroup_Omonoid__mult(X3) ),
c_0_2136,
[final] ).
cnf(c_0_2769,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
c_0_2137,
[final] ).
cnf(c_0_2770,plain,
( c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X1,X2,X4),X3,X4) = c_Power_Opower__class_Opower(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4)
| ~ class_OrderedGroup_Omonoid__mult(X4) ),
c_0_2138,
[final] ).
cnf(c_0_2771,plain,
( c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X1,X2,X3),X4,X3) = c_Power_Opower__class_Opower(X1,c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_2139,
[final] ).
cnf(c_0_2772,plain,
c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat),
c_0_2140,
[final] ).
cnf(c_0_2773,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_2141,
[final] ).
cnf(c_0_2774,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_2142,
[final] ).
cnf(c_0_2775,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_2143,
[final] ).
cnf(c_0_2776,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_2144,
[final] ).
cnf(c_0_2777,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_2145,
[final] ).
cnf(c_0_2778,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_2146,
[final] ).
cnf(c_0_2779,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(X2,X3,tc_nat) ),
c_0_2147,
[final] ).
cnf(c_0_2780,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_2148,
[final] ).
cnf(c_0_2781,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_2149,
[final] ).
cnf(c_0_2782,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_2150,
[final] ).
cnf(c_0_2783,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_2151,
[final] ).
cnf(c_0_2784,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_2152,
[final] ).
cnf(c_0_2785,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
c_0_2153,
[final] ).
cnf(c_0_2786,plain,
c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(X1,X2,tc_nat),X3,tc_nat) = c_Divides_Odiv__class_Odiv(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
c_0_2154,
[final] ).
cnf(c_0_2787,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X1,X2,tc_nat),tc_nat) ),
c_0_2155,
[final] ).
cnf(c_0_2788,plain,
( c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X4,X2,X3),X1,X3) = c_Divides_Odiv__class_Omod(X4,X1,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_2156,
[final] ).
cnf(c_0_2789,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(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
c_0_2157,
[final] ).
cnf(c_0_2790,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),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
c_0_2158,
[final] ).
cnf(c_0_2791,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
c_0_2159,
[final] ).
cnf(c_0_2792,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
c_0_2160,
[final] ).
cnf(c_0_2793,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
c_0_2161,
[final] ).
cnf(c_0_2794,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
c_0_2162,
[final] ).
cnf(c_0_2795,plain,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X3,X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
c_0_2163,
[final] ).
cnf(c_0_2796,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X3,X1),X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
c_0_2164,
[final] ).
cnf(c_0_2797,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2),c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X2),X2),X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_2165,
[final] ).
cnf(c_0_2798,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_2166,
[final] ).
cnf(c_0_2799,plain,
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_2167,
[final] ).
cnf(c_0_2800,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,c_Suc(X3),X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_2168,
[final] ).
cnf(c_0_2801,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_2169,
[final] ).
cnf(c_0_2802,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat) ),
c_0_2170,
[final] ).
cnf(c_0_2803,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_2171,
[final] ).
cnf(c_0_2804,plain,
( X1 = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| c_Power_Opower__class_Opower(X4,X1,X3) != c_Power_Opower__class_Opower(X4,X2,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
c_0_2172,
[final] ).
cnf(c_0_2805,plain,
( c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) = X2
| c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) = c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat) ),
c_0_2173,
[final] ).
cnf(c_0_2806,plain,
c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_2174,
[final] ).
cnf(c_0_2807,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
c_0_2175,
[final] ).
cnf(c_0_2808,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
c_0_2176,
[final] ).
cnf(c_0_2809,plain,
c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat),tc_nat),
c_0_2177,
[final] ).
cnf(c_0_2810,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_2178,
[final] ).
cnf(c_0_2811,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_2179,
[final] ).
cnf(c_0_2812,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_2180,
[final] ).
cnf(c_0_2813,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_2181,
[final] ).
cnf(c_0_2814,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_2182,
[final] ).
cnf(c_0_2815,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_2183,
[final] ).
cnf(c_0_2816,plain,
c_List_Omap(X2,c_List_Olist_ONil(X3),X3,X1) = c_List_Olist_ONil(X1),
c_0_2184,
[final] ).
cnf(c_0_2817,plain,
c_List_Omap(X1,c_List_Olist_ONil(X2),X2,X3) = c_List_Olist_ONil(X3),
c_0_2185,
[final] ).
cnf(c_0_2818,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_Power_Opower__class_Opower(X2,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_2186,
[final] ).
cnf(c_0_2819,plain,
( X1 = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| c_HOL_Otimes__class_Otimes(X3,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat) ),
c_0_2187,
[final] ).
cnf(c_0_2820,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
c_0_2188,
[final] ).
cnf(c_0_2821,plain,
( c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X2,X1,X3),X3) = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_2189,
[final] ).
cnf(c_0_2822,plain,
( c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X1,X3) = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_2190,
[final] ).
cnf(c_0_2823,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_2191,
[final] ).
cnf(c_0_2824,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_2192,
[final] ).
cnf(c_0_2825,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1)),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_2193,
[final] ).
cnf(c_0_2826,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
c_0_2194,
[final] ).
cnf(c_0_2827,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
c_0_2195,
[final] ).
cnf(c_0_2828,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
c_0_2196,
[final] ).
cnf(c_0_2829,plain,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X1,tc_nat) = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
c_0_2197,
[final] ).
cnf(c_0_2830,plain,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),X1,tc_nat) = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
c_0_2198,
[final] ).
cnf(c_0_2831,plain,
( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X2,X1,tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
c_0_2199,
[final] ).
cnf(c_0_2832,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_2200,
[final] ).
cnf(c_0_2833,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),tc_nat),
c_0_2201,
[final] ).
cnf(c_0_2834,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1)),tc_nat),
c_0_2202,
[final] ).
cnf(c_0_2835,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),tc_nat),
c_0_2203,
[final] ).
cnf(c_0_2836,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_2204,
[final] ).
cnf(c_0_2837,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_2205,
[final] ).
cnf(c_0_2838,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_2206,
[final] ).
cnf(c_0_2839,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_2207,
[final] ).
cnf(c_0_2840,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_2208,
[final] ).
cnf(c_0_2841,plain,
( c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) != X2 ),
c_0_2209,
[final] ).
cnf(c_0_2842,plain,
( c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3)
| ~ class_Ring__and__Field_Osemiring__1(X3) ),
c_0_2210,
[final] ).
cnf(c_0_2843,plain,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),X1,X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_2211,
[final] ).
cnf(c_0_2844,plain,
( c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_2212,
[final] ).
cnf(c_0_2845,plain,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),X1,X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
| ~ class_OrderedGroup_Omonoid__mult(X3) ),
c_0_2213,
[final] ).
cnf(c_0_2846,plain,
( c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
| ~ class_Power_Opower(X3) ),
c_0_2214,
[final] ).
cnf(c_0_2847,plain,
( c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_2215,
[final] ).
cnf(c_0_2848,plain,
( c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_2216,
[final] ).
cnf(c_0_2849,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_2217,
[final] ).
cnf(c_0_2850,plain,
( c_Divides_Odiv__class_Odiv(X2,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
c_0_2218,
[final] ).
cnf(c_0_2851,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_2219,
[final] ).
cnf(c_0_2852,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
c_0_2220,
[final] ).
cnf(c_0_2853,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_2221,
[final] ).
cnf(c_0_2854,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_2222,
[final] ).
cnf(c_0_2855,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_2223,
[final] ).
cnf(c_0_2856,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_2224,
[final] ).
cnf(c_0_2857,plain,
~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X2,tc_nat),
c_0_2225,
[final] ).
cnf(c_0_2858,plain,
~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X1,tc_nat),
c_0_2226,
[final] ).
cnf(c_0_2859,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) = c_HOL_Otimes__class_Otimes(X1,X2,X3)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3) ),
c_0_2227,
[final] ).
cnf(c_0_2860,plain,
( c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X1,X2,X3),X2,X3) = c_Divides_Odiv__class_Omod(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_2228,
[final] ).
cnf(c_0_2861,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
c_0_2229,
[final] ).
cnf(c_0_2862,plain,
( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X2,X1) = c_Divides_Odiv__class_Omod(X3,X2,X1)
| ~ class_Divides_Osemiring__div(X1) ),
c_0_2230,
[final] ).
cnf(c_0_2863,plain,
( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1)
| ~ class_Divides_Osemiring__div(X1) ),
c_0_2231,
[final] ).
cnf(c_0_2864,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X1),X2)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
c_0_2232,
[final] ).
cnf(c_0_2865,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)) = c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat),
c_0_2233,
[final] ).
cnf(c_0_2866,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)) = c_HOL_Otimes__class_Otimes(X1,c_Suc(X2),tc_nat),
c_0_2234,
[final] ).
cnf(c_0_2867,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_2235,
[final] ).
cnf(c_0_2868,plain,
( c_Power_Opower__class_Opower(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),X2,X3) = c_Nat_Osemiring__1__class_Oof__nat(c_Power_Opower__class_Opower(X1,X2,tc_nat),X3)
| ~ class_Ring__and__Field_Osemiring__1(X3) ),
c_0_2236,
[final] ).
cnf(c_0_2869,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_2237,
[final] ).
cnf(c_0_2870,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_2238,
[final] ).
cnf(c_0_2871,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_2239,
[final] ).
cnf(c_0_2872,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_2240,
[final] ).
cnf(c_0_2873,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X1,c_Suc(v_sko__Nat__Xnat__Xinducts__1(X1)))) ),
c_0_2241,
[final] ).
cnf(c_0_2874,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X1,c_Suc(v_sko__Nat__Xnat__Xinduct__1(X1)))) ),
c_0_2242,
[final] ).
cnf(c_0_2875,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X1,c_Suc(v_sko__List__Xupt__Xinduct__1(X1)))) ),
c_0_2243,
[final] ).
cnf(c_0_2876,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X1,c_Suc(v_sko__List__Xreplicate__Xinduct__1(X1)))) ),
c_0_2244,
[final] ).
cnf(c_0_2877,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X1,c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X1)))) ),
c_0_2245,
[final] ).
cnf(c_0_2878,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X1,c_Suc(v_sko__List__Xlexn__Xinduct__1(X1)))) ),
c_0_2246,
[final] ).
cnf(c_0_2879,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_2247,
[final] ).
cnf(c_0_2880,plain,
( X1 = X2
| c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat) ),
c_0_2248,
[final] ).
cnf(c_0_2881,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_2249,
[final] ).
cnf(c_0_2882,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_2250,
[final] ).
cnf(c_0_2883,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_2251,
[final] ).
cnf(c_0_2884,plain,
( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3))
| ~ c_Lambda_Obeta(X1,X2) ),
c_0_2252,
[final] ).
cnf(c_0_2885,plain,
( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2))
| ~ c_Lambda_Obeta(X1,X2) ),
c_0_2253,
[final] ).
cnf(c_0_2886,plain,
( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_Olift,X1),X3),hAPP(hAPP(c_Lambda_Olift,X2),X3))
| ~ c_Lambda_Obeta(X1,X2) ),
c_0_2254,
[final] ).
cnf(c_0_2887,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_2255,
[final] ).
cnf(c_0_2888,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_2256,
[final] ).
cnf(c_0_2889,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_2257,
[final] ).
cnf(c_0_2890,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_2258,
[final] ).
cnf(c_0_2891,plain,
( ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
c_0_2259,
[final] ).
cnf(c_0_2892,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_2260,
[final] ).
cnf(c_0_2893,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X3,X2),X1,X2) = X3
| ~ class_Divides_Osemiring__div(X2) ),
c_0_2261,
[final] ).
cnf(c_0_2894,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X1,X2),X1,X2) = X3
| ~ class_Divides_Osemiring__div(X2) ),
c_0_2262,
[final] ).
cnf(c_0_2895,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_2263,
[final] ).
cnf(c_0_2896,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_2264,
[final] ).
cnf(c_0_2897,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_2265,
[final] ).
cnf(c_0_2898,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X1,X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_2266,
[final] ).
cnf(c_0_2899,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_2267,
[final] ).
cnf(c_0_2900,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = X3
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) ),
c_0_2268,
[final] ).
cnf(c_0_2901,plain,
( X1 = X2
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(X3,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat) ),
c_0_2269,
[final] ).
cnf(c_0_2902,plain,
( X1 = X2
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) != c_HOL_Otimes__class_Otimes(X2,X3,tc_nat) ),
c_0_2270,
[final] ).
cnf(c_0_2903,plain,
( c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X1,X2,X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_2271,
[final] ).
cnf(c_0_2904,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_2272,
[final] ).
cnf(c_0_2905,plain,
( X1 = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
c_0_2273,
[final] ).
cnf(c_0_2906,plain,
( X1 = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
c_0_2274,
[final] ).
cnf(c_0_2907,plain,
( X2 = X1
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
c_0_2275,
[final] ).
cnf(c_0_2908,plain,
( X1 = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
c_0_2276,
[final] ).
cnf(c_0_2909,plain,
( X1 = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
c_0_2277,
[final] ).
cnf(c_0_2910,plain,
( X1 = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
c_0_2278,
[final] ).
cnf(c_0_2911,plain,
( X1 = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
c_0_2279,
[final] ).
cnf(c_0_2912,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
c_0_2280,
[final] ).
cnf(c_0_2913,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_2281,
[final] ).
cnf(c_0_2914,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_2282,
[final] ).
cnf(c_0_2915,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat),
c_0_2283,
[final] ).
cnf(c_0_2916,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_2284,
[final] ).
cnf(c_0_2917,plain,
( c_Type_Otyping(X1,X4,X3)
| ~ c_Type_Otyping(X1,X2,X3)
| ~ c_Lambda_Obeta(X2,X4) ),
c_0_2285,
[final] ).
cnf(c_0_2918,plain,
c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_2286,
[final] ).
cnf(c_0_2919,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_2287,
[final] ).
cnf(c_0_2920,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Divides_Odiv__class_Omod(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_2288,
[final] ).
cnf(c_0_2921,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_2289,
[final] ).
cnf(c_0_2922,plain,
( c_Divides_Odiv__class_Omod(X2,X1,X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_2290,
[final] ).
cnf(c_0_2923,plain,
( hBOOL(hAPP(X1,c_Suc(c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X1))))
| hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_2291,
[final] ).
cnf(c_0_2924,plain,
( hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X1))) ),
c_0_2292,
[final] ).
cnf(c_0_2925,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_2293,
[final] ).
cnf(c_0_2926,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_2294,
[final] ).
cnf(c_0_2927,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_2295,
[final] ).
cnf(c_0_2928,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_2296,
[final] ).
cnf(c_0_2929,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_2297,
[final] ).
cnf(c_0_2930,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_2298,
[final] ).
cnf(c_0_2931,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_2299,
[final] ).
cnf(c_0_2932,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_2300,
[final] ).
cnf(c_0_2933,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_2301,
[final] ).
cnf(c_0_2934,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat) ),
c_0_2302,
[final] ).
cnf(c_0_2935,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_2303,
[final] ).
cnf(c_0_2936,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_2304,
[final] ).
cnf(c_0_2937,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_2305,
[final] ).
cnf(c_0_2938,plain,
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_2306,
[final] ).
cnf(c_0_2939,plain,
( c_Divides_Odiv__class_Odiv(X1,X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_2307,
[final] ).
cnf(c_0_2940,plain,
( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = X1
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_2308,
[final] ).
cnf(c_0_2941,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_2309,
[final] ).
cnf(c_0_2942,plain,
( hBOOL(hAPP(X1,v_sko__List__Xupt__Xinduct__1(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
c_0_2310,
[final] ).
cnf(c_0_2943,plain,
( hBOOL(hAPP(X1,v_sko__Nat__Xnat__Xinduct__1(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
c_0_2311,
[final] ).
cnf(c_0_2944,plain,
( hBOOL(hAPP(X1,v_sko__Nat__Xnat__Xinducts__1(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
c_0_2312,
[final] ).
cnf(c_0_2945,plain,
( hBOOL(hAPP(X1,v_sko__List__Xreplicate__Xinduct__1(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
c_0_2313,
[final] ).
cnf(c_0_2946,plain,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
c_0_2314,
[final] ).
cnf(c_0_2947,plain,
( hBOOL(hAPP(X1,v_sko__List__Xlexn__Xinduct__1(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
c_0_2315,
[final] ).
cnf(c_0_2948,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
c_0_2316,
[final] ).
cnf(c_0_2949,plain,
( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
c_0_2317,
[final] ).
cnf(c_0_2950,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X1,tc_Lambda_OdB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X1),tc_Lambda_OdB),
c_0_2318,
[final] ).
cnf(c_0_2951,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_2319,
[final] ).
cnf(c_0_2952,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_2320,
[final] ).
cnf(c_0_2953,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_2321,
[final] ).
cnf(c_0_2954,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_2322,
[final] ).
cnf(c_0_2955,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_2323,
[final] ).
cnf(c_0_2956,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_2324,
[final] ).
cnf(c_0_2957,plain,
( X1 = X2
| hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X4),X2) ),
c_0_2325,
[final] ).
cnf(c_0_2958,plain,
( X1 = X2
| hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4) ),
c_0_2326,
[final] ).
cnf(c_0_2959,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_2327,
[final] ).
cnf(c_0_2960,plain,
( c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X2,X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_2328,
[final] ).
cnf(c_0_2961,plain,
( c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X2,X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_2329,
[final] ).
cnf(c_0_2962,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
c_0_2330,
[final] ).
cnf(c_0_2963,plain,
( c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
c_0_2331,
[final] ).
cnf(c_0_2964,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_2332,
[final] ).
cnf(c_0_2965,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat),
c_0_2333,
[final] ).
cnf(c_0_2966,plain,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_2334,
[final] ).
cnf(c_0_2967,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_2335,
[final] ).
cnf(c_0_2968,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_2336,
[final] ).
cnf(c_0_2969,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_2337,
[final] ).
cnf(c_0_2970,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
c_0_2338,
[final] ).
cnf(c_0_2971,plain,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1) = X2,
c_0_2339,
[final] ).
cnf(c_0_2972,plain,
( hAPP(X1,X2) = X3
| ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3) ),
c_0_2340,
[final] ).
cnf(c_0_2973,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_2341,
[final] ).
cnf(c_0_2974,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
c_0_2342,
[final] ).
cnf(c_0_2975,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
c_0_2343,
[final] ).
cnf(c_0_2976,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
c_0_2344,
[final] ).
cnf(c_0_2977,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
c_0_2345,
[final] ).
cnf(c_0_2978,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
c_0_2346,
[final] ).
cnf(c_0_2979,plain,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_2347,
[final] ).
cnf(c_0_2980,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_2348,
[final] ).
cnf(c_0_2981,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_Power_Opower__class_Opower(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_2349,
[final] ).
cnf(c_0_2982,plain,
c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) = c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),
c_0_2350,
[final] ).
cnf(c_0_2983,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X2) ),
c_0_2351,
[final] ).
cnf(c_0_2984,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_2352,
[final] ).
cnf(c_0_2985,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_2353,
[final] ).
cnf(c_0_2986,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_2354,
[final] ).
cnf(c_0_2987,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_2355,
[final] ).
cnf(c_0_2988,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_2356,
[final] ).
cnf(c_0_2989,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_2357,
[final] ).
cnf(c_0_2990,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
c_0_2358,
[final] ).
cnf(c_0_2991,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_2359,
[final] ).
cnf(c_0_2992,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_2360,
[final] ).
cnf(c_0_2993,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_2361,
[final] ).
cnf(c_0_2994,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_2362,
[final] ).
cnf(c_0_2995,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_2363,
[final] ).
cnf(c_0_2996,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_2364,
[final] ).
cnf(c_0_2997,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
c_0_2365,
[final] ).
cnf(c_0_2998,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_2366,
[final] ).
cnf(c_0_2999,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
c_0_2367,
[final] ).
cnf(c_0_3000,plain,
( X1 = c_HOL_Oone__class_Oone(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != X2 ),
c_0_2368,
[final] ).
cnf(c_0_3001,plain,
( X1 = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
c_0_2369,
[final] ).
cnf(c_0_3002,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_2370,
[final] ).
cnf(c_0_3003,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_2371,
[final] ).
cnf(c_0_3004,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_2372,
[final] ).
cnf(c_0_3005,plain,
( X1 = c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
c_0_2373,
[final] ).
cnf(c_0_3006,plain,
( X1 = c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
c_0_2374,
[final] ).
cnf(c_0_3007,plain,
( X1 = c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
c_0_2375,
[final] ).
cnf(c_0_3008,plain,
( X1 = c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
c_0_2376,
[final] ).
cnf(c_0_3009,plain,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_2377,
[final] ).
cnf(c_0_3010,plain,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_2378,
[final] ).
cnf(c_0_3011,plain,
( X1 = X2
| ~ c_fequal(X1,X2,X3) ),
c_0_2379,
[final] ).
cnf(c_0_3012,plain,
c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),hAPP(X1,X2)),
c_0_2380,
[final] ).
cnf(c_0_3013,plain,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Suc(X2),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Power_Opower(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
c_0_2381,
[final] ).
cnf(c_0_3014,plain,
c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_2382,
[final] ).
cnf(c_0_3015,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
c_0_2383,
[final] ).
cnf(c_0_3016,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
c_0_2384,
[final] ).
cnf(c_0_3017,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Osemiring__0(X2) ),
c_0_2385,
[final] ).
cnf(c_0_3018,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
c_0_2386,
[final] ).
cnf(c_0_3019,plain,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Power_Opower(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
c_0_2387,
[final] ).
cnf(c_0_3020,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_2388,
[final] ).
cnf(c_0_3021,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_2389,
[final] ).
cnf(c_0_3022,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_2390,
[final] ).
cnf(c_0_3023,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X1)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X1)),
c_0_2391,
[final] ).
cnf(c_0_3024,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_2392,
[final] ).
cnf(c_0_3025,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_2393,
[final] ).
cnf(c_0_3026,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != X2 ),
c_0_2394,
[final] ).
cnf(c_0_3027,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != X2 ),
c_0_2395,
[final] ).
cnf(c_0_3028,plain,
c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
c_0_2396,
[final] ).
cnf(c_0_3029,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_2397,
[final] ).
cnf(c_0_3030,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_2398,
[final] ).
cnf(c_0_3031,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_2399,
[final] ).
cnf(c_0_3032,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
c_0_2400,
[final] ).
cnf(c_0_3033,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_2401,
[final] ).
cnf(c_0_3034,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_2402,
[final] ).
cnf(c_0_3035,plain,
c_Power_Opower__class_Opower(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_2403,
[final] ).
cnf(c_0_3036,plain,
c_Power_Opower__class_Opower(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_2404,
[final] ).
cnf(c_0_3037,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
c_0_2405,
[final] ).
cnf(c_0_3038,plain,
( c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
c_0_2406,
[final] ).
cnf(c_0_3039,plain,
( c_Divides_Odiv__class_Odiv(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
c_0_2407,
[final] ).
cnf(c_0_3040,plain,
( c_Divides_Odiv__class_Omod(X1,c_HOL_Oone__class_Oone(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
c_0_2408,
[final] ).
cnf(c_0_3041,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_2409,
[final] ).
cnf(c_0_3042,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
c_0_2410,
[final] ).
cnf(c_0_3043,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
c_0_2411,
[final] ).
cnf(c_0_3044,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
c_0_2412,
[final] ).
cnf(c_0_3045,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Omult__zero(X2) ),
c_0_2413,
[final] ).
cnf(c_0_3046,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Omult__zero(X1) ),
c_0_2414,
[final] ).
cnf(c_0_3047,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_2415,
[final] ).
cnf(c_0_3048,plain,
( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
c_0_2416,
[final] ).
cnf(c_0_3049,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_2417,
[final] ).
cnf(c_0_3050,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_2418,
[final] ).
cnf(c_0_3051,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(X1,X1,X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Divides_Osemiring__div(X2) ),
c_0_2419,
[final] ).
cnf(c_0_3052,plain,
( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
c_0_2420,
[final] ).
cnf(c_0_3053,plain,
( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Power_Opower(X2) ),
c_0_2421,
[final] ).
cnf(c_0_3054,plain,
( c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_Divides_Osemiring__div(X2) ),
c_0_2422,
[final] ).
cnf(c_0_3055,plain,
( c_Divides_Odiv__class_Odiv(X1,c_HOL_Oone__class_Oone(X2),X2) = X1
| ~ class_Divides_Osemiring__div(X2) ),
c_0_2423,
[final] ).
cnf(c_0_3056,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_2424,
[final] ).
cnf(c_0_3057,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
c_0_2425,
[final] ).
cnf(c_0_3058,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
c_0_2426,
[final] ).
cnf(c_0_3059,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X2),X2) = X1
| ~ class_OrderedGroup_Omonoid__mult(X2) ),
c_0_2427,
[final] ).
cnf(c_0_3060,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X2),X2) = X1
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
c_0_2428,
[final] ).
cnf(c_0_3061,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_2429,
[final] ).
cnf(c_0_3062,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_2430,
[final] ).
cnf(c_0_3063,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_2431,
[final] ).
cnf(c_0_3064,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
c_0_2432,
[final] ).
cnf(c_0_3065,plain,
c_Divides_Odiv__class_Omod(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_2433,
[final] ).
cnf(c_0_3066,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_2434,
[final] ).
cnf(c_0_3067,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
c_0_2435,
[final] ).
cnf(c_0_3068,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_2436,
[final] ).
cnf(c_0_3069,plain,
c_Divides_Odiv__class_Odiv(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = X1,
c_0_2437,
[final] ).
cnf(c_0_3070,plain,
( c_Divides_Odiv__class_Omod(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
c_0_2438,
[final] ).
cnf(c_0_3071,plain,
( c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X2) = X1
| ~ class_OrderedGroup_Omonoid__mult(X2) ),
c_0_2439,
[final] ).
cnf(c_0_3072,plain,
( c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X2) = X1
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
c_0_2440,
[final] ).
cnf(c_0_3073,plain,
c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat),
c_0_2441,
[final] ).
cnf(c_0_3074,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OVar(X3),
c_0_2442,
[final] ).
cnf(c_0_3075,plain,
c_Lambda_OdB_OVar(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
c_0_2443,
[final] ).
cnf(c_0_3076,plain,
c_Lambda_OdB_OAbs(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
c_0_2444,
[final] ).
cnf(c_0_3077,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OAbs(X3),
c_0_2445,
[final] ).
cnf(c_0_3078,plain,
c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_2446,
[final] ).
cnf(c_0_3079,plain,
( c_HOL_Otimes__class_Otimes(X1,X1,X2) = X1
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2) ),
c_0_2447,
[final] ).
cnf(c_0_3080,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
c_0_2448,
[final] ).
cnf(c_0_3081,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
c_0_2449,
[final] ).
cnf(c_0_3082,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X1,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
c_0_2450,
[final] ).
cnf(c_0_3083,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat),
c_0_2451,
[final] ).
cnf(c_0_3084,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat),
c_0_2452,
[final] ).
cnf(c_0_3085,plain,
c_List_Olistsp(X1,c_List_Olist_ONil(X2),X2),
c_0_2453,
[final] ).
cnf(c_0_3086,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_2454,
[final] ).
cnf(c_0_3087,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
c_0_2455,
[final] ).
cnf(c_0_3088,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
c_0_2456,
[final] ).
cnf(c_0_3089,plain,
c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
c_0_2457,
[final] ).
cnf(c_0_3090,plain,
c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat),
c_0_2458,
[final] ).
cnf(c_0_3091,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_2459,
[final] ).
cnf(c_0_3092,plain,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_2460,
[final] ).
cnf(c_0_3093,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_2461,
[final] ).
cnf(c_0_3094,plain,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1,
c_0_2462,
[final] ).
cnf(c_0_3095,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) = X1,
c_0_2463,
[final] ).
cnf(c_0_3096,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X1) = c_Suc(X1),
c_0_2464,
[final] ).
cnf(c_0_3097,plain,
c_fequal(X1,X1,X2),
c_0_2465,
[final] ).
cnf(c_0_3098,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_2466,
[final] ).
cnf(c_0_3099,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1) = X1,
c_0_2467,
[final] ).
cnf(c_0_3100,plain,
c_Ring__and__Field_Odvd__class_Odvd(X1,X1,tc_nat),
c_0_2468,
[final] ).
cnf(c_0_3101,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)) = c_Suc(X1),
c_0_2469,
[final] ).
cnf(c_0_3102,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)) = X1,
c_0_2470,
[final] ).
cnf(c_0_3103,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)) = X1,
c_0_2471,
[final] ).
cnf(c_0_3104,plain,
( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X1),c_Lambda_OdB_OAbs(X2))
| ~ c_Lambda_Obeta(X1,X2) ),
c_0_2472,
[final] ).
cnf(c_0_3105,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
c_0_2473,
[final] ).
cnf(c_0_3106,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
c_0_2474,
[final] ).
cnf(c_0_3107,plain,
~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X1),X2),
c_0_2475,
[final] ).
cnf(c_0_3108,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_2476,
[final] ).
cnf(c_0_3109,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_2477,
[final] ).
cnf(c_0_3110,plain,
c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(X1),tc_Lambda_OdB) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_2478,
[final] ).
cnf(c_0_3111,plain,
( c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
c_0_2479,
[final] ).
cnf(c_0_3112,plain,
( c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
c_0_2480,
[final] ).
cnf(c_0_3113,plain,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
c_0_2481,
[final] ).
cnf(c_0_3114,plain,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
c_0_2482,
[final] ).
cnf(c_0_3115,plain,
( X1 = X2
| c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
c_0_2483,
[final] ).
cnf(c_0_3116,plain,
( X1 = X2
| c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
c_0_2484,
[final] ).
cnf(c_0_3117,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_ATP__Linkup_Osko__Nat__Xnot0__implies__Suc__1__1(X1)) = X1 ),
c_0_2485,
[final] ).
cnf(c_0_3118,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__Xnchotomy__1__1(X1)) = X1 ),
c_0_2486,
[final] ).
cnf(c_0_3119,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__Xexhaust__1__1(X1)) = X1 ),
c_0_2487,
[final] ).
cnf(c_0_3120,plain,
c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OAbs(X2),
c_0_2488,
[final] ).
cnf(c_0_3121,plain,
c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OVar(X2),
c_0_2489,
[final] ).
cnf(c_0_3122,plain,
c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(X1)) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_2490,
[final] ).
cnf(c_0_3123,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_2491,
[final] ).
cnf(c_0_3124,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_2492,
[final] ).
cnf(c_0_3125,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_2493,
[final] ).
cnf(c_0_3126,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_2494,
[final] ).
cnf(c_0_3127,plain,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat),
c_0_2495,
[final] ).
cnf(c_0_3128,plain,
c_Suc(X1) != X1,
c_0_2496,
[final] ).
cnf(c_0_3129,plain,
c_Suc(X1) != X1,
c_0_2497,
[final] ).
cnf(c_0_3130,plain,
class_Power_Opower(tc_nat),
c_0_2498,
[final] ).
cnf(c_0_3131,plain,
class_Orderings_Oorder(tc_nat),
c_0_2499,
[final] ).
cnf(c_0_3132,plain,
class_Orderings_Olinorder(tc_nat),
c_0_2500,
[final] ).
cnf(c_0_3133,plain,
class_Orderings_Opreorder(tc_nat),
c_0_2501,
[final] ).
cnf(c_0_3134,plain,
class_Ring__and__Field_Odvd(tc_nat),
c_0_2502,
[final] ).
cnf(c_0_3135,plain,
class_Nat_Osemiring__char__0(tc_nat),
c_0_2503,
[final] ).
cnf(c_0_3136,plain,
class_Divides_Osemiring__div(tc_nat),
c_0_2504,
[final] ).
cnf(c_0_3137,plain,
class_OrderedGroup_Omonoid__add(tc_nat),
c_0_2505,
[final] ).
cnf(c_0_3138,plain,
class_Ring__and__Field_Osemiring(tc_nat),
c_0_2506,
[final] ).
cnf(c_0_3139,plain,
class_OrderedGroup_Omonoid__mult(tc_nat),
c_0_2507,
[final] ).
cnf(c_0_3140,plain,
class_Ring__and__Field_Omult__zero(tc_nat),
c_0_2508,
[final] ).
cnf(c_0_3141,plain,
class_Ring__and__Field_Osemiring__0(tc_nat),
c_0_2509,
[final] ).
cnf(c_0_3142,plain,
class_Ring__and__Field_Osemiring__1(tc_nat),
c_0_2510,
[final] ).
cnf(c_0_3143,plain,
class_OrderedGroup_Osemigroup__add(tc_nat),
c_0_2511,
[final] ).
cnf(c_0_3144,plain,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
c_0_2512,
[final] ).
cnf(c_0_3145,plain,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
c_0_2513,
[final] ).
cnf(c_0_3146,plain,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
c_0_2514,
[final] ).
cnf(c_0_3147,plain,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
c_0_2515,
[final] ).
cnf(c_0_3148,plain,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
c_0_2516,
[final] ).
cnf(c_0_3149,plain,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
c_0_2517,
[final] ).
cnf(c_0_3150,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
c_0_2518,
[final] ).
cnf(c_0_3151,plain,
class_Ring__and__Field_Oordered__semidom(tc_nat),
c_0_2519,
[final] ).
cnf(c_0_3152,plain,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
c_0_2520,
[final] ).
cnf(c_0_3153,plain,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
c_0_2521,
[final] ).
cnf(c_0_3154,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
c_0_2522,
[final] ).
cnf(c_0_3155,plain,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
c_0_2523,
[final] ).
cnf(c_0_3156,plain,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
c_0_2524,
[final] ).
cnf(c_0_3157,plain,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
c_0_2525,
[final] ).
cnf(c_0_3158,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
c_0_2526,
[final] ).
cnf(c_0_3159,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
c_0_2527,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_2529_0,axiom,
( c_Type_Otypings(X1,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X2,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X5,tc_Lambda_OdB,tc_Lambda_OdB),X6)
| ~ c_Type_Otyping(X1,X2,X3)
| ~ c_Type_Otypings(c_Type_Oshift(X1,X4,X3,tc_Type_Otype),X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2529]) ).
cnf(c_0_2529_1,axiom,
( ~ c_Type_Otyping(X1,X2,X3)
| c_Type_Otypings(X1,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X2,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X5,tc_Lambda_OdB,tc_Lambda_OdB),X6)
| ~ c_Type_Otypings(c_Type_Oshift(X1,X4,X3,tc_Type_Otype),X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2529]) ).
cnf(c_0_2529_2,axiom,
( ~ c_Type_Otypings(c_Type_Oshift(X1,X4,X3,tc_Type_Otype),X5,X6)
| ~ c_Type_Otyping(X1,X2,X3)
| c_Type_Otypings(X1,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X2,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X5,tc_Lambda_OdB,tc_Lambda_OdB),X6) ),
inference(literals_permutation,[status(thm)],[c_0_2529]) ).
cnf(c_0_2530_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_2530]) ).
cnf(c_0_2530_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_2530]) ).
cnf(c_0_2530_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_2530]) ).
cnf(c_0_2532_0,axiom,
( X4 = X5
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X5) ),
inference(literals_permutation,[status(thm)],[c_0_2532]) ).
cnf(c_0_2532_1,axiom,
( ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
| X4 = X5
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X5) ),
inference(literals_permutation,[status(thm)],[c_0_2532]) ).
cnf(c_0_2532_2,axiom,
( ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X5)
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
| X4 = X5 ),
inference(literals_permutation,[status(thm)],[c_0_2532]) ).
cnf(c_0_2534_0,axiom,
( c_Type_Otypings(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3)
| ~ c_Type_Otypings(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2534]) ).
cnf(c_0_2534_1,axiom,
( ~ c_Type_Otypings(X1,X2,X3)
| c_Type_Otypings(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2534]) ).
cnf(c_0_2535_0,axiom,
( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_2535]) ).
cnf(c_0_2535_1,axiom,
( ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB)
| c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_2535]) ).
cnf(c_0_2536_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_2536]) ).
cnf(c_0_2536_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_2536]) ).
cnf(c_0_2537_0,axiom,
( 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))
| ~ c_Lambda_Obeta(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2537]) ).
cnf(c_0_2537_1,axiom,
( ~ c_Lambda_Obeta(X1,X2)
| 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_2537]) ).
cnf(c_0_2538_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_2538]) ).
cnf(c_0_2538_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_2538]) ).
cnf(c_0_2539_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_2539]) ).
cnf(c_0_2539_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_2539]) ).
cnf(c_0_2540_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_2540]) ).
cnf(c_0_2540_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_2540]) ).
cnf(c_0_2541_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_2541]) ).
cnf(c_0_2541_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_2541]) ).
cnf(c_0_2542_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_2542]) ).
cnf(c_0_2542_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_2542]) ).
cnf(c_0_2544_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_2544]) ).
cnf(c_0_2544_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_2544]) ).
cnf(c_0_2545_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_2545]) ).
cnf(c_0_2545_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_2545]) ).
cnf(c_0_2546_0,axiom,
( hBOOL(hAPP(X1,X2))
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat)),X4),X3,tc_nat)))
| ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2546]) ).
cnf(c_0_2546_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat)),X4),X3,tc_nat)))
| ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2546]) ).
cnf(c_0_2546_2,axiom,
( ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat)),X4),X3,tc_nat)))
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| hBOOL(hAPP(X1,X2))
| ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2546]) ).
cnf(c_0_2546_3,axiom,
( ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat)),X4),X3,tc_nat)))
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2546]) ).
cnf(c_0_2547_0,axiom,
( hBOOL(hAPP(X1,X2))
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat)),X2),X3,tc_nat)))
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2547]) ).
cnf(c_0_2547_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat)),X2),X3,tc_nat)))
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2547]) ).
cnf(c_0_2547_2,axiom,
( ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat)),X2),X3,tc_nat)))
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| hBOOL(hAPP(X1,X2))
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2547]) ).
cnf(c_0_2547_3,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat)),X2),X3,tc_nat)))
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2547]) ).
cnf(c_0_2548_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1)),c_Divides_Odiv__class_Omod(X2,X3,X1))),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2548]) ).
cnf(c_0_2548_1,axiom,
( ~ class_Divides_Osemiring__div(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1)),c_Divides_Odiv__class_Omod(X2,X3,X1))),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2548]) ).
cnf(c_0_2549_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X3,X2,X1),X1)),c_Divides_Odiv__class_Omod(X3,X2,X1))),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2549]) ).
cnf(c_0_2549_1,axiom,
( ~ class_Divides_Osemiring__div(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X3,X2,X1),X1)),c_Divides_Odiv__class_Omod(X3,X2,X1))),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2549]) ).
cnf(c_0_2550_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_2550]) ).
cnf(c_0_2550_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_2550]) ).
cnf(c_0_2554_0,axiom,
( hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) = X3
| hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_2554]) ).
cnf(c_0_2554_1,axiom,
( hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2554]) ).
cnf(c_0_2556_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_2556]) ).
cnf(c_0_2556_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_2556]) ).
cnf(c_0_2557_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_2557]) ).
cnf(c_0_2557_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_2557]) ).
cnf(c_0_2558_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_2558]) ).
cnf(c_0_2558_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_2558]) ).
cnf(c_0_2559_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_2559]) ).
cnf(c_0_2559_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_2559]) ).
cnf(c_0_2560_0,axiom,
( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| c_Lambda_OdB_OVar(X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_2560]) ).
cnf(c_0_2560_1,axiom,
( c_Lambda_OdB_OVar(X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB)
| X1 = c_List_Olist_ONil(tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_2560]) ).
cnf(c_0_2561_0,axiom,
( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2561]) ).
cnf(c_0_2561_1,axiom,
( c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X3)
| X1 = c_List_Olist_ONil(tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_2561]) ).
cnf(c_0_2562_0,axiom,
( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_2562]) ).
cnf(c_0_2562_1,axiom,
( c_Lambda_OdB_OAbs(X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB)
| X1 = c_List_Olist_ONil(tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_2562]) ).
cnf(c_0_2564_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(X4,X1,tc_nat),tc_nat)),X2),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2564]) ).
cnf(c_0_2564_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(X4,X1,tc_nat),tc_nat)),X2),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2564]) ).
cnf(c_0_2564_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(X4,X1,tc_nat),tc_nat)),X2),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2564]) ).
cnf(c_0_2566_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2566]) ).
cnf(c_0_2566_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2566]) ).
cnf(c_0_2568_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X4,X3,X1)),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X3,X1)),X5)
| ~ class_Ring__and__Field_Osemiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2568]) ).
cnf(c_0_2568_1,axiom,
( ~ class_Ring__and__Field_Osemiring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X4,X3,X1)),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X3,X1)),X5) ),
inference(literals_permutation,[status(thm)],[c_0_2568]) ).
cnf(c_0_2571_0,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X2,X1)),c_HOL_Otimes__class_Otimes(X3,X3,X1)),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2571]) ).
cnf(c_0_2571_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X2,X1)),c_HOL_Otimes__class_Otimes(X3,X3,X1)),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2571]) ).
cnf(c_0_2572_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_2572]) ).
cnf(c_0_2572_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_2572]) ).
cnf(c_0_2577_0,axiom,
( X1 = X2
| X3 = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X3,X5)),c_HOL_Otimes__class_Otimes(X2,X4,X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X4,X5)),c_HOL_Otimes__class_Otimes(X2,X3,X5))
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_2577]) ).
cnf(c_0_2577_1,axiom,
( X3 = X4
| X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X3,X5)),c_HOL_Otimes__class_Otimes(X2,X4,X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X4,X5)),c_HOL_Otimes__class_Otimes(X2,X3,X5))
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_2577]) ).
cnf(c_0_2577_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X3,X5)),c_HOL_Otimes__class_Otimes(X2,X4,X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X4,X5)),c_HOL_Otimes__class_Otimes(X2,X3,X5))
| X3 = X4
| X1 = X2
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_2577]) ).
cnf(c_0_2577_3,axiom,
( ~ class_Int_Onumber__ring(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X3,X5)),c_HOL_Otimes__class_Otimes(X2,X4,X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X4,X5)),c_HOL_Otimes__class_Otimes(X2,X3,X5))
| X3 = X4
| X1 = X2
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_2577]) ).
cnf(c_0_2577_4,axiom,
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X3,X5)),c_HOL_Otimes__class_Otimes(X2,X4,X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X4,X5)),c_HOL_Otimes__class_Otimes(X2,X3,X5))
| X3 = X4
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2577]) ).
cnf(c_0_2578_0,axiom,
( X1 = X2
| X3 = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X3,X5)),c_HOL_Otimes__class_Otimes(X2,X4,X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X4,X5)),c_HOL_Otimes__class_Otimes(X2,X3,X5))
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_2578]) ).
cnf(c_0_2578_1,axiom,
( X3 = X4
| X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X3,X5)),c_HOL_Otimes__class_Otimes(X2,X4,X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X4,X5)),c_HOL_Otimes__class_Otimes(X2,X3,X5))
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_2578]) ).
cnf(c_0_2578_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X3,X5)),c_HOL_Otimes__class_Otimes(X2,X4,X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X4,X5)),c_HOL_Otimes__class_Otimes(X2,X3,X5))
| X3 = X4
| X1 = X2
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_2578]) ).
cnf(c_0_2578_3,axiom,
( ~ class_Int_Onumber__ring(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X3,X5)),c_HOL_Otimes__class_Otimes(X2,X4,X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X4,X5)),c_HOL_Otimes__class_Otimes(X2,X3,X5))
| X3 = X4
| X1 = X2
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_2578]) ).
cnf(c_0_2578_4,axiom,
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X3,X5)),c_HOL_Otimes__class_Otimes(X2,X4,X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X4,X5)),c_HOL_Otimes__class_Otimes(X2,X3,X5))
| X3 = X4
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2578]) ).
cnf(c_0_2579_0,axiom,
( c_Type_Otyping(X1,hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4),X5)
| ~ c_Type_Otyping(c_Type_Oshift(X1,X4,X6,tc_Type_Otype),X2,X5)
| ~ c_Type_Otyping(X1,X3,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2579]) ).
cnf(c_0_2579_1,axiom,
( ~ c_Type_Otyping(c_Type_Oshift(X1,X4,X6,tc_Type_Otype),X2,X5)
| c_Type_Otyping(X1,hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4),X5)
| ~ c_Type_Otyping(X1,X3,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2579]) ).
cnf(c_0_2579_2,axiom,
( ~ c_Type_Otyping(X1,X3,X6)
| ~ c_Type_Otyping(c_Type_Oshift(X1,X4,X6,tc_Type_Otype),X2,X5)
| c_Type_Otyping(X1,hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4),X5) ),
inference(literals_permutation,[status(thm)],[c_0_2579]) ).
cnf(c_0_2581_0,axiom,
( X1 = X2
| X3 = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X4,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_2581]) ).
cnf(c_0_2581_1,axiom,
( X3 = X4
| X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X4,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_2581]) ).
cnf(c_0_2581_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X4,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat))
| X3 = X4
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2581]) ).
cnf(c_0_2582_0,axiom,
( X1 = X2
| X3 = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X4,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_2582]) ).
cnf(c_0_2582_1,axiom,
( X3 = X4
| X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X4,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_2582]) ).
cnf(c_0_2582_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X4,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat))
| X3 = X4
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2582]) ).
cnf(c_0_2583_0,axiom,
( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X4,X1)),c_Divides_Odiv__class_Omod(X3,X4,X1)),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2583]) ).
cnf(c_0_2583_1,axiom,
( ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X4,X1)),c_Divides_Odiv__class_Omod(X3,X4,X1)),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2583]) ).
cnf(c_0_2585_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X3,X3,X2)),c_HOL_Otimes__class_Otimes(X1,X1,X2)),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2585]) ).
cnf(c_0_2585_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X3,X3,X2)),c_HOL_Otimes__class_Otimes(X1,X1,X2)),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2585]) ).
cnf(c_0_2585_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X3,X3,X2)),c_HOL_Otimes__class_Otimes(X1,X1,X2)),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2585]) ).
cnf(c_0_2586_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X1,X1,X2)),c_HOL_Otimes__class_Otimes(X3,X3,X2)),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2586]) ).
cnf(c_0_2586_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X1,X1,X2)),c_HOL_Otimes__class_Otimes(X3,X3,X2)),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2586]) ).
cnf(c_0_2586_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X1,X1,X2)),c_HOL_Otimes__class_Otimes(X3,X3,X2)),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2586]) ).
cnf(c_0_2587_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X3,X2),X3,X2)),c_Divides_Odiv__class_Omod(X1,X3,X2)) = X1
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2587]) ).
cnf(c_0_2587_1,axiom,
( ~ class_Divides_Osemiring__div(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X3,X2),X3,X2)),c_Divides_Odiv__class_Omod(X1,X3,X2)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2587]) ).
cnf(c_0_2588_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1)),c_Divides_Odiv__class_Omod(X2,X3,X1)) = X2
| ~ class_Divides_Osemiring__div(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2588]) ).
cnf(c_0_2588_1,axiom,
( ~ class_Divides_Osemiring__div(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1)),c_Divides_Odiv__class_Omod(X2,X3,X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2588]) ).
cnf(c_0_2589_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X3,X2,X1),X1)),c_Divides_Odiv__class_Omod(X3,X2,X1)) = X3
| ~ class_Divides_Osemiring__div(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2589]) ).
cnf(c_0_2589_1,axiom,
( ~ class_Divides_Osemiring__div(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X3,X2,X1),X1)),c_Divides_Odiv__class_Omod(X3,X2,X1)) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2589]) ).
cnf(c_0_2591_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),c_HOL_Otimes__class_Otimes(X2,X4,X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X2,X3,X1))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2591]) ).
cnf(c_0_2591_1,axiom,
( ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),c_HOL_Otimes__class_Otimes(X2,X4,X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X2,X3,X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2591]) ).
cnf(c_0_2591_2,axiom,
( ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),c_HOL_Otimes__class_Otimes(X2,X4,X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X2,X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2591]) ).
cnf(c_0_2592_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),c_HOL_Otimes__class_Otimes(X2,X4,X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X2,X3,X1))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2592]) ).
cnf(c_0_2592_1,axiom,
( ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),c_HOL_Otimes__class_Otimes(X2,X4,X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X2,X3,X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2592]) ).
cnf(c_0_2592_2,axiom,
( ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),c_HOL_Otimes__class_Otimes(X2,X4,X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X2,X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2592]) ).
cnf(c_0_2593_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X4,X3),c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2593]) ).
cnf(c_0_2593_1,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X4,X3),c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2593]) ).
cnf(c_0_2594_0,axiom,
( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X3,X1)),X4),X3,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X3,X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2594]) ).
cnf(c_0_2594_1,axiom,
( ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X3,X1)),X4),X3,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2594]) ).
cnf(c_0_2595_0,axiom,
( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X4,X1)),X3),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2595]) ).
cnf(c_0_2595_1,axiom,
( ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X4,X1)),X3),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2595]) ).
cnf(c_0_2596_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_2596]) ).
cnf(c_0_2596_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_2596]) ).
cnf(c_0_2597_0,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X5,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X5,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2597]) ).
cnf(c_0_2597_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X5,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X5,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2597]) ).
cnf(c_0_2597_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X5,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X5,X4,X3),X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2597]) ).
cnf(c_0_2597_3,axiom,
( ~ class_Divides_Osemiring__div(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X5,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X5,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2597]) ).
cnf(c_0_2600_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Odiv(X2,X1,X3)),c_Divides_Odiv__class_Odiv(X4,X1,X3)) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X1,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2600]) ).
cnf(c_0_2600_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Odiv(X2,X1,X3)),c_Divides_Odiv__class_Odiv(X4,X1,X3)) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X1,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2600]) ).
cnf(c_0_2600_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Odiv(X2,X1,X3)),c_Divides_Odiv__class_Odiv(X4,X1,X3)) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X1,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2600]) ).
cnf(c_0_2600_3,axiom,
( ~ class_Divides_Osemiring__div(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Odiv(X2,X1,X3)),c_Divides_Odiv__class_Odiv(X4,X1,X3)) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2600]) ).
cnf(c_0_2601_0,axiom,
( c_Type_Otyping(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X2),X4),X3)
| ~ c_Type_Otyping(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2601]) ).
cnf(c_0_2601_1,axiom,
( ~ c_Type_Otyping(X1,X2,X3)
| c_Type_Otyping(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X2),X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2601]) ).
cnf(c_0_2602_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2602]) ).
cnf(c_0_2602_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2602]) ).
cnf(c_0_2602_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2602]) ).
cnf(c_0_2602_3,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),c_Power_Opower__class_Opower(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2602]) ).
cnf(c_0_2603_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Suc(c_Divides_Odiv__class_Odiv(X1,X2,tc_nat)),tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2603]) ).
cnf(c_0_2603_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Suc(c_Divides_Odiv__class_Odiv(X1,X2,tc_nat)),tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2603]) ).
cnf(c_0_2604_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X6,X3),X4,X3)
| c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X5,X4,X3)
| c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X6,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2604]) ).
cnf(c_0_2604_1,axiom,
( c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X5,X4,X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X6,X3),X4,X3)
| c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X6,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2604]) ).
cnf(c_0_2604_2,axiom,
( c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X6,X4,X3)
| c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X5,X4,X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X6,X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2604]) ).
cnf(c_0_2604_3,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X6,X4,X3)
| c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X5,X4,X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X6,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2604]) ).
cnf(c_0_2605_0,axiom,
( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X6),X4,X1)
| c_Divides_Odiv__class_Omod(X2,X4,X1) != c_Divides_Odiv__class_Omod(X5,X4,X1)
| c_Divides_Odiv__class_Omod(X3,X4,X1) != c_Divides_Odiv__class_Omod(X6,X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2605]) ).
cnf(c_0_2605_1,axiom,
( c_Divides_Odiv__class_Omod(X2,X4,X1) != c_Divides_Odiv__class_Omod(X5,X4,X1)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X6),X4,X1)
| c_Divides_Odiv__class_Omod(X3,X4,X1) != c_Divides_Odiv__class_Omod(X6,X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2605]) ).
cnf(c_0_2605_2,axiom,
( c_Divides_Odiv__class_Omod(X3,X4,X1) != c_Divides_Odiv__class_Omod(X6,X4,X1)
| c_Divides_Odiv__class_Omod(X2,X4,X1) != c_Divides_Odiv__class_Omod(X5,X4,X1)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X6),X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2605]) ).
cnf(c_0_2605_3,axiom,
( ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(X3,X4,X1) != c_Divides_Odiv__class_Omod(X6,X4,X1)
| c_Divides_Odiv__class_Omod(X2,X4,X1) != c_Divides_Odiv__class_Omod(X5,X4,X1)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X6),X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2605]) ).
cnf(c_0_2606_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2606]) ).
cnf(c_0_2606_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2606]) ).
cnf(c_0_2606_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2606]) ).
cnf(c_0_2606_3,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2606]) ).
cnf(c_0_2606_4,axiom,
( ~ class_Divides_Osemiring__div(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2606]) ).
cnf(c_0_2607_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2607]) ).
cnf(c_0_2607_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X5,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2607]) ).
cnf(c_0_2608_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X4,X5,X3),X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2608]) ).
cnf(c_0_2608_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X4,X5,X3),X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2608]) ).
cnf(c_0_2610_0,axiom,
( hAPP(c_Type_Oshift(X3,X2,X4,X5),X1) = hAPP(X3,X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2610]) ).
cnf(c_0_2610_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| hAPP(c_Type_Oshift(X3,X2,X4,X5),X1) = hAPP(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2610]) ).
cnf(c_0_2611_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X1,X1,X2)),c_HOL_Otimes__class_Otimes(X3,X3,X2)) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2611]) ).
cnf(c_0_2611_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X1,X1,X2)),c_HOL_Otimes__class_Otimes(X3,X3,X2)) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2611]) ).
cnf(c_0_2611_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X1,X1,X2)),c_HOL_Otimes__class_Otimes(X3,X3,X2)) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2611]) ).
cnf(c_0_2612_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X3,X3,X2)),c_HOL_Otimes__class_Otimes(X1,X1,X2)) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2612]) ).
cnf(c_0_2612_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X3,X3,X2)),c_HOL_Otimes__class_Otimes(X1,X1,X2)) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2612]) ).
cnf(c_0_2612_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X3,X3,X2)),c_HOL_Otimes__class_Otimes(X1,X1,X2)) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2612]) ).
cnf(c_0_2613_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_2613]) ).
cnf(c_0_2613_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_2613]) ).
cnf(c_0_2615_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X3,X1)),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1)) = X2
| ~ class_Divides_Osemiring__div(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2615]) ).
cnf(c_0_2615_1,axiom,
( ~ class_Divides_Osemiring__div(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X3,X1)),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2615]) ).
cnf(c_0_2616_0,axiom,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2616]) ).
cnf(c_0_2616_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2616]) ).
cnf(c_0_2616_2,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2616]) ).
cnf(c_0_2617_0,axiom,
( c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2617]) ).
cnf(c_0_2617_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2617]) ).
cnf(c_0_2617_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2617]) ).
cnf(c_0_2617_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2617]) ).
cnf(c_0_2618_0,axiom,
( c_HOL_Oord__class_Oless(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2618]) ).
cnf(c_0_2618_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2618]) ).
cnf(c_0_2618_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(X4,X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2618]) ).
cnf(c_0_2618_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(X4,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2618]) ).
cnf(c_0_2619_0,axiom,
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2619]) ).
cnf(c_0_2619_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2619]) ).
cnf(c_0_2619_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2619]) ).
cnf(c_0_2619_3,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2619]) ).
cnf(c_0_2620_0,axiom,
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2620]) ).
cnf(c_0_2620_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2620]) ).
cnf(c_0_2620_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2620]) ).
cnf(c_0_2620_3,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2620]) ).
cnf(c_0_2621_0,axiom,
( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(X3,X2,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Otimes__class_Otimes(X2,X5,tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_2621]) ).
cnf(c_0_2621_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Otimes__class_Otimes(X2,X5,tc_nat))
| c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(X3,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2621]) ).
cnf(c_0_2622_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2622]) ).
cnf(c_0_2622_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2622]) ).
cnf(c_0_2622_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2622]) ).
cnf(c_0_2623_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2623]) ).
cnf(c_0_2623_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2623]) ).
cnf(c_0_2623_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2623]) ).
cnf(c_0_2624_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,tc_nat),c_Power_Opower__class_Opower(X1,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2624]) ).
cnf(c_0_2624_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,tc_nat),c_Power_Opower__class_Opower(X1,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2624]) ).
cnf(c_0_2624_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,tc_nat),c_Power_Opower__class_Opower(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2624]) ).
cnf(c_0_2625_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2625]) ).
cnf(c_0_2625_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2625]) ).
cnf(c_0_2625_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2625]) ).
cnf(c_0_2626_0,axiom,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X2,X3),c_Power_Opower__class_Opower(X4,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(X3),X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2626]) ).
cnf(c_0_2626_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X2,X3),c_Power_Opower__class_Opower(X4,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(X3),X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2626]) ).
cnf(c_0_2626_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X2,X3),c_Power_Opower__class_Opower(X4,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(X3),X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2626]) ).
cnf(c_0_2626_3,axiom,
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X2,X3),c_Power_Opower__class_Opower(X4,X1,X3),X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2626]) ).
cnf(c_0_2626_4,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X2,X3),c_Power_Opower__class_Opower(X4,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2626]) ).
cnf(c_0_2627_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2627]) ).
cnf(c_0_2627_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2627]) ).
cnf(c_0_2627_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2627]) ).
cnf(c_0_2627_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2627]) ).
cnf(c_0_2628_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2628]) ).
cnf(c_0_2628_1,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2628]) ).
cnf(c_0_2628_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2628]) ).
cnf(c_0_2628_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2628]) ).
cnf(c_0_2629_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2629]) ).
cnf(c_0_2629_1,axiom,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2629]) ).
cnf(c_0_2629_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2629]) ).
cnf(c_0_2629_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2629]) ).
cnf(c_0_2630_0,axiom,
( c_HOL_Oord__class_Oless(X2,X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2630]) ).
cnf(c_0_2630_1,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2630]) ).
cnf(c_0_2630_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2630]) ).
cnf(c_0_2630_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X2,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2630]) ).
cnf(c_0_2631_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2631]) ).
cnf(c_0_2631_1,axiom,
( c_HOL_Oord__class_Oless(X4,X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2631]) ).
cnf(c_0_2631_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X4,X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2631]) ).
cnf(c_0_2631_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X4,X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2631]) ).
cnf(c_0_2632_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2632]) ).
cnf(c_0_2632_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2632]) ).
cnf(c_0_2632_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2632]) ).
cnf(c_0_2632_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2632]) ).
cnf(c_0_2633_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2633]) ).
cnf(c_0_2633_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2633]) ).
cnf(c_0_2634_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2634]) ).
cnf(c_0_2634_1,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2634]) ).
cnf(c_0_2635_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2635]) ).
cnf(c_0_2635_1,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2635]) ).
cnf(c_0_2636_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X2,X3),X4,X3),X2,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X4,X3),X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2636]) ).
cnf(c_0_2636_1,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X2,X3),X4,X3),X2,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X4,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2636]) ).
cnf(c_0_2637_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),c_HOL_Otimes__class_Otimes(X4,X1,X2)),X1,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X4),c_Divides_Odiv__class_Odiv(X3,X1,X2))
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2637]) ).
cnf(c_0_2637_1,axiom,
( c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),c_HOL_Otimes__class_Otimes(X4,X1,X2)),X1,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X4),c_Divides_Odiv__class_Odiv(X3,X1,X2))
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2637]) ).
cnf(c_0_2637_2,axiom,
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),c_HOL_Otimes__class_Otimes(X4,X1,X2)),X1,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X4),c_Divides_Odiv__class_Odiv(X3,X1,X2))
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2637]) ).
cnf(c_0_2638_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),c_HOL_Otimes__class_Otimes(X1,X4,X2)),X1,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X4),c_Divides_Odiv__class_Odiv(X3,X1,X2))
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2638]) ).
cnf(c_0_2638_1,axiom,
( c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),c_HOL_Otimes__class_Otimes(X1,X4,X2)),X1,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X4),c_Divides_Odiv__class_Odiv(X3,X1,X2))
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2638]) ).
cnf(c_0_2638_2,axiom,
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),c_HOL_Otimes__class_Otimes(X1,X4,X2)),X1,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X4),c_Divides_Odiv__class_Odiv(X3,X1,X2))
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2638]) ).
cnf(c_0_2639_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2639]) ).
cnf(c_0_2639_1,axiom,
( c_HOL_Oord__class_Oless(X4,X1,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2639]) ).
cnf(c_0_2639_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X4,X1,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2639]) ).
cnf(c_0_2639_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X4,X1,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2639]) ).
cnf(c_0_2640_0,axiom,
( c_HOL_Oord__class_Oless(X2,X4,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2640]) ).
cnf(c_0_2640_1,axiom,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2640]) ).
cnf(c_0_2640_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2640]) ).
cnf(c_0_2640_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| c_HOL_Oord__class_Oless(X2,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2640]) ).
cnf(c_0_2641_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2)),c_HOL_Otimes__class_Otimes(X1,X4,X2)) = c_HOL_Otimes__class_Otimes(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X4),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2641]) ).
cnf(c_0_2641_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2)),c_HOL_Otimes__class_Otimes(X1,X4,X2)) = c_HOL_Otimes__class_Otimes(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2641]) ).
cnf(c_0_2642_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X3,X4,X1)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2642]) ).
cnf(c_0_2642_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X3,X4,X1)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2642]) ).
cnf(c_0_2643_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X3,X4,X1)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2643]) ).
cnf(c_0_2643_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X3,X4,X1)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2643]) ).
cnf(c_0_2644_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),c_HOL_Otimes__class_Otimes(X4,X3,X1)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2644]) ).
cnf(c_0_2644_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),c_HOL_Otimes__class_Otimes(X4,X3,X1)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2644]) ).
cnf(c_0_2645_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2645]) ).
cnf(c_0_2645_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2645]) ).
cnf(c_0_2645_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2645]) ).
cnf(c_0_2645_3,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2645]) ).
cnf(c_0_2645_4,axiom,
( ~ class_Divides_Osemiring__div(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2645]) ).
cnf(c_0_2646_0,axiom,
( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_Divides_Odiv__class_Omod(X3,X4,X1)),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2646]) ).
cnf(c_0_2646_1,axiom,
( ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_Divides_Odiv__class_Omod(X3,X4,X1)),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2646]) ).
cnf(c_0_2647_0,axiom,
( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_Divides_Odiv__class_Omod(X3,X4,X1)),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2647]) ).
cnf(c_0_2647_1,axiom,
( ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_Divides_Odiv__class_Omod(X3,X4,X1)),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2647]) ).
cnf(c_0_2648_0,axiom,
( c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(X2,X4,X3),c_Power_Opower__class_Opower(X1,X4,X3),X3) = c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(X2,X1,X3),X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2648]) ).
cnf(c_0_2648_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(X2,X4,X3),c_Power_Opower__class_Opower(X1,X4,X3),X3) = c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(X2,X1,X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2648]) ).
cnf(c_0_2648_2,axiom,
( ~ class_Divides_Osemiring__div(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(X2,X4,X3),c_Power_Opower__class_Opower(X1,X4,X3),X3) = c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(X2,X1,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2648]) ).
cnf(c_0_2649_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),c_HOL_Otimes__class_Otimes(X1,X3,X2)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),c_HOL_Otimes__class_Otimes(X1,X4,X2))
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2649]) ).
cnf(c_0_2649_1,axiom,
( X3 = X4
| X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),c_HOL_Otimes__class_Otimes(X1,X3,X2)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),c_HOL_Otimes__class_Otimes(X1,X4,X2))
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2649]) ).
cnf(c_0_2649_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),c_HOL_Otimes__class_Otimes(X1,X3,X2)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),c_HOL_Otimes__class_Otimes(X1,X4,X2))
| X3 = X4
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2649]) ).
cnf(c_0_2649_3,axiom,
( ~ class_Int_Onumber__ring(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),c_HOL_Otimes__class_Otimes(X1,X3,X2)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),c_HOL_Otimes__class_Otimes(X1,X4,X2))
| X3 = X4
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2649]) ).
cnf(c_0_2649_4,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),c_HOL_Otimes__class_Otimes(X1,X3,X2)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),c_HOL_Otimes__class_Otimes(X1,X4,X2))
| X3 = X4
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2649]) ).
cnf(c_0_2650_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_2650]) ).
cnf(c_0_2650_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_2650]) ).
cnf(c_0_2652_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X1),X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2652]) ).
cnf(c_0_2652_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X1),X3,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2652]) ).
cnf(c_0_2655_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2655]) ).
cnf(c_0_2655_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| X2 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2655]) ).
cnf(c_0_2655_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| X2 = c_HOL_Ozero__class_Ozero(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2655]) ).
cnf(c_0_2655_3,axiom,
( ~ class_Ring__and__Field_Oidom(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2655]) ).
cnf(c_0_2656_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2656]) ).
cnf(c_0_2656_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| X1 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2656]) ).
cnf(c_0_2656_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| X1 = c_HOL_Ozero__class_Ozero(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2656]) ).
cnf(c_0_2656_3,axiom,
( ~ class_Ring__and__Field_Oidom(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| X1 = c_HOL_Ozero__class_Ozero(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2656]) ).
cnf(c_0_2657_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2657]) ).
cnf(c_0_2657_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2657]) ).
cnf(c_0_2657_2,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2657]) ).
cnf(c_0_2659_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_2659]) ).
cnf(c_0_2659_1,axiom,
( X2 = X3
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_2659]) ).
cnf(c_0_2659_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat))
| X2 = X3
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2659]) ).
cnf(c_0_2660_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_2660]) ).
cnf(c_0_2660_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_2660]) ).
cnf(c_0_2660_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_2660]) ).
cnf(c_0_2661_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_2661]) ).
cnf(c_0_2661_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_2661]) ).
cnf(c_0_2661_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_2661]) ).
cnf(c_0_2662_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2662]) ).
cnf(c_0_2662_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2662]) ).
cnf(c_0_2662_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2662]) ).
cnf(c_0_2663_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2663]) ).
cnf(c_0_2663_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2663]) ).
cnf(c_0_2664_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2664]) ).
cnf(c_0_2664_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2664]) ).
cnf(c_0_2665_0,axiom,
( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2665]) ).
cnf(c_0_2665_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2665]) ).
cnf(c_0_2666_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2666]) ).
cnf(c_0_2666_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2666]) ).
cnf(c_0_2667_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2667]) ).
cnf(c_0_2667_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2667]) ).
cnf(c_0_2667_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2667]) ).
cnf(c_0_2667_3,axiom,
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2667]) ).
cnf(c_0_2668_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2668]) ).
cnf(c_0_2668_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2668]) ).
cnf(c_0_2668_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2668]) ).
cnf(c_0_2668_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2668]) ).
cnf(c_0_2669_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2669]) ).
cnf(c_0_2669_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2669]) ).
cnf(c_0_2669_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(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2669]) ).
cnf(c_0_2669_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2669]) ).
cnf(c_0_2670_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2670]) ).
cnf(c_0_2670_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2670]) ).
cnf(c_0_2670_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2670]) ).
cnf(c_0_2670_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2670]) ).
cnf(c_0_2671_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2671]) ).
cnf(c_0_2671_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2671]) ).
cnf(c_0_2671_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2671]) ).
cnf(c_0_2671_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2671]) ).
cnf(c_0_2672_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2672]) ).
cnf(c_0_2672_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2672]) ).
cnf(c_0_2672_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2672]) ).
cnf(c_0_2672_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2672]) ).
cnf(c_0_2673_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2673]) ).
cnf(c_0_2673_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2673]) ).
cnf(c_0_2673_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(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2673]) ).
cnf(c_0_2673_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2673]) ).
cnf(c_0_2674_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2674]) ).
cnf(c_0_2674_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2674]) ).
cnf(c_0_2674_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2674]) ).
cnf(c_0_2674_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2674]) ).
cnf(c_0_2675_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2675]) ).
cnf(c_0_2675_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2675]) ).
cnf(c_0_2675_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2675]) ).
cnf(c_0_2675_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2675]) ).
cnf(c_0_2676_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2676]) ).
cnf(c_0_2676_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2676]) ).
cnf(c_0_2676_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(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2676]) ).
cnf(c_0_2676_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2676]) ).
cnf(c_0_2677_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2677]) ).
cnf(c_0_2677_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2677]) ).
cnf(c_0_2677_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2677]) ).
cnf(c_0_2677_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2677]) ).
cnf(c_0_2678_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2678]) ).
cnf(c_0_2678_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2678]) ).
cnf(c_0_2679_0,axiom,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X1,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2679]) ).
cnf(c_0_2679_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X1,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2679]) ).
cnf(c_0_2679_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X1,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2679]) ).
cnf(c_0_2679_3,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X1,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2679]) ).
cnf(c_0_2680_0,axiom,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2680]) ).
cnf(c_0_2680_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2680]) ).
cnf(c_0_2680_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2680]) ).
cnf(c_0_2680_3,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2680]) ).
cnf(c_0_2681_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2681]) ).
cnf(c_0_2681_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2681]) ).
cnf(c_0_2681_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2681]) ).
cnf(c_0_2681_3,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2681]) ).
cnf(c_0_2682_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),X3) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Oone__class_Oone(X1)),X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2682]) ).
cnf(c_0_2682_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),X3) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Oone__class_Oone(X1)),X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2682]) ).
cnf(c_0_2683_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1),X1,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_Divides_Odiv__class_Odiv(X3,X1,X2)),c_HOL_Oone__class_Oone(X2))
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2683]) ).
cnf(c_0_2683_1,axiom,
( c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1),X1,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_Divides_Odiv__class_Odiv(X3,X1,X2)),c_HOL_Oone__class_Oone(X2))
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2683]) ).
cnf(c_0_2683_2,axiom,
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1),X1,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_Divides_Odiv__class_Odiv(X3,X1,X2)),c_HOL_Oone__class_Oone(X2))
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2683]) ).
cnf(c_0_2684_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),X1,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_Divides_Odiv__class_Odiv(X3,X1,X2)),c_HOL_Oone__class_Oone(X2))
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2684]) ).
cnf(c_0_2684_1,axiom,
( c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),X1,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_Divides_Odiv__class_Odiv(X3,X1,X2)),c_HOL_Oone__class_Oone(X2))
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2684]) ).
cnf(c_0_2684_2,axiom,
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),X1,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_Divides_Odiv__class_Odiv(X3,X1,X2)),c_HOL_Oone__class_Oone(X2))
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2684]) ).
cnf(c_0_2685_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_2685]) ).
cnf(c_0_2685_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_2685]) ).
cnf(c_0_2685_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_2685]) ).
cnf(c_0_2685_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_2685]) ).
cnf(c_0_2686_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2686]) ).
cnf(c_0_2686_1,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2686]) ).
cnf(c_0_2687_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2687]) ).
cnf(c_0_2687_1,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2687]) ).
cnf(c_0_2688_0,axiom,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3) = c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2688]) ).
cnf(c_0_2688_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3) = c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2688]) ).
cnf(c_0_2689_0,axiom,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3) = c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2689]) ).
cnf(c_0_2689_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__mult(X3)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3) = c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2689]) ).
cnf(c_0_2690_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2690]) ).
cnf(c_0_2690_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2690]) ).
cnf(c_0_2690_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2690]) ).
cnf(c_0_2691_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2691]) ).
cnf(c_0_2691_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2691]) ).
cnf(c_0_2691_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2691]) ).
cnf(c_0_2692_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2692]) ).
cnf(c_0_2692_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2692]) ).
cnf(c_0_2692_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2692]) ).
cnf(c_0_2693_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2693]) ).
cnf(c_0_2693_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2693]) ).
cnf(c_0_2693_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2693]) ).
cnf(c_0_2694_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2694]) ).
cnf(c_0_2694_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2694]) ).
cnf(c_0_2694_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2694]) ).
cnf(c_0_2695_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2695]) ).
cnf(c_0_2695_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2695]) ).
cnf(c_0_2695_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2695]) ).
cnf(c_0_2697_0,axiom,
( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Otimes__class_Otimes(X3,X4,X1)),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2697]) ).
cnf(c_0_2697_1,axiom,
( ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Otimes__class_Otimes(X3,X4,X1)),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2697]) ).
cnf(c_0_2698_0,axiom,
( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Otimes__class_Otimes(X3,X4,X1)),X4,X1) = c_Divides_Odiv__class_Omod(X2,X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2698]) ).
cnf(c_0_2698_1,axiom,
( ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Otimes__class_Otimes(X3,X4,X1)),X4,X1) = c_Divides_Odiv__class_Omod(X2,X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2698]) ).
cnf(c_0_2699_0,axiom,
( hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
inference(literals_permutation,[status(thm)],[c_0_2699]) ).
cnf(c_0_2699_1,axiom,
( ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
| hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(literals_permutation,[status(thm)],[c_0_2699]) ).
cnf(c_0_2700_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2700]) ).
cnf(c_0_2700_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2700]) ).
cnf(c_0_2700_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2700]) ).
cnf(c_0_2700_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2700]) ).
cnf(c_0_2701_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),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2701]) ).
cnf(c_0_2701_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2701]) ).
cnf(c_0_2701_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),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2701]) ).
cnf(c_0_2701_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2701]) ).
cnf(c_0_2702_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
inference(literals_permutation,[status(thm)],[c_0_2702]) ).
cnf(c_0_2702_1,axiom,
( ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2702]) ).
cnf(c_0_2703_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_2703]) ).
cnf(c_0_2703_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_2703]) ).
cnf(c_0_2704_0,axiom,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X3),X3) = c_Power_Opower__class_Opower(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X4),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2704]) ).
cnf(c_0_2704_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X3),X3) = c_Power_Opower__class_Opower(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2704]) ).
cnf(c_0_2705_0,axiom,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X4),c_Power_Opower__class_Opower(X1,X3,X4),X4) = c_Power_Opower__class_Opower(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X4)
| ~ class_OrderedGroup_Omonoid__mult(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2705]) ).
cnf(c_0_2705_1,axiom,
( ~ class_OrderedGroup_Omonoid__mult(X4)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X4),c_Power_Opower__class_Opower(X1,X3,X4),X4) = c_Power_Opower__class_Opower(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2705]) ).
cnf(c_0_2706_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_2706]) ).
cnf(c_0_2706_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_2706]) ).
cnf(c_0_2707_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_2707]) ).
cnf(c_0_2707_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_2707]) ).
cnf(c_0_2708_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_2708]) ).
cnf(c_0_2708_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_2708]) ).
cnf(c_0_2709_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_2709]) ).
cnf(c_0_2709_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_2709]) ).
cnf(c_0_2710_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_2710]) ).
cnf(c_0_2710_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_2710]) ).
cnf(c_0_2713_0,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2713]) ).
cnf(c_0_2713_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2713]) ).
cnf(c_0_2713_2,axiom,
( ~ class_Divides_Osemiring__div(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2713]) ).
cnf(c_0_2714_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2714]) ).
cnf(c_0_2714_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2714]) ).
cnf(c_0_2714_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2714]) ).
cnf(c_0_2714_3,axiom,
( ~ class_Divides_Osemiring__div(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2714]) ).
cnf(c_0_2715_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X3,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X4)
| ~ class_Divides_Osemiring__div(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2715]) ).
cnf(c_0_2715_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X3,X4),X4)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X4)
| ~ class_Divides_Osemiring__div(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2715]) ).
cnf(c_0_2715_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X3,X4),X4)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X4)
| ~ class_Divides_Osemiring__div(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2715]) ).
cnf(c_0_2715_3,axiom,
( ~ class_Divides_Osemiring__div(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X3,X4),X4)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2715]) ).
cnf(c_0_2716_0,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2716]) ).
cnf(c_0_2716_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2716]) ).
cnf(c_0_2717_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_2717]) ).
cnf(c_0_2717_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_2717]) ).
cnf(c_0_2717_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_2717]) ).
cnf(c_0_2718_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Omap(X4,X1,X2,X3) != c_List_Olist_ONil(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2718]) ).
cnf(c_0_2718_1,axiom,
( c_List_Omap(X4,X1,X2,X3) != c_List_Olist_ONil(X3)
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2718]) ).
cnf(c_0_2719_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Omap(X3,X1,X2,X4) != c_List_Olist_ONil(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2719]) ).
cnf(c_0_2719_1,axiom,
( c_List_Omap(X3,X1,X2,X4) != c_List_Olist_ONil(X4)
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2719]) ).
cnf(c_0_2721_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_2721]) ).
cnf(c_0_2721_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_2721]) ).
cnf(c_0_2721_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_2721]) ).
cnf(c_0_2722_0,axiom,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,c_Suc(X3),X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2722]) ).
cnf(c_0_2722_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,c_Suc(X3),X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2722]) ).
cnf(c_0_2722_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,c_Suc(X3),X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2722]) ).
cnf(c_0_2722_3,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,c_Suc(X3),X1),c_HOL_Oone__class_Oone(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2722]) ).
cnf(c_0_2723_0,axiom,
( c_Lambda_Obeta(hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4))
| ~ c_Lambda_Obeta(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2723]) ).
cnf(c_0_2723_1,axiom,
( ~ c_Lambda_Obeta(X1,X2)
| 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_2723]) ).
cnf(c_0_2724_0,axiom,
( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2724]) ).
cnf(c_0_2724_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2724]) ).
cnf(c_0_2724_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2724]) ).
cnf(c_0_2726_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2726]) ).
cnf(c_0_2726_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2726]) ).
cnf(c_0_2727_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2727]) ).
cnf(c_0_2727_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2727]) ).
cnf(c_0_2727_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2727]) ).
cnf(c_0_2727_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2727]) ).
cnf(c_0_2728_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2728]) ).
cnf(c_0_2728_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2728]) ).
cnf(c_0_2728_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2728]) ).
cnf(c_0_2728_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2728]) ).
cnf(c_0_2729_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2729]) ).
cnf(c_0_2729_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2729]) ).
cnf(c_0_2729_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2729]) ).
cnf(c_0_2729_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2729]) ).
cnf(c_0_2730_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,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_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2730]) ).
cnf(c_0_2730_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2730]) ).
cnf(c_0_2730_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2730]) ).
cnf(c_0_2730_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2730]) ).
cnf(c_0_2731_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2731]) ).
cnf(c_0_2731_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2731]) ).
cnf(c_0_2731_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),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2731]) ).
cnf(c_0_2731_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2731]) ).
cnf(c_0_2732_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2732]) ).
cnf(c_0_2732_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2732]) ).
cnf(c_0_2732_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2732]) ).
cnf(c_0_2732_3,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2732]) ).
cnf(c_0_2734_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2734]) ).
cnf(c_0_2734_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2734]) ).
cnf(c_0_2734_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2734]) ).
cnf(c_0_2735_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2735]) ).
cnf(c_0_2735_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2735]) ).
cnf(c_0_2735_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2735]) ).
cnf(c_0_2737_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_2737]) ).
cnf(c_0_2737_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_2737]) ).
cnf(c_0_2737_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_2737]) ).
cnf(c_0_2737_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_2737]) ).
cnf(c_0_2738_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_2738]) ).
cnf(c_0_2738_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_2738]) ).
cnf(c_0_2738_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_2738]) ).
cnf(c_0_2738_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_2738]) ).
cnf(c_0_2739_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2739]) ).
cnf(c_0_2739_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2739]) ).
cnf(c_0_2739_2,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2739]) ).
cnf(c_0_2740_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2740]) ).
cnf(c_0_2740_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2740]) ).
cnf(c_0_2740_2,axiom,
( ~ class_Ring__and__Field_Oidom(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2740]) ).
cnf(c_0_2741_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2741]) ).
cnf(c_0_2741_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2741]) ).
cnf(c_0_2741_2,axiom,
( ~ class_Ring__and__Field_Oidom(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2741]) ).
cnf(c_0_2742_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2742]) ).
cnf(c_0_2742_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2742]) ).
cnf(c_0_2742_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2742]) ).
cnf(c_0_2742_3,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2742]) ).
cnf(c_0_2743_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2743]) ).
cnf(c_0_2743_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2743]) ).
cnf(c_0_2743_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2743]) ).
cnf(c_0_2743_3,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2743]) ).
cnf(c_0_2743_4,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2743]) ).
cnf(c_0_2744_0,axiom,
( c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),X1,tc_nat) = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2744]) ).
cnf(c_0_2744_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat)
| c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),X1,tc_nat) = c_HOL_Oone__class_Oone(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2744]) ).
cnf(c_0_2745_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_2745]) ).
cnf(c_0_2745_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_2745]) ).
cnf(c_0_2745_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_2745]) ).
cnf(c_0_2746_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_2746]) ).
cnf(c_0_2746_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_2746]) ).
cnf(c_0_2746_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_2746]) ).
cnf(c_0_2747_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_2747]) ).
cnf(c_0_2747_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_2747]) ).
cnf(c_0_2747_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_2747]) ).
cnf(c_0_2748_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_2748]) ).
cnf(c_0_2748_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_2748]) ).
cnf(c_0_2748_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_2748]) ).
cnf(c_0_2749_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_2749]) ).
cnf(c_0_2749_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_2749]) ).
cnf(c_0_2749_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_2749]) ).
cnf(c_0_2749_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_2749]) ).
cnf(c_0_2750_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2750]) ).
cnf(c_0_2750_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2750]) ).
cnf(c_0_2751_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_2751]) ).
cnf(c_0_2751_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_2751]) ).
cnf(c_0_2751_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_2751]) ).
cnf(c_0_2752_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2752]) ).
cnf(c_0_2752_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2752]) ).
cnf(c_0_2752_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2752]) ).
cnf(c_0_2752_3,axiom,
( ~ class_Divides_Osemiring__div(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2752]) ).
cnf(c_0_2753_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2753]) ).
cnf(c_0_2753_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2753]) ).
cnf(c_0_2753_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2753]) ).
cnf(c_0_2753_3,axiom,
( ~ class_Divides_Osemiring__div(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2753]) ).
cnf(c_0_2754_0,axiom,
( X2 = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2754]) ).
cnf(c_0_2754_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| X2 = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2754]) ).
cnf(c_0_2754_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| X2 = c_HOL_Oone__class_Oone(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2754]) ).
cnf(c_0_2755_0,axiom,
( X2 = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2755]) ).
cnf(c_0_2755_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| X2 = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2755]) ).
cnf(c_0_2755_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| X2 = c_HOL_Oone__class_Oone(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2755]) ).
cnf(c_0_2756_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),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_2756]) ).
cnf(c_0_2756_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),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2756]) ).
cnf(c_0_2756_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_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2756]) ).
cnf(c_0_2757_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2757]) ).
cnf(c_0_2757_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2757]) ).
cnf(c_0_2757_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2757]) ).
cnf(c_0_2757_3,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2757]) ).
cnf(c_0_2758_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Otimes__class_Otimes(X3,X2,X1)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),c_HOL_Oone__class_Oone(X1)),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2758]) ).
cnf(c_0_2758_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Otimes__class_Otimes(X3,X2,X1)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),c_HOL_Oone__class_Oone(X1)),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2758]) ).
cnf(c_0_2759_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X4,X1,X2),X2) = c_Divides_Odiv__class_Odiv(X3,X4,X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2759]) ).
cnf(c_0_2759_1,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X4,X1,X2),X2) = c_Divides_Odiv__class_Odiv(X3,X4,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2759]) ).
cnf(c_0_2759_2,axiom,
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X4,X1,X2),X2) = c_Divides_Odiv__class_Odiv(X3,X4,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2759]) ).
cnf(c_0_2760_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2) = c_Divides_Odiv__class_Odiv(X3,X4,X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2760]) ).
cnf(c_0_2760_1,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2) = c_Divides_Odiv__class_Odiv(X3,X4,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2760]) ).
cnf(c_0_2760_2,axiom,
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2) = c_Divides_Odiv__class_Odiv(X3,X4,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2760]) ).
cnf(c_0_2761_0,axiom,
( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Odiv(X2,X1,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(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_2761]) ).
cnf(c_0_2761_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Odiv(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_2761]) ).
cnf(c_0_2761_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Odiv(X2,X1,tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2761]) ).
cnf(c_0_2762_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X4),X3,X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2762]) ).
cnf(c_0_2762_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X4),X3,X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2762]) ).
cnf(c_0_2763_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X1,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2763]) ).
cnf(c_0_2763_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X1,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2763]) ).
cnf(c_0_2764_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X4),X3,X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2764]) ).
cnf(c_0_2764_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X4),X3,X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2764]) ).
cnf(c_0_2765_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2765]) ).
cnf(c_0_2765_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2765]) ).
cnf(c_0_2766_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X4,X3),X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2766]) ).
cnf(c_0_2766_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X4,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2766]) ).
cnf(c_0_2767_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ class_OrderedGroup_Oab__semigroup__mult(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2767]) ).
cnf(c_0_2767_1,axiom,
( ~ class_OrderedGroup_Oab__semigroup__mult(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2767]) ).
cnf(c_0_2768_0,axiom,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),X1,X3) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3)
| ~ class_OrderedGroup_Omonoid__mult(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2768]) ).
cnf(c_0_2768_1,axiom,
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),X1,X3) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2768]) ).
cnf(c_0_2769_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2769]) ).
cnf(c_0_2769_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2769]) ).
cnf(c_0_2769_2,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2769]) ).
cnf(c_0_2769_3,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2769]) ).
cnf(c_0_2769_4,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2769]) ).
cnf(c_0_2770_0,axiom,
( c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X1,X2,X4),X3,X4) = c_Power_Opower__class_Opower(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4)
| ~ class_OrderedGroup_Omonoid__mult(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2770]) ).
cnf(c_0_2770_1,axiom,
( ~ class_OrderedGroup_Omonoid__mult(X4)
| c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X1,X2,X4),X3,X4) = c_Power_Opower__class_Opower(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2770]) ).
cnf(c_0_2771_0,axiom,
( c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X1,X2,X3),X4,X3) = c_Power_Opower__class_Opower(X1,c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2771]) ).
cnf(c_0_2771_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X1,X2,X3),X4,X3) = c_Power_Opower__class_Opower(X1,c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2771]) ).
cnf(c_0_2773_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_2773]) ).
cnf(c_0_2773_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_2773]) ).
cnf(c_0_2773_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_2773]) ).
cnf(c_0_2774_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_2774]) ).
cnf(c_0_2774_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_2774]) ).
cnf(c_0_2774_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_2774]) ).
cnf(c_0_2775_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_2775]) ).
cnf(c_0_2775_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_2775]) ).
cnf(c_0_2775_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_2775]) ).
cnf(c_0_2777_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_2777]) ).
cnf(c_0_2777_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_2777]) ).
cnf(c_0_2778_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_2778]) ).
cnf(c_0_2778_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_2778]) ).
cnf(c_0_2779_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2779]) ).
cnf(c_0_2779_1,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(X2,X3,tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2779]) ).
cnf(c_0_2780_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2780]) ).
cnf(c_0_2780_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2780]) ).
cnf(c_0_2780_2,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2780]) ).
cnf(c_0_2781_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2781]) ).
cnf(c_0_2781_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2781]) ).
cnf(c_0_2781_2,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2781]) ).
cnf(c_0_2782_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_2782]) ).
cnf(c_0_2782_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_2782]) ).
cnf(c_0_2783_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_2783]) ).
cnf(c_0_2783_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_2783]) ).
cnf(c_0_2784_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_2784]) ).
cnf(c_0_2784_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_2784]) ).
cnf(c_0_2787_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X1,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2787]) ).
cnf(c_0_2787_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(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),c_Power_Opower__class_Opower(X1,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2787]) ).
cnf(c_0_2787_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X1,X2,tc_nat),tc_nat)
| X2 = 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_2787]) ).
cnf(c_0_2788_0,axiom,
( c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X4,X2,X3),X1,X3) = c_Divides_Odiv__class_Omod(X4,X1,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2788]) ).
cnf(c_0_2788_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X4,X2,X3),X1,X3) = c_Divides_Odiv__class_Omod(X4,X1,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2788]) ).
cnf(c_0_2788_2,axiom,
( ~ class_Divides_Osemiring__div(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X4,X2,X3),X1,X3) = c_Divides_Odiv__class_Omod(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2788]) ).
cnf(c_0_2789_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(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2789]) ).
cnf(c_0_2789_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2789]) ).
cnf(c_0_2790_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),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2790]) ).
cnf(c_0_2790_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2790]) ).
cnf(c_0_2791_0,axiom,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(literals_permutation,[status(thm)],[c_0_2791]) ).
cnf(c_0_2791_1,axiom,
( ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
inference(literals_permutation,[status(thm)],[c_0_2791]) ).
cnf(c_0_2792_0,axiom,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(literals_permutation,[status(thm)],[c_0_2792]) ).
cnf(c_0_2792_1,axiom,
( ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
inference(literals_permutation,[status(thm)],[c_0_2792]) ).
cnf(c_0_2793_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2793]) ).
cnf(c_0_2793_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2793]) ).
cnf(c_0_2793_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2793]) ).
cnf(c_0_2793_3,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2793]) ).
cnf(c_0_2794_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2794]) ).
cnf(c_0_2794_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2794]) ).
cnf(c_0_2794_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2794]) ).
cnf(c_0_2794_3,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2794]) ).
cnf(c_0_2795_0,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X3,X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2795]) ).
cnf(c_0_2795_1,axiom,
( ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X3,X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2795]) ).
cnf(c_0_2796_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X3,X1),X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2796]) ).
cnf(c_0_2796_1,axiom,
( ~ class_Ring__and__Field_Oidom(X1)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2796]) ).
cnf(c_0_2797_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2),c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X2),X2),X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2797]) ).
cnf(c_0_2797_1,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2),c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X2),X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2797]) ).
cnf(c_0_2798_0,axiom,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2798]) ).
cnf(c_0_2798_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
inference(literals_permutation,[status(thm)],[c_0_2798]) ).
cnf(c_0_2800_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,c_Suc(X3),X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2800]) ).
cnf(c_0_2800_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,c_Suc(X3),X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2800]) ).
cnf(c_0_2800_2,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,c_Suc(X3),X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2800]) ).
cnf(c_0_2801_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_2801]) ).
cnf(c_0_2801_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_2801]) ).
cnf(c_0_2801_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_2801]) ).
cnf(c_0_2802_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2802]) ).
cnf(c_0_2802_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2802]) ).
cnf(c_0_2803_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_2803]) ).
cnf(c_0_2803_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_2803]) ).
cnf(c_0_2804_0,axiom,
( X1 = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| c_Power_Opower__class_Opower(X4,X1,X3) != c_Power_Opower__class_Opower(X4,X2,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2804]) ).
cnf(c_0_2804_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| X1 = X2
| c_Power_Opower__class_Opower(X4,X1,X3) != c_Power_Opower__class_Opower(X4,X2,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2804]) ).
cnf(c_0_2804_2,axiom,
( c_Power_Opower__class_Opower(X4,X1,X3) != c_Power_Opower__class_Opower(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| X1 = X2
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2804]) ).
cnf(c_0_2804_3,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_Power_Opower__class_Opower(X4,X1,X3) != c_Power_Opower__class_Opower(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2804]) ).
cnf(c_0_2805_0,axiom,
( c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) = X2
| c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) = c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2805]) ).
cnf(c_0_2805_1,axiom,
( c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) = c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat)
| c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2805]) ).
cnf(c_0_2807_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2807]) ).
cnf(c_0_2807_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2807]) ).
cnf(c_0_2807_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2807]) ).
cnf(c_0_2807_3,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2807]) ).
cnf(c_0_2808_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2808]) ).
cnf(c_0_2808_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2808]) ).
cnf(c_0_2808_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2808]) ).
cnf(c_0_2808_3,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2808]) ).
cnf(c_0_2811_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2811]) ).
cnf(c_0_2811_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2811]) ).
cnf(c_0_2811_2,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2811]) ).
cnf(c_0_2812_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2812]) ).
cnf(c_0_2812_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2812]) ).
cnf(c_0_2813_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_2813]) ).
cnf(c_0_2813_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_2813]) ).
cnf(c_0_2813_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_2813]) ).
cnf(c_0_2814_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_2814]) ).
cnf(c_0_2814_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_2814]) ).
cnf(c_0_2814_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_2814]) ).
cnf(c_0_2815_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_2815]) ).
cnf(c_0_2815_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_2815]) ).
cnf(c_0_2815_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_2815]) ).
cnf(c_0_2818_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_Power_Opower__class_Opower(X2,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2818]) ).
cnf(c_0_2818_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_Power_Opower__class_Opower(X2,X1,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2818]) ).
cnf(c_0_2818_2,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_Power_Opower__class_Opower(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2818]) ).
cnf(c_0_2819_0,axiom,
( X1 = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| c_HOL_Otimes__class_Otimes(X3,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2819]) ).
cnf(c_0_2819_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| X1 = X2
| c_HOL_Otimes__class_Otimes(X3,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2819]) ).
cnf(c_0_2819_2,axiom,
( c_HOL_Otimes__class_Otimes(X3,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2819]) ).
cnf(c_0_2820_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2820]) ).
cnf(c_0_2820_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2820]) ).
cnf(c_0_2820_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(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_2820]) ).
cnf(c_0_2821_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X2,X1,X3),X3) = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2821]) ).
cnf(c_0_2821_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X2,X1,X3),X3) = X2
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2821]) ).
cnf(c_0_2821_2,axiom,
( ~ class_Divides_Osemiring__div(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X2,X1,X3),X3) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2821]) ).
cnf(c_0_2822_0,axiom,
( c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X1,X3) = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2822]) ).
cnf(c_0_2822_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X1,X3) = X2
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2822]) ).
cnf(c_0_2822_2,axiom,
( ~ class_Divides_Osemiring__div(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X1,X3) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2822]) ).
cnf(c_0_2823_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2823]) ).
cnf(c_0_2823_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2823]) ).
cnf(c_0_2823_2,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2823]) ).
cnf(c_0_2824_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2824]) ).
cnf(c_0_2824_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2824]) ).
cnf(c_0_2824_2,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2824]) ).
cnf(c_0_2825_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1)),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2825]) ).
cnf(c_0_2825_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1)),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2825]) ).
cnf(c_0_2826_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X1,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_2826]) ).
cnf(c_0_2826_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2826]) ).
cnf(c_0_2827_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(tc_nat),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_2827]) ).
cnf(c_0_2827_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2827]) ).
cnf(c_0_2828_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2828]) ).
cnf(c_0_2828_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),c_Power_Opower__class_Opower(X1,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2828]) ).
cnf(c_0_2829_0,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X1,tc_nat) = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2829]) ).
cnf(c_0_2829_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X1,tc_nat) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2829]) ).
cnf(c_0_2830_0,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),X1,tc_nat) = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2830]) ).
cnf(c_0_2830_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),X1,tc_nat) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2830]) ).
cnf(c_0_2831_0,axiom,
( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X2,X1,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_2831]) ).
cnf(c_0_2831_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X2,X1,tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2831]) ).
cnf(c_0_2832_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_2832]) ).
cnf(c_0_2832_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_2832]) ).
cnf(c_0_2836_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_2836]) ).
cnf(c_0_2836_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_2836]) ).
cnf(c_0_2837_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_2837]) ).
cnf(c_0_2837_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_2837]) ).
cnf(c_0_2838_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2838]) ).
cnf(c_0_2838_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2838]) ).
cnf(c_0_2838_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2838]) ).
cnf(c_0_2838_3,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2838]) ).
cnf(c_0_2839_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_2839]) ).
cnf(c_0_2839_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_2839]) ).
cnf(c_0_2839_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_2839]) ).
cnf(c_0_2839_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_2839]) ).
cnf(c_0_2840_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_2840]) ).
cnf(c_0_2840_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_2840]) ).
cnf(c_0_2840_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_2840]) ).
cnf(c_0_2840_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_2840]) ).
cnf(c_0_2841_0,axiom,
( c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2841]) ).
cnf(c_0_2841_1,axiom,
( c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) != X2
| c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2841]) ).
cnf(c_0_2842_0,axiom,
( c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3)
| ~ class_Ring__and__Field_Osemiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2842]) ).
cnf(c_0_2842_1,axiom,
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2842]) ).
cnf(c_0_2843_0,axiom,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),X1,X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2843]) ).
cnf(c_0_2843_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),X1,X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2843]) ).
cnf(c_0_2844_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2844]) ).
cnf(c_0_2844_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2844]) ).
cnf(c_0_2845_0,axiom,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),X1,X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
| ~ class_OrderedGroup_Omonoid__mult(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2845]) ).
cnf(c_0_2845_1,axiom,
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),X1,X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2845]) ).
cnf(c_0_2846_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
| ~ class_Power_Opower(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2846]) ).
cnf(c_0_2846_1,axiom,
( ~ class_Power_Opower(X3)
| c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2846]) ).
cnf(c_0_2847_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2847]) ).
cnf(c_0_2847_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2847]) ).
cnf(c_0_2848_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2848]) ).
cnf(c_0_2848_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2848]) ).
cnf(c_0_2849_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_2849]) ).
cnf(c_0_2849_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_2849]) ).
cnf(c_0_2849_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_2849]) ).
cnf(c_0_2850_0,axiom,
( c_Divides_Odiv__class_Odiv(X2,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2850]) ).
cnf(c_0_2850_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_Divides_Odiv__class_Odiv(X2,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2850]) ).
cnf(c_0_2850_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_Divides_Odiv__class_Odiv(X2,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2850]) ).
cnf(c_0_2851_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_2851]) ).
cnf(c_0_2851_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_2851]) ).
cnf(c_0_2851_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_2851]) ).
cnf(c_0_2852_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2852]) ).
cnf(c_0_2852_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2852]) ).
cnf(c_0_2853_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_2853]) ).
cnf(c_0_2853_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_2853]) ).
cnf(c_0_2854_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_2854]) ).
cnf(c_0_2854_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_2854]) ).
cnf(c_0_2855_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_2855]) ).
cnf(c_0_2855_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_2855]) ).
cnf(c_0_2856_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_2856]) ).
cnf(c_0_2856_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_2856]) ).
cnf(c_0_2859_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) = c_HOL_Otimes__class_Otimes(X1,X2,X3)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2859]) ).
cnf(c_0_2859_1,axiom,
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) = c_HOL_Otimes__class_Otimes(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2859]) ).
cnf(c_0_2860_0,axiom,
( c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X1,X2,X3),X2,X3) = c_Divides_Odiv__class_Omod(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2860]) ).
cnf(c_0_2860_1,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X1,X2,X3),X2,X3) = c_Divides_Odiv__class_Omod(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2860]) ).
cnf(c_0_2861_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2861]) ).
cnf(c_0_2861_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2861]) ).
cnf(c_0_2861_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2861]) ).
cnf(c_0_2862_0,axiom,
( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X2,X1) = c_Divides_Odiv__class_Omod(X3,X2,X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2862]) ).
cnf(c_0_2862_1,axiom,
( ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X2,X1) = c_Divides_Odiv__class_Omod(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2862]) ).
cnf(c_0_2863_0,axiom,
( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2863]) ).
cnf(c_0_2863_1,axiom,
( ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2863]) ).
cnf(c_0_2864_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_2864]) ).
cnf(c_0_2864_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_2864]) ).
cnf(c_0_2867_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_2867]) ).
cnf(c_0_2867_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_2867]) ).
cnf(c_0_2868_0,axiom,
( c_Power_Opower__class_Opower(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),X2,X3) = c_Nat_Osemiring__1__class_Oof__nat(c_Power_Opower__class_Opower(X1,X2,tc_nat),X3)
| ~ class_Ring__and__Field_Osemiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2868]) ).
cnf(c_0_2868_1,axiom,
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_Power_Opower__class_Opower(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),X2,X3) = c_Nat_Osemiring__1__class_Oof__nat(c_Power_Opower__class_Opower(X1,X2,tc_nat),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2868]) ).
cnf(c_0_2869_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_2869]) ).
cnf(c_0_2869_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_2869]) ).
cnf(c_0_2870_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_2870]) ).
cnf(c_0_2870_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_2870]) ).
cnf(c_0_2870_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_2870]) ).
cnf(c_0_2871_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_2871]) ).
cnf(c_0_2871_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_2871]) ).
cnf(c_0_2872_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_2872]) ).
cnf(c_0_2872_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_2872]) ).
cnf(c_0_2872_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_2872]) ).
cnf(c_0_2873_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X1,c_Suc(v_sko__Nat__Xnat__Xinducts__1(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_2873]) ).
cnf(c_0_2873_1,axiom,
( ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_Suc(v_sko__Nat__Xnat__Xinducts__1(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_2873]) ).
cnf(c_0_2873_2,axiom,
( ~ hBOOL(hAPP(X1,c_Suc(v_sko__Nat__Xnat__Xinducts__1(X1))))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2873]) ).
cnf(c_0_2874_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X1,c_Suc(v_sko__Nat__Xnat__Xinduct__1(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_2874]) ).
cnf(c_0_2874_1,axiom,
( ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_Suc(v_sko__Nat__Xnat__Xinduct__1(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_2874]) ).
cnf(c_0_2874_2,axiom,
( ~ hBOOL(hAPP(X1,c_Suc(v_sko__Nat__Xnat__Xinduct__1(X1))))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2874]) ).
cnf(c_0_2875_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X1,c_Suc(v_sko__List__Xupt__Xinduct__1(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_2875]) ).
cnf(c_0_2875_1,axiom,
( ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_Suc(v_sko__List__Xupt__Xinduct__1(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_2875]) ).
cnf(c_0_2875_2,axiom,
( ~ hBOOL(hAPP(X1,c_Suc(v_sko__List__Xupt__Xinduct__1(X1))))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2875]) ).
cnf(c_0_2876_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X1,c_Suc(v_sko__List__Xreplicate__Xinduct__1(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_2876]) ).
cnf(c_0_2876_1,axiom,
( ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_Suc(v_sko__List__Xreplicate__Xinduct__1(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_2876]) ).
cnf(c_0_2876_2,axiom,
( ~ hBOOL(hAPP(X1,c_Suc(v_sko__List__Xreplicate__Xinduct__1(X1))))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2876]) ).
cnf(c_0_2877_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X1,c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_2877]) ).
cnf(c_0_2877_1,axiom,
( ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_2877]) ).
cnf(c_0_2877_2,axiom,
( ~ hBOOL(hAPP(X1,c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X1))))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2877]) ).
cnf(c_0_2878_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X1,c_Suc(v_sko__List__Xlexn__Xinduct__1(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_2878]) ).
cnf(c_0_2878_1,axiom,
( ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_Suc(v_sko__List__Xlexn__Xinduct__1(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_2878]) ).
cnf(c_0_2878_2,axiom,
( ~ hBOOL(hAPP(X1,c_Suc(v_sko__List__Xlexn__Xinduct__1(X1))))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2878]) ).
cnf(c_0_2879_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_2879]) ).
cnf(c_0_2879_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_2879]) ).
cnf(c_0_2879_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_2879]) ).
cnf(c_0_2879_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_2879]) ).
cnf(c_0_2880_0,axiom,
( X1 = X2
| c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2880]) ).
cnf(c_0_2880_1,axiom,
( c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2880]) ).
cnf(c_0_2881_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2881]) ).
cnf(c_0_2881_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2881]) ).
cnf(c_0_2882_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_2882]) ).
cnf(c_0_2882_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_2882]) ).
cnf(c_0_2882_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_2882]) ).
cnf(c_0_2883_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_2883]) ).
cnf(c_0_2883_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_2883]) ).
cnf(c_0_2883_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_2883]) ).
cnf(c_0_2883_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_2883]) ).
cnf(c_0_2884_0,axiom,
( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3))
| ~ c_Lambda_Obeta(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2884]) ).
cnf(c_0_2884_1,axiom,
( ~ c_Lambda_Obeta(X1,X2)
| 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_2884]) ).
cnf(c_0_2885_0,axiom,
( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2))
| ~ c_Lambda_Obeta(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2885]) ).
cnf(c_0_2885_1,axiom,
( ~ c_Lambda_Obeta(X1,X2)
| 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_2885]) ).
cnf(c_0_2886_0,axiom,
( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_Olift,X1),X3),hAPP(hAPP(c_Lambda_Olift,X2),X3))
| ~ c_Lambda_Obeta(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2886]) ).
cnf(c_0_2886_1,axiom,
( ~ c_Lambda_Obeta(X1,X2)
| c_Lambda_Obeta(hAPP(hAPP(c_Lambda_Olift,X1),X3),hAPP(hAPP(c_Lambda_Olift,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2886]) ).
cnf(c_0_2887_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_2887]) ).
cnf(c_0_2887_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_2887]) ).
cnf(c_0_2887_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_2887]) ).
cnf(c_0_2888_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_2888]) ).
cnf(c_0_2888_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_2888]) ).
cnf(c_0_2888_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_2888]) ).
cnf(c_0_2889_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_2889]) ).
cnf(c_0_2889_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_2889]) ).
cnf(c_0_2889_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_2889]) ).
cnf(c_0_2890_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_2890]) ).
cnf(c_0_2890_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_2890]) ).
cnf(c_0_2890_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_2890]) ).
cnf(c_0_2891_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_2891]) ).
cnf(c_0_2891_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_2891]) ).
cnf(c_0_2892_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_2892]) ).
cnf(c_0_2892_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_2892]) ).
cnf(c_0_2893_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X3,X2),X1,X2) = X3
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2893]) ).
cnf(c_0_2893_1,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X3,X2),X1,X2) = X3
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2893]) ).
cnf(c_0_2893_2,axiom,
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X3,X2),X1,X2) = X3
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2893]) ).
cnf(c_0_2894_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X1,X2),X1,X2) = X3
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2894]) ).
cnf(c_0_2894_1,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X1,X2),X1,X2) = X3
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2894]) ).
cnf(c_0_2894_2,axiom,
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X1,X2),X1,X2) = X3
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2894]) ).
cnf(c_0_2895_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_2895]) ).
cnf(c_0_2895_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_2895]) ).
cnf(c_0_2895_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_2895]) ).
cnf(c_0_2896_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_2896]) ).
cnf(c_0_2896_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_2896]) ).
cnf(c_0_2896_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_2896]) ).
cnf(c_0_2897_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_2897]) ).
cnf(c_0_2897_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_2897]) ).
cnf(c_0_2897_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_2897]) ).
cnf(c_0_2898_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X1,X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2898]) ).
cnf(c_0_2898_1,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X1,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2898]) ).
cnf(c_0_2899_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2899]) ).
cnf(c_0_2899_1,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2899]) ).
cnf(c_0_2900_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = X3
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2900]) ).
cnf(c_0_2900_1,axiom,
( X2 = X3
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2900]) ).
cnf(c_0_2900_2,axiom,
( c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)
| X2 = X3
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2900]) ).
cnf(c_0_2901_0,axiom,
( X1 = X2
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(X3,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2901]) ).
cnf(c_0_2901_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = X2
| c_HOL_Otimes__class_Otimes(X3,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2901]) ).
cnf(c_0_2901_2,axiom,
( c_HOL_Otimes__class_Otimes(X3,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat)
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2901]) ).
cnf(c_0_2902_0,axiom,
( X1 = X2
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) != c_HOL_Otimes__class_Otimes(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2902]) ).
cnf(c_0_2902_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = X2
| c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) != c_HOL_Otimes__class_Otimes(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2902]) ).
cnf(c_0_2902_2,axiom,
( c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) != c_HOL_Otimes__class_Otimes(X2,X3,tc_nat)
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2902]) ).
cnf(c_0_2903_0,axiom,
( c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X1,X2,X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2903]) ).
cnf(c_0_2903_1,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X1,X2,X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2903]) ).
cnf(c_0_2904_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_2904]) ).
cnf(c_0_2904_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_2904]) ).
cnf(c_0_2904_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_2904]) ).
cnf(c_0_2905_0,axiom,
( X1 = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2905]) ).
cnf(c_0_2905_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| X1 = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2905]) ).
cnf(c_0_2905_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2905]) ).
cnf(c_0_2906_0,axiom,
( X1 = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2906]) ).
cnf(c_0_2906_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| X1 = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2906]) ).
cnf(c_0_2906_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2906]) ).
cnf(c_0_2907_0,axiom,
( X2 = X1
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2907]) ).
cnf(c_0_2907_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| X2 = X1
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2907]) ).
cnf(c_0_2907_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2907]) ).
cnf(c_0_2908_0,axiom,
( X1 = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2908]) ).
cnf(c_0_2908_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| X1 = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2908]) ).
cnf(c_0_2908_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2908]) ).
cnf(c_0_2909_0,axiom,
( X1 = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2909]) ).
cnf(c_0_2909_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| X1 = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2909]) ).
cnf(c_0_2909_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2909]) ).
cnf(c_0_2910_0,axiom,
( X1 = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2910]) ).
cnf(c_0_2910_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| X1 = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2910]) ).
cnf(c_0_2910_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2910]) ).
cnf(c_0_2911_0,axiom,
( X1 = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2911]) ).
cnf(c_0_2911_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| X1 = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2911]) ).
cnf(c_0_2911_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2911]) ).
cnf(c_0_2912_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2912]) ).
cnf(c_0_2912_1,axiom,
( ~ class_Ring__and__Field_Odvd(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2912]) ).
cnf(c_0_2913_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2913]) ).
cnf(c_0_2913_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2913]) ).
cnf(c_0_2914_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2914]) ).
cnf(c_0_2914_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2914]) ).
cnf(c_0_2916_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_2916]) ).
cnf(c_0_2916_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_2916]) ).
cnf(c_0_2917_0,axiom,
( c_Type_Otyping(X1,X4,X3)
| ~ c_Type_Otyping(X1,X2,X3)
| ~ c_Lambda_Obeta(X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2917]) ).
cnf(c_0_2917_1,axiom,
( ~ c_Type_Otyping(X1,X2,X3)
| c_Type_Otyping(X1,X4,X3)
| ~ c_Lambda_Obeta(X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2917]) ).
cnf(c_0_2917_2,axiom,
( ~ c_Lambda_Obeta(X2,X4)
| ~ c_Type_Otyping(X1,X2,X3)
| c_Type_Otyping(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2917]) ).
cnf(c_0_2919_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_2919]) ).
cnf(c_0_2919_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_2919]) ).
cnf(c_0_2920_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Divides_Odiv__class_Omod(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2920]) ).
cnf(c_0_2920_1,axiom,
( c_Divides_Odiv__class_Omod(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2920]) ).
cnf(c_0_2920_2,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2920]) ).
cnf(c_0_2922_0,axiom,
( c_Divides_Odiv__class_Omod(X2,X1,X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2922]) ).
cnf(c_0_2922_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Divides_Odiv__class_Omod(X2,X1,X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2922]) ).
cnf(c_0_2922_2,axiom,
( ~ class_Divides_Osemiring__div(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Divides_Odiv__class_Omod(X2,X1,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2922]) ).
cnf(c_0_2923_0,axiom,
( hBOOL(hAPP(X1,c_Suc(c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X1))))
| hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2923]) ).
cnf(c_0_2923_1,axiom,
( hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X1,c_Suc(c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X1))))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2923]) ).
cnf(c_0_2923_2,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X1,c_Suc(c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_2923]) ).
cnf(c_0_2924_0,axiom,
( hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2924]) ).
cnf(c_0_2924_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2924]) ).
cnf(c_0_2924_2,axiom,
( ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X1)))
| ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(literals_permutation,[status(thm)],[c_0_2924]) ).
cnf(c_0_2925_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_2925]) ).
cnf(c_0_2925_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_2925]) ).
cnf(c_0_2926_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_2926]) ).
cnf(c_0_2926_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_2926]) ).
cnf(c_0_2927_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_2927]) ).
cnf(c_0_2927_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_2927]) ).
cnf(c_0_2927_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_2927]) ).
cnf(c_0_2928_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_2928]) ).
cnf(c_0_2928_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_2928]) ).
cnf(c_0_2928_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_2928]) ).
cnf(c_0_2929_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_2929]) ).
cnf(c_0_2929_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_2929]) ).
cnf(c_0_2929_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_2929]) ).
cnf(c_0_2930_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_2930]) ).
cnf(c_0_2930_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_2930]) ).
cnf(c_0_2930_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_2930]) ).
cnf(c_0_2931_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_2931]) ).
cnf(c_0_2931_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_2931]) ).
cnf(c_0_2932_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_2932]) ).
cnf(c_0_2932_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_2932]) ).
cnf(c_0_2933_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_2933]) ).
cnf(c_0_2933_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_2933]) ).
cnf(c_0_2934_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_2934]) ).
cnf(c_0_2934_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_2934]) ).
cnf(c_0_2937_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_2937]) ).
cnf(c_0_2937_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_2937]) ).
cnf(c_0_2938_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_2938]) ).
cnf(c_0_2938_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_2938]) ).
cnf(c_0_2939_0,axiom,
( c_Divides_Odiv__class_Odiv(X1,X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2939]) ).
cnf(c_0_2939_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Divides_Odiv__class_Odiv(X1,X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2939]) ).
cnf(c_0_2940_0,axiom,
( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = X1
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2940]) ).
cnf(c_0_2940_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2940]) ).
cnf(c_0_2941_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_2941]) ).
cnf(c_0_2941_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_2941]) ).
cnf(c_0_2942_0,axiom,
( hBOOL(hAPP(X1,v_sko__List__Xupt__Xinduct__1(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(literals_permutation,[status(thm)],[c_0_2942]) ).
cnf(c_0_2942_1,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,v_sko__List__Xupt__Xinduct__1(X1)))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(literals_permutation,[status(thm)],[c_0_2942]) ).
cnf(c_0_2942_2,axiom,
( ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,v_sko__List__Xupt__Xinduct__1(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2942]) ).
cnf(c_0_2943_0,axiom,
( hBOOL(hAPP(X1,v_sko__Nat__Xnat__Xinduct__1(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(literals_permutation,[status(thm)],[c_0_2943]) ).
cnf(c_0_2943_1,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,v_sko__Nat__Xnat__Xinduct__1(X1)))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(literals_permutation,[status(thm)],[c_0_2943]) ).
cnf(c_0_2943_2,axiom,
( ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,v_sko__Nat__Xnat__Xinduct__1(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2943]) ).
cnf(c_0_2944_0,axiom,
( hBOOL(hAPP(X1,v_sko__Nat__Xnat__Xinducts__1(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(literals_permutation,[status(thm)],[c_0_2944]) ).
cnf(c_0_2944_1,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,v_sko__Nat__Xnat__Xinducts__1(X1)))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(literals_permutation,[status(thm)],[c_0_2944]) ).
cnf(c_0_2944_2,axiom,
( ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,v_sko__Nat__Xnat__Xinducts__1(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2944]) ).
cnf(c_0_2945_0,axiom,
( hBOOL(hAPP(X1,v_sko__List__Xreplicate__Xinduct__1(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(literals_permutation,[status(thm)],[c_0_2945]) ).
cnf(c_0_2945_1,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,v_sko__List__Xreplicate__Xinduct__1(X1)))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(literals_permutation,[status(thm)],[c_0_2945]) ).
cnf(c_0_2945_2,axiom,
( ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,v_sko__List__Xreplicate__Xinduct__1(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2945]) ).
cnf(c_0_2946_0,axiom,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(literals_permutation,[status(thm)],[c_0_2946]) ).
cnf(c_0_2946_1,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X1)))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(literals_permutation,[status(thm)],[c_0_2946]) ).
cnf(c_0_2946_2,axiom,
( ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2946]) ).
cnf(c_0_2947_0,axiom,
( hBOOL(hAPP(X1,v_sko__List__Xlexn__Xinduct__1(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(literals_permutation,[status(thm)],[c_0_2947]) ).
cnf(c_0_2947_1,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,v_sko__List__Xlexn__Xinduct__1(X1)))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(literals_permutation,[status(thm)],[c_0_2947]) ).
cnf(c_0_2947_2,axiom,
( ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,v_sko__List__Xlexn__Xinduct__1(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2947]) ).
cnf(c_0_2948_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2948]) ).
cnf(c_0_2948_1,axiom,
( c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2948]) ).
cnf(c_0_2948_2,axiom,
( ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2948]) ).
cnf(c_0_2948_3,axiom,
( ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2948]) ).
cnf(c_0_2948_4,axiom,
( ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2948]) ).
cnf(c_0_2948_5,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2948]) ).
cnf(c_0_2949_0,axiom,
( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2949]) ).
cnf(c_0_2949_1,axiom,
( ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2949]) ).
cnf(c_0_2949_2,axiom,
( ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2949]) ).
cnf(c_0_2949_3,axiom,
( ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2949]) ).
cnf(c_0_2949_4,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) != c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2949]) ).
cnf(c_0_2951_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_2951]) ).
cnf(c_0_2951_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_2951]) ).
cnf(c_0_2951_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_2951]) ).
cnf(c_0_2952_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_2952]) ).
cnf(c_0_2952_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_2952]) ).
cnf(c_0_2952_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_2952]) ).
cnf(c_0_2952_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_2952]) ).
cnf(c_0_2953_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_2953]) ).
cnf(c_0_2953_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_2953]) ).
cnf(c_0_2953_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_2953]) ).
cnf(c_0_2953_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_2953]) ).
cnf(c_0_2954_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_2954]) ).
cnf(c_0_2954_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_2954]) ).
cnf(c_0_2954_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_2954]) ).
cnf(c_0_2954_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_2954]) ).
cnf(c_0_2955_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_2955]) ).
cnf(c_0_2955_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_2955]) ).
cnf(c_0_2955_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_2955]) ).
cnf(c_0_2955_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_2955]) ).
cnf(c_0_2956_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_2956]) ).
cnf(c_0_2956_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_2956]) ).
cnf(c_0_2956_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_2956]) ).
cnf(c_0_2956_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_2956]) ).
cnf(c_0_2957_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_2957]) ).
cnf(c_0_2957_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_2957]) ).
cnf(c_0_2958_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_2958]) ).
cnf(c_0_2958_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_2958]) ).
cnf(c_0_2959_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_2959]) ).
cnf(c_0_2959_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_2959]) ).
cnf(c_0_2960_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X2,X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2960]) ).
cnf(c_0_2960_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2960]) ).
cnf(c_0_2961_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X2,X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2961]) ).
cnf(c_0_2961_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2961]) ).
cnf(c_0_2962_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_2962]) ).
cnf(c_0_2962_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_2962]) ).
cnf(c_0_2963_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_2963]) ).
cnf(c_0_2963_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_2963]) ).
cnf(c_0_2964_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_2964]) ).
cnf(c_0_2964_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_2964]) ).
cnf(c_0_2967_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_2967]) ).
cnf(c_0_2967_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_2967]) ).
cnf(c_0_2968_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_2968]) ).
cnf(c_0_2968_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_2968]) ).
cnf(c_0_2969_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_2969]) ).
cnf(c_0_2969_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_2969]) ).
cnf(c_0_2970_0,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2970]) ).
cnf(c_0_2970_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_2970]) ).
cnf(c_0_2972_0,axiom,
( hAPP(X1,X2) = X3
| ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2972]) ).
cnf(c_0_2972_1,axiom,
( ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3)
| hAPP(X1,X2) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2972]) ).
cnf(c_0_2974_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2974]) ).
cnf(c_0_2974_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2974]) ).
cnf(c_0_2974_2,axiom,
( c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2974]) ).
cnf(c_0_2974_3,axiom,
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X2)
| c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2974]) ).
cnf(c_0_2975_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2975]) ).
cnf(c_0_2975_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2975]) ).
cnf(c_0_2975_2,axiom,
( c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2975]) ).
cnf(c_0_2975_3,axiom,
( ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2975]) ).
cnf(c_0_2976_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2976]) ).
cnf(c_0_2976_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2976]) ).
cnf(c_0_2976_2,axiom,
( c_HOL_Otimes__class_Otimes(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2976]) ).
cnf(c_0_2976_3,axiom,
( ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| c_HOL_Otimes__class_Otimes(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2976]) ).
cnf(c_0_2977_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_2977]) ).
cnf(c_0_2977_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_2977]) ).
cnf(c_0_2977_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_2977]) ).
cnf(c_0_2978_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_2978]) ).
cnf(c_0_2978_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_2978]) ).
cnf(c_0_2978_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_2978]) ).
cnf(c_0_2979_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2979]) ).
cnf(c_0_2979_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2979]) ).
cnf(c_0_2979_2,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| X2 = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2979]) ).
cnf(c_0_2980_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_2980]) ).
cnf(c_0_2980_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_2980]) ).
cnf(c_0_2981_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_Power_Opower__class_Opower(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_2981]) ).
cnf(c_0_2981_1,axiom,
( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_2981]) ).
cnf(c_0_2981_2,axiom,
( c_Power_Opower__class_Opower(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2981]) ).
cnf(c_0_2983_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2983]) ).
cnf(c_0_2983_1,axiom,
( c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2983]) ).
cnf(c_0_2983_2,axiom,
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2983]) ).
cnf(c_0_2984_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_2984]) ).
cnf(c_0_2984_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_2984]) ).
cnf(c_0_2984_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_2984]) ).
cnf(c_0_2984_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_2984]) ).
cnf(c_0_2985_0,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_2985]) ).
cnf(c_0_2985_1,axiom,
( c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != 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_2985]) ).
cnf(c_0_2986_0,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_2986]) ).
cnf(c_0_2986_1,axiom,
( c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != 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_2986]) ).
cnf(c_0_2987_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_2987]) ).
cnf(c_0_2987_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_2987]) ).
cnf(c_0_2987_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_2987]) ).
cnf(c_0_2988_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_2988]) ).
cnf(c_0_2988_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_2988]) ).
cnf(c_0_2988_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_2988]) ).
cnf(c_0_2989_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_2989]) ).
cnf(c_0_2989_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_2989]) ).
cnf(c_0_2989_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_2989]) ).
cnf(c_0_2990_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2990]) ).
cnf(c_0_2990_1,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2990]) ).
cnf(c_0_2990_2,axiom,
( ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2990]) ).
cnf(c_0_2990_3,axiom,
( ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2990]) ).
cnf(c_0_2990_4,axiom,
( ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2990]) ).
cnf(c_0_2990_5,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2990]) ).
cnf(c_0_2991_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_2991]) ).
cnf(c_0_2991_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_2991]) ).
cnf(c_0_2991_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_2991]) ).
cnf(c_0_2992_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_2992]) ).
cnf(c_0_2992_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_2992]) ).
cnf(c_0_2992_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_2992]) ).
cnf(c_0_2993_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_2993]) ).
cnf(c_0_2993_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_2993]) ).
cnf(c_0_2993_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_2993]) ).
cnf(c_0_2994_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_2994]) ).
cnf(c_0_2994_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_2994]) ).
cnf(c_0_2994_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_2994]) ).
cnf(c_0_2995_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2995]) ).
cnf(c_0_2995_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2995]) ).
cnf(c_0_2995_2,axiom,
( c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != 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_2995]) ).
cnf(c_0_2997_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2997]) ).
cnf(c_0_2997_1,axiom,
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2997]) ).
cnf(c_0_2998_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2998]) ).
cnf(c_0_2998_1,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2998]) ).
cnf(c_0_2999_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2999]) ).
cnf(c_0_2999_1,axiom,
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2999]) ).
cnf(c_0_3000_0,axiom,
( X1 = c_HOL_Oone__class_Oone(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_3000]) ).
cnf(c_0_3000_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_3000]) ).
cnf(c_0_3000_2,axiom,
( c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != X2
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Oone__class_Oone(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_3000]) ).
cnf(c_0_3001_0,axiom,
( X1 = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_3001]) ).
cnf(c_0_3001_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| X1 = c_HOL_Oone__class_Oone(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_3001]) ).
cnf(c_0_3003_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_3003]) ).
cnf(c_0_3003_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_3003]) ).
cnf(c_0_3003_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_3003]) ).
cnf(c_0_3004_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_3004]) ).
cnf(c_0_3004_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_3004]) ).
cnf(c_0_3004_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_3004]) ).
cnf(c_0_3005_0,axiom,
( X1 = c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_3005]) ).
cnf(c_0_3005_1,axiom,
( c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
| X1 = c_HOL_Oone__class_Oone(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_3005]) ).
cnf(c_0_3006_0,axiom,
( X1 = c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_3006]) ).
cnf(c_0_3006_1,axiom,
( c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
| X1 = c_HOL_Oone__class_Oone(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_3006]) ).
cnf(c_0_3007_0,axiom,
( X1 = c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_3007]) ).
cnf(c_0_3007_1,axiom,
( c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
| X1 = c_HOL_Oone__class_Oone(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_3007]) ).
cnf(c_0_3008_0,axiom,
( X1 = c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_3008]) ).
cnf(c_0_3008_1,axiom,
( c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
| X1 = c_HOL_Oone__class_Oone(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_3008]) ).
cnf(c_0_3011_0,axiom,
( X1 = X2
| ~ c_fequal(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3011]) ).
cnf(c_0_3011_1,axiom,
( ~ c_fequal(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3011]) ).
cnf(c_0_3013_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Suc(X2),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Power_Opower(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3013]) ).
cnf(c_0_3013_1,axiom,
( ~ class_Power_Opower(X1)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Suc(X2),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3013]) ).
cnf(c_0_3013_2,axiom,
( ~ class_Ring__and__Field_Osemiring__0(X1)
| ~ class_Power_Opower(X1)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Suc(X2),X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3013]) ).
cnf(c_0_3017_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Osemiring__0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3017]) ).
cnf(c_0_3017_1,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Osemiring__0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3017]) ).
cnf(c_0_3017_2,axiom,
( ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Osemiring__0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3017]) ).
cnf(c_0_3017_3,axiom,
( ~ class_Ring__and__Field_Osemiring__0(X2)
| ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_3017]) ).
cnf(c_0_3018_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_3018]) ).
cnf(c_0_3018_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_3018]) ).
cnf(c_0_3019_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Power_Opower(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3019]) ).
cnf(c_0_3019_1,axiom,
( ~ class_Power_Opower(X1)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3019]) ).
cnf(c_0_3019_2,axiom,
( ~ class_Ring__and__Field_Osemiring__0(X1)
| ~ class_Power_Opower(X1)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3019]) ).
cnf(c_0_3020_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_3020]) ).
cnf(c_0_3020_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_3020]) ).
cnf(c_0_3024_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_3024]) ).
cnf(c_0_3024_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_3024]) ).
cnf(c_0_3025_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_3025]) ).
cnf(c_0_3025_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_3025]) ).
cnf(c_0_3026_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_3026]) ).
cnf(c_0_3026_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_3026]) ).
cnf(c_0_3027_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_3027]) ).
cnf(c_0_3027_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_3027]) ).
cnf(c_0_3029_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_3029]) ).
cnf(c_0_3029_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_3029]) ).
cnf(c_0_3030_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_3030]) ).
cnf(c_0_3030_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_3030]) ).
cnf(c_0_3030_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_3030]) ).
cnf(c_0_3031_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_3031]) ).
cnf(c_0_3031_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_3031]) ).
cnf(c_0_3032_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_3032]) ).
cnf(c_0_3032_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_3032]) ).
cnf(c_0_3033_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_3033]) ).
cnf(c_0_3033_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_3033]) ).
cnf(c_0_3034_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_3034]) ).
cnf(c_0_3034_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_3034]) ).
cnf(c_0_3037_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3037]) ).
cnf(c_0_3037_1,axiom,
( ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3037]) ).
cnf(c_0_3038_0,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3038]) ).
cnf(c_0_3038_1,axiom,
( ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3038]) ).
cnf(c_0_3039_0,axiom,
( c_Divides_Odiv__class_Odiv(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3039]) ).
cnf(c_0_3039_1,axiom,
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Odiv(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3039]) ).
cnf(c_0_3040_0,axiom,
( c_Divides_Odiv__class_Omod(X1,c_HOL_Oone__class_Oone(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3040]) ).
cnf(c_0_3040_1,axiom,
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Omod(X1,c_HOL_Oone__class_Oone(X2),X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3040]) ).
cnf(c_0_3041_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3041]) ).
cnf(c_0_3041_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3041]) ).
cnf(c_0_3042_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3042]) ).
cnf(c_0_3042_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3042]) ).
cnf(c_0_3043_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3043]) ).
cnf(c_0_3043_1,axiom,
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X2)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3043]) ).
cnf(c_0_3044_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3044]) ).
cnf(c_0_3044_1,axiom,
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3044]) ).
cnf(c_0_3045_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Omult__zero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3045]) ).
cnf(c_0_3045_1,axiom,
( ~ class_Ring__and__Field_Omult__zero(X2)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3045]) ).
cnf(c_0_3046_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Omult__zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3046]) ).
cnf(c_0_3046_1,axiom,
( ~ class_Ring__and__Field_Omult__zero(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3046]) ).
cnf(c_0_3047_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3047]) ).
cnf(c_0_3047_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3047]) ).
cnf(c_0_3048_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3048]) ).
cnf(c_0_3048_1,axiom,
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1) = c_HOL_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3048]) ).
cnf(c_0_3051_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(X1,X1,X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3051]) ).
cnf(c_0_3051_1,axiom,
( c_Divides_Odiv__class_Odiv(X1,X1,X2) = c_HOL_Oone__class_Oone(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3051]) ).
cnf(c_0_3051_2,axiom,
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Odiv(X1,X1,X2) = c_HOL_Oone__class_Oone(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3051]) ).
cnf(c_0_3052_0,axiom,
( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3052]) ).
cnf(c_0_3052_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) = c_HOL_Oone__class_Oone(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3052]) ).
cnf(c_0_3053_0,axiom,
( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Power_Opower(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3053]) ).
cnf(c_0_3053_1,axiom,
( ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) = c_HOL_Oone__class_Oone(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3053]) ).
cnf(c_0_3054_0,axiom,
( c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3054]) ).
cnf(c_0_3054_1,axiom,
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3054]) ).
cnf(c_0_3055_0,axiom,
( c_Divides_Odiv__class_Odiv(X1,c_HOL_Oone__class_Oone(X2),X2) = X1
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3055]) ).
cnf(c_0_3055_1,axiom,
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Odiv(X1,c_HOL_Oone__class_Oone(X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3055]) ).
cnf(c_0_3056_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3056]) ).
cnf(c_0_3056_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3056]) ).
cnf(c_0_3057_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3057]) ).
cnf(c_0_3057_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3057]) ).
cnf(c_0_3058_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3058]) ).
cnf(c_0_3058_1,axiom,
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3058]) ).
cnf(c_0_3059_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X2),X2) = X1
| ~ class_OrderedGroup_Omonoid__mult(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3059]) ).
cnf(c_0_3059_1,axiom,
( ~ class_OrderedGroup_Omonoid__mult(X2)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3059]) ).
cnf(c_0_3060_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X2),X2) = X1
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3060]) ).
cnf(c_0_3060_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3060]) ).
cnf(c_0_3061_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3061]) ).
cnf(c_0_3061_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3061]) ).
cnf(c_0_3063_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3063]) ).
cnf(c_0_3063_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_3063]) ).
cnf(c_0_3064_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3064]) ).
cnf(c_0_3064_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_3064]) ).
cnf(c_0_3066_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_3066]) ).
cnf(c_0_3066_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_3066]) ).
cnf(c_0_3067_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_3067]) ).
cnf(c_0_3067_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_3067]) ).
cnf(c_0_3068_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_3068]) ).
cnf(c_0_3068_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_3068]) ).
cnf(c_0_3070_0,axiom,
( c_Divides_Odiv__class_Omod(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3070]) ).
cnf(c_0_3070_1,axiom,
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Omod(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3070]) ).
cnf(c_0_3071_0,axiom,
( c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X2) = X1
| ~ class_OrderedGroup_Omonoid__mult(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3071]) ).
cnf(c_0_3071_1,axiom,
( ~ class_OrderedGroup_Omonoid__mult(X2)
| c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3071]) ).
cnf(c_0_3072_0,axiom,
( c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X2) = X1
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3072]) ).
cnf(c_0_3072_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3072]) ).
cnf(c_0_3079_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,X1,X2) = X1
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3079]) ).
cnf(c_0_3079_1,axiom,
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2)
| c_HOL_Otimes__class_Otimes(X1,X1,X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3079]) ).
cnf(c_0_3082_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X1,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3082]) ).
cnf(c_0_3082_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3082]) ).
cnf(c_0_3086_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_3086]) ).
cnf(c_0_3086_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_3086]) ).
cnf(c_0_3098_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_3098]) ).
cnf(c_0_3098_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_3098]) ).
cnf(c_0_3098_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_3098]) ).
cnf(c_0_3104_0,axiom,
( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X1),c_Lambda_OdB_OAbs(X2))
| ~ c_Lambda_Obeta(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3104]) ).
cnf(c_0_3104_1,axiom,
( ~ c_Lambda_Obeta(X1,X2)
| c_Lambda_Obeta(c_Lambda_OdB_OAbs(X1),c_Lambda_OdB_OAbs(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3104]) ).
cnf(c_0_3105_0,axiom,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3105]) ).
cnf(c_0_3105_1,axiom,
( ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3105]) ).
cnf(c_0_3106_0,axiom,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3106]) ).
cnf(c_0_3106_1,axiom,
( ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3106]) ).
cnf(c_0_3108_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_3108]) ).
cnf(c_0_3108_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_3108]) ).
cnf(c_0_3109_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_3109]) ).
cnf(c_0_3109_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_3109]) ).
cnf(c_0_3111_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_3111]) ).
cnf(c_0_3111_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_3111]) ).
cnf(c_0_3112_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_3112]) ).
cnf(c_0_3112_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_3112]) ).
cnf(c_0_3113_0,axiom,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3113]) ).
cnf(c_0_3113_1,axiom,
( c_Suc(X1) != c_Suc(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3113]) ).
cnf(c_0_3114_0,axiom,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3114]) ).
cnf(c_0_3114_1,axiom,
( c_Suc(X1) != c_Suc(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3114]) ).
cnf(c_0_3115_0,axiom,
( X1 = X2
| c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3115]) ).
cnf(c_0_3115_1,axiom,
( c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3115]) ).
cnf(c_0_3116_0,axiom,
( X1 = X2
| c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3116]) ).
cnf(c_0_3116_1,axiom,
( c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3116]) ).
cnf(c_0_3117_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_ATP__Linkup_Osko__Nat__Xnot0__implies__Suc__1__1(X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3117]) ).
cnf(c_0_3117_1,axiom,
( c_Suc(c_ATP__Linkup_Osko__Nat__Xnot0__implies__Suc__1__1(X1)) = X1
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_3117]) ).
cnf(c_0_3118_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__Xnchotomy__1__1(X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3118]) ).
cnf(c_0_3118_1,axiom,
( c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__Xnchotomy__1__1(X1)) = X1
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_3118]) ).
cnf(c_0_3119_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__Xexhaust__1__1(X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3119]) ).
cnf(c_0_3119_1,axiom,
( c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__Xexhaust__1__1(X1)) = X1
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_3119]) ).
cnf(c_0_2543_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_2543]) ).
cnf(c_0_2555_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_2555]) ).
cnf(c_0_2857_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_2857]) ).
cnf(c_0_2858_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_2858]) ).
cnf(c_0_2996_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_2996]) ).
cnf(c_0_3009_0,axiom,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3009]) ).
cnf(c_0_3010_0,axiom,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3010]) ).
cnf(c_0_3015_0,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3015]) ).
cnf(c_0_3016_0,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3016]) ).
cnf(c_0_3074_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OVar(X3),
inference(literals_permutation,[status(thm)],[c_0_3074]) ).
cnf(c_0_3075_0,axiom,
c_Lambda_OdB_OVar(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
inference(literals_permutation,[status(thm)],[c_0_3075]) ).
cnf(c_0_3076_0,axiom,
c_Lambda_OdB_OAbs(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
inference(literals_permutation,[status(thm)],[c_0_3076]) ).
cnf(c_0_3077_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OAbs(X3),
inference(literals_permutation,[status(thm)],[c_0_3077]) ).
cnf(c_0_3107_0,axiom,
~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X1),X2),
inference(literals_permutation,[status(thm)],[c_0_3107]) ).
cnf(c_0_3120_0,axiom,
c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OAbs(X2),
inference(literals_permutation,[status(thm)],[c_0_3120]) ).
cnf(c_0_3121_0,axiom,
c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OVar(X2),
inference(literals_permutation,[status(thm)],[c_0_3121]) ).
cnf(c_0_3123_0,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3123]) ).
cnf(c_0_3124_0,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3124]) ).
cnf(c_0_3125_0,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3125]) ).
cnf(c_0_3126_0,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3126]) ).
cnf(c_0_3128_0,axiom,
c_Suc(X1) != X1,
inference(literals_permutation,[status(thm)],[c_0_3128]) ).
cnf(c_0_3129_0,axiom,
c_Suc(X1) != X1,
inference(literals_permutation,[status(thm)],[c_0_3129]) ).
cnf(c_0_2528_0,axiom,
c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X3,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = 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_2528]) ).
cnf(c_0_2531_0,axiom,
c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X1),X3),c_List_Omap(c_COMBC(c_Lambda_Olift,X3,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),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_2531]) ).
cnf(c_0_2533_0,axiom,
c_COMBB(X1,X2,X3,X4,X5,X6) = hAPP(X1,hAPP(X2,X3)),
inference(literals_permutation,[status(thm)],[c_0_2533]) ).
cnf(c_0_2551_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(X1,X3,tc_nat)),c_Divides_Odiv__class_Odiv(X2,X3,tc_nat))),c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(X1,X3,tc_nat)),c_Divides_Odiv__class_Omod(X2,X3,tc_nat)),X3,tc_nat)) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2551]) ).
cnf(c_0_2552_0,axiom,
hAPP(c_COMBC(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X1,X6),X2),
inference(literals_permutation,[status(thm)],[c_0_2552]) ).
cnf(c_0_2553_0,axiom,
hAPP(c_COMBC(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X1,X6),X2),
inference(literals_permutation,[status(thm)],[c_0_2553]) ).
cnf(c_0_2563_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Odiv(X1,X2,tc_nat),X3,tc_nat),tc_nat)),c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) = c_Divides_Odiv__class_Omod(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2563]) ).
cnf(c_0_2565_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X2,X3,tc_nat),tc_nat)),c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X3,tc_nat),tc_nat),X3,tc_nat)) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2565]) ).
cnf(c_0_2567_0,axiom,
c_Type_Oshift(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),X5,X4),c_Suc(X2),X3,X4) = c_Type_Oshift(c_Type_Oshift(X1,X2,X3,X4),c_HOL_Ozero__class_Ozero(tc_nat),X5,X4),
inference(literals_permutation,[status(thm)],[c_0_2567]) ).
cnf(c_0_2569_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat)),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),X2,tc_nat)),X4),
inference(literals_permutation,[status(thm)],[c_0_2569]) ).
cnf(c_0_2570_0,axiom,
c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),
inference(literals_permutation,[status(thm)],[c_0_2570]) ).
cnf(c_0_2573_0,axiom,
c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OVar(X1),
inference(literals_permutation,[status(thm)],[c_0_2573]) ).
cnf(c_0_2574_0,axiom,
c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OAbs(X1),
inference(literals_permutation,[status(thm)],[c_0_2574]) ).
cnf(c_0_2575_0,axiom,
c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OAbs(X1),
inference(literals_permutation,[status(thm)],[c_0_2575]) ).
cnf(c_0_2576_0,axiom,
c_List_Ofoldl(X1,X2,c_List_Olist_ONil(X3),X4,X3) = X2,
inference(literals_permutation,[status(thm)],[c_0_2576]) ).
cnf(c_0_2580_0,axiom,
c_Divides_Odiv__class_Omod(c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),X3)),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X3),X2,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2580]) ).
cnf(c_0_2584_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_2584]) ).
cnf(c_0_2590_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_2590]) ).
cnf(c_0_2598_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),
inference(literals_permutation,[status(thm)],[c_0_2598]) ).
cnf(c_0_2599_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),
inference(literals_permutation,[status(thm)],[c_0_2599]) ).
cnf(c_0_2609_0,axiom,
c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),X3),X2,tc_nat) = c_Divides_Odiv__class_Omod(X3,X2,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2609]) ).
cnf(c_0_2614_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_Lambda_OdB)),c_Nat_Osize__class_Osize(X2,tc_Lambda_OdB))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),tc_Lambda_OdB),
inference(literals_permutation,[status(thm)],[c_0_2614]) ).
cnf(c_0_2651_0,axiom,
hAPP(c_Type_Oshift(X1,X2,X3,X4),X2) = X3,
inference(literals_permutation,[status(thm)],[c_0_2651]) ).
cnf(c_0_2653_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)) = c_HOL_Otimes__class_Otimes(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2653]) ).
cnf(c_0_2654_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2654]) ).
cnf(c_0_2658_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_2658]) ).
cnf(c_0_2696_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_2696]) ).
cnf(c_0_2711_0,axiom,
c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X3,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2711]) ).
cnf(c_0_2712_0,axiom,
c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X3,tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2712]) ).
cnf(c_0_2720_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X1)),c_Lambda_OdB_OdB__size(X2))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),
inference(literals_permutation,[status(thm)],[c_0_2720]) ).
cnf(c_0_2725_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_2725]) ).
cnf(c_0_2733_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_2733]) ).
cnf(c_0_2736_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_2736]) ).
cnf(c_0_2772_0,axiom,
c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2772]) ).
cnf(c_0_2776_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_2776]) ).
cnf(c_0_2785_0,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2785]) ).
cnf(c_0_2786_0,axiom,
c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(X1,X2,tc_nat),X3,tc_nat) = c_Divides_Odiv__class_Odiv(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2786]) ).
cnf(c_0_2799_0,axiom,
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_2799]) ).
cnf(c_0_2806_0,axiom,
c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2806]) ).
cnf(c_0_2809_0,axiom,
c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2809]) ).
cnf(c_0_2810_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_2810]) ).
cnf(c_0_2816_0,axiom,
c_List_Omap(X2,c_List_Olist_ONil(X3),X3,X1) = c_List_Olist_ONil(X1),
inference(literals_permutation,[status(thm)],[c_0_2816]) ).
cnf(c_0_2817_0,axiom,
c_List_Omap(X1,c_List_Olist_ONil(X2),X2,X3) = c_List_Olist_ONil(X3),
inference(literals_permutation,[status(thm)],[c_0_2817]) ).
cnf(c_0_2833_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_2833]) ).
cnf(c_0_2834_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_2834]) ).
cnf(c_0_2835_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_2835]) ).
cnf(c_0_2865_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)) = c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2865]) ).
cnf(c_0_2866_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)) = c_HOL_Otimes__class_Otimes(X1,c_Suc(X2),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2866]) ).
cnf(c_0_2915_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2915]) ).
cnf(c_0_2918_0,axiom,
c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2918]) ).
cnf(c_0_2921_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_2921]) ).
cnf(c_0_2935_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_2935]) ).
cnf(c_0_2936_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_2936]) ).
cnf(c_0_2950_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X1,tc_Lambda_OdB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X1),tc_Lambda_OdB),
inference(literals_permutation,[status(thm)],[c_0_2950]) ).
cnf(c_0_2965_0,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2965]) ).
cnf(c_0_2966_0,axiom,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2966]) ).
cnf(c_0_2971_0,axiom,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1) = X2,
inference(literals_permutation,[status(thm)],[c_0_2971]) ).
cnf(c_0_2973_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_2973]) ).
cnf(c_0_2982_0,axiom,
c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) = c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2982]) ).
cnf(c_0_3002_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_3002]) ).
cnf(c_0_3012_0,axiom,
c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),hAPP(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_3012]) ).
cnf(c_0_3014_0,axiom,
c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(literals_permutation,[status(thm)],[c_0_3014]) ).
cnf(c_0_3021_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_3021]) ).
cnf(c_0_3022_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_3022]) ).
cnf(c_0_3023_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X1)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X1)),
inference(literals_permutation,[status(thm)],[c_0_3023]) ).
cnf(c_0_3028_0,axiom,
c_Ring__and__Field_Odvd__class_Odvd(c_Suc(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_3028]) ).
cnf(c_0_3035_0,axiom,
c_Power_Opower__class_Opower(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(literals_permutation,[status(thm)],[c_0_3035]) ).
cnf(c_0_3036_0,axiom,
c_Power_Opower__class_Opower(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(literals_permutation,[status(thm)],[c_0_3036]) ).
cnf(c_0_3049_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_3049]) ).
cnf(c_0_3050_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_3050]) ).
cnf(c_0_3062_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_3062]) ).
cnf(c_0_3065_0,axiom,
c_Divides_Odiv__class_Omod(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3065]) ).
cnf(c_0_3069_0,axiom,
c_Divides_Odiv__class_Odiv(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = X1,
inference(literals_permutation,[status(thm)],[c_0_3069]) ).
cnf(c_0_3073_0,axiom,
c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3073]) ).
cnf(c_0_3078_0,axiom,
c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(literals_permutation,[status(thm)],[c_0_3078]) ).
cnf(c_0_3080_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_3080]) ).
cnf(c_0_3081_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_3081]) ).
cnf(c_0_3083_0,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3083]) ).
cnf(c_0_3084_0,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3084]) ).
cnf(c_0_3085_0,axiom,
c_List_Olistsp(X1,c_List_Olist_ONil(X2),X2),
inference(literals_permutation,[status(thm)],[c_0_3085]) ).
cnf(c_0_3087_0,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3087]) ).
cnf(c_0_3088_0,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3088]) ).
cnf(c_0_3089_0,axiom,
c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3089]) ).
cnf(c_0_3090_0,axiom,
c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3090]) ).
cnf(c_0_3091_0,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3091]) ).
cnf(c_0_3092_0,axiom,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3092]) ).
cnf(c_0_3093_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_3093]) ).
cnf(c_0_3094_0,axiom,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1,
inference(literals_permutation,[status(thm)],[c_0_3094]) ).
cnf(c_0_3095_0,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) = X1,
inference(literals_permutation,[status(thm)],[c_0_3095]) ).
cnf(c_0_3096_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_3096]) ).
cnf(c_0_3097_0,axiom,
c_fequal(X1,X1,X2),
inference(literals_permutation,[status(thm)],[c_0_3097]) ).
cnf(c_0_3099_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_3099]) ).
cnf(c_0_3100_0,axiom,
c_Ring__and__Field_Odvd__class_Odvd(X1,X1,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3100]) ).
cnf(c_0_3101_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_3101]) ).
cnf(c_0_3102_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_3102]) ).
cnf(c_0_3103_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_3103]) ).
cnf(c_0_3110_0,axiom,
c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(X1),tc_Lambda_OdB) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3110]) ).
cnf(c_0_3122_0,axiom,
c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(X1)) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3122]) ).
cnf(c_0_3127_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_3127]) ).
cnf(c_0_3130_0,axiom,
class_Power_Opower(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3130]) ).
cnf(c_0_3131_0,axiom,
class_Orderings_Oorder(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3131]) ).
cnf(c_0_3132_0,axiom,
class_Orderings_Olinorder(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3132]) ).
cnf(c_0_3133_0,axiom,
class_Orderings_Opreorder(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3133]) ).
cnf(c_0_3134_0,axiom,
class_Ring__and__Field_Odvd(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3134]) ).
cnf(c_0_3135_0,axiom,
class_Nat_Osemiring__char__0(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3135]) ).
cnf(c_0_3136_0,axiom,
class_Divides_Osemiring__div(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3136]) ).
cnf(c_0_3137_0,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3137]) ).
cnf(c_0_3138_0,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3138]) ).
cnf(c_0_3139_0,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3139]) ).
cnf(c_0_3140_0,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3140]) ).
cnf(c_0_3141_0,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3141]) ).
cnf(c_0_3142_0,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3142]) ).
cnf(c_0_3143_0,axiom,
class_OrderedGroup_Osemigroup__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3143]) ).
cnf(c_0_3144_0,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3144]) ).
cnf(c_0_3145_0,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3145]) ).
cnf(c_0_3146_0,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3146]) ).
cnf(c_0_3147_0,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3147]) ).
cnf(c_0_3148_0,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3148]) ).
cnf(c_0_3149_0,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3149]) ).
cnf(c_0_3150_0,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3150]) ).
cnf(c_0_3151_0,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3151]) ).
cnf(c_0_3152_0,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3152]) ).
cnf(c_0_3153_0,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3153]) ).
cnf(c_0_3154_0,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3154]) ).
cnf(c_0_3155_0,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3155]) ).
cnf(c_0_3156_0,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3156]) ).
cnf(c_0_3157_0,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3157]) ).
cnf(c_0_3158_0,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3158]) ).
cnf(c_0_3159_0,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_3159]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_001,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(v_ia))),c_Suc(v_ja)))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file('<stdin>',cls_conjecture_4) ).
fof(c_0_1_002,negated_conjecture,
! [X1,X2] : hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(X2))),c_Suc(X1))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X2)),X1)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(X2),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X1,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file('<stdin>',cls_conjecture_1) ).
fof(c_0_2_003,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB))),
file('<stdin>',cls_conjecture_0) ).
fof(c_0_3_004,negated_conjecture,
! [X1,X2] : hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X2)),X1))),
file('<stdin>',cls_conjecture_3) ).
fof(c_0_4_005,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,v_s)),
file('<stdin>',cls_conjecture_2) ).
fof(c_0_5_006,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(v_ia))),c_Suc(v_ja)))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_6_007,negated_conjecture,
! [X1,X2] : hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(X2))),c_Suc(X1))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X2)),X1)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(X2),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X1,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
c_0_1 ).
fof(c_0_7_008,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB))),
c_0_2 ).
fof(c_0_8_009,negated_conjecture,
! [X1,X2] : hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X2)),X1))),
c_0_3 ).
fof(c_0_9_010,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,v_s)),
c_0_4 ).
fof(c_0_10_011,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(v_ia))),c_Suc(v_ja)))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
c_0_5 ).
fof(c_0_11_012,negated_conjecture,
! [X3,X4] : hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(X4))),c_Suc(X3))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X4)),X3)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(X4),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X3,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(variable_rename,[status(thm)],[c_0_6]) ).
fof(c_0_12_013,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB))),
c_0_7 ).
fof(c_0_13_014,negated_conjecture,
! [X3,X4] : hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X4)),X3))),
inference(variable_rename,[status(thm)],[c_0_8]) ).
fof(c_0_14_015,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,v_s)),
c_0_9 ).
cnf(c_0_15_016,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(v_ia))),c_Suc(v_ja)))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16_017,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(X1))),c_Suc(X2))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X1)),X2)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X2,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17_018,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB))),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18_019,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X1)),X2))),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19_020,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,v_s)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20_021,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(v_ia))),c_Suc(v_ja)))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
c_0_15,
[final] ).
cnf(c_0_21_022,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(X1))),c_Suc(X2))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X1)),X2)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X2,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
c_0_16,
[final] ).
cnf(c_0_22_023,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB))),
c_0_17,
[final] ).
cnf(c_0_23_024,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X1)),X2))),
c_0_18,
[final] ).
cnf(c_0_24_025,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,v_s)),
c_0_19,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_1443,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X0)),X1))),
file('/export/starexec/sandbox2/tmp/iprover_modulo_e66390.p',c_0_23) ).
cnf(c_1891,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X0)),X1))),
inference(copy,[status(esa)],[c_1443]) ).
cnf(c_1908,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X0)),X1))),
inference(copy,[status(esa)],[c_1891]) ).
cnf(c_1911,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X0)),X1))),
inference(copy,[status(esa)],[c_1908]) ).
cnf(c_1915,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X0)),X1))),
inference(copy,[status(esa)],[c_1911]) ).
cnf(c_6171,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X0)),X1))),
inference(copy,[status(esa)],[c_1915]) ).
cnf(c_1434,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X0)),X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X0),X1),c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_e66390.p',c_0_2530_2) ).
cnf(c_6159,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X0)),X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X0),X1),c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(copy,[status(esa)],[c_1434]) ).
cnf(c_6160,plain,
( ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X0),X1),c_HOL_Ozero__class_Ozero(tc_nat)),X2,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(X0)),X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(rewriting,[status(thm)],[c_6159]) ).
cnf(c_6203,plain,
( ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X0),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(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(X0)),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X1)),X2)),X3,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(resolution,[status(thm)],[c_6171,c_6160]) ).
cnf(c_6204,plain,
( ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X0),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(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(X0)),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X1)),X2)),X3,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(rewriting,[status(thm)],[c_6203]) ).
cnf(c_1441,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(X0))),c_Suc(X1))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X0)),X1)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(X0),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X1,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file('/export/starexec/sandbox2/tmp/iprover_modulo_e66390.p',c_0_21) ).
cnf(c_1887,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(X0))),c_Suc(X1))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X0)),X1)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(X0),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X1,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(copy,[status(esa)],[c_1441]) ).
cnf(c_1906,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(X0))),c_Suc(X1))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X0)),X1)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(X0),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X1,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(copy,[status(esa)],[c_1887]) ).
cnf(c_1913,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(X0))),c_Suc(X1))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X0)),X1)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(X0),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X1,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(copy,[status(esa)],[c_1906]) ).
cnf(c_1918,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(X0))),c_Suc(X1))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X0)),X1)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(X0),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X1,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(copy,[status(esa)],[c_1913]) ).
cnf(c_6177,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(X0))),c_Suc(X1))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X0)),X1)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(X0),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X1,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(copy,[status(esa)],[c_1918]) ).
cnf(c_6407,plain,
hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(X0))),c_Suc(X1)))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X0)),X1)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(X0),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X1,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(resolution,[status(thm)],[c_6204,c_6177]) ).
cnf(c_6408,plain,
hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(X0))),c_Suc(X1)))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X0)),X1)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(X0),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X1,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(rewriting,[status(thm)],[c_6407]) ).
cnf(c_1440,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(v_ia))),c_Suc(v_ja)))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file('/export/starexec/sandbox2/tmp/iprover_modulo_e66390.p',c_0_20) ).
cnf(c_1885,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(v_ia))),c_Suc(v_ja)))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(copy,[status(esa)],[c_1440]) ).
cnf(c_1905,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(v_ia))),c_Suc(v_ja)))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(copy,[status(esa)],[c_1885]) ).
cnf(c_1914,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(v_ia))),c_Suc(v_ja)))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(copy,[status(esa)],[c_1905]) ).
cnf(c_1917,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(v_ia))),c_Suc(v_ja)))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(copy,[status(esa)],[c_1914]) ).
cnf(c_6175,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(v_ia))),c_Suc(v_ja)))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(copy,[status(esa)],[c_1917]) ).
cnf(c_6423,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_6408,c_6175]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL759-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : iprover_modulo %s %d
% 0.10/0.35 % Computer : n019.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Fri Sep 4 21:56:53 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.36 % Running in mono-core mode
% 0.20/0.53 % Orienting using strategy Equiv(ClausalAll)
% 0.20/0.53 % Orientation found
% 0.20/0.53 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_b9ee26.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_e66390.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_3d0d61 | grep -v "SZS"
% 0.20/0.56
% 0.20/0.56 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.20/0.56
% 0.20/0.56 %
% 0.20/0.56 % ------ iProver source info
% 0.20/0.56
% 0.20/0.56 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.20/0.56 % git: non_committed_changes: true
% 0.20/0.56 % git: last_make_outside_of_git: true
% 0.20/0.56
% 0.20/0.56 %
% 0.20/0.56 % ------ Input Options
% 0.20/0.56
% 0.20/0.56 % --out_options all
% 0.20/0.56 % --tptp_safe_out true
% 0.20/0.56 % --problem_path ""
% 0.20/0.56 % --include_path ""
% 0.20/0.56 % --clausifier .//eprover
% 0.20/0.56 % --clausifier_options --tstp-format
% 0.20/0.56 % --stdin false
% 0.20/0.56 % --dbg_backtrace false
% 0.20/0.56 % --dbg_dump_prop_clauses false
% 0.20/0.56 % --dbg_dump_prop_clauses_file -
% 0.20/0.56 % --dbg_out_stat false
% 0.20/0.56
% 0.20/0.56 % ------ General Options
% 0.20/0.56
% 0.20/0.56 % --fof false
% 0.20/0.56 % --time_out_real 150.
% 0.20/0.56 % --time_out_prep_mult 0.2
% 0.20/0.56 % --time_out_virtual -1.
% 0.20/0.56 % --schedule none
% 0.20/0.56 % --ground_splitting input
% 0.33/0.56 % --splitting_nvd 16
% 0.33/0.56 % --non_eq_to_eq false
% 0.33/0.56 % --prep_gs_sim true
% 0.33/0.56 % --prep_unflatten false
% 0.33/0.56 % --prep_res_sim true
% 0.33/0.56 % --prep_upred true
% 0.33/0.56 % --res_sim_input true
% 0.33/0.56 % --clause_weak_htbl true
% 0.33/0.56 % --gc_record_bc_elim false
% 0.33/0.56 % --symbol_type_check false
% 0.33/0.56 % --clausify_out false
% 0.33/0.56 % --large_theory_mode false
% 0.33/0.56 % --prep_sem_filter none
% 0.33/0.56 % --prep_sem_filter_out false
% 0.33/0.56 % --preprocessed_out false
% 0.33/0.56 % --sub_typing false
% 0.33/0.56 % --brand_transform false
% 0.33/0.56 % --pure_diseq_elim true
% 0.33/0.56 % --min_unsat_core false
% 0.33/0.56 % --pred_elim true
% 0.33/0.56 % --add_important_lit false
% 0.33/0.56 % --soft_assumptions false
% 0.33/0.56 % --reset_solvers false
% 0.33/0.56 % --bc_imp_inh []
% 0.33/0.56 % --conj_cone_tolerance 1.5
% 0.33/0.56 % --prolific_symb_bound 500
% 0.33/0.56 % --lt_threshold 2000
% 0.33/0.56
% 0.33/0.56 % ------ SAT Options
% 0.33/0.56
% 0.33/0.56 % --sat_mode false
% 0.33/0.56 % --sat_fm_restart_options ""
% 0.33/0.56 % --sat_gr_def false
% 0.33/0.56 % --sat_epr_types true
% 0.33/0.56 % --sat_non_cyclic_types false
% 0.33/0.56 % --sat_finite_models false
% 0.33/0.56 % --sat_fm_lemmas false
% 0.33/0.56 % --sat_fm_prep false
% 0.33/0.56 % --sat_fm_uc_incr true
% 0.33/0.56 % --sat_out_model small
% 0.33/0.56 % --sat_out_clauses false
% 0.33/0.56
% 0.33/0.56 % ------ QBF Options
% 0.33/0.56
% 0.33/0.56 % --qbf_mode false
% 0.33/0.56 % --qbf_elim_univ true
% 0.33/0.56 % --qbf_sk_in true
% 0.33/0.56 % --qbf_pred_elim true
% 0.33/0.56 % --qbf_split 32
% 0.33/0.56
% 0.33/0.56 % ------ BMC1 Options
% 0.33/0.56
% 0.33/0.56 % --bmc1_incremental false
% 0.33/0.56 % --bmc1_axioms reachable_all
% 0.33/0.56 % --bmc1_min_bound 0
% 0.33/0.56 % --bmc1_max_bound -1
% 0.33/0.56 % --bmc1_max_bound_default -1
% 0.33/0.56 % --bmc1_symbol_reachability true
% 0.33/0.56 % --bmc1_property_lemmas false
% 0.33/0.56 % --bmc1_k_induction false
% 0.33/0.56 % --bmc1_non_equiv_states false
% 0.33/0.56 % --bmc1_deadlock false
% 0.33/0.56 % --bmc1_ucm false
% 0.33/0.56 % --bmc1_add_unsat_core none
% 0.33/0.56 % --bmc1_unsat_core_children false
% 0.33/0.56 % --bmc1_unsat_core_extrapolate_axioms false
% 0.33/0.56 % --bmc1_out_stat full
% 0.33/0.56 % --bmc1_ground_init false
% 0.33/0.56 % --bmc1_pre_inst_next_state false
% 0.33/0.56 % --bmc1_pre_inst_state false
% 0.33/0.56 % --bmc1_pre_inst_reach_state false
% 0.33/0.56 % --bmc1_out_unsat_core false
% 0.33/0.56 % --bmc1_aig_witness_out false
% 0.33/0.56 % --bmc1_verbose false
% 0.33/0.56 % --bmc1_dump_clauses_tptp false
% 150.25/150.57 % --bmc1_dump_unsat_core_tptp false
% 150.25/150.57 % --bmc1_dump_file -
% 150.25/150.57 % --bmc1_ucm_expand_uc_limit 128
% 150.25/150.57 % --bmc1_ucm_n_expand_iterations 6
% 150.25/150.57 % --bmc1_ucm_extend_mode 1
% 150.25/150.57 % --bmc1_ucm_init_mode 2
% 150.25/150.57 % --bmc1_ucm_cone_mode none
% 150.25/150.57 % --bmc1_ucm_reduced_relation_type 0
% 150.25/150.57 % --bmc1_ucm_relax_model 4
% 150.25/150.57 % --bmc1_ucm_full_tr_after_sat true
% 150.25/150.57 % --bmc1_ucm_expand_neg_assumptions false
% 150.25/150.57 % --bmc1_ucm_layered_model none
% 150.25/150.57 % --bmc1_ucm_max_lemma_size 10
% 150.25/150.57
% 150.25/150.57 % ------ AIG Options
% 150.25/150.57
% 150.25/150.57 % --aig_mode false
% 150.25/150.57
% 150.25/150.57 % ------ Instantiation Options
% 150.25/150.57
% 150.25/150.57 % --instantiation_flag true
% 150.25/150.57 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 150.25/150.57 % --inst_solver_per_active 750
% 150.25/150.57 % --inst_solver_calls_frac 0.5
% 150.25/150.57 % --inst_passive_queue_type priority_queues
% 150.25/150.57 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 150.25/150.57 % --inst_passive_queues_freq [25;2]
% 150.25/150.57 % --inst_dismatching true
% 150.25/150.57 % --inst_eager_unprocessed_to_passive true
% 150.25/150.57 % --inst_prop_sim_given true
% 150.25/150.57 % --inst_prop_sim_new false
% 150.25/150.57 % --inst_orphan_elimination true
% 150.25/150.57 % --inst_learning_loop_flag true
% 150.25/150.57 % --inst_learning_start 3000
% 150.25/150.57 % --inst_learning_factor 2
% 150.25/150.57 % --inst_start_prop_sim_after_learn 3
% 150.25/150.57 % --inst_sel_renew solver
% 150.25/150.57 % --inst_lit_activity_flag true
% 150.25/150.57 % --inst_out_proof true
% 150.25/150.57
% 150.25/150.57 % ------ Resolution Options
% 150.25/150.57
% 150.25/150.57 % --resolution_flag true
% 150.25/150.57 % --res_lit_sel kbo_max
% 150.25/150.57 % --res_to_prop_solver none
% 150.25/150.57 % --res_prop_simpl_new false
% 150.25/150.57 % --res_prop_simpl_given false
% 150.25/150.57 % --res_passive_queue_type priority_queues
% 150.25/150.57 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 150.25/150.57 % --res_passive_queues_freq [15;5]
% 150.25/150.57 % --res_forward_subs full
% 150.25/150.57 % --res_backward_subs full
% 150.25/150.57 % --res_forward_subs_resolution true
% 150.25/150.57 % --res_backward_subs_resolution true
% 150.25/150.57 % --res_orphan_elimination false
% 150.25/150.57 % --res_time_limit 1000.
% 150.25/150.57 % --res_out_proof true
% 150.25/150.57 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_b9ee26.s
% 150.25/150.57 % --modulo true
% 150.25/150.57
% 150.25/150.57 % ------ Combination Options
% 150.25/150.57
% 150.25/150.57 % --comb_res_mult 1000
% 150.25/150.57 % --comb_inst_mult 300
% 150.25/150.57 % ------
% 150.25/150.57
% 150.25/150.57 % ------ Parsing...% successful
% 150.25/150.57
% 150.25/150.57 % ------ 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 %
% 150.25/150.57
% 150.25/150.57 % ------ Proving...
% 150.25/150.57 % ------ Problem Properties
% 150.25/150.57
% 150.25/150.57 %
% 150.25/150.57 % EPR false
% 150.25/150.57 % Horn false
% 150.25/150.57 % Has equality true
% 150.25/150.57
% 150.25/150.57 % % ------ Input Options Time Limit: Unbounded
% 150.25/150.57
% 150.25/150.57
% 150.25/150.57 Compiling...
% 150.25/150.57 Loading plugin: done.
% 150.25/150.57 %
% 150.25/150.57
% 150.25/150.57
% 150.25/150.57 % Time Out Real
% 150.25/150.57
% 150.25/150.57 % ------ Statistics
% 150.25/150.57
% 150.25/150.57 % ------ General
% 150.25/150.57
% 150.25/150.57 % num_of_input_clauses: 1445
% 150.25/150.57 % num_of_input_neg_conjectures: 5
% 150.25/150.57 % num_of_splits: 0
% 150.25/150.57 % num_of_split_atoms: 0
% 150.25/150.57 % num_of_sem_filtered_clauses: 0
% 150.25/150.57 % num_of_subtypes: 0
% 150.25/150.57 % monotx_restored_types: 0
% 150.25/150.57 % sat_num_of_epr_types: 0
% 150.25/150.57 % sat_num_of_non_cyclic_types: 0
% 150.25/150.57 % sat_guarded_non_collapsed_types: 0
% 150.25/150.57 % is_epr: 0
% 150.25/150.57 % is_horn: 0
% 150.25/150.57 % has_eq: 1
% 150.25/150.57 % num_pure_diseq_elim: 0
% 150.25/150.57 % simp_replaced_by: 0
% 150.25/150.57 % res_preprocessed: 10
% 150.25/150.57 % prep_upred: 0
% 150.25/150.57 % prep_unflattend: 0
% 150.25/150.57 % pred_elim_cands: 0
% 150.25/150.57 % pred_elim: 0
% 150.25/150.57 % pred_elim_cl: 0
% 150.25/150.57 % pred_elim_cycles: 0
% 0.31/150.60 % forced_gc_time: 0
% 0.31/150.60 % gc_basic_clause_elim: 0
% 0.31/150.60 % parsing_time: 0.1
% 0.31/150.60 % sem_filter_time: 0.
% 0.31/150.60 % pred_elim_time: 0.
% 0.31/150.60 % out_proof_time: 0.
% 0.31/150.60 % monotx_time: 0.
% 0.31/150.60 % subtype_inf_time: 0.
% 0.31/150.60 % unif_index_cands_time: 0.
% 0.31/150.60 % unif_index_add_time: 0.001
% 0.31/150.60 % total_time: 150.042
% 0.31/150.60 % num_of_symbols: 116
% 0.31/150.60 % num_of_terms: 4082
% 0.31/150.60
% 0.31/150.60 % ------ Propositional Solver
% 0.31/150.60
% 0.31/150.60 % prop_solver_calls: 1
% 0.31/150.60 % prop_fast_solver_calls: 15
% 0.31/150.60 % prop_num_of_clauses: 1233
% 0.31/150.60 % prop_preprocess_simplified: 4511
% 0.31/150.60 % prop_fo_subsumed: 0
% 0.31/150.60 % prop_solver_time: 0.
% 0.31/150.60 % prop_fast_solver_time: 0.
% 0.31/150.60 % prop_unsat_core_time: 0.
% 0.31/150.60
% 0.31/150.60 % ------ QBF
% 0.31/150.60
% 0.31/150.60 % qbf_q_res: 0
% 0.31/150.61 % qbf_num_tautologies: 0
% 0.31/150.61 % qbf_prep_cycles: 0
% 0.31/150.61
% 0.31/150.61 % ------ BMC1
% 0.31/150.61
% 0.31/150.61 % bmc1_current_bound: -1
% 0.31/150.61 % bmc1_last_solved_bound: -1
% 0.31/150.61 % bmc1_unsat_core_size: -1
% 0.31/150.61 % bmc1_unsat_core_parents_size: -1
% 0.31/150.61 % bmc1_merge_next_fun: 0
% 0.31/150.61 % bmc1_unsat_core_clauses_time: 0.
% 0.31/150.61
% 0.31/150.61 % ------ Instantiation
% 0.31/150.61
% 0.31/150.61 % inst_num_of_clauses: 1305
% 0.31/150.61 % inst_num_in_passive: 0
% 0.31/150.61 % inst_num_in_active: 0
% 0.31/150.61 % inst_num_in_unprocessed: 1445
% 0.31/150.61 % inst_num_of_loops: 0
% 0.31/150.61 % inst_num_of_learning_restarts: 0
% 0.31/150.61 % inst_num_moves_active_passive: 0
% 0.31/150.61 % inst_lit_activity: 0
% 0.31/150.61 % inst_lit_activity_moves: 0
% 0.31/150.61 % inst_num_tautologies: 0
% 0.31/150.61 % inst_num_prop_implied: 0
% 0.31/150.61 % inst_num_existing_simplified: 0
% 0.31/150.61 % inst_num_eq_res_simplified: 0
% 0.31/150.61 % inst_num_child_elim: 0
% 0.31/150.61 % inst_num_of_dismatching_blockings: 0
% 0.31/150.61 % inst_num_of_non_proper_insts: 0
% 0.31/150.61 % inst_num_of_duplicates: 0
% 0.31/150.61 % inst_inst_num_from_inst_to_res: 0
% 0.31/150.61 % inst_dismatching_checking_time: 0.
% 0.31/150.61
% 0.31/150.61 % ------ Resolution
% 0.31/150.61
% 0.31/150.61 % res_num_of_clauses: 1263
% 0.31/150.61 % res_num_in_passive: 0
% 0.31/150.61 % res_num_in_active: 484
% 0.31/150.61 % res_num_of_loops: 0
% 0.31/150.61 % res_forward_subset_subsumed: 797
% 0.31/150.61 % res_backward_subset_subsumed: 8
% 0.31/150.61 % res_forward_subsumed: 0
% 0.31/150.61 % res_backward_subsumed: 0
% 0.31/150.61 % res_forward_subsumption_resolution: 0
% 0.31/150.61 % res_backward_subsumption_resolution: 0
% 0.31/150.61 % res_clause_to_clause_subsumption: 0
% 0.31/150.61 % res_orphan_elimination: 0
% 0.31/150.61 % res_tautology_del: 0
% 0.31/150.61 % res_num_eq_res_simplified: 0
% 0.31/150.61 % res_num_sel_changes: 0
% 0.31/150.61 % res_moves_from_active_to_pass: 0
% 0.31/150.61
% 0.31/150.61 % Status Unknown
% 150.39/150.75 % Orienting using strategy ClausalAll
% 150.39/150.75 % Orientation found
% 150.39/150.75 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_b9ee26.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_e66390.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_ac89a1 | grep -v "SZS"
% 150.39/150.79
% 150.39/150.79 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 150.39/150.79
% 150.39/150.79 %
% 150.39/150.79 % ------ iProver source info
% 150.39/150.79
% 150.39/150.79 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 150.39/150.79 % git: non_committed_changes: true
% 150.39/150.79 % git: last_make_outside_of_git: true
% 150.39/150.79
% 150.39/150.79 %
% 150.39/150.79 % ------ Input Options
% 150.39/150.79
% 150.39/150.79 % --out_options all
% 150.39/150.79 % --tptp_safe_out true
% 150.39/150.79 % --problem_path ""
% 150.39/150.79 % --include_path ""
% 150.39/150.79 % --clausifier .//eprover
% 150.39/150.79 % --clausifier_options --tstp-format
% 150.39/150.79 % --stdin false
% 150.39/150.79 % --dbg_backtrace false
% 150.39/150.79 % --dbg_dump_prop_clauses false
% 150.39/150.79 % --dbg_dump_prop_clauses_file -
% 150.39/150.79 % --dbg_out_stat false
% 150.39/150.79
% 150.39/150.79 % ------ General Options
% 150.39/150.79
% 150.39/150.79 % --fof false
% 150.39/150.79 % --time_out_real 150.
% 150.39/150.79 % --time_out_prep_mult 0.2
% 150.39/150.79 % --time_out_virtual -1.
% 150.39/150.79 % --schedule none
% 150.39/150.79 % --ground_splitting input
% 150.39/150.79 % --splitting_nvd 16
% 150.39/150.79 % --non_eq_to_eq false
% 150.39/150.79 % --prep_gs_sim true
% 150.39/150.79 % --prep_unflatten false
% 150.39/150.79 % --prep_res_sim true
% 150.39/150.79 % --prep_upred true
% 150.39/150.79 % --res_sim_input true
% 150.39/150.79 % --clause_weak_htbl true
% 150.39/150.79 % --gc_record_bc_elim false
% 150.39/150.79 % --symbol_type_check false
% 150.39/150.79 % --clausify_out false
% 150.39/150.79 % --large_theory_mode false
% 150.39/150.79 % --prep_sem_filter none
% 150.39/150.79 % --prep_sem_filter_out false
% 150.39/150.79 % --preprocessed_out false
% 150.39/150.79 % --sub_typing false
% 150.39/150.79 % --brand_transform false
% 150.39/150.79 % --pure_diseq_elim true
% 150.39/150.79 % --min_unsat_core false
% 150.39/150.79 % --pred_elim true
% 150.39/150.79 % --add_important_lit false
% 150.39/150.79 % --soft_assumptions false
% 150.39/150.79 % --reset_solvers false
% 150.39/150.79 % --bc_imp_inh []
% 150.39/150.79 % --conj_cone_tolerance 1.5
% 150.39/150.79 % --prolific_symb_bound 500
% 150.39/150.79 % --lt_threshold 2000
% 150.39/150.79
% 150.39/150.79 % ------ SAT Options
% 150.39/150.79
% 150.39/150.79 % --sat_mode false
% 150.39/150.79 % --sat_fm_restart_options ""
% 150.39/150.79 % --sat_gr_def false
% 150.39/150.79 % --sat_epr_types true
% 150.39/150.79 % --sat_non_cyclic_types false
% 150.39/150.79 % --sat_finite_models false
% 150.39/150.79 % --sat_fm_lemmas false
% 150.39/150.79 % --sat_fm_prep false
% 150.39/150.79 % --sat_fm_uc_incr true
% 150.39/150.79 % --sat_out_model small
% 150.39/150.79 % --sat_out_clauses false
% 150.39/150.79
% 150.39/150.79 % ------ QBF Options
% 150.39/150.79
% 150.39/150.79 % --qbf_mode false
% 150.39/150.79 % --qbf_elim_univ true
% 150.39/150.79 % --qbf_sk_in true
% 150.39/150.79 % --qbf_pred_elim true
% 150.39/150.79 % --qbf_split 32
% 150.39/150.79
% 150.39/150.79 % ------ BMC1 Options
% 150.39/150.79
% 150.39/150.79 % --bmc1_incremental false
% 150.39/150.79 % --bmc1_axioms reachable_all
% 150.39/150.79 % --bmc1_min_bound 0
% 150.39/150.79 % --bmc1_max_bound -1
% 150.39/150.79 % --bmc1_max_bound_default -1
% 150.39/150.79 % --bmc1_symbol_reachability true
% 150.39/150.79 % --bmc1_property_lemmas false
% 150.39/150.79 % --bmc1_k_induction false
% 150.39/150.79 % --bmc1_non_equiv_states false
% 150.39/150.79 % --bmc1_deadlock false
% 150.39/150.79 % --bmc1_ucm false
% 150.39/150.79 % --bmc1_add_unsat_core none
% 150.39/150.79 % --bmc1_unsat_core_children false
% 150.39/150.79 % --bmc1_unsat_core_extrapolate_axioms false
% 150.39/150.79 % --bmc1_out_stat full
% 150.39/150.79 % --bmc1_ground_init false
% 150.39/150.79 % --bmc1_pre_inst_next_state false
% 150.39/150.79 % --bmc1_pre_inst_state false
% 150.39/150.79 % --bmc1_pre_inst_reach_state false
% 150.39/150.79 % --bmc1_out_unsat_core false
% 150.39/150.79 % --bmc1_aig_witness_out false
% 150.39/150.79 % --bmc1_verbose false
% 150.39/150.79 % --bmc1_dump_clauses_tptp false
% 154.21/154.55 % --bmc1_dump_unsat_core_tptp false
% 154.21/154.55 % --bmc1_dump_file -
% 154.21/154.55 % --bmc1_ucm_expand_uc_limit 128
% 154.21/154.55 % --bmc1_ucm_n_expand_iterations 6
% 154.21/154.55 % --bmc1_ucm_extend_mode 1
% 154.21/154.55 % --bmc1_ucm_init_mode 2
% 154.21/154.55 % --bmc1_ucm_cone_mode none
% 154.21/154.55 % --bmc1_ucm_reduced_relation_type 0
% 154.21/154.55 % --bmc1_ucm_relax_model 4
% 154.21/154.55 % --bmc1_ucm_full_tr_after_sat true
% 154.21/154.55 % --bmc1_ucm_expand_neg_assumptions false
% 154.21/154.55 % --bmc1_ucm_layered_model none
% 154.21/154.55 % --bmc1_ucm_max_lemma_size 10
% 154.21/154.55
% 154.21/154.55 % ------ AIG Options
% 154.21/154.55
% 154.21/154.55 % --aig_mode false
% 154.21/154.55
% 154.21/154.55 % ------ Instantiation Options
% 154.21/154.55
% 154.21/154.55 % --instantiation_flag true
% 154.21/154.55 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 154.21/154.55 % --inst_solver_per_active 750
% 154.21/154.55 % --inst_solver_calls_frac 0.5
% 154.21/154.55 % --inst_passive_queue_type priority_queues
% 154.21/154.55 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 154.21/154.55 % --inst_passive_queues_freq [25;2]
% 154.21/154.55 % --inst_dismatching true
% 154.21/154.55 % --inst_eager_unprocessed_to_passive true
% 154.21/154.55 % --inst_prop_sim_given true
% 154.21/154.55 % --inst_prop_sim_new false
% 154.21/154.55 % --inst_orphan_elimination true
% 154.21/154.55 % --inst_learning_loop_flag true
% 154.21/154.55 % --inst_learning_start 3000
% 154.21/154.55 % --inst_learning_factor 2
% 154.21/154.55 % --inst_start_prop_sim_after_learn 3
% 154.21/154.55 % --inst_sel_renew solver
% 154.21/154.55 % --inst_lit_activity_flag true
% 154.21/154.55 % --inst_out_proof true
% 154.21/154.55
% 154.21/154.55 % ------ Resolution Options
% 154.21/154.55
% 154.21/154.55 % --resolution_flag true
% 154.21/154.55 % --res_lit_sel kbo_max
% 154.21/154.55 % --res_to_prop_solver none
% 154.21/154.55 % --res_prop_simpl_new false
% 154.21/154.55 % --res_prop_simpl_given false
% 154.21/154.55 % --res_passive_queue_type priority_queues
% 154.21/154.55 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 154.21/154.55 % --res_passive_queues_freq [15;5]
% 154.21/154.55 % --res_forward_subs full
% 154.21/154.55 % --res_backward_subs full
% 154.21/154.55 % --res_forward_subs_resolution true
% 154.21/154.55 % --res_backward_subs_resolution true
% 154.21/154.55 % --res_orphan_elimination false
% 154.21/154.55 % --res_time_limit 1000.
% 154.21/154.55 % --res_out_proof true
% 154.21/154.55 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_b9ee26.s
% 154.21/154.55 % --modulo true
% 154.21/154.55
% 154.21/154.55 % ------ Combination Options
% 154.21/154.55
% 154.21/154.55 % --comb_res_mult 1000
% 154.21/154.55 % --comb_inst_mult 300
% 154.21/154.55 % ------
% 154.21/154.55
% 154.21/154.55 % ------ Parsing...% successful
% 154.21/154.55
% 154.21/154.55 % ------ 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 %
% 154.21/154.55
% 154.21/154.55 % ------ Proving...
% 154.21/154.55 % ------ Problem Properties
% 154.21/154.55
% 154.21/154.55 %
% 154.21/154.55 % EPR false
% 154.21/154.55 % Horn false
% 154.21/154.55 % Has equality true
% 154.21/154.55
% 154.21/154.55 % % ------ Input Options Time Limit: Unbounded
% 154.21/154.55
% 154.21/154.55
% 154.21/154.55 Compiling...
% 154.21/154.55 Loading plugin: done.
% 154.21/154.55 Compiling...
% 154.21/154.55 Loading plugin: done.
% 154.21/154.55 Compiling...
% 154.21/154.55 Loading plugin: done.
% 154.21/154.55 Compiling...
% 154.21/154.55 Loading plugin: done.
% 154.21/154.55 Compiling...
% 154.21/154.55 Loading plugin: done.
% 154.21/154.55 Compiling...
% 154.21/154.55 Loading plugin: done.
% 154.21/154.55 Compiling...
% 154.21/154.55 Loading plugin: done.
% 154.21/154.55 Compiling...
% 154.21/154.55 Loading plugin: done.
% 154.21/154.55 Compiling...
% 154.21/154.55 Loading plugin: done.
% 154.21/154.55 Compiling...
% 154.21/154.55 Loading plugin: done.
% 154.21/154.55 Compiling...
% 154.21/154.55 Loading plugin: done.
% 154.21/154.55 Compiling...
% 154.21/154.55 Loading plugin: done.
% 154.21/154.55 Compiling...
% 154.21/154.55 Loading plugin: done.
% 154.21/154.55 Compiling...
% 154.21/154.55 Loading plugin: done.
% 154.21/154.55 Compiling...
% 154.21/154.55 Loading plugin: done.
% 154.21/154.55 % % ------ Current options:
% 154.21/154.55
% 154.21/154.55 % ------ Input Options
% 154.21/154.55
% 154.21/154.55 % --out_options all
% 154.21/154.55 % --tptp_safe_out true
% 154.21/154.55 % --problem_path ""
% 154.21/154.55 % --include_path ""
% 154.21/154.55 % --clausifier .//eprover
% 154.21/154.55 % --clausifier_options --tstp-format
% 154.21/154.55 % --stdin false
% 154.21/154.55 % --dbg_backtrace false
% 154.21/154.55 % --dbg_dump_prop_clauses false
% 154.21/154.55 % --dbg_dump_prop_clauses_file -
% 154.21/154.55 % --dbg_out_stat false
% 154.21/154.55
% 154.21/154.55 % ------ General Options
% 154.21/154.55
% 154.21/154.55 % --fof false
% 154.21/154.55 % --time_out_real 150.
% 154.21/154.55 % --time_out_prep_mult 0.2
% 154.21/154.55 % --time_out_virtual -1.
% 154.21/154.55 % --schedule none
% 154.21/154.55 % --ground_splitting input
% 154.21/154.55 % --splitting_nvd 16
% 154.21/154.55 % --non_eq_to_eq false
% 154.21/154.55 % --prep_gs_sim true
% 154.21/154.55 % --prep_unflatten false
% 154.21/154.55 % --prep_res_sim true
% 154.21/154.55 % --prep_upred true
% 154.21/154.55 % --res_sim_input true
% 154.21/154.55 % --clause_weak_htbl true
% 154.21/154.55 % --gc_record_bc_elim false
% 154.21/154.55 % --symbol_type_check false
% 154.21/154.55 % --clausify_out false
% 154.21/154.55 % --large_theory_mode false
% 154.21/154.55 % --prep_sem_filter none
% 154.21/154.55 % --prep_sem_filter_out false
% 154.21/154.55 % --preprocessed_out false
% 154.21/154.55 % --sub_typing false
% 154.21/154.55 % --brand_transform false
% 154.21/154.55 % --pure_diseq_elim true
% 154.21/154.55 % --min_unsat_core false
% 154.21/154.55 % --pred_elim true
% 154.21/154.55 % --add_important_lit false
% 154.21/154.55 % --soft_assumptions false
% 154.21/154.55 % --reset_solvers false
% 154.21/154.55 % --bc_imp_inh []
% 154.21/154.55 % --conj_cone_tolerance 1.5
% 154.21/154.55 % --prolific_symb_bound 500
% 154.21/154.55 % --lt_threshold 2000
% 154.21/154.55
% 154.21/154.55 % ------ SAT Options
% 154.21/154.55
% 154.21/154.55 % --sat_mode false
% 154.21/154.55 % --sat_fm_restart_options ""
% 154.21/154.55 % --sat_gr_def false
% 154.21/154.55 % --sat_epr_types true
% 154.21/154.55 % --sat_non_cyclic_types false
% 154.21/154.55 % --sat_finite_models false
% 154.21/154.55 % --sat_fm_lemmas false
% 154.21/154.55 % --sat_fm_prep false
% 154.21/154.55 % --sat_fm_uc_incr true
% 154.21/154.55 % --sat_out_model small
% 154.21/154.55 % --sat_out_clauses false
% 154.21/154.55
% 154.21/154.55 % ------ QBF Options
% 154.21/154.55
% 154.21/154.55 % --qbf_mode false
% 154.21/154.55 % --qbf_elim_univ true
% 154.21/154.55 % --qbf_sk_in true
% 154.21/154.55 % --qbf_pred_elim true
% 154.21/154.55 % --qbf_split 32
% 154.21/154.55
% 154.21/154.55 % ------ BMC1 Options
% 154.21/154.55
% 154.21/154.55 % --bmc1_incremental false
% 154.21/154.55 % --bmc1_axioms reachable_all
% 154.21/154.55 % --bmc1_min_bound 0
% 154.21/154.55 % --bmc1_max_bound -1
% 154.21/154.55 % --bmc1_max_bound_default -1
% 154.21/154.55 % --bmc1_symbol_reachability true
% 154.21/154.55 % --bmc1_property_lemmas false
% 154.21/154.55 % --bmc1_k_induction false
% 154.21/154.55 % --bmc1_non_equiv_states false
% 154.21/154.55 % --bmc1_deadlock false
% 154.21/154.55 % --bmc1_ucm false
% 154.21/154.55 % --bmc1_add_unsat_core none
% 154.21/154.55 % --bmc1_unsat_core_children false
% 154.21/154.55 % --bmc1_unsat_core_extrapolate_axioms false
% 154.21/154.55 % --bmc1_out_stat full
% 154.21/154.55 % --bmc1_ground_init false
% 154.21/154.55 % --bmc1_pre_inst_next_state false
% 154.21/154.55 % --bmc1_pre_inst_state false
% 154.21/154.55 % --bmc1_pre_inst_reach_state false
% 154.21/154.55 % --bmc1_out_unsat_core false
% 154.21/154.55 % --bmc1_aig_witness_out false
% 154.21/154.55 % --bmc1_verbose false
% 154.21/154.55 % --bmc1_dump_clauses_tptp false
% 154.21/154.55 % --bmc1_dump_unsat_core_tptp false
% 154.21/154.55 % --bmc1_dump_file -
% 154.21/154.55 % --bmc1_ucm_expand_uc_limit 128
% 154.21/154.55 % --bmc1_ucm_n_expand_iterations 6
% 154.21/154.55 % --bmc1_ucm_extend_mode 1
% 154.21/154.55 % --bmc1_ucm_init_mode 2
% 154.21/154.55 % --bmc1_ucm_cone_mode none
% 154.21/154.55 % --bmc1_ucm_reduced_relation_type 0
% 154.21/154.55 % --bmc1_ucm_relax_model 4
% 154.21/154.55 % --bmc1_ucm_full_tr_after_sat true
% 154.21/154.55 % --bmc1_ucm_expand_neg_assumptions false
% 154.21/154.55 % --bmc1_ucm_layered_model none
% 154.21/154.55 % --bmc1_ucm_max_lemma_size 10
% 154.21/154.55
% 154.21/154.55 % ------ AIG Options
% 154.21/154.55
% 154.21/154.55 % --aig_mode false
% 154.21/154.55
% 154.21/154.55 % ------ Instantiation Options
% 154.21/154.57
% 154.21/154.57 % --instantiation_flag true
% 154.21/154.57 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 154.21/154.57 % --inst_solver_per_active 750
% 154.21/154.57 % --inst_solver_calls_frac 0.5
% 154.21/154.57 % --inst_passive_queue_type priority_queues
% 154.21/154.57 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 154.21/154.57 % --inst_passive_queues_freq [25;2]
% 154.21/154.57 % --inst_dismatching true
% 154.21/154.57 % --inst_eager_unprocessed_to_passive true
% 154.21/154.57 % --inst_prop_sim_given true
% 154.21/154.57 % --inst_prop_sim_new false
% 154.21/154.57 % --inst_orphan_elimination true
% 154.21/154.57 % --inst_learning_loop_flag true
% 154.21/154.57 % --inst_learning_start 3000
% 154.21/154.57 % --inst_learning_factor 2
% 154.21/154.57 % --inst_start_prop_sim_after_learn 3
% 154.21/154.57 % --inst_sel_renew solver
% 154.21/154.57 % --inst_lit_activity_flag true
% 154.21/154.57 % --inst_out_proof true
% 154.21/154.57
% 154.21/154.57 % ------ Resolution Options
% 154.21/154.57
% 154.21/154.57 % --resolution_flag true
% 154.21/154.57 % --res_lit_sel kbo_max
% 154.21/154.57 % --res_to_prop_solver none
% 154.21/154.57 % --res_prop_simpl_new false
% 154.21/154.57 % --res_prop_simpl_given false
% 154.21/154.57 % --res_passive_queue_type priority_queues
% 154.21/154.57 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 154.21/154.57 % --res_passive_queues_freq [15;5]
% 154.21/154.57 % --res_forward_subs full
% 154.21/154.57 % --res_backward_subs full
% 154.21/154.57 % --res_forward_subs_resolution true
% 154.21/154.57 % --res_backward_subs_resolution true
% 154.21/154.57 % --res_orphan_elimination false
% 154.21/154.57 % --res_time_limit 1000.
% 154.21/154.57 % --res_out_proof true
% 154.21/154.57 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_b9ee26.s
% 154.21/154.57 % --modulo true
% 154.21/154.57
% 154.21/154.57 % ------ Combination Options
% 154.21/154.57
% 154.21/154.57 % --comb_res_mult 1000
% 154.21/154.57 % --comb_inst_mult 300
% 154.21/154.57 % ------
% 154.21/154.57
% 154.21/154.57
% 154.21/154.57
% 154.21/154.57 % ------ Proving...
% 154.21/154.57 %
% 154.21/154.57
% 154.21/154.57
% 154.21/154.57 % Resolution empty clause
% 154.21/154.57
% 154.21/154.57 % ------ Statistics
% 154.21/154.57
% 154.21/154.57 % ------ General
% 154.21/154.57
% 154.21/154.57 % num_of_input_clauses: 1445
% 154.21/154.57 % num_of_input_neg_conjectures: 5
% 154.21/154.57 % num_of_splits: 0
% 154.21/154.57 % num_of_split_atoms: 0
% 154.21/154.57 % num_of_sem_filtered_clauses: 0
% 154.21/154.57 % num_of_subtypes: 0
% 154.21/154.57 % monotx_restored_types: 0
% 154.21/154.57 % sat_num_of_epr_types: 0
% 154.21/154.57 % sat_num_of_non_cyclic_types: 0
% 154.21/154.57 % sat_guarded_non_collapsed_types: 0
% 154.21/154.57 % is_epr: 0
% 154.21/154.57 % is_horn: 0
% 154.21/154.57 % has_eq: 1
% 154.21/154.57 % num_pure_diseq_elim: 0
% 154.21/154.57 % simp_replaced_by: 0
% 154.21/154.57 % res_preprocessed: 10
% 154.21/154.57 % prep_upred: 0
% 154.21/154.57 % prep_unflattend: 0
% 154.21/154.57 % pred_elim_cands: 0
% 154.21/154.57 % pred_elim: 0
% 154.21/154.57 % pred_elim_cl: 0
% 154.21/154.57 % pred_elim_cycles: 0
% 154.21/154.57 % forced_gc_time: 0
% 154.21/154.57 % gc_basic_clause_elim: 0
% 154.21/154.57 % parsing_time: 0.099
% 154.21/154.57 % sem_filter_time: 0.
% 154.21/154.57 % pred_elim_time: 0.
% 154.21/154.57 % out_proof_time: 0.003
% 154.21/154.57 % monotx_time: 0.
% 154.21/154.57 % subtype_inf_time: 0.
% 154.21/154.57 % unif_index_cands_time: 0.
% 154.21/154.57 % unif_index_add_time: 0.001
% 154.21/154.57 % total_time: 3.808
% 154.21/154.57 % num_of_symbols: 116
% 154.21/154.57 % num_of_terms: 3800
% 154.21/154.57
% 154.21/154.57 % ------ Propositional Solver
% 154.21/154.57
% 154.21/154.57 % prop_solver_calls: 1
% 154.21/154.57 % prop_fast_solver_calls: 15
% 154.21/154.57 % prop_num_of_clauses: 1335
% 154.21/154.57 % prop_preprocess_simplified: 4409
% 154.21/154.57 % prop_fo_subsumed: 0
% 154.21/154.57 % prop_solver_time: 0.
% 154.21/154.57 % prop_fast_solver_time: 0.
% 154.21/154.57 % prop_unsat_core_time: 0.
% 154.21/154.57
% 154.21/154.57 % ------ QBF
% 154.21/154.57
% 154.21/154.57 % qbf_q_res: 0
% 154.21/154.57 % qbf_num_tautologies: 0
% 154.21/154.57 % qbf_prep_cycles: 0
% 154.21/154.57
% 154.21/154.57 % ------ BMC1
% 154.21/154.57
% 154.21/154.57 % bmc1_current_bound: -1
% 154.21/154.57 % bmc1_last_solved_bound: -1
% 154.21/154.57 % bmc1_unsat_core_size: -1
% 154.21/154.57 % bmc1_unsat_core_parents_size: -1
% 154.21/154.57 % bmc1_merge_next_fun: 0
% 154.21/154.57 % bmc1_unsat_core_clauses_time: 0.
% 154.21/154.57
% 154.21/154.57 % ------ Instantiation
% 154.21/154.57
% 154.21/154.57 % inst_num_of_clauses: 1298
% 154.21/154.57 % inst_num_in_passive: 0
% 154.21/154.57 % inst_num_in_active: 0
% 154.21/154.57 % inst_num_in_unprocessed: 1445
% 154.21/154.57 % inst_num_of_loops: 0
% 154.21/154.57 % inst_num_of_learning_restarts: 0
% 154.21/154.57 % inst_num_moves_active_passive: 0
% 154.21/154.57 % inst_lit_activity: 0
% 154.21/154.57 % inst_lit_activity_moves: 0
% 154.21/154.57 % inst_num_tautologies: 0
% 154.21/154.57 % inst_num_prop_implied: 0
% 154.21/154.57 % inst_num_existing_simplified: 0
% 154.21/154.57 % inst_num_eq_res_simplified: 0
% 154.21/154.57 % inst_num_child_elim: 0
% 154.21/154.57 % inst_num_of_dismatching_blockings: 0
% 154.21/154.57 % inst_num_of_non_proper_insts: 0
% 154.21/154.57 % inst_num_of_duplicates: 0
% 154.21/154.57 % inst_inst_num_from_inst_to_res: 0
% 154.21/154.57 % inst_dismatching_checking_time: 0.
% 154.21/154.57
% 154.21/154.57 % ------ Resolution
% 154.21/154.57
% 154.21/154.57 % res_num_of_clauses: 1472
% 154.21/154.57 % res_num_in_passive: 58
% 154.21/154.57 % res_num_in_active: 565
% 154.21/154.57 % res_num_of_loops: 22
% 154.21/154.57 % res_forward_subset_subsumed: 843
% 154.21/154.57 % res_backward_subset_subsumed: 0
% 154.21/154.57 % res_forward_subsumed: 0
% 154.21/154.57 % res_backward_subsumed: 0
% 154.21/154.57 % res_forward_subsumption_resolution: 0
% 154.21/154.57 % res_backward_subsumption_resolution: 1
% 154.21/154.57 % res_clause_to_clause_subsumption: 1
% 154.21/154.57 % res_orphan_elimination: 0
% 154.21/154.57 % res_tautology_del: 0
% 154.21/154.57 % res_num_eq_res_simplified: 0
% 154.21/154.57 % res_num_sel_changes: 0
% 154.21/154.57 % res_moves_from_active_to_pass: 0
% 154.21/154.57
% 154.21/154.58 % Status Unsatisfiable
% 154.21/154.58 % SZS status Unsatisfiable
% 154.21/154.58 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------