TSTP Solution File: SWV884-1 by iProverMo---2.5-0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : SWV884-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Wed Jul 20 19:22:58 EDT 2022
% Result : Unsatisfiable 157.44s 157.60s
% Output : CNFRefutation 157.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1126
% Syntax : Number of formulae : 8366 (1378 unt; 0 def)
% Number of atoms : 21701 (4625 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 25723 (12388 ~;13335 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 68 ( 66 usr; 1 prp; 0-4 aty)
% Number of functors : 47 ( 47 usr; 9 con; 0-5 aty)
% Number of variables : 25633 (1079 sgn9996 !; 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,
! [X20,X6,X7,X14,X4] :
( c_lessequals(c_Set_Oimage(X20,X7,X4,X14),X6,tc_fun(X14,tc_bool))
| ~ c_in(hAPP(X20,c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1(X7,X6,X20,X4,X14)),X6,X14) ),
file('<stdin>',cls_image__subsetI_1) ).
fof(c_0_1,axiom,
! [X20,X6,X7,X14,X4] :
( c_lessequals(c_Set_Oimage(X20,X7,X14,X4),X6,tc_fun(X4,tc_bool))
| ~ c_in(hAPP(X20,c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1(X7,X6,X20,X14,X4)),X6,X4) ),
file('<stdin>',cls_image__subset__iff_2) ).
fof(c_0_2,axiom,
! [X9,X42,X20,X14,X4] :
( hAPP(X20,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X9,X20,X42,X4,X14)) != hAPP(X42,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X9,X20,X42,X4,X14))
| c_Set_Oimage(X20,X9,X4,X14) = c_Set_Oimage(X42,X9,X4,X14) ),
file('<stdin>',cls_image__cong_1) ).
fof(c_0_3,axiom,
! [X1,X17,X11,X10,X3,X14,X4] :
( c_Fun_Ofun__upd(c_Fun_Ofun__upd(X1,X3,X10,X4,X14),X11,X17,X4,X14) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X1,X11,X17,X4,X14),X3,X10,X4,X14)
| X3 = X11 ),
file('<stdin>',cls_fun__upd__twist_0) ).
fof(c_0_4,axiom,
! [X15,X8,X9,X20,X14,X4] : c_Fun_Ofun__upd(c_Fun_Ofun__upd(X20,X9,X8,X4,X14),X9,X15,X4,X14) = c_Fun_Ofun__upd(X20,X9,X15,X4,X14),
file('<stdin>',cls_fun__upd__upd_0) ).
fof(c_0_5,axiom,
! [X8,X9,X20,X7,X14,X4] :
( c_Set_Oimage(c_Fun_Ofun__upd(X20,X9,X8,X14,X4),X7,X14,X4) = c_Set_Oinsert(X8,c_Set_Oimage(X20,c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool)),X14),tc_fun(X14,tc_bool)),X14,X4),X4)
| ~ c_in(X9,X7,X14) ),
file('<stdin>',cls_fun__upd__image_0) ).
fof(c_0_6,axiom,
! [X8,X9,X7,X4] :
( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4),c_Finite__Set_Ocard(X7,X4),tc_nat)
| ~ c_in(X8,X7,X4)
| ~ c_in(X9,X7,X4)
| ~ c_Finite__Set_Ofinite(X7,X4) ),
file('<stdin>',cls_card__Diff2__less_0) ).
fof(c_0_7,axiom,
! [X8,X9,X20,X7,X14,X4] :
( c_Fun_Oinj__on(c_Fun_Ofun__upd(X20,X9,X8,X4,X14),X7,X4,X14)
| c_in(X8,c_Set_Oimage(X20,X7,X4,X14),X14)
| ~ c_Fun_Oinj__on(X20,X7,X4,X14) ),
file('<stdin>',cls_inj__on__fun__updI_0) ).
fof(c_0_8,axiom,
! [X20,X6,X7,X14,X4] :
( X6 = c_Set_Oimage(X20,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X7,X6,X20,X14,X4),X14,X4)
| ~ c_lessequals(X6,c_Set_Oimage(X20,X7,X14,X4),tc_fun(X4,tc_bool))
| ~ c_Finite__Set_Ofinite(X6,X4) ),
file('<stdin>',cls_finite__subset__image_2) ).
fof(c_0_9,axiom,
! [X20,X6,X7,X14,X4] :
( X6 = c_Set_Oimage(X20,c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(X7,X6,X20,X14,X4),X14,X4)
| ~ c_lessequals(X6,c_Set_Oimage(X20,X7,X14,X4),tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_subset__image__iff_1) ).
fof(c_0_10,axiom,
! [X20,X6,X7,X14,X4] :
( c_lessequals(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X7,X6,X20,X14,X4),X7,tc_fun(X14,tc_bool))
| ~ c_lessequals(X6,c_Set_Oimage(X20,X7,X14,X4),tc_fun(X4,tc_bool))
| ~ c_Finite__Set_Ofinite(X6,X4) ),
file('<stdin>',cls_finite__subset__image_0) ).
fof(c_0_11,axiom,
! [X20,X6,X7,X14,X4] :
( c_lessequals(c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(X7,X6,X20,X14,X4),X7,tc_fun(X14,tc_bool))
| ~ c_lessequals(X6,c_Set_Oimage(X20,X7,X14,X4),tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_subset__image__iff_0) ).
fof(c_0_12,axiom,
! [X20,X6,X7,X14,X4] :
( c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X7,X6,X20,X14,X4),X14)
| ~ c_lessequals(X6,c_Set_Oimage(X20,X7,X14,X4),tc_fun(X4,tc_bool))
| ~ c_Finite__Set_Ofinite(X6,X4) ),
file('<stdin>',cls_finite__subset__image_1) ).
fof(c_0_13,axiom,
! [X15,X20,X7,X14,X4] :
( c_in(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(X7,X20,X15,X14,X4),X7,X14)
| ~ c_in(X15,c_Set_Oimage(X20,X7,X14,X4),X4) ),
file('<stdin>',cls_image__iff_0) ).
fof(c_0_14,axiom,
! [X20,X10,X7,X14,X4] :
( c_in(c_ATP__Linkup_Osko__Set__XimageE__1__1(X7,X10,X20,X14,X4),X7,X14)
| ~ c_in(X10,c_Set_Oimage(X20,X7,X14,X4),X4) ),
file('<stdin>',cls_imageE_1) ).
fof(c_0_15,axiom,
! [X8,X9,X20,X7,X14,X4] :
( hAPP(c_Hilbert__Choice_Oinv__into(X7,X20,X4,X14),X9) != hAPP(c_Hilbert__Choice_Oinv__into(X7,X20,X4,X14),X8)
| X9 = X8
| ~ c_in(X8,c_Set_Oimage(X20,X7,X4,X14),X14)
| ~ c_in(X9,c_Set_Oimage(X20,X7,X4,X14),X14) ),
file('<stdin>',cls_inv__into__injective_0) ).
fof(c_0_16,axiom,
! [X20,X10,X7,X14,X4] :
( X10 = hAPP(X20,c_ATP__Linkup_Osko__Set__XimageE__1__1(X7,X10,X20,X14,X4))
| ~ c_in(X10,c_Set_Oimage(X20,X7,X14,X4),X4) ),
file('<stdin>',cls_imageE_0) ).
fof(c_0_17,axiom,
! [X15,X20,X7,X14,X4] :
( X15 = hAPP(X20,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(X7,X20,X15,X14,X4))
| ~ c_in(X15,c_Set_Oimage(X20,X7,X14,X4),X4) ),
file('<stdin>',cls_image__iff_1) ).
fof(c_0_18,axiom,
! [X20,X3,X7,X14,X4] :
( ~ c_in(hAPP(X20,X3),c_Set_Oimage(X20,c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4,X14),X14)
| ~ c_Fun_Oinj__on(X20,c_Set_Oinsert(X3,X7,X4),X4,X14) ),
file('<stdin>',cls_inj__on__insert_1) ).
fof(c_0_19,axiom,
! [X20,X6,X7,X14,X4] :
( c_lessequals(c_Set_Oimage(X20,X7,X14,X4),X6,tc_fun(X4,tc_bool))
| c_in(c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1(X7,X6,X20,X14,X4),X7,X14) ),
file('<stdin>',cls_image__subset__iff_1) ).
fof(c_0_20,axiom,
! [X20,X6,X7,X14,X4] :
( c_lessequals(c_Set_Oimage(X20,X7,X4,X14),X6,tc_fun(X14,tc_bool))
| c_in(c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1(X7,X6,X20,X4,X14),X7,X4) ),
file('<stdin>',cls_image__subsetI_0) ).
fof(c_0_21,axiom,
! [X20,X6,X7,X14,X4] : c_lessequals(c_Set_Oimage(X20,c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X14,tc_bool)),X14,X4),c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X20,X7,X14,X4),c_Set_Oimage(X20,X6,X14,X4),tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
file('<stdin>',cls_image__Int__subset_0) ).
fof(c_0_22,axiom,
! [X20,X6,X7,X14,X4] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(X20,X7,X14,X4),c_Set_Oimage(X20,X6,X14,X4),tc_fun(X4,tc_bool)),c_Set_Oimage(X20,c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X14,tc_bool)),X14,X4),tc_fun(X4,tc_bool)),
file('<stdin>',cls_image__diff__subset_0) ).
fof(c_0_23,axiom,
! [X8,X9,X20,X7,X14,X4] :
( c_Set_Oimage(c_Fun_Ofun__upd(X20,X9,X8,X14,X4),X7,X14,X4) = c_Set_Oimage(X20,X7,X14,X4)
| c_in(X9,X7,X14) ),
file('<stdin>',cls_fun__upd__image_1) ).
fof(c_0_24,axiom,
! [X9,X42,X20,X14,X4] :
( c_Set_Oimage(X20,X9,X4,X14) = c_Set_Oimage(X42,X9,X4,X14)
| c_in(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X9,X20,X42,X4,X14),X9,X4) ),
file('<stdin>',cls_image__cong_0) ).
fof(c_0_25,axiom,
! [X42,X20,X3,X25,X14,X4] :
( c_in(hAPP(X42,X3),c_Inductive_Ocomplete__lattice__class_Ogfp(X20,tc_fun(X14,tc_bool)),X14)
| ~ c_lessequals(c_Set_Oimage(X42,X25,X4,X14),hAPP(X20,c_Set_Oimage(X42,X25,X4,X14)),tc_fun(X14,tc_bool))
| ~ c_in(X3,X25,X4) ),
file('<stdin>',cls_weak__coinduct__image_0) ).
fof(c_0_26,axiom,
! [X42,X20,X6,X7,X14,X4] :
( c_Finite__Set_Ocard(X7,X4) = c_Finite__Set_Ocard(X6,X14)
| ~ c_Finite__Set_Ofinite(X6,X14)
| ~ c_Finite__Set_Ofinite(X7,X4)
| ~ c_lessequals(c_Set_Oimage(X42,X6,X14,X4),X7,tc_fun(X4,tc_bool))
| ~ c_Fun_Oinj__on(X42,X6,X14,X4)
| ~ c_lessequals(c_Set_Oimage(X20,X7,X4,X14),X6,tc_fun(X14,tc_bool))
| ~ c_Fun_Oinj__on(X20,X7,X4,X14) ),
file('<stdin>',cls_card__bij__eq_0) ).
fof(c_0_27,axiom,
! [X20,X3,X7,X14,X4] :
( c_Fun_Oinj__on(X20,c_Set_Oinsert(X3,X7,X4),X4,X14)
| c_in(hAPP(X20,X3),c_Set_Oimage(X20,c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4,X14),X14)
| ~ c_Fun_Oinj__on(X20,X7,X4,X14) ),
file('<stdin>',cls_inj__on__insert_2) ).
fof(c_0_28,axiom,
! [X5,X21,X22,X26] :
( ~ c_HOL_Oord__class_Oless(X21,X5,tc_nat)
| X5 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ hBOOL(hAPP(X26,c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X22,tc_nat),X21,tc_nat),X5,tc_nat)))
| hBOOL(hAPP(X26,X21)) ),
file('<stdin>',cls_split__mod_1) ).
fof(c_0_29,axiom,
! [X15,X8,X9,X20,X14,X4] :
( hAPP(c_Fun_Ofun__upd(X20,X9,X8,X4,X14),X15) = hAPP(X20,X15)
| X15 = X9 ),
file('<stdin>',cls_fun__upd__other_0) ).
fof(c_0_30,axiom,
! [X15,X8,X9,X20,X14,X4] :
( hAPP(c_Fun_Ofun__upd(X20,X9,X8,X14,X4),X15) = hAPP(X20,X15)
| X15 = X9 ),
file('<stdin>',cls_fun__upd__apply_1) ).
fof(c_0_31,axiom,
! [X8,X9,X20,X23,X4] : hAPP(c_Fun_Ofun__upd(X20,X9,X8,X4,X23),X9) = X8,
file('<stdin>',cls_fun__upd__apply_0) ).
fof(c_0_32,axiom,
! [X8,X9,X20,X14,X4] : hAPP(c_Fun_Ofun__upd(X20,X9,X8,X14,X4),X9) = X8,
file('<stdin>',cls_fun__upd__same_0) ).
fof(c_0_33,axiom,
! [X20,X6,X7,X14,X4] :
( c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| ~ c_lessequals(c_Set_Oimage(X20,X7,X4,X14),c_Set_Oimage(X20,X6,X4,X14),tc_fun(X14,tc_bool))
| ~ c_Fun_Oinj__on(X20,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X14) ),
file('<stdin>',cls_inj__image__subset__iff_0) ).
fof(c_0_34,axiom,
! [X20,X16,X6,X7,X14,X4] :
( c_Set_Oimage(X20,c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),X4,X14) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X20,X7,X4,X14),c_Set_Oimage(X20,X6,X4,X14),tc_fun(X14,tc_bool))
| ~ c_lessequals(X6,X16,tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,X16,tc_fun(X4,tc_bool))
| ~ c_Fun_Oinj__on(X20,X16,X4,X14) ),
file('<stdin>',cls_inj__on__image__Int_0) ).
fof(c_0_35,axiom,
! [X20,X16,X6,X7,X14,X4] :
( c_Set_Oimage(X20,c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),X4,X14) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X20,X7,X4,X14),c_Set_Oimage(X20,X6,X4,X14),tc_fun(X14,tc_bool))
| ~ c_lessequals(X6,X16,tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,X16,tc_fun(X4,tc_bool))
| ~ c_Fun_Oinj__on(X20,X16,X4,X14) ),
file('<stdin>',cls_inj__on__image__set__diff_0) ).
fof(c_0_36,axiom,
! [X18,X2,X1,X21,X22] :
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),X2,tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X22,X21,tc_nat),X18,tc_nat),X1,tc_nat),X2,tc_nat)
| ~ c_lessequals(X21,X22,tc_nat) ),
file('<stdin>',cls_nat__le__add__iff1_1) ).
fof(c_0_37,axiom,
! [X18,X2,X1,X21,X22] :
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X21,X22,tc_nat),X18,tc_nat),X2,tc_nat),tc_nat)
| ~ c_lessequals(X22,X21,tc_nat) ),
file('<stdin>',cls_nat__le__add__iff2_1) ).
fof(c_0_38,axiom,
! [X18,X2,X1,X21,X22] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X21,X22,tc_nat),X18,tc_nat),X2,tc_nat),tc_nat)
| ~ c_lessequals(X22,X21,tc_nat) ),
file('<stdin>',cls_nat__less__add__iff2_1) ).
fof(c_0_39,axiom,
! [X18,X2,X1,X21,X22] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X22,X21,tc_nat),X18,tc_nat),X1,tc_nat),X2,tc_nat)
| ~ c_lessequals(X21,X22,tc_nat) ),
file('<stdin>',cls_nat__less__add__iff1_1) ).
fof(c_0_40,axiom,
! [X19,X17,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X19,X4),X11,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X19,X4),X17,X4),X4)
| ~ c_lessequals(X11,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X3,X4),X19,X4),X17,X4),X4) ),
file('<stdin>',cls_le__add__iff2_1) ).
fof(c_0_41,axiom,
! [X19,X17,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X19,X4),X11,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X19,X4),X17,X4),X4)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X10,X4),X19,X4),X11,X4),X17,X4) ),
file('<stdin>',cls_le__add__iff1_1) ).
fof(c_0_42,axiom,
! [X19,X17,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X19,X4),X11,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X19,X4),X17,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X10,X4),X19,X4),X11,X4),X17,X4) ),
file('<stdin>',cls_less__add__iff1_1) ).
fof(c_0_43,axiom,
! [X19,X17,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X19,X4),X11,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X19,X4),X17,X4),X4)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X3,X4),X19,X4),X17,X4),X4) ),
file('<stdin>',cls_less__add__iff2_1) ).
fof(c_0_44,axiom,
! [X20,X6,X7,X14,X4] :
( c_lessequals(c_Set_Ovimage(X20,X6,X4,X14),X7,tc_fun(X4,tc_bool))
| ~ c_lessequals(X6,c_Set_Oimage(X20,X7,X4,X14),tc_fun(X14,tc_bool))
| ~ c_Fun_Oinj__on(X20,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X14) ),
file('<stdin>',cls_vimage__subsetI_0) ).
fof(c_0_45,axiom,
! [X20,X6,X7,X14,X4] :
( c_Set_Oimage(X20,c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),X4,X14) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X20,X7,X4,X14),c_Set_Oimage(X20,X6,X4,X14),tc_fun(X14,tc_bool))
| ~ c_Fun_Oinj__on(X20,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X14) ),
file('<stdin>',cls_image__set__diff_0) ).
fof(c_0_46,axiom,
! [X20,X6,X7,X14,X4] :
( c_Set_Oimage(X20,c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),X4,X14) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X20,X7,X4,X14),c_Set_Oimage(X20,X6,X4,X14),tc_fun(X14,tc_bool))
| ~ c_Fun_Oinj__on(X20,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X14) ),
file('<stdin>',cls_image__Int_0) ).
fof(c_0_47,axiom,
! [X9,X20,X7,X14,X4] :
( c_in(hAPP(c_Hilbert__Choice_Oinv__into(X7,X20,X14,X4),X9),X7,X14)
| ~ c_in(X9,c_Set_Oimage(X20,X7,X14,X4),X4) ),
file('<stdin>',cls_inv__into__into_0) ).
fof(c_0_48,axiom,
! [X18,X2,X1,X21,X22] :
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X22,X21,tc_nat),X18,tc_nat),X1,tc_nat),X2,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),X2,tc_nat),tc_nat)
| ~ c_lessequals(X21,X22,tc_nat) ),
file('<stdin>',cls_nat__le__add__iff1_0) ).
fof(c_0_49,axiom,
! [X18,X2,X1,X21,X22] :
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X21,X22,tc_nat),X18,tc_nat),X2,tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),X2,tc_nat),tc_nat)
| ~ c_lessequals(X22,X21,tc_nat) ),
file('<stdin>',cls_nat__le__add__iff2_0) ).
fof(c_0_50,axiom,
! [X18,X2,X1,X21,X22] :
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X21,X22,tc_nat),X18,tc_nat),X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),X2,tc_nat),tc_nat)
| ~ c_lessequals(X22,X21,tc_nat) ),
file('<stdin>',cls_nat__less__add__iff2_0) ).
fof(c_0_51,axiom,
! [X18,X2,X1,X21,X22] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X22,X21,tc_nat),X18,tc_nat),X1,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),X2,tc_nat),tc_nat)
| ~ c_lessequals(X21,X22,tc_nat) ),
file('<stdin>',cls_nat__less__add__iff1_0) ).
fof(c_0_52,axiom,
! [X8,X9,X20,X14,X4] :
( c_Fun_Ofun__upd(X20,X9,X8,X4,X14) != X20
| hAPP(X20,X9) = X8 ),
file('<stdin>',cls_fun__upd__idem__iff_0) ).
fof(c_0_53,axiom,
! [X19,X17,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X4)
| c_lessequals(X11,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X3,X4),X19,X4),X17,X4),X4)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X19,X4),X11,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X19,X4),X17,X4),X4) ),
file('<stdin>',cls_le__add__iff2_0) ).
fof(c_0_54,axiom,
! [X19,X17,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X10,X4),X19,X4),X11,X4),X17,X4)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X19,X4),X11,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X19,X4),X17,X4),X4) ),
file('<stdin>',cls_le__add__iff1_0) ).
fof(c_0_55,axiom,
! [X19,X17,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X10,X4),X19,X4),X11,X4),X17,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X19,X4),X11,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X19,X4),X17,X4),X4) ),
file('<stdin>',cls_less__add__iff1_0) ).
fof(c_0_56,axiom,
! [X19,X17,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X4)
| c_HOL_Oord__class_Oless(X11,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X3,X4),X19,X4),X17,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X19,X4),X11,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X19,X4),X17,X4),X4) ),
file('<stdin>',cls_less__add__iff2_0) ).
fof(c_0_57,axiom,
! [X8,X20,X7,X14,X4] :
( hAPP(X20,hAPP(c_Hilbert__Choice_Oinv__into(X7,X20,X14,X4),X8)) = X8
| ~ c_in(X8,c_Set_Oimage(X20,X7,X14,X4),X4) ),
file('<stdin>',cls_f__inv__into__f_0) ).
fof(c_0_58,axiom,
! [X20,X7,X14,X4] :
( c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X20,X4,X14),c_Set_Oimage(X20,X7,X4,X14),X14,X4) = X7
| ~ c_Fun_Oinj__on(X20,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X14) ),
file('<stdin>',cls_image__inv__f__f_0) ).
fof(c_0_59,axiom,
! [X20,X25,X14,X4] :
( c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X20,X4,X14),c_Set_Oimage(X20,X25,X4,X14),X14,X4) = X25
| ~ c_Fun_Oinj__on(X20,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X14) ),
file('<stdin>',cls_inv__image__comp_0) ).
fof(c_0_60,axiom,
! [X20,X47,X7,X14,X4] :
( c_Set_Oimage(c_Hilbert__Choice_Oinv__into(X7,X20,X4,X14),c_Set_Oimage(X20,X47,X4,X14),X14,X4) = X47
| ~ c_lessequals(X47,X7,tc_fun(X4,tc_bool))
| ~ c_Fun_Oinj__on(X20,X7,X4,X14) ),
file('<stdin>',cls_inv__into__image__cancel_0) ).
fof(c_0_61,axiom,
! [X9,X20,X7,X14,X4] :
( hBOOL(hAPP(X7,hAPP(X20,X9)))
| ~ hBOOL(hAPP(c_Set_Ovimage(X20,X7,X4,X14),X9)) ),
file('<stdin>',cls_vimage__code_0) ).
fof(c_0_62,axiom,
! [X20,X6,X7,X14,X4] :
( c_lessequals(c_Set_Oimage(X20,X7,X4,X14),c_Set_Oimage(X20,X6,X4,X14),tc_fun(X14,tc_bool))
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| ~ c_Fun_Oinj__on(X20,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X14) ),
file('<stdin>',cls_inj__image__subset__iff_1) ).
fof(c_0_63,axiom,
! [X20,X6,X7,X14,X4] :
( c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X7,X20,X14,X4),X6,X4,X14)
| ~ c_lessequals(X6,c_Set_Oimage(X20,X7,X14,X4),tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_inj__on__inv__into_0) ).
fof(c_0_64,axiom,
! [X20,X7,X4] :
( c_Set_Oimage(X20,X7,X4,X4) = X7
| ~ c_Fun_Oinj__on(X20,X7,X4,X4)
| ~ c_lessequals(c_Set_Oimage(X20,X7,X4,X4),X7,tc_fun(X4,tc_bool))
| ~ c_Finite__Set_Ofinite(X7,X4) ),
file('<stdin>',cls_endo__inj__surj_0) ).
fof(c_0_65,axiom,
! [X20,X7,X14,X4] : c_lessequals(c_Set_Oimage(X20,c_Set_Ovimage(X20,X7,X14,X4),X14,X4),X7,tc_fun(X4,tc_bool)),
file('<stdin>',cls_image__vimage__subset_0) ).
fof(c_0_66,axiom,
! [X18,X2,X1,X21,X22] :
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),X2,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X22,X21,tc_nat),X18,tc_nat),X1,tc_nat),X2,tc_nat)
| ~ c_lessequals(X21,X22,tc_nat) ),
file('<stdin>',cls_nat__diff__add__eq1_0) ).
fof(c_0_67,axiom,
! [X18,X2,X1,X21,X22] :
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),X2,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X21,X22,tc_nat),X18,tc_nat),X2,tc_nat),tc_nat)
| ~ c_lessequals(X22,X21,tc_nat) ),
file('<stdin>',cls_nat__diff__add__eq2_0) ).
fof(c_0_68,axiom,
! [X20,X10,X3,X14,X4] :
( hAPP(X20,X3) = X10
| ~ c_in(X3,c_Set_Ovimage(X20,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool)),X14),X4,X14),X4) ),
file('<stdin>',cls_vimage__singleton__eq_0) ).
fof(c_0_69,axiom,
! [X9,X43,X5,X17,X44,X4] :
( ~ class_Ring__and__Field_Odvd(X4)
| ~ class_Ring__and__Field_Ocomm__ring(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X17,c_HOL_Oplus__class_Oplus(X9,X43,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X9,c_HOL_Otimes__class_Otimes(X5,X44,X4),X4),X43,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X44,X4) ),
file('<stdin>',cls_inf__period_I4_J_1) ).
fof(c_0_70,axiom,
! [X20,X6,X7,X14,X4] : c_Set_Ovimage(X20,c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X14,tc_bool)),X4,X14) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Ovimage(X20,X7,X4,X14),c_Set_Ovimage(X20,X6,X4,X14),tc_fun(X4,tc_bool)),
file('<stdin>',cls_vimage__Int_0) ).
fof(c_0_71,axiom,
! [X20,X6,X7,X14,X4] : c_Set_Ovimage(X20,c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X14,tc_bool)),X4,X14) = c_HOL_Ominus__class_Ominus(c_Set_Ovimage(X20,X7,X4,X14),c_Set_Ovimage(X20,X6,X4,X14),tc_fun(X4,tc_bool)),
file('<stdin>',cls_vimage__Diff_0) ).
fof(c_0_72,axiom,
! [X9,X6,X7,X4] :
( c_HOL_Oord__class_Oless(X7,c_Set_Oinsert(X9,X6,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X6,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(X7,X6,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_psubset__insert__iff_9) ).
fof(c_0_73,axiom,
! [X20,X3,X7,X14,X4] :
( c_in(X3,X7,X4)
| ~ c_in(hAPP(X20,X3),c_Set_Oimage(X20,X7,X4,X14),X14)
| ~ c_Fun_Oinj__on(X20,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X14) ),
file('<stdin>',cls_inj__image__mem__iff_0) ).
fof(c_0_74,axiom,
! [X9,X6,X7,X4] :
( c_HOL_Oord__class_Oless(X7,c_Set_Oinsert(X9,X6,X4),tc_fun(X4,tc_bool))
| ~ c_in(X9,X7,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X6,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(X7,X6,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_psubset__insert__iff_8) ).
fof(c_0_75,axiom,
! [X20,X6,X7,X14,X4] :
( c_lessequals(c_Finite__Set_Ocard(X7,X4),c_Finite__Set_Ocard(X6,X14),tc_nat)
| ~ c_Finite__Set_Ofinite(X6,X14)
| ~ c_lessequals(c_Set_Oimage(X20,X7,X4,X14),X6,tc_fun(X14,tc_bool))
| ~ c_Fun_Oinj__on(X20,X7,X4,X14) ),
file('<stdin>',cls_card__inj__on__le_0) ).
fof(c_0_76,axiom,
! [X20,X7,X14,X4] : c_Set_Oimage(X20,c_Set_Ovimage(X20,X7,X14,X4),X14,X4) = c_Lattices_Olower__semilattice__class_Oinf(X7,c_Set_Oimage(X20,c_Orderings_Otop__class_Otop(tc_fun(X14,tc_bool)),X14,X4),tc_fun(X4,tc_bool)),
file('<stdin>',cls_image__vimage__eq_0) ).
fof(c_0_77,axiom,
! [X9,X6,X7,X4] :
( c_HOL_Oord__class_Oless(X7,c_Set_Oinsert(X9,X6,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X6,tc_fun(X4,tc_bool))
| c_in(X9,X6,X4) ),
file('<stdin>',cls_psubset__insert__iff_5) ).
fof(c_0_78,axiom,
! [X9,X7,X4] :
( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4),c_Finite__Set_Ocard(X7,X4),tc_nat)
| ~ c_in(X9,X7,X4)
| ~ c_Finite__Set_Ofinite(X7,X4) ),
file('<stdin>',cls_card__Diff1__less_0) ).
fof(c_0_79,axiom,
! [X9,X6,X7,X4] :
( c_HOL_Oord__class_Oless(X7,c_Set_Oinsert(X9,X6,X4),tc_fun(X4,tc_bool))
| ~ c_in(X9,X7,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X6,tc_fun(X4,tc_bool))
| c_in(X9,X6,X4) ),
file('<stdin>',cls_psubset__insert__iff_4) ).
fof(c_0_80,axiom,
! [X9,X6,X7,X4] :
( c_lessequals(X7,c_Set_Oinsert(X9,X6,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X6,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_subset__insert__iff_4) ).
fof(c_0_81,axiom,
! [X9,X7,X4] :
( c_Finite__Set_Ocard(c_Set_Oinsert(X9,X7,X4),X4) = c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4))
| ~ c_Finite__Set_Ofinite(X7,X4) ),
file('<stdin>',cls_card__insert_0) ).
fof(c_0_82,axiom,
! [X9,X7,X4] :
( c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4)) = c_Finite__Set_Ocard(X7,X4)
| ~ c_in(X9,X7,X4)
| ~ c_Finite__Set_Ofinite(X7,X4) ),
file('<stdin>',cls_card__Suc__Diff1_0) ).
fof(c_0_83,axiom,
! [X9,X6,X7,X4] :
( c_lessequals(X7,c_Set_Oinsert(X9,X6,X4),tc_fun(X4,tc_bool))
| ~ c_in(X9,X7,X4)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X6,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_diff__single__insert_0) ).
fof(c_0_84,axiom,
! [X9,X6,X7,X4] :
( c_lessequals(X7,c_Set_Oinsert(X9,X6,X4),tc_fun(X4,tc_bool))
| ~ c_in(X9,X7,X4)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X6,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_subset__insert__iff_3) ).
fof(c_0_85,axiom,
! [X9,X7,X4] :
( c_lessequals(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4),c_Finite__Set_Ocard(X7,X4),tc_nat)
| ~ c_Finite__Set_Ofinite(X7,X4) ),
file('<stdin>',cls_card__Diff1__le_0) ).
fof(c_0_86,axiom,
! [X20,X6,X7,X14,X4] :
( c_Set_Oimage(X20,X7,X4,X14) != c_Set_Oimage(X20,X6,X4,X14)
| ~ c_Fun_Oinj__on(X20,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X14)
| X7 = X6 ),
file('<stdin>',cls_inj__image__eq__iff_0) ).
fof(c_0_87,axiom,
! [X9,X20,X23,X4] : c_Fun_Ofun__upd(X20,X9,hAPP(X20,X9),X23,X4) = X20,
file('<stdin>',cls_fun__upd__idem__iff_1) ).
fof(c_0_88,axiom,
! [X9,X20,X14,X4] : c_Fun_Ofun__upd(X20,X9,hAPP(X20,X9),X4,X14) = X20,
file('<stdin>',cls_fun__upd__triv_0) ).
fof(c_0_89,axiom,
! [X9,X20,X14,X4] : c_Fun_Ofun__upd(X20,X9,hAPP(X20,X9),X14,X4) = X20,
file('<stdin>',cls_fun__upd__idem_0) ).
fof(c_0_90,axiom,
! [X20,X7,X14,X4] :
( c_Set_Ovimage(X20,c_Set_Oimage(X20,X7,X4,X14),X4,X14) = X7
| ~ c_Fun_Oinj__on(X20,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X14) ),
file('<stdin>',cls_inj__vimage__image__eq_0) ).
fof(c_0_91,axiom,
! [X20,X7,X14,X4] :
( c_Finite__Set_Ofinite(X7,X14)
| ~ c_Fun_Oinj__on(X20,X7,X14,X4)
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(X20,X7,X14,X4),X4) ),
file('<stdin>',cls_finite__imageD_0) ).
fof(c_0_92,axiom,
! [X20,X6,X7,X14,X4] :
( c_lessequals(c_Set_Oimage(X20,X7,X4,X14),c_Set_Oimage(X20,X6,X4,X14),tc_fun(X14,tc_bool))
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_image__mono_0) ).
fof(c_0_93,axiom,
! [X9,X20,X7,X14,X4] :
( ~ c_lessequals(X9,X7,tc_fun(X14,tc_bool))
| c_lessequals(c_Set_Oimage(X20,X9,X14,X4),c_Set_Oimage(X20,X7,X14,X4),tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_subset__image__iff_2) ).
fof(c_0_94,axiom,
! [X20,X6,X7,X14,X4] :
( c_lessequals(c_Set_Ovimage(X20,X7,X14,X4),c_Set_Ovimage(X20,X6,X14,X4),tc_fun(X14,tc_bool))
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_vimage__mono_0) ).
fof(c_0_95,axiom,
! [X20,X7,X4] :
( c_Fun_Oinj__on(X20,X7,X4,X4)
| ~ c_lessequals(X7,c_Set_Oimage(X20,X7,X4,X4),tc_fun(X4,tc_bool))
| ~ c_Finite__Set_Ofinite(X7,X4) ),
file('<stdin>',cls_finite__surj__inj_0) ).
fof(c_0_96,axiom,
! [X9,X43,X5,X17,X44,X4] :
( ~ class_Ring__and__Field_Odvd(X4)
| ~ class_Ring__and__Field_Ocomm__ring(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X17,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X9,c_HOL_Otimes__class_Otimes(X5,X44,X4),X4),X43,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,c_HOL_Oplus__class_Oplus(X9,X43,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X44,X4) ),
file('<stdin>',cls_inf__period_I4_J_0) ).
fof(c_0_97,axiom,
! [X9,X20,X7,X14,X4] :
( hBOOL(hAPP(c_Set_Ovimage(X20,X7,X4,X14),X9))
| ~ hBOOL(hAPP(X7,hAPP(X20,X9))) ),
file('<stdin>',cls_vimage__code_1) ).
fof(c_0_98,axiom,
! [X20,X3,X7,X14,X4] :
( c_in(hAPP(X20,X3),c_Set_Oimage(X20,X7,X4,X14),X14)
| ~ c_in(X3,X7,X4)
| ~ c_Fun_Oinj__on(X20,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X14) ),
file('<stdin>',cls_inj__image__mem__iff_1) ).
fof(c_0_99,axiom,
! [X18,X1,X21,X22] :
( ~ c_lessequals(X21,X22,tc_nat)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),X1,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X22,X21,tc_nat),X18,tc_nat),X1,tc_nat),tc_nat) ),
file('<stdin>',cls_nat__eq__add__iff1_1) ).
fof(c_0_100,axiom,
! [X18,X2,X21,X22] :
( ~ c_lessequals(X22,X21,tc_nat)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X21,X22,tc_nat),X18,tc_nat),X2,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),X2,tc_nat) ),
file('<stdin>',cls_nat__eq__add__iff2_1) ).
fof(c_0_101,axiom,
! [X20,X7,X14,X4] :
( c_lessequals(c_Finite__Set_Ocard(c_Set_Oimage(X20,X7,X4,X14),X14),c_Finite__Set_Ocard(X7,X4),tc_nat)
| ~ c_Finite__Set_Ofinite(X7,X4) ),
file('<stdin>',cls_card__image__le_0) ).
fof(c_0_102,axiom,
! [X9,X20,X23,X4] :
( ~ c_Fun_Oinj__on(X20,c_Orderings_Otop__class_Otop(tc_fun(X23,tc_bool)),X23,X4)
| hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X23,tc_bool)),X20,X23,X4),hAPP(X20,X9)) = X9 ),
file('<stdin>',cls_inv__f__eq_0) ).
fof(c_0_103,axiom,
! [X9,X20,X14,X4] :
( hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X20,X4,X14),hAPP(X20,X9)) = X9
| ~ c_Fun_Oinj__on(X20,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X14) ),
file('<stdin>',cls_inv__f__f_0) ).
fof(c_0_104,axiom,
! [X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(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),X4) ),
file('<stdin>',cls_sum__squares__gt__zero__iff_0) ).
fof(c_0_105,axiom,
! [X20,X7,X14,X4] :
( c_Finite__Set_Ocard(c_Set_Oimage(X20,X7,X4,X14),X14) != c_Finite__Set_Ocard(X7,X4)
| ~ c_Finite__Set_Ofinite(X7,X4)
| c_Fun_Oinj__on(X20,X7,X4,X14) ),
file('<stdin>',cls_eq__card__imp__inj__on_0) ).
fof(c_0_106,axiom,
! [X9,X6,X7,X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X6,tc_fun(X4,tc_bool))
| ~ c_in(X9,X7,X4)
| c_in(X9,X6,X4)
| ~ c_HOL_Oord__class_Oless(X7,c_Set_Oinsert(X9,X6,X4),tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_psubset__insert__iff_1) ).
fof(c_0_107,axiom,
! [X19,X17,X10,X3,X4] :
( ~ class_Ring__and__Field_Oring(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X19,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X3,X4),X19,X4),X17,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X19,X4),X17,X4) ),
file('<stdin>',cls_eq__add__iff2_1) ).
fof(c_0_108,axiom,
! [X19,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oring(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X19,X4),X11,X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X19,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X10,X4),X19,X4),X11,X4),X4) ),
file('<stdin>',cls_eq__add__iff1_1) ).
fof(c_0_109,axiom,
! [X20,X3,X23,X4] : c_in(X3,c_Set_Ovimage(X20,c_Set_Oinsert(hAPP(X20,X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X23,X4),X23),
file('<stdin>',cls_vimage__singleton__eq_1) ).
fof(c_0_110,axiom,
! [X9,X20,X6,X7,X14,X4] :
( c_in(hAPP(X20,X9),X6,X4)
| ~ c_in(X9,X7,X14)
| ~ c_lessequals(c_Set_Oimage(X20,X7,X14,X4),X6,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_image__subset__iff_0) ).
fof(c_0_111,axiom,
! [X17,X10,X26] :
( ~ hBOOL(hAPP(X26,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X10,X17,tc_nat),X10,tc_nat)))
| hBOOL(hAPP(X26,X17)) ),
file('<stdin>',cls_nat__diff__split_1) ).
fof(c_0_112,axiom,
! [X9,X10,X26] :
( ~ hBOOL(hAPP(X26,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X10,X9,tc_nat),X10,tc_nat)))
| hBOOL(hAPP(X26,X9)) ),
file('<stdin>',cls_nat__diff__split__asm_1) ).
fof(c_0_113,axiom,
! [X36,X37,X11,X10] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,c_Divides_Odiv__class_Omod(X37,X11,tc_nat),tc_nat),X36,tc_nat),c_HOL_Otimes__class_Otimes(X10,X11,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X36,X10,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_114,axiom,
! [X9,X6,X7,X4] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X6,tc_fun(X4,tc_bool))
| ~ c_in(X9,X7,X4)
| ~ c_lessequals(X7,c_Set_Oinsert(X9,X6,X4),tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_subset__insert__iff_0) ).
fof(c_0_115,axiom,
! [X9,X20,X7,X23,X4] :
( ~ c_in(X9,X7,X23)
| ~ c_Fun_Oinj__on(X20,X7,X23,X4)
| hAPP(c_Hilbert__Choice_Oinv__into(X7,X20,X23,X4),hAPP(X20,X9)) = X9 ),
file('<stdin>',cls_inv__into__f__eq_0) ).
fof(c_0_116,axiom,
! [X9,X20,X7,X14,X4] :
( hAPP(c_Hilbert__Choice_Oinv__into(X7,X20,X4,X14),hAPP(X20,X9)) = X9
| ~ c_in(X9,X7,X4)
| ~ c_Fun_Oinj__on(X20,X7,X4,X14) ),
file('<stdin>',cls_inv__into__f__f_0) ).
fof(c_0_117,axiom,
! [X12,X13,X14,X4] :
( c_Finite__Set_Ofinite(c_Set_Ovimage(X12,X13,X14,X4),X14)
| ~ c_Fun_Oinj__on(X12,c_Orderings_Otop__class_Otop(tc_fun(X14,tc_bool)),X14,X4)
| ~ c_Finite__Set_Ofinite(X13,X4) ),
file('<stdin>',cls_finite__vimageI_0) ).
fof(c_0_118,axiom,
! [X8,X9,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X9,X4),c_HOL_Otimes__class_Otimes(X8,X8,X4),X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_sum__squares__le__zero__iff_1) ).
fof(c_0_119,axiom,
! [X8,X9,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| X9 = c_HOL_Ozero__class_Ozero(X4)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X9,X4),c_HOL_Otimes__class_Otimes(X8,X8,X4),X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_sum__squares__le__zero__iff_0) ).
fof(c_0_120,axiom,
! [X8,X9,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X9,X4),c_HOL_Otimes__class_Otimes(X8,X8,X4),X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_not__sum__squares__lt__zero_0) ).
fof(c_0_121,axiom,
! [X18,X2,X1,X21,X22] :
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),X1,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),X2,tc_nat)
| ~ c_lessequals(X21,X22,tc_nat)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X22,X21,tc_nat),X18,tc_nat),X1,tc_nat) = X2 ),
file('<stdin>',cls_nat__eq__add__iff1_0) ).
fof(c_0_122,axiom,
! [X18,X2,X1,X21,X22] :
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),X1,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),X2,tc_nat)
| ~ c_lessequals(X22,X21,tc_nat)
| X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X21,X22,tc_nat),X18,tc_nat),X2,tc_nat) ),
file('<stdin>',cls_nat__eq__add__iff2_0) ).
fof(c_0_123,axiom,
! [X20,X3,X7,X14,X4] :
( c_in(hAPP(X20,X3),X7,X14)
| ~ c_in(X3,c_Set_Ovimage(X20,X7,X4,X14),X4) ),
file('<stdin>',cls_vimageD_0) ).
fof(c_0_124,axiom,
! [X20,X3,X6,X14,X4] :
( c_in(hAPP(X20,X3),X6,X14)
| ~ c_in(X3,c_Set_Ovimage(X20,X6,X4,X14),X4) ),
file('<stdin>',cls_vimageE_0) ).
fof(c_0_125,axiom,
! [X20,X6,X7,X14,X4] :
( c_Finite__Set_Ofinite(X6,X14)
| ~ c_lessequals(X6,c_Set_Oimage(X20,X7,X4,X14),tc_fun(X14,tc_bool))
| ~ c_Finite__Set_Ofinite(X7,X4) ),
file('<stdin>',cls_finite__surj_0) ).
fof(c_0_126,axiom,
! [X20,X7,X14,X4] :
( c_Finite__Set_Ocard(c_Set_Oimage(X20,X7,X4,X14),X14) = c_Finite__Set_Ocard(X7,X4)
| ~ c_Fun_Oinj__on(X20,X7,X4,X14)
| ~ c_Finite__Set_Ofinite(X7,X4) ),
file('<stdin>',cls_inj__on__iff__eq__card_0) ).
fof(c_0_127,axiom,
! [X3,X6,X7,X4] :
( c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X3,X6,X4),tc_fun(X4,tc_bool)),X4) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),X4),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_in(X3,X6,X4)
| ~ c_in(X3,X7,X4)
| ~ c_Finite__Set_Ofinite(X7,X4) ),
file('<stdin>',cls_card__Diff__insert_0) ).
fof(c_0_128,axiom,
! [X20,X3,X6,X14,X4] : c_Set_Oimage(X20,c_Set_Oinsert(X3,X6,X14),X14,X4) = c_Set_Oinsert(hAPP(X20,X3),c_Set_Oimage(X20,X6,X14,X4),X4),
file('<stdin>',cls_image__insert_0) ).
fof(c_0_129,axiom,
! [X20,X7,X14,X4] :
( c_Finite__Set_Ocard(c_Set_Oimage(X20,X7,X4,X14),X14) = c_Finite__Set_Ocard(X7,X4)
| ~ c_Fun_Oinj__on(X20,X7,X4,X14) ),
file('<stdin>',cls_card__image_0) ).
fof(c_0_130,axiom,
! [X9,X20,X7,X14,X4] :
( c_Set_Oinsert(hAPP(X20,X9),c_Set_Oimage(X20,X7,X4,X14),X14) = c_Set_Oimage(X20,X7,X4,X14)
| ~ c_in(X9,X7,X4) ),
file('<stdin>',cls_insert__image_0) ).
fof(c_0_131,axiom,
! [X19,X17,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oring(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X19,X4),X11,X4) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X19,X4),X17,X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X10,X4),X19,X4),X11,X4) = X17 ),
file('<stdin>',cls_eq__add__iff1_0) ).
fof(c_0_132,axiom,
! [X19,X17,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oring(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X19,X4),X11,X4) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X19,X4),X17,X4)
| X11 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X3,X4),X19,X4),X17,X4) ),
file('<stdin>',cls_eq__add__iff2_0) ).
fof(c_0_133,axiom,
! [X19,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Osemiring(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X19,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X19,X4),X11,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,X10,X4),X19,X4),X11,X4) ),
file('<stdin>',cls_combine__common__factor_0) ).
fof(c_0_134,axiom,
! [X17,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X17,X4),X4) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X17,X4),c_HOL_Otimes__class_Otimes(X10,X11,X4),X4)
| X11 = X17
| X3 = X10 ),
file('<stdin>',cls_class__ringb_Onoteq__reduce_0) ).
fof(c_0_135,axiom,
! [X15,X8,X9,X29,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X29,X8,X4),c_HOL_Otimes__class_Otimes(X9,X15,X4),X4) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X29,X15,X4),c_HOL_Otimes__class_Otimes(X9,X8,X4),X4)
| X8 = X15
| X29 = X9 ),
file('<stdin>',cls_class__ringb_Oadd__mul__solve_0) ).
fof(c_0_136,axiom,
! [X6,X7,X4] :
( c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),X4) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(X7,X4),c_Finite__Set_Ocard(c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),X4),tc_nat)
| ~ c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),X4) ),
file('<stdin>',cls_card__Diff__subset__Int_0) ).
fof(c_0_137,axiom,
! [X17,X11,X10,X3,X4] :
( c_Set_Oinsert(X3,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X11,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4)
| X3 = X17
| X3 = X11 ),
file('<stdin>',cls_doubleton__eq__iff_0) ).
fof(c_0_138,axiom,
! [X17,X11,X10,X3,X4] :
( c_Set_Oinsert(X3,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X11,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4)
| X10 = X11
| X3 = X11 ),
file('<stdin>',cls_doubleton__eq__iff_1) ).
fof(c_0_139,axiom,
! [X17,X11,X10,X3,X4] :
( c_Set_Oinsert(X3,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X11,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4)
| X3 = X17
| X10 = X17 ),
file('<stdin>',cls_doubleton__eq__iff_2) ).
fof(c_0_140,axiom,
! [X17,X11,X10,X3,X4] :
( c_Set_Oinsert(X3,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X11,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4)
| X10 = X11
| X10 = X17 ),
file('<stdin>',cls_doubleton__eq__iff_3) ).
fof(c_0_141,axiom,
! [X3,X6,X7,X4] : c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X3,X6,X4),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X6,tc_fun(X4,tc_bool)),
file('<stdin>',cls_Diff__insert2_0) ).
fof(c_0_142,axiom,
! [X18,X5,X21,X22] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),X5,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X22,X21,tc_nat),X18,tc_nat),X5,tc_nat),
file('<stdin>',cls_left__add__mult__distrib_0) ).
fof(c_0_143,axiom,
! [X15,X8,X9,X29] :
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X29,X8,tc_nat),c_HOL_Otimes__class_Otimes(X9,X15,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X29,X15,tc_nat),c_HOL_Otimes__class_Otimes(X9,X8,tc_nat),tc_nat)
| X8 = X15
| X29 = X9 ),
file('<stdin>',cls_natgb_Oadd__mul__solve_0) ).
fof(c_0_144,axiom,
! [X17,X11,X10,X3] :
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X11,tc_nat),c_HOL_Otimes__class_Otimes(X10,X17,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X17,tc_nat),c_HOL_Otimes__class_Otimes(X10,X11,tc_nat),tc_nat)
| X11 = X17
| X3 = X10 ),
file('<stdin>',cls_natgb_Onoteq__reduce_0) ).
fof(c_0_145,axiom,
! [X20,X3,X7,X14,X4] :
( c_Fun_Oinj__on(X20,X7,X4,X14)
| ~ c_Fun_Oinj__on(X20,c_Set_Oinsert(X3,X7,X4),X4,X14) ),
file('<stdin>',cls_inj__on__insert_0) ).
fof(c_0_146,axiom,
! [X20,X6,X7,X14,X4] :
( c_Fun_Oinj__on(X20,c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),X4,X14)
| ~ c_Fun_Oinj__on(X20,X7,X4,X14) ),
file('<stdin>',cls_inj__on__diff_0) ).
fof(c_0_147,axiom,
! [X9,X7,X4] :
( c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(X7,X4),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ c_in(X9,X7,X4)
| ~ c_Finite__Set_Ofinite(X7,X4) ),
file('<stdin>',cls_card__Diff__singleton_0) ).
fof(c_0_148,axiom,
! [X3,X6,X7,X4] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),X4)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X3,X6,X4),tc_fun(X4,tc_bool)),X4) ),
file('<stdin>',cls_finite__Diff__insert_0) ).
fof(c_0_149,axiom,
! [X20,X6,X7,X14,X4] :
( c_Fun_Oinj__on(X20,X7,X4,X14)
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| ~ c_Fun_Oinj__on(X20,X6,X4,X14) ),
file('<stdin>',cls_subset__inj__on_0) ).
fof(c_0_150,axiom,
! [X11,X10,X3,X4] :
( ~ class_Divides_Oring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X3,X10,X4),X11,X4) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X3,X11,X4),c_Divides_Odiv__class_Omod(X10,X11,X4),X4),X11,X4) ),
file('<stdin>',cls_mod__diff__eq_0) ).
fof(c_0_151,axiom,
! [X11,X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X10,X4),X11,X4) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X3,X11,X4),c_Divides_Odiv__class_Omod(X10,X11,X4),X4),X11,X4) ),
file('<stdin>',cls_mod__mult__eq_0) ).
fof(c_0_152,axiom,
! [X11,X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,X10,X4),X11,X4) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X3,X11,X4),c_Divides_Odiv__class_Omod(X10,X11,X4),X4),X11,X4) ),
file('<stdin>',cls_mod__add__eq_0) ).
fof(c_0_153,axiom,
! [X2,X1,X5] : c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,tc_nat),X1,tc_nat)),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat),
file('<stdin>',cls_mod__mult__self4_0) ).
fof(c_0_154,axiom,
! [X3,X7,X4] :
( c_Set_Oinsert(X3,c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4) = X7
| ~ c_in(X3,X7,X4) ),
file('<stdin>',cls_insert__Diff_0) ).
fof(c_0_155,axiom,
! [X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(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),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_sum__squares__le__zero__iff_2) ).
fof(c_0_156,axiom,
! [X3,X7,X4] : c_Set_Oinsert(X3,c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4) = c_Set_Oinsert(X3,X7,X4),
file('<stdin>',cls_insert__Diff__single_0) ).
fof(c_0_157,axiom,
! [X9,X7,X4] :
( c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4) = c_Finite__Set_Ocard(X7,X4)
| c_in(X9,X7,X4)
| ~ c_Finite__Set_Ofinite(X7,X4) ),
file('<stdin>',cls_card__Diff__singleton__if_1) ).
fof(c_0_158,axiom,
! [X9,X20,X14,X4] : c_in(hAPP(X20,X9),c_Set_Oimage(X20,c_Orderings_Otop__class_Otop(tc_fun(X14,tc_bool)),X14,X4),X4),
file('<stdin>',cls_rangeI_0) ).
fof(c_0_159,axiom,
! [X20,X3,X6,X14,X4] :
( c_in(X3,c_Set_Ovimage(X20,X6,X14,X4),X14)
| ~ c_in(hAPP(X20,X3),X6,X4) ),
file('<stdin>',cls_vimageI_0) ).
fof(c_0_160,axiom,
! [X20,X3,X7,X14,X4] :
( c_in(X3,c_Set_Ovimage(X20,X7,X14,X4),X14)
| ~ c_in(hAPP(X20,X3),X7,X4) ),
file('<stdin>',cls_vimageI2_0) ).
fof(c_0_161,axiom,
! [X20,X3,X6,X14,X4] :
( c_in(X3,c_Set_Ovimage(X20,X6,X4,X14),X4)
| ~ c_in(hAPP(X20,X3),X6,X14) ),
file('<stdin>',cls_vimage__eq_1) ).
fof(c_0_162,axiom,
! [X11,X27,X10,X28,X3,X4] :
( ~ class_Divides_Oring__div(X4)
| c_Divides_Odiv__class_Omod(X10,X11,X4) != c_Divides_Odiv__class_Omod(X27,X11,X4)
| c_Divides_Odiv__class_Omod(X3,X11,X4) != c_Divides_Odiv__class_Omod(X28,X11,X4)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X3,X10,X4),X11,X4) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X28,X27,X4),X11,X4) ),
file('<stdin>',cls_mod__diff__cong_0) ).
fof(c_0_163,axiom,
! [X11,X27,X10,X28,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(X10,X11,X4) != c_Divides_Odiv__class_Omod(X27,X11,X4)
| c_Divides_Odiv__class_Omod(X3,X11,X4) != c_Divides_Odiv__class_Omod(X28,X11,X4)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X10,X4),X11,X4) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X28,X27,X4),X11,X4) ),
file('<stdin>',cls_mod__mult__cong_0) ).
fof(c_0_164,axiom,
! [X11,X27,X10,X28,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(X10,X11,X4) != c_Divides_Odiv__class_Omod(X27,X11,X4)
| c_Divides_Odiv__class_Omod(X3,X11,X4) != c_Divides_Odiv__class_Omod(X28,X11,X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,X10,X4),X11,X4) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X28,X27,X4),X11,X4) ),
file('<stdin>',cls_mod__add__cong_0) ).
fof(c_0_165,axiom,
! [X9,X20,X7,X14,X4] :
( c_in(hAPP(X20,X9),c_Set_Oimage(X20,X7,X4,X14),X14)
| ~ c_in(X9,X7,X4) ),
file('<stdin>',cls_imageI_0) ).
fof(c_0_166,axiom,
! [X9,X20,X7,X14,X4] :
( c_in(hAPP(X20,X9),c_Set_Oimage(X20,X7,X14,X4),X4)
| ~ c_in(X9,X7,X14) ),
file('<stdin>',cls_image__eqI_0) ).
fof(c_0_167,axiom,
! [X9,X20,X7,X14,X4] :
( ~ c_in(X9,X7,X14)
| c_in(hAPP(X20,X9),c_Set_Oimage(X20,X7,X14,X4),X4) ),
file('<stdin>',cls_image__iff_2) ).
fof(c_0_168,axiom,
! [X9,X20,X7,X23,X4] :
( ~ c_in(X9,X7,X23)
| c_in(hAPP(X20,X9),c_Set_Oimage(X20,X7,X23,X4),X4) ),
file('<stdin>',cls_rev__image__eqI_0) ).
fof(c_0_169,axiom,
! [X30,X31,X32,X33,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X33,X32,X4),c_HOL_Otimes__class_Otimes(X31,X30,X4),X4) = c_HOL_Otimes__class_Otimes(X31,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X33,X32,X4),X30,X4),X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I15_J_0) ).
fof(c_0_170,axiom,
! [X30,X31,X32,X33,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X33,X32,X4),c_HOL_Otimes__class_Otimes(X31,X30,X4),X4) = c_HOL_Otimes__class_Otimes(X33,c_HOL_Otimes__class_Otimes(X32,c_HOL_Otimes__class_Otimes(X31,X30,X4),X4),X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I14_J_0) ).
fof(c_0_171,axiom,
! [X3,X6,X7,X4] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X3,X6,X4),tc_fun(X4,tc_bool)),X4)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),X4) ),
file('<stdin>',cls_finite__Diff__insert_1) ).
fof(c_0_172,axiom,
! [X17,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X17,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X11,X17,X4)
| ~ c_HOL_Oord__class_Oless(X3,X10,X4) ),
file('<stdin>',cls_mult__strict__mono_H_0) ).
fof(c_0_173,axiom,
! [X17,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X17,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X11,X17,X4)
| ~ c_lessequals(X3,X10,X4) ),
file('<stdin>',cls_mult__le__less__imp__less_0) ).
fof(c_0_174,axiom,
! [X17,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X17,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(X11,X17,X4)
| ~ c_HOL_Oord__class_Oless(X3,X10,X4) ),
file('<stdin>',cls_mult__less__le__imp__less_0) ).
fof(c_0_175,axiom,
! [X17,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__semiring(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X17,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(X11,X17,X4)
| ~ c_lessequals(X3,X10,X4) ),
file('<stdin>',cls_mult__mono_H_0) ).
fof(c_0_176,axiom,
! [X17,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__semiring(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X17,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X10,X4)
| ~ c_lessequals(X11,X17,X4)
| ~ c_lessequals(X3,X10,X4) ),
file('<stdin>',cls_mult__mono_0) ).
fof(c_0_177,axiom,
! [X17,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X17,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X10,X4)
| ~ c_HOL_Oord__class_Oless(X11,X17,X4)
| ~ c_HOL_Oord__class_Oless(X3,X10,X4) ),
file('<stdin>',cls_mult__strict__mono_0) ).
fof(c_0_178,axiom,
! [X2,X1,X5] :
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X5,tc_nat),c_HOL_Ominus__class_Ominus(X2,X5,tc_nat),tc_nat)
| ~ c_lessequals(X5,X2,tc_nat)
| ~ c_lessequals(X5,X1,tc_nat) ),
file('<stdin>',cls_le__diff__iff_0) ).
fof(c_0_179,axiom,
! [X2,X1,X5] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X5,tc_nat),c_HOL_Ominus__class_Ominus(X2,X5,tc_nat),tc_nat)
| ~ c_lessequals(X5,X2,tc_nat)
| ~ c_lessequals(X5,X1,tc_nat) ),
file('<stdin>',cls_less__diff__iff_0) ).
fof(c_0_180,axiom,
! [X49,X2,X20,X4] :
( ~ class_Orderings_Oorder(X4)
| c_lessequals(hAPP(X20,X2),hAPP(X20,X49),X4)
| ~ c_lessequals(X2,X49,tc_nat)
| ~ c_lessequals(hAPP(X20,c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1(X20,X4)),hAPP(X20,c_Suc(c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1(X20,X4))),X4) ),
file('<stdin>',cls_lift__Suc__mono__le_0) ).
fof(c_0_181,axiom,
! [X44,X16,X6,X7,X4] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),c_HOL_Ominus__class_Ominus(X16,X44,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
| ~ c_lessequals(X44,X6,tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,X16,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_Diff__mono_0) ).
fof(c_0_182,axiom,
! [X44,X16,X6,X7,X4] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X16,X44,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
| ~ c_lessequals(X6,X44,tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,X16,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_Int__mono_0) ).
fof(c_0_183,axiom,
! [X3,X6,X7,X4] : c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X3,X6,X4),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),
file('<stdin>',cls_Diff__insert_0) ).
fof(c_0_184,axiom,
! [X16,X6,X7,X4] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X7,X16,tc_fun(X4,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X6,X16,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X7,X16,tc_fun(X4,tc_bool)),X6,tc_fun(X4,tc_bool)),
file('<stdin>',cls_Diff__Int2_0) ).
fof(c_0_185,axiom,
! [X16,X6,X7,X4] : c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),X16,tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X7,X16,tc_fun(X4,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X6,X16,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
file('<stdin>',cls_Diff__Int__distrib2_0) ).
fof(c_0_186,axiom,
! [X16,X6,X7,X4] : c_Lattices_Olower__semilattice__class_Oinf(X16,c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X16,X7,tc_fun(X4,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X16,X6,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
file('<stdin>',cls_Diff__Int__distrib_0) ).
fof(c_0_187,axiom,
! [X8,X9,X20,X7,X14,X4] :
( hAPP(X20,X9) != hAPP(X20,X8)
| ~ c_Fun_Oinj__on(X20,X7,X4,X14)
| X9 = X8
| ~ c_in(X8,X7,X4)
| ~ c_in(X9,X7,X4) ),
file('<stdin>',cls_inj__onD_0) ).
fof(c_0_188,axiom,
! [X34,X9,X20,X7,X14,X4] :
( hAPP(X20,X9) != hAPP(X20,X34)
| ~ c_in(X34,X7,X4)
| ~ c_in(X9,X7,X4)
| ~ c_Fun_Oinj__on(X20,X7,X4,X14)
| X9 = X34 ),
file('<stdin>',cls_inj__on__def_0) ).
fof(c_0_189,axiom,
! [X8,X9,X20,X7,X14,X4] :
( hAPP(X20,X9) != hAPP(X20,X8)
| ~ c_in(X8,X7,X4)
| ~ c_in(X9,X7,X4)
| ~ c_Fun_Oinj__on(X20,X7,X4,X14)
| X9 = X8 ),
file('<stdin>',cls_inj__on__iff_0) ).
fof(c_0_190,axiom,
! [X8,X9,X20,X7,X14,X4] :
( hAPP(X20,X9) != hAPP(X20,X8)
| ~ c_in(X8,X7,X4)
| ~ c_in(X9,X7,X4)
| X9 = X8
| ~ c_Fun_Oinj__on(X20,X7,X4,X14) ),
file('<stdin>',cls_inj__on__contraD_0) ).
fof(c_0_191,axiom,
! [X8,X9,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X9,X4),c_HOL_Otimes__class_Otimes(X8,X8,X4),X4),X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_sum__squares__gt__zero__iff_2) ).
fof(c_0_192,axiom,
! [X8,X9,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X9,X4),c_HOL_Otimes__class_Otimes(X8,X8,X4),X4),X4)
| X9 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_sum__squares__gt__zero__iff_1) ).
fof(c_0_193,axiom,
! [X8,X9,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X9,X4),c_HOL_Otimes__class_Otimes(X8,X8,X4),X4),X4) ),
file('<stdin>',cls_sum__squares__ge__zero_0) ).
fof(c_0_194,axiom,
! [X8,X35,X34,X9,X2] :
( c_HOL_Oplus__class_Oplus(X9,c_HOL_Otimes__class_Otimes(X2,X34,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X8,c_HOL_Otimes__class_Otimes(X2,X35,tc_nat),tc_nat)
| c_Divides_Odiv__class_Omod(X9,X2,tc_nat) = c_Divides_Odiv__class_Omod(X8,X2,tc_nat) ),
file('<stdin>',cls_nat__mod__eq__iff_1) ).
fof(c_0_195,axiom,
! [X9,X7,X4] :
( X7 = c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4)
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_subset__singletonD_0) ).
fof(c_0_196,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(X3,X10,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X11,X4) ),
file('<stdin>',cls_mult__less__cancel__left__pos_0) ).
fof(c_0_197,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(X10,X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_mult__less__cancel__left__neg_0) ).
fof(c_0_198,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_lessequals(X3,X10,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X11,X4),X4) ),
file('<stdin>',cls_mult__right__le__imp__le_0) ).
fof(c_0_199,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_lessequals(X3,X10,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4) ),
file('<stdin>',cls_mult__left__le__imp__le_0) ).
fof(c_0_200,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(X3,X10,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X11,X4) ),
file('<stdin>',cls_mult__le__cancel__left__pos_0) ).
fof(c_0_201,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(X10,X3,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_mult__le__cancel__left__neg_0) ).
fof(c_0_202,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semiring(X4)
| c_HOL_Oord__class_Oless(X3,X10,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4) ),
file('<stdin>',cls_mult__left__less__imp__less_0) ).
fof(c_0_203,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semiring(X4)
| c_HOL_Oord__class_Oless(X3,X10,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X11,X4),X4) ),
file('<stdin>',cls_mult__right__less__imp__less_0) ).
fof(c_0_204,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(X3,X10,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4) ),
file('<stdin>',cls_mult__less__imp__less__left_0) ).
fof(c_0_205,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(X3,X10,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X11,X4),X4) ),
file('<stdin>',cls_mult__less__imp__less__right_0) ).
fof(c_0_206,axiom,
! [X9,X6,X7,X4] :
( hBOOL(hAPP(X7,X9))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),X9)) ),
file('<stdin>',cls_inf1E_0) ).
fof(c_0_207,axiom,
! [X9,X6,X7,X4] :
( hBOOL(hAPP(X6,X9))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),X9)) ),
file('<stdin>',cls_inf1E_1) ).
fof(c_0_208,axiom,
! [X2,X1,X5] :
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ 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,X1,tc_nat),c_HOL_Otimes__class_Otimes(X5,X2,tc_nat),tc_nat) ),
file('<stdin>',cls_dvd__mult__cancel_0) ).
fof(c_0_209,axiom,
! [X2,X1,X5] :
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,X1,tc_nat),c_HOL_Otimes__class_Otimes(X5,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
file('<stdin>',cls_nat__mult__dvd__cancel1_0) ).
fof(c_0_210,axiom,
! [X2,X1,X5] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X1,tc_nat),c_HOL_Otimes__class_Otimes(X5,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
file('<stdin>',cls_nat__mult__less__cancel1_0) ).
fof(c_0_211,axiom,
! [X2,X1,X5] :
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X5,X1,tc_nat),c_HOL_Otimes__class_Otimes(X5,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
file('<stdin>',cls_nat__mult__le__cancel1_0) ).
fof(c_0_212,axiom,
! [X2,X1,X5] :
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X5,X1,tc_nat),c_HOL_Otimes__class_Otimes(X5,X2,tc_nat),tc_nat) ),
file('<stdin>',cls_mult__le__cancel1_0) ).
fof(c_0_213,axiom,
! [X2,X1,X5] :
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X5,tc_nat),c_HOL_Otimes__class_Otimes(X2,X5,tc_nat),tc_nat) ),
file('<stdin>',cls_mult__le__cancel2_0) ).
fof(c_0_214,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X11,X4),X4) ),
file('<stdin>',cls_mult__less__cancel__right__disj_0) ).
fof(c_0_215,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4) ),
file('<stdin>',cls_mult__less__cancel__left__disj_0) ).
fof(c_0_216,axiom,
! [X9,X17,X11,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X11,X4),c_HOL_Otimes__class_Otimes(X9,X17,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X17,X4),c_HOL_Otimes__class_Otimes(X9,X11,X4),X4) ),
file('<stdin>',cls_class__ringb_Onoteq__reduce_1) ).
fof(c_0_217,axiom,
! [X15,X8,X9,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X8,X4),c_HOL_Otimes__class_Otimes(X9,X15,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X15,X4),c_HOL_Otimes__class_Otimes(X9,X8,X4),X4) ),
file('<stdin>',cls_class__ringb_Oadd__mul__solve_1) ).
fof(c_0_218,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(X10,X3,X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4) ),
file('<stdin>',cls_mult__less__cancel__left__disj_1) ).
fof(c_0_219,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X3,X10,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4) ),
file('<stdin>',cls_mult__less__cancel__left__disj_2) ).
fof(c_0_220,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(X10,X3,X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X11,X4),X4) ),
file('<stdin>',cls_mult__less__cancel__right__disj_1) ).
fof(c_0_221,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X3,X10,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X11,X4),X4) ),
file('<stdin>',cls_mult__less__cancel__right__disj_2) ).
fof(c_0_222,axiom,
! [X11,X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,c_Divides_Odiv__class_Omod(X10,X11,X4),X4),X11,X4) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,X10,X4),X11,X4) ),
file('<stdin>',cls_zmod__simps_I2_J_0) ).
fof(c_0_223,axiom,
! [X11,X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X3,X11,X4),X10,X4),X11,X4) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,X10,X4),X11,X4) ),
file('<stdin>',cls_zmod__simps_I1_J_0) ).
fof(c_0_224,axiom,
! [X11,X10,X3,X4] :
( ~ class_Divides_Oring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X3,X10,X4),X11,X4) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X3,c_Divides_Odiv__class_Omod(X10,X11,X4),X4),X11,X4) ),
file('<stdin>',cls_mod__diff__right__eq_0) ).
fof(c_0_225,axiom,
! [X11,X10,X3,X4] :
( ~ class_Divides_Oring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X3,X10,X4),X11,X4) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X3,X11,X4),X10,X4),X11,X4) ),
file('<stdin>',cls_mod__diff__left__eq_0) ).
fof(c_0_226,axiom,
! [X30,X31,X32,X33,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X33,X32,X4),c_HOL_Otimes__class_Otimes(X31,X30,X4),X4) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X33,X31,X4),c_HOL_Otimes__class_Otimes(X32,X30,X4),X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I13_J_0) ).
fof(c_0_227,axiom,
! [X17,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X10,X4),c_HOL_Oplus__class_Oplus(X11,X17,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X11,X4),c_HOL_Oplus__class_Oplus(X10,X17,X4),X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I20_J_0) ).
fof(c_0_228,axiom,
! [X11,X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X10,X4),X11,X4) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(X10,X11,X4),X4),X11,X4) ),
file('<stdin>',cls_mod__mult__right__eq_0) ).
fof(c_0_229,axiom,
! [X11,X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X10,X4),X11,X4) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X3,X11,X4),X10,X4),X11,X4) ),
file('<stdin>',cls_mod__mult__left__eq_0) ).
fof(c_0_230,axiom,
! [X11,X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X3,X11,X4),X10,X4),X11,X4) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X10,X4),X11,X4) ),
file('<stdin>',cls_zmod__simps_I4_J_0) ).
fof(c_0_231,axiom,
! [X11,X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,X10,X4),X11,X4) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,c_Divides_Odiv__class_Omod(X10,X11,X4),X4),X11,X4) ),
file('<stdin>',cls_mod__add__right__eq_0) ).
fof(c_0_232,axiom,
! [X11,X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,X10,X4),X11,X4) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X3,X11,X4),X10,X4),X11,X4) ),
file('<stdin>',cls_mod__add__left__eq_0) ).
fof(c_0_233,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(X10,X3,X4)
| c_HOL_Oord__class_Oless(X3,X10,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X11,X4),X4) ),
file('<stdin>',cls_mult__less__cancel__right__disj_3) ).
fof(c_0_234,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(X10,X3,X4)
| c_HOL_Oord__class_Oless(X3,X10,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4) ),
file('<stdin>',cls_mult__less__cancel__left__disj_3) ).
fof(c_0_235,axiom,
! [X34,X9,X4] : c_Set_Oinsert(X34,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) = c_Set_Oinsert(X9,c_Set_Oinsert(X34,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4),
file('<stdin>',cls_doubleton__eq__iff_4) ).
fof(c_0_236,axiom,
! [X12,X13,X14,X4] :
( c_Finite__Set_Ofinite(c_Set_Oimage(X12,X13,X4,X14),X14)
| ~ c_Finite__Set_Ofinite(X13,X4) ),
file('<stdin>',cls_finite__imageI_0) ).
fof(c_0_237,axiom,
! [X9,X36,X17,X11,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| c_HOL_Oplus__class_Oplus(X9,c_HOL_Otimes__class_Otimes(X36,X11,X4),X4) != c_HOL_Oplus__class_Oplus(X9,c_HOL_Otimes__class_Otimes(X36,X17,X4),X4)
| X11 = X17
| X36 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
fof(c_0_238,axiom,
! [X15,X8,X9] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X8,tc_nat),c_HOL_Otimes__class_Otimes(X9,X15,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X15,tc_nat),c_HOL_Otimes__class_Otimes(X9,X8,tc_nat),tc_nat),
file('<stdin>',cls_natgb_Oadd__mul__solve_1) ).
fof(c_0_239,axiom,
! [X9,X17,X11] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X11,tc_nat),c_HOL_Otimes__class_Otimes(X9,X17,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X17,tc_nat),c_HOL_Otimes__class_Otimes(X9,X11,tc_nat),tc_nat),
file('<stdin>',cls_natgb_Onoteq__reduce_1) ).
fof(c_0_240,axiom,
! [X8,X9,X20,X14,X4] :
( hAPP(X20,X9) != hAPP(X20,X8)
| ~ c_Fun_Oinj__on(X20,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X14)
| X9 = X8 ),
file('<stdin>',cls_injD_0) ).
fof(c_0_241,axiom,
! [X1,X5,X21] :
( c_HOL_Ominus__class_Ominus(X1,c_Suc(c_HOL_Ominus__class_Ominus(X21,X5,tc_nat)),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X5,tc_nat),c_Suc(X21),tc_nat)
| ~ c_lessequals(X5,X21,tc_nat) ),
file('<stdin>',cls_diff__Suc__diff__eq1_0) ).
fof(c_0_242,axiom,
! [X1,X5,X21] :
( c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ominus__class_Ominus(X21,X5,tc_nat)),X1,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X21),c_HOL_Oplus__class_Oplus(X5,X1,tc_nat),tc_nat)
| ~ c_lessequals(X5,X21,tc_nat) ),
file('<stdin>',cls_diff__Suc__diff__eq2_0) ).
fof(c_0_243,axiom,
! [X2,X1,X5] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X5,tc_nat),c_HOL_Ominus__class_Ominus(X2,X5,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X5,X2,tc_nat)
| ~ c_lessequals(X5,X1,tc_nat) ),
file('<stdin>',cls_le__diff__iff_1) ).
fof(c_0_244,axiom,
! [X2,X1,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X5,tc_nat),c_HOL_Ominus__class_Ominus(X2,X5,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(X5,X2,tc_nat)
| ~ c_lessequals(X5,X1,tc_nat) ),
file('<stdin>',cls_less__diff__iff_1) ).
fof(c_0_245,axiom,
! [X17,X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_lessequals(X3,c_HOL_Oplus__class_Oplus(X10,X17,X4),X4)
| ~ c_lessequals(X11,X17,X4)
| ~ c_lessequals(X3,c_HOL_Oplus__class_Oplus(X10,X11,X4),X4) ),
file('<stdin>',cls_le__add__right__mono_0) ).
fof(c_0_246,axiom,
! [X2,X1,X5] :
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X5),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X5),X2,tc_nat),tc_nat) ),
file('<stdin>',cls_Suc__mult__le__cancel1_0) ).
fof(c_0_247,axiom,
! [X2,X1,X5] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X5),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X5),X2,tc_nat),tc_nat) ),
file('<stdin>',cls_Suc__mult__less__cancel1_0) ).
fof(c_0_248,axiom,
! [X9,X36,X17,X11] :
( c_HOL_Oplus__class_Oplus(X9,c_HOL_Otimes__class_Otimes(X36,X11,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X9,c_HOL_Otimes__class_Otimes(X36,X17,tc_nat),tc_nat)
| X11 = X17
| X36 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_natgb_Oadd__scale__eq__noteq_0) ).
fof(c_0_249,axiom,
! [X3,X6,X7,X4] : c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X3,X7,X4),c_Set_Oinsert(X3,X6,X4),tc_fun(X4,tc_bool)) = c_Set_Oinsert(X3,c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),X4),
file('<stdin>',cls_insert__inter__insert_0) ).
fof(c_0_250,axiom,
! [X10,X3,X26] :
( hBOOL(hAPP(X26,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X3,X10,tc_nat)
| ~ hBOOL(hAPP(X26,c_HOL_Ominus__class_Ominus(X3,X10,tc_nat))) ),
file('<stdin>',cls_nat__diff__split_0) ).
fof(c_0_251,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X10,X4)
| X11 = c_HOL_Ozero__class_Ozero(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X11,X4),X4) ),
file('<stdin>',cls_dvd__mult__cancel__right_0) ).
fof(c_0_252,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X10,X4)
| X11 = c_HOL_Ozero__class_Ozero(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4) ),
file('<stdin>',cls_dvd__mult__cancel__left_0) ).
fof(c_0_253,axiom,
! [X5,X21,X22] :
( c_lessequals(X22,c_HOL_Ominus__class_Ominus(X21,X5,tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X22,X5,tc_nat),X21,tc_nat)
| ~ c_lessequals(X5,X21,tc_nat) ),
file('<stdin>',cls_le__diff__conv2_1) ).
fof(c_0_254,axiom,
! [X5,X21,X22] :
( c_lessequals(c_HOL_Oplus__class_Oplus(X22,X5,tc_nat),X21,tc_nat)
| ~ c_lessequals(X22,c_HOL_Ominus__class_Ominus(X21,X5,tc_nat),tc_nat)
| ~ c_lessequals(X5,X21,tc_nat) ),
file('<stdin>',cls_le__diff__conv2_0) ).
fof(c_0_255,axiom,
! [X9,X6,X7,X4] :
( c_HOL_Oord__class_Oless(X7,c_Set_Oinsert(X9,X6,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| c_in(X9,X7,X4)
| ~ c_HOL_Oord__class_Oless(X7,X6,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_psubset__insert__iff_7) ).
fof(c_0_256,axiom,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| c_HOL_Oord__class_Oless(X3,X10,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X3,X4),c_HOL_Oplus__class_Oplus(X11,X10,X4),X4) ),
file('<stdin>',cls_add__less__cancel__left_0) ).
fof(c_0_257,axiom,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| c_HOL_Oord__class_Oless(X3,X10,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X11,X4),c_HOL_Oplus__class_Oplus(X10,X11,X4),X4) ),
file('<stdin>',cls_add__less__cancel__right_0) ).
fof(c_0_258,axiom,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| c_lessequals(X3,X10,X4)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X11,X4),c_HOL_Oplus__class_Oplus(X10,X11,X4),X4) ),
file('<stdin>',cls_add__le__cancel__right_0) ).
fof(c_0_259,axiom,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| c_lessequals(X3,X10,X4)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X11,X3,X4),c_HOL_Oplus__class_Oplus(X11,X10,X4),X4) ),
file('<stdin>',cls_add__le__cancel__left_0) ).
fof(c_0_260,axiom,
! [X2,X1,X5] :
( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X5,tc_nat),c_HOL_Ominus__class_Ominus(X2,X5,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)
| ~ c_lessequals(X5,X2,tc_nat)
| ~ c_lessequals(X5,X1,tc_nat) ),
file('<stdin>',cls_Nat_Odiff__diff__eq_0) ).
fof(c_0_261,axiom,
! [X9,X6,X7,X4] :
( c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| c_in(X9,X7,X4)
| c_in(X9,X6,X4)
| ~ c_HOL_Oord__class_Oless(X7,c_Set_Oinsert(X9,X6,X4),tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_psubset__insert__iff_2) ).
fof(c_0_262,axiom,
! [X3,X6,X7,X4] :
( c_Lattices_Olower__semilattice__class_Oinf(X7,c_Set_Oinsert(X3,X6,X4),tc_fun(X4,tc_bool)) = c_Set_Oinsert(X3,c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),X4)
| ~ c_in(X3,X7,X4) ),
file('<stdin>',cls_Int__insert__right_0) ).
fof(c_0_263,axiom,
! [X3,X16,X6,X4] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X3,X6,X4),X16,tc_fun(X4,tc_bool)) = c_Set_Oinsert(X3,c_Lattices_Olower__semilattice__class_Oinf(X6,X16,tc_fun(X4,tc_bool)),X4)
| ~ c_in(X3,X16,X4) ),
file('<stdin>',cls_Int__insert__left_0) ).
fof(c_0_264,axiom,
! [X16,X6,X7,X4] :
( c_HOL_Ominus__class_Ominus(X6,c_HOL_Ominus__class_Ominus(X16,X7,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = X7
| ~ c_lessequals(X6,X16,tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_double__diff_0) ).
fof(c_0_265,axiom,
! [X16,X6,X7,X4] :
( c_lessequals(X16,c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
| ~ c_lessequals(X16,X6,tc_fun(X4,tc_bool))
| ~ c_lessequals(X16,X7,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_Int__greatest_0) ).
fof(c_0_266,axiom,
! [X16,X6,X7,X4] :
( c_lessequals(X16,c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
| ~ c_lessequals(X16,X6,tc_fun(X4,tc_bool))
| ~ c_lessequals(X16,X7,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_Int__subset__iff_2) ).
fof(c_0_267,axiom,
! [X2,X1,X5] :
( c_Ring__and__Field_Odvd__class_Odvd(X5,X2,tc_nat)
| ~ c_lessequals(X2,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ),
file('<stdin>',cls_dvd__diffD1_0) ).
fof(c_0_268,axiom,
! [X2,X1,X5] :
( c_Ring__and__Field_Odvd__class_Odvd(X5,X1,tc_nat)
| ~ c_lessequals(X2,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ),
file('<stdin>',cls_dvd__diffD_0) ).
fof(c_0_269,axiom,
! [X2,X1,X5] :
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| X5 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,X1,tc_nat),c_HOL_Otimes__class_Otimes(X5,X2,tc_nat),tc_nat) ),
file('<stdin>',cls_nat__mult__dvd__cancel__disj_0) ).
fof(c_0_270,axiom,
! [X2,X1,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X1,tc_nat),c_HOL_Otimes__class_Otimes(X5,X2,tc_nat),tc_nat) ),
file('<stdin>',cls_mult__less__cancel1_0) ).
fof(c_0_271,axiom,
! [X2,X1,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X5,tc_nat),c_HOL_Otimes__class_Otimes(X2,X5,tc_nat),tc_nat) ),
file('<stdin>',cls_mult__less__cancel2_0) ).
fof(c_0_272,axiom,
! [X9,X4] :
( c_in(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4)
| c_Finite__Set_Ocard(c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) = c_Suc(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4)) ),
file('<stdin>',cls_card__Suc__eq_5) ).
fof(c_0_273,axiom,
! [X2,X1,X5] :
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X5,X1,tc_nat),c_HOL_Oplus__class_Oplus(X5,X2,tc_nat),tc_nat) ),
file('<stdin>',cls_nat__add__left__cancel__le_0) ).
fof(c_0_274,axiom,
! [X2,X1,X5] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X1,tc_nat),c_HOL_Oplus__class_Oplus(X5,X2,tc_nat),tc_nat) ),
file('<stdin>',cls_nat__add__left__cancel__less_0) ).
fof(c_0_275,axiom,
! [X2,X1,X5] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X5,tc_nat),c_HOL_Otimes__class_Otimes(X2,X5,tc_nat),tc_nat) ),
file('<stdin>',cls_mult__less__cancel2_1) ).
fof(c_0_276,axiom,
! [X2,X1,X5] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X1,tc_nat),c_HOL_Otimes__class_Otimes(X5,X2,tc_nat),tc_nat) ),
file('<stdin>',cls_mult__less__cancel1_1) ).
fof(c_0_277,axiom,
! [X16,X6,X7,X4] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),X16,tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X7,c_HOL_Ominus__class_Ominus(X6,X16,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
file('<stdin>',cls_Int__Diff_0) ).
fof(c_0_278,axiom,
! [X16,X6,X7,X4] : c_Lattices_Olower__semilattice__class_Oinf(X7,c_Lattices_Olower__semilattice__class_Oinf(X6,X16,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X16,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
file('<stdin>',cls_Int__left__commute_0) ).
fof(c_0_279,axiom,
! [X16,X6,X7,X4] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),X16,tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X7,c_Lattices_Olower__semilattice__class_Oinf(X6,X16,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
file('<stdin>',cls_Int__assoc_0) ).
fof(c_0_280,axiom,
! [X20,X7,X14,X4] :
( c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) != c_Set_Oimage(X20,X7,X14,X4)
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool)) ),
file('<stdin>',cls_empty__is__image_0) ).
fof(c_0_281,axiom,
! [X20,X7,X14,X4] :
( c_Set_Oimage(X20,X7,X14,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool)) ),
file('<stdin>',cls_image__is__empty_0) ).
fof(c_0_282,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Omult__mono1(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_lessequals(X3,X10,X4) ),
file('<stdin>',cls_mult__mono1_0) ).
fof(c_0_283,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Omult__mono(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_lessequals(X3,X10,X4) ),
file('<stdin>',cls_mult__left__mono_0) ).
fof(c_0_284,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Omult__mono(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X11,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_lessequals(X3,X10,X4) ),
file('<stdin>',cls_mult__right__mono_0) ).
fof(c_0_285,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X10,X3,X4) ),
file('<stdin>',cls_mult__left__mono__neg_0) ).
fof(c_0_286,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X11,X4),X4)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X10,X3,X4) ),
file('<stdin>',cls_mult__right__mono__neg_0) ).
fof(c_0_287,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_HOL_Oord__class_Oless(X3,X10,X4) ),
file('<stdin>',cls_mult__strict__left__mono__comm_0) ).
fof(c_0_288,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X11,X4),X4)
| ~ c_HOL_Oord__class_Oless(X10,X3,X4)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_mult__less__cancel__right__disj_5) ).
fof(c_0_289,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X11,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,X10,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X11,X4) ),
file('<stdin>',cls_mult__less__cancel__right__disj_4) ).
fof(c_0_290,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X11,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_HOL_Oord__class_Oless(X3,X10,X4) ),
file('<stdin>',cls_mult__strict__right__mono_0) ).
fof(c_0_291,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X11,X4),X4)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X10,X3,X4) ),
file('<stdin>',cls_mult__strict__right__mono__neg_0) ).
fof(c_0_292,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4)
| ~ c_HOL_Oord__class_Oless(X10,X3,X4)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_mult__less__cancel__left__disj_5) ).
fof(c_0_293,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,X10,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X11,X4) ),
file('<stdin>',cls_mult__less__cancel__left__disj_4) ).
fof(c_0_294,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_HOL_Oord__class_Oless(X3,X10,X4) ),
file('<stdin>',cls_mult__strict__left__mono_0) ).
fof(c_0_295,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X10,X3,X4) ),
file('<stdin>',cls_mult__strict__left__mono__neg_0) ).
fof(c_0_296,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,X10,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X11,X4) ),
file('<stdin>',cls_mult__less__cancel__left__pos_1) ).
fof(c_0_297,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4)
| ~ c_HOL_Oord__class_Oless(X10,X3,X4)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_mult__less__cancel__left__neg_1) ).
fof(c_0_298,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4)
| ~ c_lessequals(X3,X10,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X11,X4) ),
file('<stdin>',cls_mult__le__cancel__left__pos_1) ).
fof(c_0_299,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4)
| ~ c_lessequals(X10,X3,X4)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_mult__le__cancel__left__neg_1) ).
fof(c_0_300,axiom,
! [X8,X9,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X9,X4),X9,X4)
| ~ c_lessequals(X8,c_HOL_Oone__class_Oone(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X9,X4) ),
file('<stdin>',cls_mult__left__le__one__le_0) ).
fof(c_0_301,axiom,
! [X8,X9,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X9,X8,X4),X9,X4)
| ~ c_lessequals(X8,c_HOL_Oone__class_Oone(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X9,X4) ),
file('<stdin>',cls_mult__right__le__one__le_0) ).
fof(c_0_302,axiom,
! [X9,X6,X7,X4] :
( c_HOL_Oord__class_Oless(X7,X6,tc_fun(X4,tc_bool))
| ~ c_in(X9,X6,X4)
| ~ c_HOL_Oord__class_Oless(X7,c_Set_Oinsert(X9,X6,X4),tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_psubset__insert__iff_0) ).
fof(c_0_303,axiom,
! [X9,X7,X4] :
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X9,X7,X4),c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)) = X7
| c_in(X9,X7,X4) ),
file('<stdin>',cls_Diff__insert__absorb_0) ).
fof(c_0_304,axiom,
! [X2,X1,X5] :
( c_lessequals(X1,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),X5,tc_nat),tc_nat)
| ~ c_lessequals(X5,X2,tc_nat) ),
file('<stdin>',cls_le__add__diff_0) ).
fof(c_0_305,axiom,
! [X17,X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(X3,X11,X4),c_HOL_Oplus__class_Oplus(X10,X17,X4),X4)
| ~ c_lessequals(X11,X17,X4)
| ~ c_lessequals(X3,X10,X4) ),
file('<stdin>',cls_add__mono_0) ).
fof(c_0_306,axiom,
! [X17,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X17,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X17,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X10,X4) ),
file('<stdin>',cls_mult__dvd__mono_0) ).
fof(c_0_307,axiom,
! [X17,X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X11,X4),c_HOL_Oplus__class_Oplus(X10,X17,X4),X4)
| ~ c_HOL_Oord__class_Oless(X11,X17,X4)
| ~ c_HOL_Oord__class_Oless(X3,X10,X4) ),
file('<stdin>',cls_add__strict__mono_0) ).
fof(c_0_308,axiom,
! [X17,X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X11,X4),c_HOL_Oplus__class_Oplus(X10,X17,X4),X4)
| ~ c_lessequals(X11,X17,X4)
| ~ c_HOL_Oord__class_Oless(X3,X10,X4) ),
file('<stdin>',cls_add__less__le__mono_0) ).
fof(c_0_309,axiom,
! [X17,X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X11,X4),c_HOL_Oplus__class_Oplus(X10,X17,X4),X4)
| ~ c_HOL_Oord__class_Oless(X11,X17,X4)
| ~ c_lessequals(X3,X10,X4) ),
file('<stdin>',cls_add__le__less__mono_0) ).
fof(c_0_310,axiom,
! [X9,X6,X7,X4] :
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X9,X7,X4),X6,tc_fun(X4,tc_bool)) = c_Set_Oinsert(X9,c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),X4)
| c_in(X9,X6,X4) ),
file('<stdin>',cls_insert__Diff__if_1) ).
fof(c_0_311,axiom,
! [X8,X9,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X9,X4),c_HOL_Otimes__class_Otimes(X8,X8,X4),X4) != c_HOL_Ozero__class_Ozero(X4)
| X9 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_sum__squares__eq__zero__iff_0) ).
fof(c_0_312,axiom,
! [X8,X9,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X9,X4),c_HOL_Otimes__class_Otimes(X8,X8,X4),X4) != c_HOL_Ozero__class_Ozero(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_sum__squares__eq__zero__iff_1) ).
fof(c_0_313,axiom,
! [X16,X6,X7,X4] :
( c_lessequals(X16,X7,tc_fun(X4,tc_bool))
| ~ c_lessequals(X16,c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_Int__subset__iff_0) ).
fof(c_0_314,axiom,
! [X16,X6,X7,X4] :
( c_lessequals(X16,X6,tc_fun(X4,tc_bool))
| ~ c_lessequals(X16,c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_Int__subset__iff_1) ).
fof(c_0_315,axiom,
! [X15,X8,X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(X9,c_HOL_Oplus__class_Oplus(X8,X15,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X8,X4),c_HOL_Otimes__class_Otimes(X9,X15,X4),X4) ),
file('<stdin>',cls_class__semiring_Omul__d_0) ).
fof(c_0_316,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,X10,X4),X11,X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X11,X4),X4) ),
file('<stdin>',cls_comm__semiring__class_Odistrib_0) ).
fof(c_0_317,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,X10,X4),X11,X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X11,X4),X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I8_J_0) ).
fof(c_0_318,axiom,
! [X11,X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4) = c_HOL_Otimes__class_Otimes(X11,c_Divides_Odiv__class_Omod(X3,X10,X4),X4) ),
file('<stdin>',cls_mod__mult__mult1_0) ).
fof(c_0_319,axiom,
! [X11,X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X11,X4),X4) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X3,X10,X4),X11,X4) ),
file('<stdin>',cls_mod__mult__mult2_0) ).
fof(c_0_320,axiom,
! [X1,X10,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X1,X4),c_HOL_Otimes__class_Otimes(X10,X1,X4),X4) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,X10,X4),X1,X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I1_J_0) ).
fof(c_0_321,axiom,
! [X11,X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X10,X11,X4),X4),X10,X4) = c_Divides_Odiv__class_Omod(X3,X10,X4) ),
file('<stdin>',cls_mod__mult__self2_0) ).
fof(c_0_322,axiom,
! [X11,X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X11,X10,X4),X4),X10,X4) = c_Divides_Odiv__class_Omod(X3,X10,X4) ),
file('<stdin>',cls_mod__mult__self1_0) ).
fof(c_0_323,axiom,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X3,X10,X4),X11,X4) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X3,X11,X4),c_HOL_Oplus__class_Oplus(X10,X11,X4),X4) ),
file('<stdin>',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0) ).
fof(c_0_324,axiom,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_HOL_Oplus__class_Oplus(X3,c_Lattices_Olower__semilattice__class_Oinf(X10,X11,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X3,X10,X4),c_HOL_Oplus__class_Oplus(X3,X11,X4),X4) ),
file('<stdin>',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0) ).
fof(c_0_325,axiom,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(X4)
| c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X3,X10,X4),X11,X4) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X3,X11,X4),c_HOL_Oplus__class_Oplus(X10,X11,X4),X4) ),
file('<stdin>',cls_add__inf__distrib__right_0) ).
fof(c_0_326,axiom,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(X4)
| c_HOL_Oplus__class_Oplus(X3,c_Lattices_Olower__semilattice__class_Oinf(X10,X11,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X3,X10,X4),c_HOL_Oplus__class_Oplus(X3,X11,X4),X4) ),
file('<stdin>',cls_add__inf__distrib__left_0) ).
fof(c_0_327,axiom,
! [X2,X1,X5] :
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,X1,tc_nat),c_HOL_Otimes__class_Otimes(X5,X2,tc_nat),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
file('<stdin>',cls_nat__mult__dvd__cancel1_1) ).
fof(c_0_328,axiom,
! [X2,X1,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X1,tc_nat),c_HOL_Otimes__class_Otimes(X5,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),X5,tc_nat) ),
file('<stdin>',cls_nat__mult__less__cancel1_1) ).
fof(c_0_329,axiom,
! [X5,X21,X22] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X22,X5,tc_nat),c_HOL_Otimes__class_Otimes(X21,X5,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(X22,X21,tc_nat) ),
file('<stdin>',cls_mult__less__mono1_0) ).
fof(c_0_330,axiom,
! [X5,X21,X22] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X22,tc_nat),c_HOL_Otimes__class_Otimes(X5,X21,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(X22,X21,tc_nat) ),
file('<stdin>',cls_mult__less__mono2_0) ).
fof(c_0_331,axiom,
! [X2,X1,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X1,tc_nat),c_HOL_Otimes__class_Otimes(X5,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),X5,tc_nat) ),
file('<stdin>',cls_mult__less__cancel1_2) ).
fof(c_0_332,axiom,
! [X2,X1,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X5,tc_nat),c_HOL_Otimes__class_Otimes(X2,X5,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),X5,tc_nat) ),
file('<stdin>',cls_mult__less__cancel2_2) ).
fof(c_0_333,axiom,
! [X2,X1,X5] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X5,X1,tc_nat),c_HOL_Otimes__class_Otimes(X5,X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
file('<stdin>',cls_nat__mult__le__cancel1_1) ).
fof(c_0_334,axiom,
! [X2,X1] :
( c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_mult__eq__if_1) ).
fof(c_0_335,axiom,
! [X9,X6,X7,X4] :
( hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),X9))
| ~ hBOOL(hAPP(X6,X9))
| ~ hBOOL(hAPP(X7,X9)) ),
file('<stdin>',cls_inf1I_0) ).
fof(c_0_336,axiom,
! [X11,X10,X3] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X11,tc_nat),c_HOL_Ominus__class_Ominus(X10,X11,tc_nat),tc_nat)
| ~ c_lessequals(X11,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X10,tc_nat) ),
file('<stdin>',cls_diff__less__mono_0) ).
fof(c_0_337,axiom,
! [X2,X1,X24] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X24,X2,tc_nat),c_HOL_Ominus__class_Ominus(X24,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X24,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('<stdin>',cls_diff__less__mono2_0) ).
fof(c_0_338,axiom,
! [X24,X5,X21,X22] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X22,X5,tc_nat),c_HOL_Otimes__class_Otimes(X21,X24,tc_nat),tc_nat)
| ~ c_lessequals(X5,X24,tc_nat)
| ~ c_lessequals(X22,X21,tc_nat) ),
file('<stdin>',cls_mult__le__mono_0) ).
fof(c_0_339,axiom,
! [X24,X5,X21,X22] :
( c_lessequals(c_HOL_Oplus__class_Oplus(X22,X5,tc_nat),c_HOL_Oplus__class_Oplus(X21,X24,tc_nat),tc_nat)
| ~ c_lessequals(X5,X24,tc_nat)
| ~ c_lessequals(X22,X21,tc_nat) ),
file('<stdin>',cls_add__le__mono_0) ).
fof(c_0_340,axiom,
! [X24,X5,X21,X22] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X22,X5,tc_nat),c_HOL_Oplus__class_Oplus(X21,X24,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X24,tc_nat)
| ~ c_HOL_Oord__class_Oless(X22,X21,tc_nat) ),
file('<stdin>',cls_add__less__mono_0) ).
fof(c_0_341,axiom,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X10,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X3,X10,X4),X4) ),
file('<stdin>',cls_zero__less__mult__pos_0) ).
fof(c_0_342,axiom,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X10,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X10,X3,X4),X4) ),
file('<stdin>',cls_zero__less__mult__pos2_0) ).
fof(c_0_343,axiom,
! [X2,X26] :
( ~ hBOOL(hAPP(X26,c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
| hBOOL(hAPP(X26,X2)) ),
file('<stdin>',cls_split__mod_0) ).
fof(c_0_344,axiom,
! [X9,X6,X7,X4] :
( c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,c_Set_Oinsert(X9,X6,X4),tc_fun(X4,tc_bool))
| c_in(X9,X7,X4) ),
file('<stdin>',cls_subset__insert_0) ).
fof(c_0_345,axiom,
! [X9,X6,X7,X4] :
( c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| c_in(X9,X7,X4)
| ~ c_lessequals(X7,c_Set_Oinsert(X9,X6,X4),tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_subset__insert__iff_1) ).
fof(c_0_346,axiom,
! [X10,X3,X4] :
( X10 = X3
| ~ c_in(X10,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
file('<stdin>',cls_singletonE_0) ).
fof(c_0_347,axiom,
! [X2,X1,X5] : c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X5,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X5,tc_nat),c_HOL_Otimes__class_Otimes(X2,X5,tc_nat),tc_nat),
file('<stdin>',cls_diff__mult__distrib_0) ).
fof(c_0_348,axiom,
! [X2,X1,X5] : c_HOL_Otimes__class_Otimes(X5,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X5,X1,tc_nat),c_HOL_Otimes__class_Otimes(X5,X2,tc_nat),tc_nat),
file('<stdin>',cls_diff__mult__distrib2_0) ).
fof(c_0_349,axiom,
! [X2,X1,X5] : c_HOL_Otimes__class_Otimes(X5,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X1,tc_nat),c_HOL_Otimes__class_Otimes(X5,X2,tc_nat),tc_nat),
file('<stdin>',cls_add__mult__distrib2_0) ).
fof(c_0_350,axiom,
! [X2,X1,X5] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X5,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X5,tc_nat),c_HOL_Otimes__class_Otimes(X2,X5,tc_nat),tc_nat),
file('<stdin>',cls_add__mult__distrib_0) ).
fof(c_0_351,axiom,
! [X2,X1,X5] : c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,tc_nat),X1,tc_nat),X2,tc_nat) = c_Divides_Odiv__class_Omod(X1,X2,tc_nat),
file('<stdin>',cls_mod__mult__self3_0) ).
fof(c_0_352,axiom,
! [X2,X1,X5] : c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X5,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X5,tc_nat),c_HOL_Otimes__class_Otimes(X2,X5,tc_nat),tc_nat),
file('<stdin>',cls_mod__mult__distrib_0) ).
fof(c_0_353,axiom,
! [X2,X1,X5] : c_HOL_Otimes__class_Otimes(X5,c_Divides_Odiv__class_Omod(X1,X2,tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X1,tc_nat),c_HOL_Otimes__class_Otimes(X5,X2,tc_nat),tc_nat),
file('<stdin>',cls_mod__mult__distrib2_0) ).
fof(c_0_354,axiom,
! [X9,X6,X7,X4] :
( c_HOL_Oord__class_Oless(X7,c_Set_Oinsert(X9,X6,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| c_in(X9,X7,X4)
| c_in(X9,X6,X4) ),
file('<stdin>',cls_psubset__insert__iff_3) ).
fof(c_0_355,axiom,
! [X6,X7,X4] :
( c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),X4) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(X7,X4),c_Finite__Set_Ocard(X6,X4),tc_nat)
| ~ c_lessequals(X6,X7,tc_fun(X4,tc_bool))
| ~ c_Finite__Set_Ofinite(X6,X4) ),
file('<stdin>',cls_card__Diff__subset_0) ).
fof(c_0_356,axiom,
! [X8,X9,X7,X4] :
( hBOOL(hAPP(X7,X9))
| X8 = X9
| ~ hBOOL(hAPP(c_Set_Oinsert(X8,X7,X4),X9)) ),
file('<stdin>',cls_insert__code_0) ).
fof(c_0_357,axiom,
! [X3,X44,X16,X4] :
( c_lessequals(c_Set_Oinsert(X3,X16,X4),c_Set_Oinsert(X3,X44,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X16,X44,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_insert__mono_0) ).
fof(c_0_358,axiom,
! [X11,X6,X7,X4] :
( ~ c_in(X11,X6,X4)
| ~ c_in(X11,c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),X4) ),
file('<stdin>',cls_DiffE_1) ).
fof(c_0_359,axiom,
! [X5,X22] :
( ~ c_lessequals(X22,c_HOL_Oplus__class_Oplus(X5,X22,tc_nat),tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X5,X22,tc_nat),X22,tc_nat) = X5 ),
file('<stdin>',cls_le__imp__diff__is__add_1) ).
fof(c_0_360,axiom,
! [X5,X21,X22] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X21,X5,tc_nat),X22,tc_nat)
| ~ c_lessequals(X21,c_HOL_Oplus__class_Oplus(X22,X5,tc_nat),tc_nat) ),
file('<stdin>',cls_le__diff__conv_1) ).
fof(c_0_361,axiom,
! [X5,X21,X22] :
( c_lessequals(X21,c_HOL_Oplus__class_Oplus(X22,X5,tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X21,X5,tc_nat),X22,tc_nat) ),
file('<stdin>',cls_le__diff__conv_0) ).
fof(c_0_362,axiom,
! [X5,X21,X22] :
( c_HOL_Oord__class_Oless(X22,c_HOL_Ominus__class_Ominus(X21,X5,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X22,X5,tc_nat),X21,tc_nat) ),
file('<stdin>',cls_less__diff__conv_1) ).
fof(c_0_363,axiom,
! [X5,X21,X22] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X22,X5,tc_nat),X21,tc_nat)
| ~ c_HOL_Oord__class_Oless(X22,c_HOL_Ominus__class_Ominus(X21,X5,tc_nat),tc_nat) ),
file('<stdin>',cls_less__diff__conv_0) ).
fof(c_0_364,axiom,
! [X2,X1,X5,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X5,X1,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,c_Divides_Odiv__class_Omod(X1,X2,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X2,X4) ),
file('<stdin>',cls_dvd__mod__iff_0) ).
fof(c_0_365,axiom,
! [X2,X1,X5,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X5,X1,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X2,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,c_Divides_Odiv__class_Omod(X1,X2,X4),X4) ),
file('<stdin>',cls_dvd__mod__imp__dvd_0) ).
fof(c_0_366,axiom,
! [X15,X8,X9,X18,X4] :
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_HOL_Oplus__class_Oplus(X9,c_HOL_Oplus__class_Oplus(X8,X15,X4),X4) != c_HOL_Oplus__class_Oplus(X8,X18,X4)
| c_HOL_Oplus__class_Oplus(X9,X15,X4) = X18 ),
file('<stdin>',cls_add__cancel__21_0) ).
fof(c_0_367,axiom,
! [X5,X21,X22] :
( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X21,X5,tc_nat),X22,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X21,X22,tc_nat),X5,tc_nat)
| ~ c_lessequals(X5,X21,tc_nat) ),
file('<stdin>',cls_add__diff__assoc2_0) ).
fof(c_0_368,axiom,
! [X5,X21,X22] :
( c_HOL_Oplus__class_Oplus(X22,c_HOL_Ominus__class_Ominus(X21,X5,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X22,X21,tc_nat),X5,tc_nat)
| ~ c_lessequals(X5,X21,tc_nat) ),
file('<stdin>',cls_add__diff__assoc_0) ).
fof(c_0_369,axiom,
! [X5,X21,X22] :
( c_HOL_Ominus__class_Ominus(X22,c_HOL_Ominus__class_Ominus(X21,X5,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X22,X5,tc_nat),X21,tc_nat)
| ~ c_lessequals(X5,X21,tc_nat) ),
file('<stdin>',cls_diff__diff__right_0) ).
fof(c_0_370,axiom,
! [X5,X21,X22] :
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X21,X22,tc_nat),X5,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X21,X5,tc_nat),X22,tc_nat)
| ~ c_lessequals(X5,X21,tc_nat) ),
file('<stdin>',cls_diff__add__assoc2_0) ).
fof(c_0_371,axiom,
! [X5,X21,X22] :
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X22,X21,tc_nat),X5,tc_nat) = c_HOL_Oplus__class_Oplus(X22,c_HOL_Ominus__class_Ominus(X21,X5,tc_nat),tc_nat)
| ~ c_lessequals(X5,X21,tc_nat) ),
file('<stdin>',cls_diff__add__assoc_0) ).
fof(c_0_372,axiom,
! [X9,X6,X7,X4] :
( c_lessequals(c_Set_Oinsert(X9,X7,X4),X6,tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| ~ c_in(X9,X6,X4) ),
file('<stdin>',cls_insert__subset_2) ).
fof(c_0_373,axiom,
! [X9,X6,X7,X4] :
( c_HOL_Oord__class_Oless(X7,c_Set_Oinsert(X9,X6,X4),tc_fun(X4,tc_bool))
| ~ c_in(X9,X6,X4)
| ~ c_HOL_Oord__class_Oless(X7,X6,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_psubset__insert__iff_6) ).
fof(c_0_374,axiom,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X10,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_mult__le__0__iff_0) ).
fof(c_0_375,axiom,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X10,X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X10,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_mult__le__0__iff_1) ).
fof(c_0_376,axiom,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(X10,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X10,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_mult__le__0__iff_2) ).
fof(c_0_377,axiom,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X10,X4)
| c_lessequals(X10,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X10,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_mult__le__0__iff_3) ).
fof(c_0_378,axiom,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(X10,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X10,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X3,X10,X4),X4) ),
file('<stdin>',cls_zero__le__mult__iff_3) ).
fof(c_0_379,axiom,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X10,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X3,X10,X4),X4) ),
file('<stdin>',cls_zero__le__mult__iff_2) ).
fof(c_0_380,axiom,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(X10,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X3,X10,X4),X4) ),
file('<stdin>',cls_zero__le__mult__iff_1) ).
fof(c_0_381,axiom,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X3,X10,X4),X4) ),
file('<stdin>',cls_zero__le__mult__iff_0) ).
fof(c_0_382,axiom,
! [X6,X7,X4] :
( c_HOL_Oord__class_Oless(X7,X6,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(X7,X4),c_Finite__Set_Ocard(X6,X4),tc_nat)
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| ~ c_Finite__Set_Ofinite(X6,X4) ),
file('<stdin>',cls_card__psubset_0) ).
fof(c_0_383,axiom,
! [X2,X1] :
( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_add__eq__if_1) ).
fof(c_0_384,axiom,
! [X11,X6,X7,X4] :
( c_in(X11,X7,X4)
| ~ c_in(X11,c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),X4) ),
file('<stdin>',cls_IntE_0) ).
fof(c_0_385,axiom,
! [X11,X6,X7,X4] :
( c_in(X11,X6,X4)
| ~ c_in(X11,c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),X4) ),
file('<stdin>',cls_IntE_1) ).
fof(c_0_386,axiom,
! [X11,X6,X7,X4] :
( c_in(X11,X7,X4)
| ~ c_in(X11,c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),X4) ),
file('<stdin>',cls_DiffE_0) ).
fof(c_0_387,axiom,
! [X11,X6,X7,X4] :
( c_in(X11,c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),X4)
| ~ c_in(X11,X6,X4)
| ~ c_in(X11,X7,X4) ),
file('<stdin>',cls_IntI_0) ).
fof(c_0_388,axiom,
! [X11,X6,X7,X4] :
( c_in(X11,c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),X4)
| ~ c_in(X11,X6,X4)
| ~ c_in(X11,X7,X4) ),
file('<stdin>',cls_Int__iff_2) ).
fof(c_0_389,axiom,
! [X20,X3,X25,X4] :
( c_in(X3,c_Inductive_Ocomplete__lattice__class_Ogfp(X20,tc_fun(X4,tc_bool)),X4)
| ~ c_lessequals(X25,hAPP(X20,X25),tc_fun(X4,tc_bool))
| ~ c_in(X3,X25,X4) ),
file('<stdin>',cls_weak__coinduct_0) ).
fof(c_0_390,axiom,
! [X2,X1] :
( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat) ),
file('<stdin>',cls_one__le__mult__iff_2) ).
fof(c_0_391,axiom,
! [X2,X1] :
( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),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) ),
file('<stdin>',cls_one__less__mult_0) ).
fof(c_0_392,axiom,
! [X2,X1,X5] :
( c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X5),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X5),X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
file('<stdin>',cls_Suc__mult__le__cancel1_1) ).
fof(c_0_393,axiom,
! [X2,X1,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X5),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X5),X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('<stdin>',cls_Suc__mult__less__cancel1_1) ).
fof(c_0_394,axiom,
! [X9,X6,X7,X4] :
( c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X9,X7,X4),X6,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_insert__subset_1) ).
fof(c_0_395,axiom,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X3,X10,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X10,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
file('<stdin>',cls_split__mult__pos__le_0) ).
fof(c_0_396,axiom,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X3,X10,X4),X4)
| ~ c_lessequals(X10,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_split__mult__pos__le_1) ).
fof(c_0_397,axiom,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X3,X10,X4),X4)
| ~ c_lessequals(X10,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_mult__nonpos__nonpos_0) ).
fof(c_0_398,axiom,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X3,X10,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X10,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
file('<stdin>',cls_zero__le__mult__iff_4) ).
fof(c_0_399,axiom,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X3,X10,X4),X4)
| ~ c_lessequals(X10,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_zero__le__mult__iff_5) ).
fof(c_0_400,axiom,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X3,X10,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X10,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
file('<stdin>',cls_mult__nonneg__nonneg_0) ).
fof(c_0_401,axiom,
! [X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(X3,X10,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X10,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_add__nonpos__nonpos_0) ).
fof(c_0_402,axiom,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X10,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X10,X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_mult__neg__pos_0) ).
fof(c_0_403,axiom,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X10,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
file('<stdin>',cls_mult__pos__neg_0) ).
fof(c_0_404,axiom,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
file('<stdin>',cls_mult__pos__neg2_0) ).
fof(c_0_405,axiom,
! [X2,X1,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),c_HOL_Otimes__class_Otimes(X1,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),X1,X4) ),
file('<stdin>',cls_less__1__mult_0) ).
fof(c_0_406,axiom,
! [X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(X3,X10,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X10,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
file('<stdin>',cls_add__pos__pos_0) ).
fof(c_0_407,axiom,
! [X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X10,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X10,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_add__neg__nonpos_0) ).
fof(c_0_408,axiom,
! [X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X10,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_add__nonpos__neg_0) ).
fof(c_0_409,axiom,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X3,X10,X4),X4)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_mult__neg__neg_0) ).
fof(c_0_410,axiom,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X3,X10,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X10,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
file('<stdin>',cls_mult__pos__pos_0) ).
fof(c_0_411,axiom,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X10,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X10,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
file('<stdin>',cls_mult__nonneg__nonpos2_0) ).
fof(c_0_412,axiom,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X10,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X10,X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_mult__nonpos__nonneg_0) ).
fof(c_0_413,axiom,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X10,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X10,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
file('<stdin>',cls_mult__nonneg__nonpos_0) ).
fof(c_0_414,axiom,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X10,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X10,X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_split__mult__neg__le_1) ).
fof(c_0_415,axiom,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X10,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X10,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
file('<stdin>',cls_split__mult__neg__le_0) ).
fof(c_0_416,axiom,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X10,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X10,X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_mult__le__0__iff_5) ).
fof(c_0_417,axiom,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X10,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X10,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
file('<stdin>',cls_mult__le__0__iff_4) ).
fof(c_0_418,axiom,
! [X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(X3,X10,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X10,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
file('<stdin>',cls_add__pos__nonneg_0) ).
fof(c_0_419,axiom,
! [X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(X3,X10,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X10,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
file('<stdin>',cls_add__nonneg__pos_0) ).
fof(c_0_420,axiom,
! [X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X10,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_add__neg__neg_0) ).
fof(c_0_421,axiom,
! [X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(X3,X10,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X10,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
file('<stdin>',cls_add__nonneg__nonneg_0) ).
fof(c_0_422,axiom,
! [X1] : c_lessequals(X1,c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X1,X1,tc_nat),tc_nat),tc_nat),
file('<stdin>',cls_le__cube_0) ).
fof(c_0_423,axiom,
! [X2,X1] :
( 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_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
file('<stdin>',cls_add__gr__0_0) ).
fof(c_0_424,axiom,
! [X2,X1] :
( c_HOL_Oord__class_Oless(X2,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) ),
file('<stdin>',cls_n__less__n__mult__m_0) ).
fof(c_0_425,axiom,
! [X2,X1] :
( c_HOL_Oord__class_Oless(X2,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) ),
file('<stdin>',cls_n__less__m__mult__n_0) ).
fof(c_0_426,axiom,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X3,X4),c_HOL_Oplus__class_Oplus(X11,X10,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,X10,X4) ),
file('<stdin>',cls_add__less__cancel__left_1) ).
fof(c_0_427,axiom,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X3,X4),c_HOL_Oplus__class_Oplus(X11,X10,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,X10,X4) ),
file('<stdin>',cls_add__strict__left__mono_0) ).
fof(c_0_428,axiom,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X11,X4),c_HOL_Oplus__class_Oplus(X10,X11,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,X10,X4) ),
file('<stdin>',cls_add__less__cancel__right_1) ).
fof(c_0_429,axiom,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X11,X4),c_HOL_Oplus__class_Oplus(X10,X11,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,X10,X4) ),
file('<stdin>',cls_add__strict__right__mono_0) ).
fof(c_0_430,axiom,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(X3,X11,X4),c_HOL_Oplus__class_Oplus(X10,X11,X4),X4)
| ~ c_lessequals(X3,X10,X4) ),
file('<stdin>',cls_add__le__cancel__right_1) ).
fof(c_0_431,axiom,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(X11,X3,X4),c_HOL_Oplus__class_Oplus(X11,X10,X4),X4)
| ~ c_lessequals(X3,X10,X4) ),
file('<stdin>',cls_add__le__cancel__left_1) ).
fof(c_0_432,axiom,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(X3,X11,X4),c_HOL_Oplus__class_Oplus(X10,X11,X4),X4)
| ~ c_lessequals(X3,X10,X4) ),
file('<stdin>',cls_add__right__mono_0) ).
fof(c_0_433,axiom,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(X11,X3,X4),c_HOL_Oplus__class_Oplus(X11,X10,X4),X4)
| ~ c_lessequals(X3,X10,X4) ),
file('<stdin>',cls_add__left__mono_0) ).
fof(c_0_434,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X10,X4) ),
file('<stdin>',cls_dvd__mult__cancel__left_2) ).
fof(c_0_435,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X11,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X10,X4) ),
file('<stdin>',cls_dvd__mult__cancel__right_2) ).
fof(c_0_436,axiom,
! [X9,X6,X7,X4] :
( c_lessequals(X7,c_Set_Oinsert(X9,X6,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| c_in(X9,X7,X4) ),
file('<stdin>',cls_subset__insert_1) ).
fof(c_0_437,axiom,
! [X9,X6,X7,X4] :
( c_lessequals(X7,c_Set_Oinsert(X9,X6,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| c_in(X9,X7,X4) ),
file('<stdin>',cls_subset__insert__iff_2) ).
fof(c_0_438,axiom,
! [X15,X8,X9] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X9,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X15,X8,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X15,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X8,X9,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X8,tc_nat) ),
file('<stdin>',cls_dvd_Oless__trans_1) ).
fof(c_0_439,axiom,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_lessequals(X10,c_HOL_Oplus__class_Oplus(X3,X11,X4),X4)
| ~ c_lessequals(X10,X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X11,X4) ),
file('<stdin>',cls_add__increasing2_0) ).
fof(c_0_440,axiom,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_lessequals(X10,c_HOL_Oplus__class_Oplus(X3,X11,X4),X4)
| ~ c_lessequals(X10,X11,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
file('<stdin>',cls_add__increasing_0) ).
fof(c_0_441,axiom,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_HOL_Oord__class_Oless(X10,c_HOL_Oplus__class_Oplus(X3,X11,X4),X4)
| ~ c_lessequals(X10,X11,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
file('<stdin>',cls_add__strict__increasing_0) ).
fof(c_0_442,axiom,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_HOL_Oord__class_Oless(X10,c_HOL_Oplus__class_Oplus(X3,X11,X4),X4)
| ~ c_HOL_Oord__class_Oless(X10,X11,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
file('<stdin>',cls_add__strict__increasing2_0) ).
fof(c_0_443,axiom,
! [X1,X5] :
( c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Otimes__class_Otimes(X5,X1,tc_nat)),X5,tc_nat) = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X5,tc_nat) ),
file('<stdin>',cls_Suc__times__mod__eq_0) ).
fof(c_0_444,axiom,
! [X2,X48,X26] :
( hBOOL(hAPP(X26,X48))
| ~ hBOOL(hAPP(X26,c_Suc(c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1(X26,X2))))
| ~ c_lessequals(c_Suc(X2),X48,tc_nat) ),
file('<stdin>',cls_Suc__le__D__lemma_1) ).
fof(c_0_445,axiom,
! [X5,X22,X26] :
( hBOOL(hAPP(X26,c_HOL_Ominus__class_Ominus(X5,X22,tc_nat)))
| hBOOL(hAPP(X26,c_Suc(c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1(X26))))
| ~ hBOOL(hAPP(X26,X5)) ),
file('<stdin>',cls_zero__induct__lemma_0) ).
fof(c_0_446,axiom,
! [X5,X22,X26] :
( hBOOL(hAPP(X26,c_HOL_Ominus__class_Ominus(X5,X22,tc_nat)))
| ~ hBOOL(hAPP(X26,c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1(X26)))
| ~ hBOOL(hAPP(X26,X5)) ),
file('<stdin>',cls_zero__induct__lemma_1) ).
fof(c_0_447,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(X10,c_HOL_Oplus__class_Oplus(X3,X11,X4),X4)
| ~ c_HOL_Oord__class_Oless(X10,X11,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
file('<stdin>',cls_pos__add__strict_0) ).
fof(c_0_448,axiom,
! [X11,X6,X7,X4] :
( c_in(X11,c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),X4)
| c_in(X11,X6,X4)
| ~ c_in(X11,X7,X4) ),
file('<stdin>',cls_DiffI_0) ).
fof(c_0_449,axiom,
! [X11,X6,X7,X4] :
( c_in(X11,c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),X4)
| c_in(X11,X6,X4)
| ~ c_in(X11,X7,X4) ),
file('<stdin>',cls_Diff__iff_2) ).
fof(c_0_450,axiom,
! [X9,X6,X7,X4] :
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X9,X7,X4),X6,tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool))
| ~ c_in(X9,X6,X4) ),
file('<stdin>',cls_insert__Diff1_0) ).
fof(c_0_451,axiom,
! [X9,X6,X7,X4] :
( c_in(X9,X6,X4)
| ~ c_lessequals(c_Set_Oinsert(X9,X7,X4),X6,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_insert__subset_0) ).
fof(c_0_452,axiom,
! [X2,X1,X24] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X24,tc_nat),c_HOL_Ominus__class_Ominus(X2,X24,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
file('<stdin>',cls_diff__le__mono_0) ).
fof(c_0_453,axiom,
! [X2,X1,X24] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X24,X2,tc_nat),c_HOL_Ominus__class_Ominus(X24,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
file('<stdin>',cls_diff__le__mono2_0) ).
fof(c_0_454,axiom,
! [X5,X21,X22] :
( c_lessequals(c_HOL_Oplus__class_Oplus(X22,X5,tc_nat),c_HOL_Oplus__class_Oplus(X21,X5,tc_nat),tc_nat)
| ~ c_lessequals(X22,X21,tc_nat) ),
file('<stdin>',cls_add__le__mono1_0) ).
fof(c_0_455,axiom,
! [X2,X1,X5] :
( c_lessequals(c_HOL_Oplus__class_Oplus(X5,X1,tc_nat),c_HOL_Oplus__class_Oplus(X5,X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
file('<stdin>',cls_nat__add__left__cancel__le_1) ).
fof(c_0_456,axiom,
! [X5,X21,X22] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X22,X5,tc_nat),c_HOL_Otimes__class_Otimes(X21,X5,tc_nat),tc_nat)
| ~ c_lessequals(X22,X21,tc_nat) ),
file('<stdin>',cls_mult__le__mono1_0) ).
fof(c_0_457,axiom,
! [X5,X21,X22] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X5,X22,tc_nat),c_HOL_Otimes__class_Otimes(X5,X21,tc_nat),tc_nat)
| ~ c_lessequals(X22,X21,tc_nat) ),
file('<stdin>',cls_mult__le__mono2_0) ).
fof(c_0_458,axiom,
! [X2,X1,X5] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X5,X1,tc_nat),c_HOL_Otimes__class_Otimes(X5,X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
file('<stdin>',cls_mult__le__cancel1_2) ).
fof(c_0_459,axiom,
! [X2,X1,X5] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X5,tc_nat),c_HOL_Otimes__class_Otimes(X2,X5,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
file('<stdin>',cls_mult__le__cancel2_2) ).
fof(c_0_460,axiom,
! [X2,X1,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X1,tc_nat),c_HOL_Oplus__class_Oplus(X5,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('<stdin>',cls_nat__add__left__cancel__less_1) ).
fof(c_0_461,axiom,
! [X5,X21,X22] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X22,X5,tc_nat),c_HOL_Oplus__class_Oplus(X21,X5,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X22,X21,tc_nat) ),
file('<stdin>',cls_add__less__mono1_0) ).
fof(c_0_462,axiom,
! [X2,X1,X5] :
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,X1,tc_nat),c_HOL_Otimes__class_Otimes(X5,X2,tc_nat),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
file('<stdin>',cls_nat__mult__dvd__cancel__disj_2) ).
fof(c_0_463,axiom,
! [X1,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X3,X1,X4),X4) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(X4),X4),X1,X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I3_J_0) ).
fof(c_0_464,axiom,
! [X1,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X1,X4),X1,X4) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(X4),X4),X1,X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I2_J_0) ).
fof(c_0_465,axiom,
! [X9,X7,X4] :
( c_lessequals(c_Finite__Set_Ocard(X7,X4),c_Finite__Set_Ocard(c_Set_Oinsert(X9,X7,X4),X4),tc_nat)
| ~ c_Finite__Set_Ofinite(X7,X4) ),
file('<stdin>',cls_card__insert__le_0) ).
fof(c_0_466,axiom,
! [X15,X8,X9,X4] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X9,c_HOL_Ominus__class_Ominus(X8,X15,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X15,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X8,X4) ),
file('<stdin>',cls_dvd__diff_0) ).
fof(c_0_467,axiom,
! [X15,X8,X9,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(X9,c_Lattices_Olower__semilattice__class_Oinf(X8,X15,X4),X4)
| ~ c_lessequals(X9,X15,X4)
| ~ c_lessequals(X9,X8,X4) ),
file('<stdin>',cls_inf__greatest_0) ).
fof(c_0_468,axiom,
! [X15,X8,X9,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(X9,c_Lattices_Olower__semilattice__class_Oinf(X8,X15,X4),X4)
| ~ c_lessequals(X9,X15,X4)
| ~ c_lessequals(X9,X8,X4) ),
file('<stdin>',cls_le__inf__iff_2) ).
fof(c_0_469,axiom,
! [X9,X10,X3,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(X9,c_Lattices_Olower__semilattice__class_Oinf(X3,X10,X4),X4)
| ~ c_lessequals(X9,X10,X4)
| ~ c_lessequals(X9,X3,X4) ),
file('<stdin>',cls_le__infI_0) ).
fof(c_0_470,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Oplus__class_Oplus(X10,X11,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X11,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X10,X4) ),
file('<stdin>',cls_dvd__add_0) ).
fof(c_0_471,axiom,
! [X2,X1,X5,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X5,c_Divides_Odiv__class_Omod(X1,X2,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X2,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X1,X4) ),
file('<stdin>',cls_dvd__mod_0) ).
fof(c_0_472,axiom,
! [X2,X1,X5,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X5,c_Divides_Odiv__class_Omod(X1,X2,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X1,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X2,X4) ),
file('<stdin>',cls_dvd__mod__iff_1) ).
fof(c_0_473,axiom,
! [X2,X1] :
( 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)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
file('<stdin>',cls_dvd__mult__cancel2_0) ).
fof(c_0_474,axiom,
! [X2,X1] :
( 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)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
file('<stdin>',cls_dvd__mult__cancel1_0) ).
fof(c_0_475,axiom,
! [X2,X1] :
( 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)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
file('<stdin>',cls_nat__0__less__mult__iff_2) ).
fof(c_0_476,axiom,
! [X9,X6,X7,X4] :
( ~ c_in(X9,X6,X4)
| ~ c_in(X9,X7,X4)
| c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_disjoint__iff__not__equal_0) ).
fof(c_0_477,axiom,
! [X2,X1,X5] :
( c_HOL_Ominus__class_Ominus(X1,X5,tc_nat) != c_HOL_Ominus__class_Ominus(X2,X5,tc_nat)
| ~ c_lessequals(X5,X2,tc_nat)
| ~ c_lessequals(X5,X1,tc_nat)
| X1 = X2 ),
file('<stdin>',cls_eq__diff__iff_0) ).
fof(c_0_478,axiom,
! [X10,X3,X4] :
( c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4) != c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4)
| X3 = X10 ),
file('<stdin>',cls_singleton__inject_0) ).
fof(c_0_479,axiom,
! [X2,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X1,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) ),
file('<stdin>',cls_diff__less_0) ).
fof(c_0_480,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
fof(c_0_481,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(X3,X3,X4),X4) ),
file('<stdin>',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
fof(c_0_482,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_even__less__0__iff_0) ).
fof(c_0_483,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_double__add__less__zero__iff__single__less__zero_0) ).
fof(c_0_484,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(X3,X3,X4),X4) ),
file('<stdin>',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
fof(c_0_485,axiom,
! [X2,X1,X5] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X1),X2,tc_nat),c_Suc(X5),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X5,tc_nat),
file('<stdin>',cls_Suc__diff__diff_0) ).
fof(c_0_486,axiom,
! [X2,X1] :
( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
file('<stdin>',cls_one__le__mult__iff_0) ).
fof(c_0_487,axiom,
! [X2,X1] :
( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
file('<stdin>',cls_one__le__mult__iff_1) ).
fof(c_0_488,axiom,
! [X15,X8,X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(X9,c_HOL_Otimes__class_Otimes(X8,X15,X4),X4) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X9,X8,X4),X15,X4) ),
file('<stdin>',cls_class__semiring_Omul__a_0) ).
fof(c_0_489,axiom,
! [X30,X31,X33,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(X33,c_HOL_Otimes__class_Otimes(X31,X30,X4),X4) = c_HOL_Otimes__class_Otimes(X31,c_HOL_Otimes__class_Otimes(X33,X30,X4),X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I19_J_0) ).
fof(c_0_490,axiom,
! [X30,X31,X33,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(X33,c_HOL_Otimes__class_Otimes(X31,X30,X4),X4) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X33,X31,X4),X30,X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I18_J_0) ).
fof(c_0_491,axiom,
! [X31,X32,X33,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X33,X32,X4),X31,X4) = c_HOL_Otimes__class_Otimes(X33,c_HOL_Otimes__class_Otimes(X32,X31,X4),X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I17_J_0) ).
fof(c_0_492,axiom,
! [X31,X32,X33,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X33,X32,X4),X31,X4) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X33,X31,X4),X32,X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I16_J_0) ).
fof(c_0_493,axiom,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X3,X10,X4),X11,X4) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X10,X11,X4),X4) ),
file('<stdin>',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
fof(c_0_494,axiom,
! [X15,X8,X9,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X9,X8,X4),X15,X4) = c_Lattices_Olower__semilattice__class_Oinf(X9,c_Lattices_Olower__semilattice__class_Oinf(X8,X15,X4),X4) ),
file('<stdin>',cls_inf__assoc_0) ).
fof(c_0_495,axiom,
! [X15,X8,X9,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X9,c_Lattices_Olower__semilattice__class_Oinf(X8,X15,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X8,c_Lattices_Olower__semilattice__class_Oinf(X9,X15,X4),X4) ),
file('<stdin>',cls_inf__left__commute_0) ).
fof(c_0_496,axiom,
! [X15,X8,X9,X4] :
( ~ class_Lattices_Olattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X9,c_Lattices_Olower__semilattice__class_Oinf(X8,X15,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X8,c_Lattices_Olower__semilattice__class_Oinf(X9,X15,X4),X4) ),
file('<stdin>',cls_inf__sup__aci_I3_J_0) ).
fof(c_0_497,axiom,
! [X15,X8,X9,X4] :
( ~ class_Lattices_Olattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X9,X8,X4),X15,X4) = c_Lattices_Olower__semilattice__class_Oinf(X9,c_Lattices_Olower__semilattice__class_Oinf(X8,X15,X4),X4) ),
file('<stdin>',cls_inf__sup__aci_I2_J_0) ).
fof(c_0_498,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X10,X4),X11,X4) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X10,X11,X4),X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I21_J_0) ).
fof(c_0_499,axiom,
! [X17,X11,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X11,X17,X4),X4) = c_HOL_Oplus__class_Oplus(X11,c_HOL_Oplus__class_Oplus(X3,X17,X4),X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I22_J_0) ).
fof(c_0_500,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X10,X4),X11,X4) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X11,X4),X10,X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I23_J_0) ).
fof(c_0_501,axiom,
! [X17,X11,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X11,X17,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X11,X4),X17,X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I25_J_0) ).
fof(c_0_502,axiom,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Oab__semigroup__add(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X10,X4),X11,X4) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X10,X11,X4),X4) ),
file('<stdin>',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
fof(c_0_503,axiom,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X10,X11,X4),X4) = c_HOL_Oplus__class_Oplus(X10,c_HOL_Oplus__class_Oplus(X3,X11,X4),X4) ),
file('<stdin>',cls_comm__monoid__add_Omult__left__commute_0) ).
fof(c_0_504,axiom,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X10,X4),X11,X4) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X10,X11,X4),X4) ),
file('<stdin>',cls_comm__monoid__add_Omult__assoc_0) ).
fof(c_0_505,axiom,
! [X15,X8,X9,X4] :
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_HOL_Oplus__class_Oplus(X9,c_HOL_Oplus__class_Oplus(X8,X15,X4),X4) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X9,X15,X4),X4) ),
file('<stdin>',cls_add__cancel__21_1) ).
fof(c_0_506,axiom,
! [X15,X8,X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(X9,c_HOL_Oplus__class_Oplus(X8,X15,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X9,X8,X4),X15,X4) ),
file('<stdin>',cls_class__semiring_Oadd__a_0) ).
fof(c_0_507,axiom,
! [X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oplus__class_Oplus(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) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_sum__squares__eq__zero__iff_2) ).
fof(c_0_508,axiom,
! [X15,X8,X9] :
( c_Ring__and__Field_Odvd__class_Odvd(X9,X15,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X15,X8,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X15,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X8,X9,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X8,tc_nat) ),
file('<stdin>',cls_dvd_Oless__trans_0) ).
fof(c_0_509,axiom,
! [X20,X14,X4] : c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) = c_Set_Oimage(X20,c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool)),X14,X4),
file('<stdin>',cls_empty__is__image_1) ).
fof(c_0_510,axiom,
! [X20,X14,X4] : c_Set_Oimage(X20,c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool)),X14,X4) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
file('<stdin>',cls_image__empty_0) ).
fof(c_0_511,axiom,
! [X20,X14,X4] : c_Set_Ovimage(X20,c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool)),X4,X14) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
file('<stdin>',cls_vimage__empty_0) ).
fof(c_0_512,axiom,
! [X20,X14,X4] : c_Set_Ovimage(X20,c_Orderings_Otop__class_Otop(tc_fun(X14,tc_bool)),X4,X14) = c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),
file('<stdin>',cls_vimage__UNIV_0) ).
fof(c_0_513,axiom,
! [X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_lessequals(X3,X10,X4)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X3,X10,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_le__iff__diff__le__0_1) ).
fof(c_0_514,axiom,
! [X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(X3,X10,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X10,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_less__iff__diff__less__0_1) ).
fof(c_0_515,axiom,
! [X2,X1] : 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),
file('<stdin>',cls_mod__Suc__eq__Suc__mod_0) ).
fof(c_0_516,axiom,
! [X2,X1,X5] :
( c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X1,tc_nat) ),
file('<stdin>',cls_dvd__diff__nat_0) ).
fof(c_0_517,axiom,
! [X8,X9,X7,X4] : c_Set_Oinsert(X9,c_Set_Oinsert(X8,X7,X4),X4) = c_Set_Oinsert(X8,c_Set_Oinsert(X9,X7,X4),X4),
file('<stdin>',cls_insert__commute_0) ).
fof(c_0_518,axiom,
! [X16,X6,X7,X4] :
( c_lessequals(X7,X16,tc_fun(X4,tc_bool))
| ~ c_lessequals(X6,X16,tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_subset__trans_0) ).
fof(c_0_519,axiom,
! [X16,X6,X7,X4] :
( c_HOL_Oord__class_Oless(X7,X16,tc_fun(X4,tc_bool))
| ~ c_lessequals(X6,X16,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(X7,X6,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_psubset__subset__trans_0) ).
fof(c_0_520,axiom,
! [X16,X6,X7,X4] :
( c_HOL_Oord__class_Oless(X7,X16,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(X6,X16,tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_subset__psubset__trans_0) ).
fof(c_0_521,axiom,
! [X16,X6,X7,X4] :
( c_HOL_Oord__class_Oless(X7,X16,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(X6,X16,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(X7,X6,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_psubset__trans_0) ).
fof(c_0_522,axiom,
! [X38,X8,X39,X9,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_HOL_Ominus__class_Ominus(X9,X8,X4) != c_HOL_Ominus__class_Ominus(X39,X38,X4)
| c_lessequals(X38,X39,X4)
| ~ c_lessequals(X8,X9,X4) ),
file('<stdin>',cls_le__eqI_0) ).
fof(c_0_523,axiom,
! [X38,X8,X39,X9,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_HOL_Ominus__class_Ominus(X9,X8,X4) != c_HOL_Ominus__class_Ominus(X39,X38,X4)
| c_lessequals(X8,X9,X4)
| ~ c_lessequals(X38,X39,X4) ),
file('<stdin>',cls_le__eqI_1) ).
fof(c_0_524,axiom,
! [X38,X8,X39,X9,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_HOL_Ominus__class_Ominus(X9,X8,X4) != c_HOL_Ominus__class_Ominus(X39,X38,X4)
| c_HOL_Oord__class_Oless(X39,X38,X4)
| ~ c_HOL_Oord__class_Oless(X9,X8,X4) ),
file('<stdin>',cls_less__eqI_0) ).
fof(c_0_525,axiom,
! [X38,X8,X39,X9,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_HOL_Ominus__class_Ominus(X9,X8,X4) != c_HOL_Ominus__class_Ominus(X39,X38,X4)
| c_HOL_Oord__class_Oless(X9,X8,X4)
| ~ c_HOL_Oord__class_Oless(X39,X38,X4) ),
file('<stdin>',cls_less__eqI_1) ).
fof(c_0_526,axiom,
! [X2,X1,X5] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X5,X1,tc_nat),c_HOL_Otimes__class_Otimes(X5,X2,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
file('<stdin>',cls_mult__le__cancel1_1) ).
fof(c_0_527,axiom,
! [X2,X1,X5] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X5,tc_nat),c_HOL_Otimes__class_Otimes(X2,X5,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
file('<stdin>',cls_mult__le__cancel2_1) ).
fof(c_0_528,axiom,
! [X3,X6,X7,X4] :
( c_Lattices_Olower__semilattice__class_Oinf(X7,c_Set_Oinsert(X3,X6,X4),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool))
| c_in(X3,X7,X4) ),
file('<stdin>',cls_Int__insert__right_1) ).
fof(c_0_529,axiom,
! [X3,X16,X6,X4] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X3,X6,X4),X16,tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,X16,tc_fun(X4,tc_bool))
| c_in(X3,X16,X4) ),
file('<stdin>',cls_Int__insert__left_1) ).
fof(c_0_530,axiom,
! [X15,X8,X9,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(X9,X15,X4)
| ~ c_lessequals(X9,c_Lattices_Olower__semilattice__class_Oinf(X8,X15,X4),X4) ),
file('<stdin>',cls_le__inf__iff_1) ).
fof(c_0_531,axiom,
! [X15,X8,X9,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(X9,X8,X4)
| ~ c_lessequals(X9,c_Lattices_Olower__semilattice__class_Oinf(X8,X15,X4),X4) ),
file('<stdin>',cls_le__inf__iff_0) ).
fof(c_0_532,axiom,
! [X9,X10,X3,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(X9,X10,X4)
| ~ c_lessequals(X9,c_Lattices_Olower__semilattice__class_Oinf(X3,X10,X4),X4) ),
file('<stdin>',cls_le__infE_1) ).
fof(c_0_533,axiom,
! [X9,X10,X3,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(X9,X3,X4)
| ~ c_lessequals(X9,c_Lattices_Olower__semilattice__class_Oinf(X3,X10,X4),X4) ),
file('<stdin>',cls_le__infE_0) ).
fof(c_0_534,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X11,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X10,X4),X11,X4) ),
file('<stdin>',cls_dvd__mult__left_0) ).
fof(c_0_535,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X10,X11,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X10,X4),X11,X4) ),
file('<stdin>',cls_dvd__mult__right_0) ).
fof(c_0_536,axiom,
! [X2,X1,X4] :
( ~ class_Ring__and__Field_Oring__1(X4)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X4) = c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(X1,X4),c_Nat_Osemiring__1__class_Oof__nat(X2,X4),X4)
| ~ c_lessequals(X2,X1,tc_nat) ),
file('<stdin>',cls_of__nat__diff_0) ).
fof(c_0_537,axiom,
! [X5,X21,X22] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X22,X21,tc_nat),X5,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X22,X5,tc_nat),X21,tc_nat),
file('<stdin>',cls_diff__commute_0) ).
fof(c_0_538,axiom,
! [X2,X1,X5] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X5,X1,tc_nat),c_HOL_Oplus__class_Oplus(X5,X2,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),
file('<stdin>',cls_diff__cancel_0) ).
fof(c_0_539,axiom,
! [X2,X1,X5] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X5,tc_nat),c_HOL_Oplus__class_Oplus(X2,X5,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),
file('<stdin>',cls_diff__cancel2_0) ).
fof(c_0_540,axiom,
! [X5,X21,X22] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X22,X21,tc_nat),X5,tc_nat) = c_HOL_Ominus__class_Ominus(X22,c_HOL_Oplus__class_Oplus(X21,X5,tc_nat),tc_nat),
file('<stdin>',cls_diff__diff__left_0) ).
fof(c_0_541,axiom,
! [X2,X1,X5] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X5,tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X5,tc_nat),tc_nat),
file('<stdin>',cls_nat__mult__assoc_0) ).
fof(c_0_542,axiom,
! [X2,X1,X5] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X5,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X5,tc_nat),tc_nat),
file('<stdin>',cls_nat__add__assoc_0) ).
fof(c_0_543,axiom,
! [X15,X8,X9] : c_HOL_Oplus__class_Oplus(X9,c_HOL_Oplus__class_Oplus(X8,X15,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X9,X15,tc_nat),tc_nat),
file('<stdin>',cls_nat__add__left__commute_0) ).
fof(c_0_544,axiom,
! [X6,X7,X4] :
( X7 = X6
| ~ c_lessequals(c_Finite__Set_Ocard(X6,X4),c_Finite__Set_Ocard(X7,X4),tc_nat)
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| ~ c_Finite__Set_Ofinite(X6,X4) ),
file('<stdin>',cls_card__seteq_0) ).
fof(c_0_545,axiom,
! [X10,X3,X7,X4] :
( c_in(X3,X7,X4)
| X3 = X10
| ~ c_in(X3,c_Set_Oinsert(X10,X7,X4),X4) ),
file('<stdin>',cls_insertE_0) ).
fof(c_0_546,axiom,
! [X11,X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X3,X10,X4),X11,X4) = c_Divides_Odiv__class_Omod(X3,X11,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X10,X4) ),
file('<stdin>',cls_mod__mod__cancel_0) ).
fof(c_0_547,axiom,
! [X21,X22,X26] :
( hBOOL(hAPP(X26,X22))
| hBOOL(hAPP(X26,c_Suc(c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X26,X21))))
| ~ hBOOL(hAPP(X26,X21))
| ~ c_lessequals(X22,X21,tc_nat) ),
file('<stdin>',cls_inc__induct_1) ).
fof(c_0_548,axiom,
! [X2,X1] :
( 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) ),
file('<stdin>',cls_nat__0__less__mult__iff_0) ).
fof(c_0_549,axiom,
! [X2,X1] :
( 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) ),
file('<stdin>',cls_nat__0__less__mult__iff_1) ).
fof(c_0_550,axiom,
! [X6,X7,X4] : c_Lattices_Olower__semilattice__class_Oinf(X7,c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),
file('<stdin>',cls_Int__left__absorb_0) ).
fof(c_0_551,axiom,
! [X6,X7,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),X6,tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),
file('<stdin>',cls_Diff__idemp_0) ).
fof(c_0_552,axiom,
! [X10,X6,X7,X4] :
( c_lessequals(X7,c_Set_Oinsert(X10,X6,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_subset__insertI2_0) ).
fof(c_0_553,axiom,
! [X2,X1] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ),
file('<stdin>',cls_zero__less__diff_0) ).
fof(c_0_554,axiom,
! [X15,X8,X9] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X9,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X15,X8,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X15,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X8,tc_nat) ),
file('<stdin>',cls_dvd_Ole__less__trans_1) ).
fof(c_0_555,axiom,
! [X15,X8,X9] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X9,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X15,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X8,X9,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X8,tc_nat) ),
file('<stdin>',cls_dvd_Oless__le__trans_1) ).
fof(c_0_556,axiom,
! [X2,X1,X24,X5] :
( c_HOL_Oplus__class_Oplus(X1,X24,tc_nat) != c_HOL_Oplus__class_Oplus(X5,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X24,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('<stdin>',cls_less__add__eq__less_0) ).
fof(c_0_557,axiom,
! [X2,X1,X5] :
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X5,tc_nat),X2,tc_nat) ),
file('<stdin>',cls_add__leE_0) ).
fof(c_0_558,axiom,
! [X2,X1,X5] :
( c_lessequals(X5,X2,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X5,tc_nat),X2,tc_nat) ),
file('<stdin>',cls_add__leE_1) ).
fof(c_0_559,axiom,
! [X2,X5] :
( c_Ring__and__Field_Odvd__class_Odvd(X5,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Oplus__class_Oplus(X2,X5,tc_nat),tc_nat) ),
file('<stdin>',cls_dvd__reduce_0) ).
fof(c_0_560,axiom,
! [X5,X21,X22] :
( c_HOL_Oord__class_Oless(X22,X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X22,X21,tc_nat),X5,tc_nat) ),
file('<stdin>',cls_add__lessD1_0) ).
fof(c_0_561,axiom,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),X3,X4),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),X10,X4),X4) ),
file('<stdin>',cls_dvd__mult__cancel__left_1) ).
fof(c_0_562,axiom,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X4),X4),c_HOL_Otimes__class_Otimes(X10,c_HOL_Ozero__class_Ozero(X4),X4),X4) ),
file('<stdin>',cls_dvd__mult__cancel__right_1) ).
fof(c_0_563,axiom,
! [X6,X7,X4] :
( c_Finite__Set_Ofinite(X7,X4)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),X4)
| ~ c_Finite__Set_Ofinite(X6,X4) ),
file('<stdin>',cls_finite__Diff2_0) ).
fof(c_0_564,axiom,
! [X20,X14,X4] : c_Fun_Oinj__on(X20,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4,X14),
file('<stdin>',cls_inj__on__empty_0) ).
fof(c_0_565,axiom,
! [X2,X26] :
( ~ hBOOL(hAPP(X26,X2))
| hBOOL(hAPP(X26,c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
file('<stdin>',cls_split__mod_5) ).
fof(c_0_566,axiom,
! [X8,X9,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_HOL_Oplus__class_Oplus(X9,X8,X4) != c_HOL_Ozero__class_Ozero(X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X9,X4)
| X9 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_add__nonneg__eq__0__iff_0) ).
fof(c_0_567,axiom,
! [X8,X9,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_HOL_Oplus__class_Oplus(X9,X8,X4) != c_HOL_Ozero__class_Ozero(X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X9,X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_add__nonneg__eq__0__iff_1) ).
fof(c_0_568,axiom,
! [X42,X20,X14,X4] :
( ~ class_HOL_Oord(X14)
| c_HOL_Oord__class_Oless(X20,X42,tc_fun(X4,X14))
| c_lessequals(X42,X20,tc_fun(X4,X14))
| ~ c_lessequals(X20,X42,tc_fun(X4,X14)) ),
file('<stdin>',cls_less__fun__def_2) ).
fof(c_0_569,axiom,
! [X2,X1] :
( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat)
| ~ c_lessequals(X2,X1,tc_nat) ),
file('<stdin>',cls_le__mod__geq_0) ).
fof(c_0_570,axiom,
! [X4] : ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_nat),
file('<stdin>',cls_card__gt__0__iff_0) ).
fof(c_0_571,axiom,
! [X8,X9,X7,X4] :
( hBOOL(hAPP(c_Set_Oinsert(X8,X7,X4),X9))
| ~ hBOOL(hAPP(X7,X9)) ),
file('<stdin>',cls_insert__code_2) ).
fof(c_0_572,axiom,
! [X21,X22,X26] :
( hBOOL(hAPP(X26,X22))
| ~ hBOOL(hAPP(X26,c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X26,X21)))
| ~ hBOOL(hAPP(X26,X21))
| ~ c_lessequals(X22,X21,tc_nat) ),
file('<stdin>',cls_inc__induct_2) ).
fof(c_0_573,axiom,
! [X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4),tc_nat)
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4) ),
file('<stdin>',cls_finite__UNIV__card__ge__0_0) ).
fof(c_0_574,axiom,
! [X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_add__nonneg__eq__0__iff_2) ).
fof(c_0_575,axiom,
! [X45,X46,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X45,X4),c_Finite__Set_Olinorder__class_OMin(X46,X4),X4)
| ~ c_Finite__Set_Ofinite(X45,X4)
| X46 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ c_lessequals(X46,X45,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_Min__antimono_0) ).
fof(c_0_576,axiom,
! [X45,X46,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_lessequals(c_Finite__Set_Olinorder__class_OMax(X46,X4),c_Finite__Set_Olinorder__class_OMax(X45,X4),X4)
| ~ c_Finite__Set_Ofinite(X45,X4)
| X46 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ c_lessequals(X46,X45,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_Max__mono_0) ).
fof(c_0_577,axiom,
! [X9,X6,X7,X4] :
( c_Set_Oinsert(X9,X7,X4) != c_Set_Oinsert(X9,X6,X4)
| c_in(X9,X6,X4)
| c_in(X9,X7,X4)
| X7 = X6 ),
file('<stdin>',cls_insert__ident_0) ).
fof(c_0_578,axiom,
! [X2,X1] :
( c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat))
| c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) = X2 ),
file('<stdin>',cls_mod__Suc_1) ).
fof(c_0_579,axiom,
! [X15,X8,X9] :
( c_Ring__and__Field_Odvd__class_Odvd(X9,X15,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X15,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X8,X9,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X8,tc_nat) ),
file('<stdin>',cls_dvd_Oless__le__trans_0) ).
fof(c_0_580,axiom,
! [X15,X8,X9] :
( c_Ring__and__Field_Odvd__class_Odvd(X9,X15,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X15,X8,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X15,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X8,tc_nat) ),
file('<stdin>',cls_dvd_Ole__less__trans_0) ).
fof(c_0_581,axiom,
! [X2,X1] : 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),
file('<stdin>',cls_nat__mult__dvd__cancel__disj_1) ).
fof(c_0_582,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(X3,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
fof(c_0_583,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(X3,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
file('<stdin>',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
fof(c_0_584,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_even__less__0__iff_1) ).
fof(c_0_585,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_double__add__less__zero__iff__single__less__zero_1) ).
fof(c_0_586,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_not__square__less__zero_0) ).
fof(c_0_587,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(X3,X3,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
file('<stdin>',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
fof(c_0_588,axiom,
! [X9,X1] : c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X1,X9,tc_nat)),tc_nat),
file('<stdin>',cls_less__iff__Suc__add_1) ).
fof(c_0_589,axiom,
! [X1,X22] : c_HOL_Oord__class_Oless(X22,c_Suc(c_HOL_Oplus__class_Oplus(X1,X22,tc_nat)),tc_nat),
file('<stdin>',cls_less__add__Suc2_0) ).
fof(c_0_590,axiom,
! [X1,X22] : c_HOL_Oord__class_Oless(X22,c_Suc(c_HOL_Oplus__class_Oplus(X22,X1,tc_nat)),tc_nat),
file('<stdin>',cls_less__add__Suc1_0) ).
fof(c_0_591,axiom,
! [X8,X9,X4] :
( ~ class_Orderings_Oorder(X4)
| c_lessequals(X8,X9,X4)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeast(X9,X4),c_SetInterval_Oord__class_OatLeast(X8,X4),tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_atLeast__subset__iff_0) ).
fof(c_0_592,axiom,
! [X9,X4] : c_in(X9,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4),
file('<stdin>',cls_singleton__iff_1) ).
fof(c_0_593,axiom,
! [X9,X6,X7,X4] :
( c_in(X9,X6,X4)
| ~ c_in(X9,X7,X4)
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_set__mp_0) ).
fof(c_0_594,axiom,
! [X11,X6,X7,X4] :
( c_in(X11,X6,X4)
| ~ c_in(X11,X7,X4)
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_subsetD_0) ).
fof(c_0_595,axiom,
! [X9,X6,X7,X4] :
( c_in(X9,X6,X4)
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| ~ c_in(X9,X7,X4) ),
file('<stdin>',cls_set__rev__mp_0) ).
fof(c_0_596,axiom,
! [X43,X6,X7,X4] :
( c_in(X43,X6,X4)
| ~ c_in(X43,X7,X4)
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_subset__iff_0) ).
fof(c_0_597,axiom,
! [X11,X6,X7,X4] :
( c_in(X11,X6,X4)
| ~ c_in(X11,X7,X4)
| ~ c_HOL_Oord__class_Oless(X7,X6,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_psubsetD_0) ).
fof(c_0_598,axiom,
! [X2,X1] :
( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('<stdin>',cls_mod__if_1) ).
fof(c_0_599,axiom,
! [X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_lessequals(c_HOL_Ominus__class_Ominus(X3,X10,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,X10,X4) ),
file('<stdin>',cls_le__iff__diff__le__0_0) ).
fof(c_0_600,axiom,
! [X42,X20,X14,X4] :
( ~ class_HOL_Oord(X14)
| ~ c_lessequals(X42,X20,tc_fun(X4,X14))
| ~ c_HOL_Oord__class_Oless(X20,X42,tc_fun(X4,X14)) ),
file('<stdin>',cls_less__fun__def_1) ).
fof(c_0_601,axiom,
! [X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X10,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,X10,X4) ),
file('<stdin>',cls_less__iff__diff__less__0_0) ).
fof(c_0_602,axiom,
! [X7,X4] :
( c_Finite__Set_Ocard(X7,X4) != c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4)
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4)
| X7 = c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_card__eq__UNIV__imp__eq__UNIV_0) ).
fof(c_0_603,axiom,
! [X2,X22] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,c_Suc(X22),tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
file('<stdin>',cls_diff__Suc__less_0) ).
fof(c_0_604,axiom,
! [X2,X1,X5] :
( c_HOL_Otimes__class_Otimes(X5,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X5,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| X1 = X2 ),
file('<stdin>',cls_nat__mult__eq__cancel1_0) ).
fof(c_0_605,axiom,
! [X6,X7,X4] : c_Lattices_Olower__semilattice__class_Oinf(X7,c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
file('<stdin>',cls_Diff__disjoint_0) ).
fof(c_0_606,axiom,
! [X2,X1] :
( ~ 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) ),
file('<stdin>',cls_nat__dvd__not__less_0) ).
fof(c_0_607,axiom,
! [X9,X10,X3,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X10,X4),X9,X4)
| ~ c_lessequals(X10,X9,X4) ),
file('<stdin>',cls_le__infI2_0) ).
fof(c_0_608,axiom,
! [X9,X10,X3,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X10,X4),X9,X4)
| ~ c_lessequals(X3,X9,X4) ),
file('<stdin>',cls_le__infI1_0) ).
fof(c_0_609,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Otimes__class_Otimes(X10,X11,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X11,X4) ),
file('<stdin>',cls_dvd__mult_0) ).
fof(c_0_610,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Otimes__class_Otimes(X10,X11,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X10,X4) ),
file('<stdin>',cls_dvd__mult2_0) ).
fof(c_0_611,axiom,
! [X9,X10,X3,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X3,X10,X4),X9,X4)
| ~ c_HOL_Oord__class_Oless(X3,X9,X4) ),
file('<stdin>',cls_less__infI1_0) ).
fof(c_0_612,axiom,
! [X9,X10,X3,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X3,X10,X4),X9,X4)
| ~ c_HOL_Oord__class_Oless(X10,X9,X4) ),
file('<stdin>',cls_less__infI2_0) ).
fof(c_0_613,axiom,
! [X1] :
( ~ 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) ),
file('<stdin>',cls_dvd__mult__cancel1_1) ).
fof(c_0_614,axiom,
! [X1] :
( ~ 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) ),
file('<stdin>',cls_dvd__mult__cancel2_1) ).
fof(c_0_615,axiom,
! [X2,X1] :
( c_HOL_Ominus__class_Ominus(c_Suc(X1),X2,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat))
| ~ c_lessequals(X2,X1,tc_nat) ),
file('<stdin>',cls_Suc__diff__le_0) ).
fof(c_0_616,axiom,
! [X6,X7,X4] :
( c_lessequals(c_Finite__Set_Ocard(X7,X4),c_Finite__Set_Ocard(X6,X4),tc_nat)
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| ~ c_Finite__Set_Ofinite(X6,X4) ),
file('<stdin>',cls_card__mono_0) ).
fof(c_0_617,axiom,
! [X6,X7,X4] :
( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(X7,X4),c_Finite__Set_Ocard(X6,X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,X6,tc_fun(X4,tc_bool))
| ~ c_Finite__Set_Ofinite(X6,X4) ),
file('<stdin>',cls_psubset__card__mono_0) ).
fof(c_0_618,axiom,
! [X2,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
file('<stdin>',cls_add__gr__0_1) ).
fof(c_0_619,axiom,
! [X2,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
file('<stdin>',cls_add__gr__0_2) ).
fof(c_0_620,axiom,
! [X10,X3,X6,X4] :
( c_in(X3,c_Set_Oinsert(X10,X6,X4),X4)
| ~ c_in(X3,X6,X4) ),
file('<stdin>',cls_insertCI_0) ).
fof(c_0_621,axiom,
! [X10,X3,X7,X4] :
( c_in(X3,c_Set_Oinsert(X10,X7,X4),X4)
| ~ c_in(X3,X7,X4) ),
file('<stdin>',cls_insert__iff_2) ).
fof(c_0_622,axiom,
! [X1,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(X1,X1,X4) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X4),c_HOL_Oone__class_Oone(X4),X4),X1,X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I4_J_0) ).
fof(c_0_623,axiom,
! [X21,X22] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X21,X22,tc_nat),X22,tc_nat),
file('<stdin>',cls_not__add__less2_0) ).
fof(c_0_624,axiom,
! [X21,X22] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X22,X21,tc_nat),X22,tc_nat),
file('<stdin>',cls_not__add__less1_0) ).
fof(c_0_625,axiom,
! [X6,X7,X4] :
( X7 = X6
| ~ c_lessequals(X6,X7,tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_equalityI_0) ).
fof(c_0_626,axiom,
! [X6,X7,X4] :
( X7 = X6
| ~ c_lessequals(X6,X7,tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_set__eq__subset_2) ).
fof(c_0_627,axiom,
! [X2,X1] :
( c_lessequals(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
file('<stdin>',cls_mod__le__divisor_0) ).
fof(c_0_628,axiom,
! [X2,X1] :
( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
file('<stdin>',cls_mod__less__divisor_0) ).
fof(c_0_629,axiom,
! [X9,X7,X4] :
( c_Finite__Set_Ocard(c_Set_Oinsert(X9,X7,X4),X4) = c_Finite__Set_Ocard(X7,X4)
| ~ c_in(X9,X7,X4)
| ~ c_Finite__Set_Ofinite(X7,X4) ),
file('<stdin>',cls_card__insert__if_0) ).
fof(c_0_630,axiom,
! [X9,X7,X4] : hBOOL(hAPP(c_Set_Oinsert(X9,X7,X4),X9)),
file('<stdin>',cls_insert__code_1) ).
fof(c_0_631,axiom,
! [X2,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('<stdin>',cls_zero__less__diff_1) ).
fof(c_0_632,axiom,
! [X6,X7,X4] :
( c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)) = X7 ),
file('<stdin>',cls_Diff__triv_0) ).
fof(c_0_633,axiom,
! [X2,X22] :
( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X2,X22,tc_nat),tc_nat) = X22
| ~ c_lessequals(X22,X2,tc_nat) ),
file('<stdin>',cls_diff__diff__cancel_0) ).
fof(c_0_634,axiom,
! [X2,X1] :
( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat) = X1
| ~ c_lessequals(X2,X1,tc_nat) ),
file('<stdin>',cls_le__add__diff__inverse2_0) ).
fof(c_0_635,axiom,
! [X2,X1] :
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) = X1
| ~ c_lessequals(X2,X1,tc_nat) ),
file('<stdin>',cls_le__add__diff__inverse_0) ).
fof(c_0_636,axiom,
! [X21,X22] :
( ~ c_lessequals(X22,X21,tc_nat)
| X21 = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X21,X22,tc_nat),X22,tc_nat) ),
file('<stdin>',cls_le__imp__diff__is__add_0) ).
fof(c_0_637,axiom,
! [X21,X22,X26] :
( hBOOL(hAPP(X26,X22))
| c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X26,X21),X21,tc_nat)
| ~ hBOOL(hAPP(X26,X21))
| ~ c_lessequals(X22,X21,tc_nat) ),
file('<stdin>',cls_inc__induct_0) ).
fof(c_0_638,axiom,
! [X9,X42,X20,X14,X4] :
( ~ class_HOL_Oord(X14)
| c_lessequals(hAPP(X20,X9),hAPP(X42,X9),X14)
| ~ c_lessequals(X20,X42,tc_fun(X4,X14)) ),
file('<stdin>',cls_le__funD_0) ).
fof(c_0_639,axiom,
! [X2,X5,X21] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X21,X2,tc_nat),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(X21,X5,tc_nat) ),
file('<stdin>',cls_less__imp__diff__less_0) ).
fof(c_0_640,axiom,
! [X15,X8,X9] :
( c_lessequals(X9,c_HOL_Oplus__class_Oplus(X8,X15,tc_nat),tc_nat)
| ~ c_lessequals(X9,X8,tc_nat) ),
file('<stdin>',cls_termination__basic__simps_I3_J_0) ).
fof(c_0_641,axiom,
! [X15,X8,X9] :
( c_lessequals(X9,c_HOL_Oplus__class_Oplus(X8,X15,tc_nat),tc_nat)
| ~ c_lessequals(X9,X15,tc_nat) ),
file('<stdin>',cls_termination__basic__simps_I4_J_0) ).
fof(c_0_642,axiom,
! [X1,X21,X22] :
( c_lessequals(X22,c_HOL_Oplus__class_Oplus(X21,X1,tc_nat),tc_nat)
| ~ c_lessequals(X22,X21,tc_nat) ),
file('<stdin>',cls_trans__le__add1_0) ).
fof(c_0_643,axiom,
! [X1,X21,X22] :
( c_lessequals(X22,c_HOL_Oplus__class_Oplus(X1,X21,tc_nat),tc_nat)
| ~ c_lessequals(X22,X21,tc_nat) ),
file('<stdin>',cls_trans__le__add2_0) ).
fof(c_0_644,axiom,
! [X2,X5] :
( c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Oplus__class_Oplus(X2,X5,tc_nat),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X2,tc_nat) ),
file('<stdin>',cls_dvd__reduce_1) ).
fof(c_0_645,axiom,
! [X1,X21,X22] :
( c_HOL_Oord__class_Oless(X22,c_HOL_Oplus__class_Oplus(X1,X21,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X22,X21,tc_nat) ),
file('<stdin>',cls_trans__less__add2_0) ).
fof(c_0_646,axiom,
! [X1,X21,X22] :
( c_HOL_Oord__class_Oless(X22,c_HOL_Oplus__class_Oplus(X21,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X22,X21,tc_nat) ),
file('<stdin>',cls_trans__less__add1_0) ).
fof(c_0_647,axiom,
! [X15,X8,X9] :
( c_HOL_Oord__class_Oless(X9,c_HOL_Oplus__class_Oplus(X8,X15,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X9,X15,tc_nat) ),
file('<stdin>',cls_termination__basic__simps_I2_J_0) ).
fof(c_0_648,axiom,
! [X15,X8,X9] :
( c_HOL_Oord__class_Oless(X9,c_HOL_Oplus__class_Oplus(X8,X15,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X9,X8,tc_nat) ),
file('<stdin>',cls_termination__basic__simps_I1_J_0) ).
fof(c_0_649,axiom,
! [X15,X8,X9,X4] :
( ~ class_Orderings_Oorder(X4)
| c_lessequals(X15,X9,X4)
| ~ c_lessequals(X15,X8,X4)
| ~ c_lessequals(X8,X9,X4) ),
file('<stdin>',cls_xt1_I6_J_0) ).
fof(c_0_650,axiom,
! [X15,X8,X9,X4] :
( ~ class_Orderings_Opreorder(X4)
| c_lessequals(X9,X15,X4)
| ~ c_lessequals(X8,X15,X4)
| ~ c_lessequals(X9,X8,X4) ),
file('<stdin>',cls_order__trans_0) ).
fof(c_0_651,axiom,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X11,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X11,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X10,X4) ),
file('<stdin>',cls_dvd__trans_0) ).
fof(c_0_652,axiom,
! [X15,X8,X9,X4] :
( ~ class_Orderings_Oorder(X4)
| c_HOL_Oord__class_Oless(X15,X9,X4)
| ~ c_lessequals(X15,X8,X4)
| ~ c_HOL_Oord__class_Oless(X8,X9,X4) ),
file('<stdin>',cls_xt1_I7_J_0) ).
fof(c_0_653,axiom,
! [X15,X8,X9,X4] :
( ~ class_Orderings_Oorder(X4)
| c_HOL_Oord__class_Oless(X15,X9,X4)
| ~ c_HOL_Oord__class_Oless(X15,X8,X4)
| ~ c_lessequals(X8,X9,X4) ),
file('<stdin>',cls_xt1_I8_J_0) ).
fof(c_0_654,axiom,
! [X15,X8,X9,X4] :
( ~ class_Orderings_Opreorder(X4)
| c_HOL_Oord__class_Oless(X9,X15,X4)
| ~ c_HOL_Oord__class_Oless(X8,X15,X4)
| ~ c_lessequals(X9,X8,X4) ),
file('<stdin>',cls_order__le__less__trans_0) ).
fof(c_0_655,axiom,
! [X15,X8,X9,X4] :
( ~ class_Orderings_Opreorder(X4)
| c_HOL_Oord__class_Oless(X9,X15,X4)
| ~ c_lessequals(X8,X15,X4)
| ~ c_HOL_Oord__class_Oless(X9,X8,X4) ),
file('<stdin>',cls_order__less__le__trans_0) ).
fof(c_0_656,axiom,
! [X15,X8,X9,X4] :
( ~ class_Orderings_Oorder(X4)
| c_HOL_Oord__class_Oless(X15,X9,X4)
| ~ c_HOL_Oord__class_Oless(X15,X8,X4)
| ~ c_HOL_Oord__class_Oless(X8,X9,X4) ),
file('<stdin>',cls_xt1_I10_J_0) ).
fof(c_0_657,axiom,
! [X15,X8,X9,X4] :
( ~ class_Orderings_Opreorder(X4)
| c_HOL_Oord__class_Oless(X9,X15,X4)
| ~ c_HOL_Oord__class_Oless(X8,X15,X4)
| ~ c_HOL_Oord__class_Oless(X9,X8,X4) ),
file('<stdin>',cls_order__less__trans_0) ).
fof(c_0_658,axiom,
! [X2,X1] :
( 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) ),
file('<stdin>',cls_mod__Suc_0) ).
fof(c_0_659,axiom,
! [X3,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) = X3 ),
file('<stdin>',cls_Min__singleton_0) ).
fof(c_0_660,axiom,
! [X3,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) = X3 ),
file('<stdin>',cls_Max__singleton_0) ).
fof(c_0_661,axiom,
! [X7,X4] :
( X7 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_subset__empty_0) ).
fof(c_0_662,axiom,
! [X2,X1,X4] :
( ~ class_Ring__and__Field_Osemiring__1(X4)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X4) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(X1,X4),c_Nat_Osemiring__1__class_Oof__nat(X2,X4),X4) ),
file('<stdin>',cls_of__nat__add_0) ).
fof(c_0_663,axiom,
! [X2,X1,X4] :
( ~ class_Ring__and__Field_Osemiring__1(X4)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X4) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(X1,X4),c_Nat_Osemiring__1__class_Oof__nat(X2,X4),X4) ),
file('<stdin>',cls_of__nat__mult_0) ).
fof(c_0_664,axiom,
! [X6,X7,X4] : c_lessequals(c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),X7,tc_fun(X4,tc_bool)),
file('<stdin>',cls_Diff__subset_0) ).
fof(c_0_665,axiom,
! [X6,X7,X4] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),X7,tc_fun(X4,tc_bool)),
file('<stdin>',cls_Int__lower1_0) ).
fof(c_0_666,axiom,
! [X6,X7,X4] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),X6,tc_fun(X4,tc_bool)),
file('<stdin>',cls_Int__lower2_0) ).
fof(c_0_667,axiom,
! [X9,X7,X4] :
( c_Finite__Set_Ocard(c_Set_Oinsert(X9,X7,X4),X4) = c_Suc(c_Finite__Set_Ocard(X7,X4))
| c_in(X9,X7,X4)
| ~ c_Finite__Set_Ofinite(X7,X4) ),
file('<stdin>',cls_card__insert__if_1) ).
fof(c_0_668,axiom,
! [X2,X1,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X4),c_Nat_Osemiring__1__class_Oof__nat(X2,X4),X4) ),
file('<stdin>',cls_of__nat__le__iff_0) ).
fof(c_0_669,axiom,
! [X2,X1,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X4),c_Nat_Osemiring__1__class_Oof__nat(X2,X4),X4) ),
file('<stdin>',cls_of__nat__less__iff_0) ).
fof(c_0_670,axiom,
! [X5,X21,X22] :
( c_HOL_Oord__class_Oless(c_Suc(X22),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(X21,X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(X22,X21,tc_nat) ),
file('<stdin>',cls_less__trans__Suc_0) ).
fof(c_0_671,axiom,
! [X2,X5] :
( c_lessequals(X5,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X2,tc_nat) ),
file('<stdin>',cls_dvd__imp__le_0) ).
fof(c_0_672,axiom,
! [X8,X9,X4] :
( ~ class_Orderings_Oorder(X4)
| c_lessequals(c_SetInterval_Oord__class_OatLeast(X9,X4),c_SetInterval_Oord__class_OatLeast(X8,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X8,X9,X4) ),
file('<stdin>',cls_atLeast__subset__iff_1) ).
fof(c_0_673,axiom,
! [X8,X9,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X9,c_Lattices_Olower__semilattice__class_Oinf(X9,X8,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X9,X8,X4) ),
file('<stdin>',cls_inf__left__idem_0) ).
fof(c_0_674,axiom,
! [X8,X9,X4] :
( ~ class_Lattices_Olattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X9,c_Lattices_Olower__semilattice__class_Oinf(X9,X8,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X9,X8,X4) ),
file('<stdin>',cls_inf__sup__aci_I4_J_0) ).
fof(c_0_675,axiom,
! [X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X10,X3,X4),X10,X4) = c_Divides_Odiv__class_Omod(X3,X10,X4) ),
file('<stdin>',cls_mod__add__self1_0) ).
fof(c_0_676,axiom,
! [X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,X10,X4),X10,X4) = c_Divides_Odiv__class_Omod(X3,X10,X4) ),
file('<stdin>',cls_mod__add__self2_0) ).
fof(c_0_677,axiom,
! [X8,X9,X4] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X4)
| c_HOL_Otimes__class_Otimes(X9,c_HOL_Otimes__class_Otimes(X9,X8,X4),X4) = c_HOL_Otimes__class_Otimes(X9,X8,X4) ),
file('<stdin>',cls_mult__left__idem_0) ).
fof(c_0_678,axiom,
! [X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X3,X10,X4),X10,X4) = c_Divides_Odiv__class_Omod(X3,X10,X4) ),
file('<stdin>',cls_mod__mod__trivial_0) ).
fof(c_0_679,axiom,
! [X34,X9,X4] :
( c_in(X9,X34,X4)
| c_Finite__Set_Ocard(c_Set_Oinsert(X9,X34,X4),X4) = c_Suc(c_Finite__Set_Ocard(X34,X4))
| c_Finite__Set_Ocard(X34,X4) = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_card__Suc__eq_4) ).
fof(c_0_680,axiom,
! [X2] :
( c_Suc(c_HOL_Ominus__class_Ominus(X2,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
file('<stdin>',cls_Suc__pred_0) ).
fof(c_0_681,axiom,
! [X2,X1] : c_HOL_Ominus__class_Ominus(X1,c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),
file('<stdin>',cls_diff__Suc__eq__diff__pred_0) ).
fof(c_0_682,axiom,
! [X5,X21,X22] :
( c_lessequals(X22,X5,tc_nat)
| ~ c_lessequals(X21,X5,tc_nat)
| ~ c_lessequals(X22,X21,tc_nat) ),
file('<stdin>',cls_le__trans_0) ).
fof(c_0_683,axiom,
! [X15,X8,X9] :
( c_Ring__and__Field_Odvd__class_Odvd(X9,X15,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X15,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X8,tc_nat) ),
file('<stdin>',cls_dvd_Oorder__trans_0) ).
fof(c_0_684,axiom,
! [X9,X7,X4] : c_Set_Oinsert(X9,c_Set_Oinsert(X9,X7,X4),X4) = c_Set_Oinsert(X9,X7,X4),
file('<stdin>',cls_insert__absorb2_0) ).
fof(c_0_685,axiom,
! [X2,X1] : c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
file('<stdin>',cls_mult__Suc_0) ).
fof(c_0_686,axiom,
! [X2,X1] : c_HOL_Otimes__class_Otimes(X1,c_Suc(X2),tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
file('<stdin>',cls_mult__Suc__right_0) ).
fof(c_0_687,axiom,
! [X9,X26,X4] :
( ~ hBOOL(hAPP(X26,X9))
| ~ c_in(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4) ),
file('<stdin>',cls_bex__empty_0) ).
fof(c_0_688,axiom,
! [X42,X20,X14,X4] :
( ~ class_HOL_Oord(X14)
| c_lessequals(X20,X42,tc_fun(X4,X14))
| ~ c_HOL_Oord__class_Oless(X20,X42,tc_fun(X4,X14)) ),
file('<stdin>',cls_less__fun__def_0) ).
fof(c_0_689,axiom,
! [X20,X25,X4] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X4)
| c_lessequals(X25,c_Inductive_Ocomplete__lattice__class_Ogfp(X20,X4),X4)
| ~ c_lessequals(X25,hAPP(X20,X25),X4) ),
file('<stdin>',cls_gfp__upperbound_0) ).
fof(c_0_690,axiom,
! [X6,X7,X4] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),X4)
| ~ c_Finite__Set_Ofinite(X7,X4)
| ~ c_Finite__Set_Ofinite(X6,X4) ),
file('<stdin>',cls_finite__Diff2_1) ).
fof(c_0_691,axiom,
! [X2,X1] :
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) = X1
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('<stdin>',cls_add__diff__inverse_0) ).
fof(c_0_692,axiom,
! [X9,X4] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X9)),
file('<stdin>',cls_bot1E_0) ).
fof(c_0_693,axiom,
! [X3,X7,X4] :
( c_Finite__Set_Ofinite(X7,X4)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X3,X7,X4),X4) ),
file('<stdin>',cls_finite__insert_0) ).
fof(c_0_694,axiom,
! [X2] :
( X2 = c_Suc(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
file('<stdin>',cls_Suc__pred_H_0) ).
fof(c_0_695,axiom,
! [X2] :
( c_Suc(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
file('<stdin>',cls_Suc__diff__1_0) ).
fof(c_0_696,axiom,
! [X7,X4] : ~ c_HOL_Oord__class_Oless(X7,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
file('<stdin>',cls_not__psubset__empty_0) ).
fof(c_0_697,axiom,
! [X2,X48,X26] :
( hBOOL(hAPP(X26,X48))
| c_lessequals(X2,c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1(X26,X2),tc_nat)
| ~ c_lessequals(c_Suc(X2),X48,tc_nat) ),
file('<stdin>',cls_Suc__le__D__lemma_0) ).
fof(c_0_698,axiom,
! [X8,X9,X4] :
( ~ class_Orderings_Opreorder(X4)
| c_HOL_Oord__class_Oless(X9,X8,X4)
| c_lessequals(X8,X9,X4)
| ~ c_lessequals(X9,X8,X4) ),
file('<stdin>',cls_less__le__not__le_2) ).
fof(c_0_699,axiom,
! [X6,X7,X4] :
( c_HOL_Oord__class_Oless(X7,X6,tc_fun(X4,tc_bool))
| X7 = X6
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_psubset__eq_2) ).
fof(c_0_700,axiom,
! [X6,X7,X4] :
( X7 = X6
| c_HOL_Oord__class_Oless(X7,X6,tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_subset__iff__psubset__eq_0) ).
fof(c_0_701,axiom,
! [X6,X7,X4] :
( c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)) = X6
| ~ c_lessequals(X6,X7,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_Int__absorb1_0) ).
fof(c_0_702,axiom,
! [X6,X7,X4] :
( c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)) = X7
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_Int__absorb2_0) ).
fof(c_0_703,axiom,
! [X9,X50,X26,X4] :
( hBOOL(hAPP(X50,X9))
| ~ hBOOL(hAPP(X26,X9))
| ~ c_lessequals(X26,X50,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_predicate1D_0) ).
fof(c_0_704,axiom,
! [X9,X50,X26,X4] :
( hBOOL(hAPP(X50,X9))
| ~ c_lessequals(X26,X50,tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(X26,X9)) ),
file('<stdin>',cls_rev__predicate1D_0) ).
fof(c_0_705,axiom,
! [X2,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| 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(X4),c_Nat_Osemiring__1__class_Oof__nat(X2,X4),X4) ),
file('<stdin>',cls_of__nat__0__less__iff_0) ).
fof(c_0_706,axiom,
! [X6,X7,X4] :
( c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(X7,X6,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_psubset__eq_0) ).
fof(c_0_707,axiom,
! [X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X4),c_HOL_Oone__class_Oone(X4),X4),X4) ),
file('<stdin>',cls_zero__less__two_0) ).
fof(c_0_708,axiom,
! [X9,X26,X4] :
( hBOOL(hAPP(X26,X9))
| ~ c_in(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4) ),
file('<stdin>',cls_ball__empty_0) ).
fof(c_0_709,axiom,
! [X2,X1,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X4),c_Nat_Osemiring__1__class_Oof__nat(X2,X4),X4)
| ~ c_lessequals(X1,X2,tc_nat) ),
file('<stdin>',cls_of__nat__le__iff_1) ).
fof(c_0_710,axiom,
! [X2,X1,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X4),c_Nat_Osemiring__1__class_Oof__nat(X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('<stdin>',cls_of__nat__less__iff_1) ).
fof(c_0_711,axiom,
! [X9,X7,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_lessequals(X9,c_Finite__Set_Olinorder__class_OMax(X7,X4),X4)
| ~ c_in(X9,X7,X4)
| ~ c_Finite__Set_Ofinite(X7,X4) ),
file('<stdin>',cls_Max__ge_0) ).
fof(c_0_712,axiom,
! [X9,X7,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X7,X4),X9,X4)
| ~ c_in(X9,X7,X4)
| ~ c_Finite__Set_Ofinite(X7,X4) ),
file('<stdin>',cls_Min__le_0) ).
fof(c_0_713,axiom,
! [X2,X1,X26] :
( hBOOL(hAPP(hAPP(X26,X2),X1))
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('<stdin>',cls_nat__less__cases_0) ).
fof(c_0_714,axiom,
! [X40,X13,X4] :
( c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X13,X40,tc_fun(X4,tc_bool)),X4)
| ~ c_Finite__Set_Ofinite(X13,X4) ),
file('<stdin>',cls_finite__Int_0) ).
fof(c_0_715,axiom,
! [X40,X13,X4] :
( c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X13,X40,tc_fun(X4,tc_bool)),X4)
| ~ c_Finite__Set_Ofinite(X40,X4) ),
file('<stdin>',cls_finite__Int_1) ).
fof(c_0_716,axiom,
! [X6,X7,X4] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),X4)
| ~ c_Finite__Set_Ofinite(X7,X4) ),
file('<stdin>',cls_finite__Diff_0) ).
fof(c_0_717,axiom,
! [X5,X22,X4] :
( ~ class_HOL_Oord(X4)
| c_lessequals(X5,X22,X4)
| ~ c_in(X22,c_SetInterval_Oord__class_OatLeast(X5,X4),X4) ),
file('<stdin>',cls_atLeast__iff_0) ).
fof(c_0_718,axiom,
! [X2,X1,X5] :
( c_HOL_Otimes__class_Otimes(c_Suc(X5),X1,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X5),X2,tc_nat)
| X1 = X2 ),
file('<stdin>',cls_Suc__mult__cancel1_0) ).
fof(c_0_719,axiom,
! [X15,X8,X9,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| c_HOL_Oplus__class_Oplus(X9,X8,X4) != c_HOL_Oplus__class_Oplus(X9,X15,X4)
| X8 = X15 ),
file('<stdin>',cls_class__ringb_Oadd__cancel_0) ).
fof(c_0_720,axiom,
! [X3,X6,X4] : c_lessequals(X6,c_Set_Oinsert(X3,X6,X4),tc_fun(X4,tc_bool)),
file('<stdin>',cls_subset__insertI_0) ).
fof(c_0_721,axiom,
! [X34,X9,X4] :
( c_Set_Oinsert(X9,X34,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| c_in(X9,X34,X4) ),
file('<stdin>',cls_comm__monoid__add_Ononempty__iff_2) ).
fof(c_0_722,axiom,
! [X2,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Nat_Osemiring__1__class_Oof__nat(X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
file('<stdin>',cls_of__nat__0__less__iff_1) ).
fof(c_0_723,axiom,
! [X8,X9,X4] :
( ~ class_Orderings_Oorder(X4)
| X9 = X8
| ~ c_lessequals(X8,X9,X4)
| ~ c_lessequals(X9,X8,X4) ),
file('<stdin>',cls_order__eq__iff_2) ).
fof(c_0_724,axiom,
! [X8,X9,X4] :
( ~ class_Orderings_Oorder(X4)
| X9 = X8
| ~ c_lessequals(X8,X9,X4)
| ~ c_lessequals(X9,X8,X4) ),
file('<stdin>',cls_order__antisym_0) ).
fof(c_0_725,axiom,
! [X8,X9,X4] :
( ~ class_Orderings_Oorder(X4)
| X9 = X8
| ~ c_lessequals(X9,X8,X4)
| ~ c_lessequals(X8,X9,X4) ),
file('<stdin>',cls_order__antisym__conv_0) ).
fof(c_0_726,axiom,
! [X4] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
file('<stdin>',cls_subset__empty_1) ).
fof(c_0_727,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(X4),X4),X4) ),
file('<stdin>',cls_less__add__one_0) ).
fof(c_0_728,axiom,
! [X38,X39,X9,X4] :
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_HOL_Ominus__class_Ominus(X9,X9,X4) != c_HOL_Ominus__class_Ominus(X39,X38,X4)
| X39 = X38 ),
file('<stdin>',cls_eq__eqI_0) ).
fof(c_0_729,axiom,
! [X8,X34,X9,X4] :
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_HOL_Ominus__class_Ominus(X34,X8,X4) != c_HOL_Ominus__class_Ominus(X9,X9,X4)
| X34 = X8 ),
file('<stdin>',cls_eq__eqI_1) ).
fof(c_0_730,axiom,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X4)
| c_HOL_Oplus__class_Oplus(X10,X3,X4) != c_HOL_Oplus__class_Oplus(X11,X3,X4)
| X10 = X11 ),
file('<stdin>',cls_add__right__cancel_0) ).
fof(c_0_731,axiom,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X4)
| c_HOL_Oplus__class_Oplus(X3,X10,X4) != c_HOL_Oplus__class_Oplus(X3,X11,X4)
| X10 = X11 ),
file('<stdin>',cls_add__left__cancel_0) ).
fof(c_0_732,axiom,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X4)
| c_HOL_Oplus__class_Oplus(X3,X10,X4) != c_HOL_Oplus__class_Oplus(X3,X11,X4)
| X10 = X11 ),
file('<stdin>',cls_add__imp__eq_0) ).
fof(c_0_733,axiom,
! [X10,X3,X4] :
( ~ class_Orderings_Opreorder(X4)
| ~ c_HOL_Oord__class_Oless(X10,X3,X4)
| ~ c_HOL_Oord__class_Oless(X3,X10,X4) ),
file('<stdin>',cls_order__less__asym_H_0) ).
fof(c_0_734,axiom,
! [X8,X9,X4] :
( ~ class_Orderings_Opreorder(X4)
| ~ c_HOL_Oord__class_Oless(X8,X9,X4)
| ~ c_HOL_Oord__class_Oless(X9,X8,X4) ),
file('<stdin>',cls_order__less__asym_0) ).
fof(c_0_735,axiom,
! [X8,X9,X4] :
( ~ class_Orderings_Olinorder(X4)
| ~ c_HOL_Oord__class_Oless(X9,X8,X4)
| ~ c_HOL_Oord__class_Oless(X8,X9,X4) ),
file('<stdin>',cls_not__less__iff__gr__or__eq_1) ).
fof(c_0_736,axiom,
! [X10,X3,X4] :
( ~ class_Orderings_Oorder(X4)
| ~ c_HOL_Oord__class_Oless(X3,X10,X4)
| ~ c_HOL_Oord__class_Oless(X10,X3,X4) ),
file('<stdin>',cls_xt1_I9_J_0) ).
fof(c_0_737,axiom,
! [X8,X9,X4] :
( ~ class_Orderings_Opreorder(X4)
| ~ c_lessequals(X8,X9,X4)
| ~ c_HOL_Oord__class_Oless(X9,X8,X4) ),
file('<stdin>',cls_less__le__not__le_1) ).
fof(c_0_738,axiom,
! [X8,X9,X4] :
( ~ class_Orderings_Olinorder(X4)
| ~ c_lessequals(X9,X8,X4)
| ~ c_HOL_Oord__class_Oless(X8,X9,X4) ),
file('<stdin>',cls_linorder__not__le_1) ).
fof(c_0_739,axiom,
! [X8,X9,X4] :
( ~ class_Orderings_Olinorder(X4)
| ~ c_HOL_Oord__class_Oless(X9,X8,X4)
| ~ c_lessequals(X8,X9,X4) ),
file('<stdin>',cls_linorder__not__less_1) ).
fof(c_0_740,axiom,
! [X9,X4] :
( ~ class_Orderings_Olinorder(X4)
| ~ c_lessequals(X9,X9,X4)
| ~ c_HOL_Oord__class_Oless(X9,X9,X4) ),
file('<stdin>',cls_linorder__antisym__conv2_1) ).
fof(c_0_741,axiom,
! [X2,X1] :
( X2 = X1
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
file('<stdin>',cls_le__less__Suc__eq_0) ).
fof(c_0_742,axiom,
! [X2,X1] :
( ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_Suc(X2),X1,tc_nat) ),
file('<stdin>',cls_not__less__eq__eq_1) ).
fof(c_0_743,axiom,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
file('<stdin>',cls_not__less__eq_1) ).
fof(c_0_744,axiom,
! [X2,X1] :
( c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = X2 ),
file('<stdin>',cls_diffs0__imp__equal_0) ).
fof(c_0_745,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X3,X3,X4),X4) ),
file('<stdin>',cls_zero__le__square_0) ).
fof(c_0_746,axiom,
! [X5,X22,X4] :
( ~ class_HOL_Oord(X4)
| c_in(X22,c_SetInterval_Oord__class_OatLeast(X5,X4),X4)
| ~ c_lessequals(X5,X22,X4) ),
file('<stdin>',cls_atLeast__iff_1) ).
fof(c_0_747,axiom,
! [X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X10,X3,X4),X10,X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_mod__mult__self1__is__0_0) ).
fof(c_0_748,axiom,
! [X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X10,X4),X10,X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_mod__mult__self2__is__0_0) ).
fof(c_0_749,axiom,
! [X2,X1,X5] :
( c_HOL_Otimes__class_Otimes(X1,X5,tc_nat) != c_HOL_Otimes__class_Otimes(X2,X5,tc_nat)
| X5 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = X2 ),
file('<stdin>',cls_mult__cancel2_0) ).
fof(c_0_750,axiom,
! [X2,X1,X5] :
( c_HOL_Otimes__class_Otimes(X5,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X5,X2,tc_nat)
| X5 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = X2 ),
file('<stdin>',cls_mult__cancel1_0) ).
fof(c_0_751,axiom,
! [X2,X1,X5] :
( c_HOL_Otimes__class_Otimes(X5,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X5,X2,tc_nat)
| X1 = X2
| X5 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_nat__mult__eq__cancel__disj_0) ).
fof(c_0_752,axiom,
! [X2,X1] :
( X1 = X2
| ~ c_lessequals(X2,X1,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
file('<stdin>',cls_le__antisym_0) ).
fof(c_0_753,axiom,
! [X10,X3] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X10,tc_nat)
| X3 = X10 ),
file('<stdin>',cls_dvd_Oneq__le__trans_0) ).
fof(c_0_754,axiom,
! [X10,X3] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X3,tc_nat)
| X3 = X10
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X10,tc_nat) ),
file('<stdin>',cls_dvd_Ole__neq__trans_0) ).
fof(c_0_755,axiom,
! [X8,X9] :
( X9 = X8
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X8,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X9,tc_nat) ),
file('<stdin>',cls_dvd_Oantisym__conv_0) ).
fof(c_0_756,axiom,
! [X2,X1] :
( X1 = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
file('<stdin>',cls_dvd__antisym_0) ).
fof(c_0_757,axiom,
! [X8,X9] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X9,tc_nat)
| X9 = X8
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X8,tc_nat) ),
file('<stdin>',cls_dvd_Oless__le_0) ).
fof(c_0_758,axiom,
! [X8,X9] :
( X9 = X8
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X9,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X8,tc_nat) ),
file('<stdin>',cls_dvd_Oantisym_0) ).
fof(c_0_759,axiom,
! [X8,X9] :
( X9 = X8
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X9,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X8,tc_nat) ),
file('<stdin>',cls_dvd_Oeq__iff_2) ).
fof(c_0_760,axiom,
! [X10,X3,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X10,X4),X10,X4) = X3 ),
file('<stdin>',cls_add__diff__cancel_0) ).
fof(c_0_761,axiom,
! [X10,X3,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X3,X10,X4),X10,X4) = X3 ),
file('<stdin>',cls_diff__add__cancel_0) ).
fof(c_0_762,axiom,
! [X8,X9,X4] :
( ~ class_Lattices_Olattice(X4)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X9,X8,X4),X9,X4) ),
file('<stdin>',cls_inf__sup__ord_I1_J_0) ).
fof(c_0_763,axiom,
! [X8,X9,X4] :
( ~ class_Lattices_Olattice(X4)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X9,X8,X4),X8,X4) ),
file('<stdin>',cls_inf__sup__ord_I2_J_0) ).
fof(c_0_764,axiom,
! [X8,X9,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X9,X8,X4),X8,X4) ),
file('<stdin>',cls_inf__le2_0) ).
fof(c_0_765,axiom,
! [X8,X9,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X9,X8,X4),X9,X4) ),
file('<stdin>',cls_inf__le1_0) ).
fof(c_0_766,axiom,
! [X2,X1,X5] :
( c_HOL_Oplus__class_Oplus(X5,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X5,X2,tc_nat)
| X1 = X2 ),
file('<stdin>',cls_nat__add__left__cancel_0) ).
fof(c_0_767,axiom,
! [X2,X1,X5] :
( c_HOL_Oplus__class_Oplus(X1,X5,tc_nat) != c_HOL_Oplus__class_Oplus(X2,X5,tc_nat)
| X1 = X2 ),
file('<stdin>',cls_nat__add__right__cancel_0) ).
fof(c_0_768,axiom,
! [X15,X8,X9] :
( c_HOL_Oplus__class_Oplus(X9,X8,tc_nat) != c_HOL_Oplus__class_Oplus(X9,X15,tc_nat)
| X8 = X15 ),
file('<stdin>',cls_natgb_Oadd__cancel_0) ).
fof(c_0_769,axiom,
! [X5,X10,X4] :
( ~ class_Ring__and__Field_Odvd(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X10,c_HOL_Otimes__class_Otimes(X10,X5,X4),X4) ),
file('<stdin>',cls_dvdI_0) ).
fof(c_0_770,axiom,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Otimes__class_Otimes(X3,X10,X4),X4) ),
file('<stdin>',cls_dvd__triv__left_0) ).
fof(c_0_771,axiom,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Otimes__class_Otimes(X10,X3,X4),X4) ),
file('<stdin>',cls_dvd__triv__right_0) ).
fof(c_0_772,axiom,
! [X3,X4] : ~ c_in(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),
file('<stdin>',cls_emptyE_0) ).
fof(c_0_773,axiom,
! [X11,X4] : ~ c_in(X11,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),
file('<stdin>',cls_empty__iff_0) ).
fof(c_0_774,axiom,
! [X9,X4] : ~ c_in(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),
file('<stdin>',cls_ex__in__conv_0) ).
fof(c_0_775,axiom,
! [X2,X1] : c_HOL_Oplus__class_Oplus(X1,c_Suc(X2),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),
file('<stdin>',cls_add__Suc__right_0) ).
fof(c_0_776,axiom,
! [X2,X1] : c_HOL_Oplus__class_Oplus(c_Suc(X1),X2,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),
file('<stdin>',cls_add__Suc_0) ).
fof(c_0_777,axiom,
! [X2,X1,X26] :
( hBOOL(hAPP(X26,X2))
| hBOOL(hAPP(X26,X1))
| ~ c_lessequals(c_Suc(X1),c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1(X26),tc_nat) ),
file('<stdin>',cls_full__nat__induct_0) ).
fof(c_0_778,axiom,
! [X2,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_Suc(X1),tc_nat),
file('<stdin>',cls_diff__less__Suc_0) ).
fof(c_0_779,axiom,
! [X9,X6,X4] : c_in(X9,c_Set_Oinsert(X9,X6,X4),X4),
file('<stdin>',cls_insertCI_1) ).
fof(c_0_780,axiom,
! [X3,X6,X4] : c_in(X3,c_Set_Oinsert(X3,X6,X4),X4),
file('<stdin>',cls_insertI1_0) ).
fof(c_0_781,axiom,
! [X9,X7,X4] : c_in(X9,c_Set_Oinsert(X9,X7,X4),X4),
file('<stdin>',cls_insert__iff_1) ).
fof(c_0_782,axiom,
! [X6,X7,X4] :
( c_Finite__Set_Ofinite(X7,X4)
| ~ c_Finite__Set_Ofinite(X6,X4)
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_finite__subset_0) ).
fof(c_0_783,axiom,
! [X6,X7,X4] :
( c_Finite__Set_Ofinite(X7,X4)
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| ~ c_Finite__Set_Ofinite(X6,X4) ),
file('<stdin>',cls_rev__finite__subset_0) ).
fof(c_0_784,axiom,
! [X9,X17] : c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X17,X9,tc_nat),X17,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_mod__eq__0__iff_1) ).
fof(c_0_785,axiom,
! [X2,X1] : c_HOL_Ominus__class_Ominus(X2,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_diff__add__0_0) ).
fof(c_0_786,axiom,
! [X2,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),X2,tc_nat) = X1,
file('<stdin>',cls_diff__add__inverse_0) ).
fof(c_0_787,axiom,
! [X2,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat) = X1,
file('<stdin>',cls_diff__add__inverse2_0) ).
fof(c_0_788,axiom,
! [X2,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X1,tc_nat),
file('<stdin>',cls_diff__le__self_0) ).
fof(c_0_789,axiom,
! [X1] : c_lessequals(X1,c_HOL_Otimes__class_Otimes(X1,X1,tc_nat),tc_nat),
file('<stdin>',cls_le__square_0) ).
fof(c_0_790,axiom,
! [X2,X1] : c_lessequals(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X1,tc_nat),
file('<stdin>',cls_mod__less__eq__dividend_0) ).
fof(c_0_791,axiom,
! [X2,X1] : c_lessequals(X2,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat),
file('<stdin>',cls_le__add1_0) ).
fof(c_0_792,axiom,
! [X2,X1] : c_lessequals(X2,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),
file('<stdin>',cls_le__add2_0) ).
fof(c_0_793,axiom,
! [X9,X1] : c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,X9,tc_nat),tc_nat),
file('<stdin>',cls_le__iff__add_1) ).
fof(c_0_794,axiom,
! [X2,X1] :
( c_lessequals(X2,X1,tc_nat)
| ~ c_lessequals(c_Suc(X2),c_Suc(X1),tc_nat) ),
file('<stdin>',cls_Suc__le__mono_0) ).
fof(c_0_795,axiom,
! [X2,X1] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat) ),
file('<stdin>',cls_Suc__less__eq_0) ).
fof(c_0_796,axiom,
! [X7,X4] : c_HOL_Ominus__class_Ominus(X7,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
file('<stdin>',cls_Diff__UNIV_0) ).
fof(c_0_797,axiom,
! [X7,X4] : c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X7,tc_fun(X4,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
file('<stdin>',cls_empty__Diff_0) ).
fof(c_0_798,axiom,
! [X7,X4] : c_Lattices_Olower__semilattice__class_Oinf(X7,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
file('<stdin>',cls_Int__empty__right_0) ).
fof(c_0_799,axiom,
! [X6,X4] : c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X6,tc_fun(X4,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
file('<stdin>',cls_Int__empty__left_0) ).
fof(c_0_800,axiom,
! [X6,X7,X4] : c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X4,tc_bool)),
file('<stdin>',cls_Int__commute_0) ).
fof(c_0_801,axiom,
! [X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(X10,X3,X4) != c_HOL_Ozero__class_Ozero(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X10,X4) ),
file('<stdin>',cls_dvd__eq__mod__eq__0_1) ).
fof(c_0_802,axiom,
! [X2,X1] :
( X1 = c_Suc(X2)
| c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X1,c_Suc(X2),tc_nat) ),
file('<stdin>',cls_le__SucE_0) ).
fof(c_0_803,axiom,
! [X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(X10,X3,X4) = c_HOL_Ozero__class_Ozero(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X10,X4) ),
file('<stdin>',cls_dvd__imp__mod__0_0) ).
fof(c_0_804,axiom,
! [X5,X7,X4] :
( c_Finite__Set_Ocard(X7,X4) != c_Suc(X5)
| c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(X7,X5,X4),X4) = X5 ),
file('<stdin>',cls_card__Suc__eq_2) ).
fof(c_0_805,axiom,
! [X5,X7,X4] :
( c_Finite__Set_Ocard(X7,X4) != c_Suc(X5)
| c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(X7,X5,X4),X4) = X5 ),
file('<stdin>',cls_card__eq__SucD_2) ).
fof(c_0_806,axiom,
! [X10,X3,X4] :
( ~ class_Orderings_Oorder(X4)
| c_HOL_Oord__class_Oless(X10,X3,X4)
| X3 = X10
| ~ c_lessequals(X10,X3,X4) ),
file('<stdin>',cls_xt1_I11_J_0) ).
fof(c_0_807,axiom,
! [X10,X3,X4] :
( ~ class_Orderings_Oorder(X4)
| c_HOL_Oord__class_Oless(X10,X3,X4)
| ~ c_lessequals(X10,X3,X4)
| X3 = X10 ),
file('<stdin>',cls_xt1_I12_J_0) ).
fof(c_0_808,axiom,
! [X8,X9,X4] :
( ~ class_Orderings_Oorder(X4)
| X9 = X8
| c_HOL_Oord__class_Oless(X9,X8,X4)
| ~ c_lessequals(X9,X8,X4) ),
file('<stdin>',cls_order__le__less_0) ).
fof(c_0_809,axiom,
! [X8,X9,X4] :
( ~ class_Orderings_Oorder(X4)
| c_HOL_Oord__class_Oless(X9,X8,X4)
| X9 = X8
| ~ c_lessequals(X9,X8,X4) ),
file('<stdin>',cls_order__less__le_2) ).
fof(c_0_810,axiom,
! [X10,X3,X4] :
( ~ class_Orderings_Oorder(X4)
| c_HOL_Oord__class_Oless(X3,X10,X4)
| X3 = X10
| ~ c_lessequals(X3,X10,X4) ),
file('<stdin>',cls_order__le__neq__trans_0) ).
fof(c_0_811,axiom,
! [X10,X3,X4] :
( ~ class_Orderings_Oorder(X4)
| c_HOL_Oord__class_Oless(X3,X10,X4)
| ~ c_lessequals(X3,X10,X4)
| X3 = X10 ),
file('<stdin>',cls_order__neq__le__trans_0) ).
fof(c_0_812,axiom,
! [X8,X9,X4] :
( ~ class_Orderings_Olinorder(X4)
| X9 = X8
| ~ c_lessequals(X9,X8,X4)
| c_HOL_Oord__class_Oless(X9,X8,X4) ),
file('<stdin>',cls_linorder__antisym__conv1_0) ).
fof(c_0_813,axiom,
! [X8,X9,X4] :
( ~ class_Orderings_Olinorder(X4)
| X9 = X8
| c_HOL_Oord__class_Oless(X9,X8,X4)
| ~ c_lessequals(X9,X8,X4) ),
file('<stdin>',cls_linorder__antisym__conv2_0) ).
fof(c_0_814,axiom,
! [X8,X9,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X9,X8,X4) != X9
| c_lessequals(X9,X8,X4) ),
file('<stdin>',cls_le__iff__inf_1) ).
fof(c_0_815,axiom,
! [X2,X1] :
( c_lessequals(c_Suc(X2),c_Suc(X1),tc_nat)
| ~ c_lessequals(X2,X1,tc_nat) ),
file('<stdin>',cls_Suc__le__mono_1) ).
fof(c_0_816,axiom,
! [X2,X1] :
( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('<stdin>',cls_Suc__mono_0) ).
fof(c_0_817,axiom,
! [X9,X2] :
( c_HOL_Oord__class_Oless(c_Suc(X9),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X9,X2,tc_nat) ),
file('<stdin>',cls_less__Suc__eq__0__disj_3) ).
fof(c_0_818,axiom,
! [X2,X1] :
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
file('<stdin>',cls_less__SucE_0) ).
fof(c_0_819,axiom,
! [X2,X1] :
( X1 = X2
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
file('<stdin>',cls_less__antisym_0) ).
fof(c_0_820,axiom,
! [X2,X1] :
( X2 = X1
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
file('<stdin>',cls_not__less__less__Suc__eq_0) ).
fof(c_0_821,axiom,
! [X8,X9,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X9,X8,X4) = X8
| ~ c_lessequals(X8,X9,X4) ),
file('<stdin>',cls_inf__absorb2_0) ).
fof(c_0_822,axiom,
! [X8,X9,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X9,X8,X4) = X9
| ~ c_lessequals(X9,X8,X4) ),
file('<stdin>',cls_le__iff__inf_0) ).
fof(c_0_823,axiom,
! [X2,X1] :
( c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
| c_Suc(X1) = X2
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('<stdin>',cls_Suc__lessI_0) ).
fof(c_0_824,axiom,
! [X8,X9,X4] :
( ~ class_Orderings_Oorder(X4)
| c_lessequals(X9,X8,X4)
| ~ c_HOL_Oord__class_Oless(X9,X8,X4) ),
file('<stdin>',cls_order__le__less_1) ).
fof(c_0_825,axiom,
! [X8,X9,X4] :
( ~ class_Orderings_Opreorder(X4)
| c_lessequals(X9,X8,X4)
| ~ c_HOL_Oord__class_Oless(X9,X8,X4) ),
file('<stdin>',cls_order__less__imp__le_0) ).
fof(c_0_826,axiom,
! [X2,X1] :
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
file('<stdin>',cls_Suc__leD_0) ).
fof(c_0_827,axiom,
! [X2,X1] :
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_lessequals(c_Suc(X2),X1,tc_nat) ),
file('<stdin>',cls_less__eq__Suc__le_1) ).
fof(c_0_828,axiom,
! [X2,X1] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
file('<stdin>',cls_Suc__le__eq_0) ).
fof(c_0_829,axiom,
! [X2,X1] :
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
file('<stdin>',cls_less__Suc__eq__le_0) ).
fof(c_0_830,axiom,
! [X2,X1] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat) ),
file('<stdin>',cls_Suc__lessD_0) ).
fof(c_0_831,axiom,
! [X3,X7,X4] :
( c_Finite__Set_Ofinite(c_Set_Oinsert(X3,X7,X4),X4)
| ~ c_Finite__Set_Ofinite(X7,X4) ),
file('<stdin>',cls_finite__insert_1) ).
fof(c_0_832,axiom,
! [X7,X4] :
( c_Finite__Set_Ofinite(X7,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(X7,X4),tc_nat) ),
file('<stdin>',cls_card__gt__0__iff_1) ).
fof(c_0_833,axiom,
! [X1,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_of__nat__less__0__iff_0) ).
fof(c_0_834,axiom,
! [X2,X1] :
( c_lessequals(X1,c_Suc(X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
file('<stdin>',cls_le__SucI_0) ).
fof(c_0_835,axiom,
! [X2,X1] :
( c_lessequals(c_Suc(X2),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
file('<stdin>',cls_less__eq__Suc__le_0) ).
fof(c_0_836,axiom,
! [X2,X1] :
( c_lessequals(c_Suc(X1),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('<stdin>',cls_Suc__leI_0) ).
fof(c_0_837,axiom,
! [X2,X1] :
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
file('<stdin>',cls_less__Suc__eq__le_1) ).
fof(c_0_838,axiom,
! [X9] :
( ~ c_lessequals(X9,X9,tc_nat)
| c_HOL_Oord__class_Oless(X9,c_Suc(X9),tc_nat) ),
file('<stdin>',cls_le__less__Suc__eq_1) ).
fof(c_0_839,axiom,
! [X2,X1] :
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('<stdin>',cls_less__SucI_0) ).
fof(c_0_840,axiom,
! [X3,X7,X4] :
( c_Set_Oinsert(X3,X7,X4) = X7
| ~ c_in(X3,X7,X4) ),
file('<stdin>',cls_insert__absorb_0) ).
fof(c_0_841,axiom,
! [X2,X1] :
( c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_lessequals(X1,X2,tc_nat) ),
file('<stdin>',cls_diff__is__0__eq_0) ).
fof(c_0_842,axiom,
! [X2,X1] :
( c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
file('<stdin>',cls_diff__is__0__eq_1) ).
fof(c_0_843,axiom,
! [X2,X1] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
file('<stdin>',cls_nat__less__le_2) ).
fof(c_0_844,axiom,
! [X2,X1] :
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
file('<stdin>',cls_le__eq__less__or__eq_0) ).
fof(c_0_845,axiom,
! [X2,X1] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
file('<stdin>',cls_le__neq__implies__less_0) ).
fof(c_0_846,axiom,
! [X7,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_in(c_Finite__Set_Olinorder__class_OMax(X7,X4),X7,X4)
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ c_Finite__Set_Ofinite(X7,X4) ),
file('<stdin>',cls_Max__in_0) ).
fof(c_0_847,axiom,
! [X7,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_in(c_Finite__Set_Olinorder__class_OMin(X7,X4),X7,X4)
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ c_Finite__Set_Ofinite(X7,X4) ),
file('<stdin>',cls_Min__in_0) ).
fof(c_0_848,axiom,
! [X2,X1] :
( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = X1
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('<stdin>',cls_mod__if_0) ).
fof(c_0_849,axiom,
! [X8,X9] :
( c_lessequals(X9,X8,tc_nat)
| ~ c_HOL_Oord__class_Oless(X9,X8,tc_nat) ),
file('<stdin>',cls_termination__basic__simps_I5_J_0) ).
fof(c_0_850,axiom,
! [X2,X1] :
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('<stdin>',cls_nat__less__le_0) ).
fof(c_0_851,axiom,
! [X9,X4] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X9)),
file('<stdin>',cls_top1I_0) ).
fof(c_0_852,axiom,
! [X7,X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(X7,X4),tc_nat)
| ~ c_Finite__Set_Ofinite(X7,X4)
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_card__gt__0__iff_2) ).
fof(c_0_853,axiom,
! [X7,X4] : c_Lattices_Olower__semilattice__class_Oinf(X7,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = X7,
file('<stdin>',cls_Int__UNIV__right_0) ).
fof(c_0_854,axiom,
! [X6,X4] : c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X6,tc_fun(X4,tc_bool)) = X6,
file('<stdin>',cls_Int__UNIV__left_0) ).
fof(c_0_855,axiom,
! [X7,X4] : c_HOL_Ominus__class_Ominus(X7,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = X7,
file('<stdin>',cls_Diff__empty_0) ).
fof(c_0_856,axiom,
! [X7,X4] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X7,tc_fun(X4,tc_bool)),
file('<stdin>',cls_empty__subsetI_0) ).
fof(c_0_857,axiom,
! [X7,X4] : c_lessequals(X7,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
file('<stdin>',cls_subset__UNIV_0) ).
fof(c_0_858,axiom,
! [X3,X7,X4] : c_Set_Oinsert(X3,X7,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
file('<stdin>',cls_insert__not__empty_0) ).
fof(c_0_859,axiom,
! [X3,X7,X4] : c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) != c_Set_Oinsert(X3,X7,X4),
file('<stdin>',cls_empty__not__insert_0) ).
fof(c_0_860,axiom,
! [X9,X4] : ~ c_HOL_Oord__class_Oless(X9,X9,tc_fun(X4,tc_bool)),
file('<stdin>',cls_psubset__eq_1) ).
fof(c_0_861,axiom,
! [X8,X9,X4] :
( ~ class_Orderings_Olinorder(X4)
| X9 = X8
| c_HOL_Oord__class_Oless(X9,X8,X4)
| c_HOL_Oord__class_Oless(X8,X9,X4) ),
file('<stdin>',cls_linorder__antisym__conv3_0) ).
fof(c_0_862,axiom,
! [X8,X9,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_HOL_Oord__class_Oless(X8,X9,X4)
| X9 = X8
| c_HOL_Oord__class_Oless(X9,X8,X4) ),
file('<stdin>',cls_linorder__less__linear_0) ).
fof(c_0_863,axiom,
! [X8,X9,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_HOL_Oord__class_Oless(X8,X9,X4)
| c_HOL_Oord__class_Oless(X9,X8,X4)
| X9 = X8 ),
file('<stdin>',cls_linorder__neqE_0) ).
fof(c_0_864,axiom,
! [X8,X9,X4] :
( ~ class_Orderings_Olinorder(X4)
| X9 = X8
| c_HOL_Oord__class_Oless(X8,X9,X4)
| c_HOL_Oord__class_Oless(X9,X8,X4) ),
file('<stdin>',cls_not__less__iff__gr__or__eq_0) ).
fof(c_0_865,axiom,
! [X8,X9,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_HOL_Oord__class_Oless(X8,X9,X4)
| c_HOL_Oord__class_Oless(X9,X8,X4)
| X9 = X8 ),
file('<stdin>',cls_linorder__neqE__ordered__idom_0) ).
fof(c_0_866,axiom,
! [X2,X1] : c_HOL_Ominus__class_Ominus(c_Suc(X1),c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),
file('<stdin>',cls_diff__Suc__Suc_0) ).
fof(c_0_867,axiom,
! [X2,X1] : c_HOL_Oplus__class_Oplus(c_Suc(X1),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_Suc(X2),tc_nat),
file('<stdin>',cls_add__Suc__shift_0) ).
fof(c_0_868,axiom,
! [X7,X4] :
( c_Finite__Set_Ocard(X7,X4) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(X7,c_HOL_Ozero__class_Ozero(tc_nat),X4) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_card__eq__SucD_3) ).
fof(c_0_869,axiom,
! [X7,X4] :
( c_Finite__Set_Ocard(X7,X4) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(X7,c_HOL_Ozero__class_Ozero(tc_nat),X4) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_card__Suc__eq_3) ).
fof(c_0_870,axiom,
! [X8,X9,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_lessequals(X8,X9,X4)
| c_lessequals(X9,X8,X4) ),
file('<stdin>',cls_linorder__linear_0) ).
fof(c_0_871,axiom,
! [X8,X9,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_HOL_Oord__class_Oless(X8,X9,X4)
| c_lessequals(X9,X8,X4) ),
file('<stdin>',cls_linorder__not__le_0) ).
fof(c_0_872,axiom,
! [X8,X9,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_lessequals(X8,X9,X4)
| c_HOL_Oord__class_Oless(X9,X8,X4) ),
file('<stdin>',cls_linorder__not__less_0) ).
fof(c_0_873,axiom,
! [X9,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_HOL_Oord__class_Oless(X9,X9,X4)
| c_lessequals(X9,X9,X4) ),
file('<stdin>',cls_linorder__antisym__conv1_1) ).
fof(c_0_874,axiom,
! [X8,X9,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_HOL_Oord__class_Oless(X9,X8,X4)
| c_lessequals(X8,X9,X4) ),
file('<stdin>',cls_not__leE_0) ).
fof(c_0_875,axiom,
! [X9,X47,X4] :
( hBOOL(hAPP(X47,X9))
| ~ c_in(X9,X47,X4) ),
file('<stdin>',cls_mem__def_0) ).
fof(c_0_876,axiom,
! [X8,X9,X4] :
( ~ class_Lattices_Olattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X9,X8,X4) = c_Lattices_Olower__semilattice__class_Oinf(X8,X9,X4) ),
file('<stdin>',cls_inf__sup__aci_I1_J_0) ).
fof(c_0_877,axiom,
! [X8,X9,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X9,X8,X4) = c_Lattices_Olower__semilattice__class_Oinf(X8,X9,X4) ),
file('<stdin>',cls_inf__commute_0) ).
fof(c_0_878,axiom,
! [X8,X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(X9,X8,X4) = c_HOL_Oplus__class_Oplus(X8,X9,X4) ),
file('<stdin>',cls_class__semiring_Oadd__c_0) ).
fof(c_0_879,axiom,
! [X10,X3,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_HOL_Oplus__class_Oplus(X3,X10,X4) = c_HOL_Oplus__class_Oplus(X10,X3,X4) ),
file('<stdin>',cls_comm__monoid__add_Omult__commute_0) ).
fof(c_0_880,axiom,
! [X11,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(X3,X11,X4) = c_HOL_Oplus__class_Oplus(X11,X3,X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I24_J_0) ).
fof(c_0_881,axiom,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(X3,X10,X4) = c_HOL_Otimes__class_Otimes(X10,X3,X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I7_J_0) ).
fof(c_0_882,axiom,
! [X8,X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(X9,X8,X4) = c_HOL_Otimes__class_Otimes(X8,X9,X4) ),
file('<stdin>',cls_class__semiring_Omul__c_0) ).
fof(c_0_883,axiom,
! [X1,X4] :
( ~ class_Ring__and__Field_Osemiring__1(X4)
| c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X1),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X4),c_Nat_Osemiring__1__class_Oof__nat(X1,X4),X4) ),
file('<stdin>',cls_of__nat__Suc_0) ).
fof(c_0_884,axiom,
! [X2,X1] :
( c_lessequals(c_Suc(X2),X1,tc_nat)
| c_lessequals(X1,X2,tc_nat) ),
file('<stdin>',cls_not__less__eq__eq_0) ).
fof(c_0_885,axiom,
! [X2,X1] :
( c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('<stdin>',cls_not__less__eq_0) ).
fof(c_0_886,axiom,
! [X9] :
( c_HOL_Oord__class_Oless(X9,X9,tc_nat)
| c_HOL_Oord__class_Oless(X9,c_Suc(X9),tc_nat) ),
file('<stdin>',cls_not__less__less__Suc__eq_1) ).
fof(c_0_887,axiom,
! [X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_not__one__le__zero_0) ).
fof(c_0_888,axiom,
! [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) ),
file('<stdin>',cls_not__one__less__zero_0) ).
fof(c_0_889,axiom,
! [X2,X1] : 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),
file('<stdin>',cls_mult__cancel2_1) ).
fof(c_0_890,axiom,
! [X2,X1] : 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),
file('<stdin>',cls_mult__cancel1_1) ).
fof(c_0_891,axiom,
! [X2,X1] :
( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != 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)) ),
file('<stdin>',cls_add__is__1_1) ).
fof(c_0_892,axiom,
! [X2,X1] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('<stdin>',cls_one__is__add_1) ).
fof(c_0_893,axiom,
! [X1] :
( 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) ),
file('<stdin>',cls_dvd__1__iff__1_0) ).
fof(c_0_894,axiom,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X4)
| c_HOL_Otimes__class_Otimes(X3,X10,X4) != c_HOL_Ozero__class_Ozero(X4)
| X3 = c_HOL_Ozero__class_Ozero(X4)
| X10 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_no__zero__divirors__neq0_0) ).
fof(c_0_895,axiom,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X4)
| c_HOL_Otimes__class_Otimes(X3,X10,X4) != c_HOL_Ozero__class_Ozero(X4)
| X10 = c_HOL_Ozero__class_Ozero(X4)
| X3 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_no__zero__divisors_0) ).
fof(c_0_896,axiom,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X4)
| c_HOL_Otimes__class_Otimes(X3,X10,X4) != c_HOL_Ozero__class_Ozero(X4)
| X10 = c_HOL_Ozero__class_Ozero(X4)
| X3 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_mult__eq__0__iff_0) ).
fof(c_0_897,axiom,
! [X8,X9] :
( c_HOL_Oord__class_Oless(X8,X9,tc_nat)
| c_HOL_Oord__class_Oless(X9,X8,tc_nat)
| X9 = X8 ),
file('<stdin>',cls_linorder__neqE__nat_0) ).
fof(c_0_898,axiom,
! [X2,X1] :
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2 ),
file('<stdin>',cls_nat__neq__iff_0) ).
fof(c_0_899,axiom,
! [X8,X9,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| c_HOL_Ominus__class_Ominus(X9,X8,X4) != c_HOL_Ozero__class_Ozero(X4)
| X9 = X8 ),
file('<stdin>',cls_class__ringb_Osubr0__iff_0) ).
fof(c_0_900,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| X3 = c_HOL_Ozero__class_Ozero(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
file('<stdin>',cls_dvd__0__left_0) ).
fof(c_0_901,axiom,
! [X9,X3,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| X9 != c_HOL_Oplus__class_Oplus(X9,X3,X4)
| X3 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_class__ringb_Oadd__r0__iff_0) ).
fof(c_0_902,axiom,
! [X2,X1] :
( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != 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)) ),
file('<stdin>',cls_add__is__1_0) ).
fof(c_0_903,axiom,
! [X2,X1] :
( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_add__is__1_3) ).
fof(c_0_904,axiom,
! [X2,X1] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('<stdin>',cls_one__is__add_0) ).
fof(c_0_905,axiom,
! [X2,X1] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_one__is__add_3) ).
fof(c_0_906,axiom,
! [X2] :
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
file('<stdin>',cls_less__Suc0_0) ).
fof(c_0_907,axiom,
! [X2,X1] :
( c_lessequals(X2,X1,tc_nat)
| c_lessequals(X1,X2,tc_nat) ),
file('<stdin>',cls_nat__le__linear_0) ).
fof(c_0_908,axiom,
! [X9,X4] : c_in(X9,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4),
file('<stdin>',cls_UNIV__I_0) ).
fof(c_0_909,axiom,
! [X2,X1] : c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),
file('<stdin>',cls_nat__add__commute_0) ).
fof(c_0_910,axiom,
! [X2,X1] : c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) = c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),
file('<stdin>',cls_nat__mult__commute_0) ).
fof(c_0_911,axiom,
! [X2,X48] :
( X48 = c_Suc(c_ATP__Linkup_Osko__Nat__XSuc__le__D__1__1(X48))
| ~ c_lessequals(c_Suc(X2),X48,tc_nat) ),
file('<stdin>',cls_Suc__le__D_0) ).
fof(c_0_912,axiom,
! [X6,X7,X4] :
( ~ class_Lattices_Obounded__lattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X7,X6,X4) != c_Orderings_Otop__class_Otop(X4)
| X7 = c_Orderings_Otop__class_Otop(X4) ),
file('<stdin>',cls_inf__eq__top__eq1_0) ).
fof(c_0_913,axiom,
! [X6,X7,X4] :
( ~ class_Lattices_Obounded__lattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X7,X6,X4) != c_Orderings_Otop__class_Otop(X4)
| X6 = c_Orderings_Otop__class_Otop(X4) ),
file('<stdin>',cls_inf__eq__top__eq2_0) ).
fof(c_0_914,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_HOL_Oplus__class_Oplus(X3,X3,X4) != c_HOL_Ozero__class_Ozero(X4)
| X3 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_double__eq__0__iff_0) ).
fof(c_0_915,axiom,
! [X7,X4] : c_HOL_Ominus__class_Ominus(X7,X7,tc_fun(X4,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
file('<stdin>',cls_Diff__cancel_0) ).
fof(c_0_916,axiom,
! [X2,X1] :
( c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('<stdin>',cls_mult__eq__1__iff_1) ).
fof(c_0_917,axiom,
! [X2,X1] :
( 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)) ),
file('<stdin>',cls_mult__eq__1__iff_0) ).
fof(c_0_918,axiom,
! [X9,X47,X4] :
( c_in(X9,X47,X4)
| ~ hBOOL(hAPP(X47,X9)) ),
file('<stdin>',cls_mem__def_1) ).
fof(c_0_919,axiom,
! [X2,X1] :
( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_add__is__1_2) ).
fof(c_0_920,axiom,
! [X2,X1] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_one__is__add_2) ).
fof(c_0_921,axiom,
! [X10,X3,X4] :
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_HOL_Ominus__class_Ominus(X3,X10,X4) != c_HOL_Ozero__class_Ozero(X4)
| X3 = X10 ),
file('<stdin>',cls_eq__iff__diff__eq__0_1) ).
fof(c_0_922,axiom,
! [X10,X3,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Ominus__class_Ominus(X3,X10,X4) != c_HOL_Ozero__class_Ozero(X4)
| X3 = X10 ),
file('<stdin>',cls_right__minus__eq_0) ).
fof(c_0_923,axiom,
! [X2,X26] :
( hBOOL(hAPP(X26,X2))
| ~ hBOOL(hAPP(X26,c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1(X26))) ),
file('<stdin>',cls_full__nat__induct_1) ).
fof(c_0_924,axiom,
! [X2,X1] :
( 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) ),
file('<stdin>',cls_mult__is__0_0) ).
fof(c_0_925,axiom,
! [X1,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_Nat_Osemiring__1__class_Oof__nat(X1,X4),X4) ),
file('<stdin>',cls_zero__le__imp__of__nat_0) ).
fof(c_0_926,axiom,
! [X2,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_Nat_Osemiring__1__class_Oof__nat(X2,X4),X4) ),
file('<stdin>',cls_of__nat__0__le__iff_0) ).
fof(c_0_927,axiom,
! [X2] : ~ c_lessequals(c_Suc(X2),X2,tc_nat),
file('<stdin>',cls_Suc__n__not__le__n_0) ).
fof(c_0_928,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_929,axiom,
! [X9,X4] :
( ~ class_Orderings_Opreorder(X4)
| ~ c_HOL_Oord__class_Oless(X9,X9,X4) ),
file('<stdin>',cls_order__less__irrefl_0) ).
fof(c_0_930,axiom,
! [X9,X4] :
( ~ class_Orderings_Olinorder(X4)
| ~ c_HOL_Oord__class_Oless(X9,X9,X4) ),
file('<stdin>',cls_linorder__neq__iff_1) ).
fof(c_0_931,axiom,
! [X9,X4] :
( ~ class_Orderings_Oorder(X4)
| ~ c_HOL_Oord__class_Oless(X9,X9,X4) ),
file('<stdin>',cls_order__less__le_1) ).
fof(c_0_932,axiom,
! [X2,X1] :
( X1 != c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Oone__class_Oone(tc_nat) ),
file('<stdin>',cls_mult__eq__self__implies__10_0) ).
fof(c_0_933,axiom,
! [X2] :
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
file('<stdin>',cls_le__0__eq_0) ).
fof(c_0_934,axiom,
! [X1] :
( 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) ),
file('<stdin>',cls_nat__dvd__1__iff__1_0) ).
fof(c_0_935,axiom,
! [X2,X1] :
( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)
| X2 = c_HOL_Oone__class_Oone(tc_nat) ),
file('<stdin>',cls_nat__1__eq__mult__iff_1) ).
fof(c_0_936,axiom,
! [X2,X1] :
( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)
| X1 = c_HOL_Oone__class_Oone(tc_nat) ),
file('<stdin>',cls_nat__1__eq__mult__iff_0) ).
fof(c_0_937,axiom,
! [X2,X1] :
( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_add__is__0_1) ).
fof(c_0_938,axiom,
! [X2,X1] :
( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_add__is__0_0) ).
fof(c_0_939,axiom,
! [X2,X1] :
( c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
| X1 = c_HOL_Oone__class_Oone(tc_nat) ),
file('<stdin>',cls_nat__mult__eq__1__iff_0) ).
fof(c_0_940,axiom,
! [X2,X1] :
( c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
| X2 = c_HOL_Oone__class_Oone(tc_nat) ),
file('<stdin>',cls_nat__mult__eq__1__iff_1) ).
fof(c_0_941,axiom,
! [X9,X3] :
( X9 != c_HOL_Oplus__class_Oplus(X9,X3,tc_nat)
| X3 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_natgb_Oadd__r0__iff_0) ).
fof(c_0_942,axiom,
! [X2,X1] :
( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != X1
| X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_add__eq__self__zero_0) ).
fof(c_0_943,axiom,
! [X2] : ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('<stdin>',cls_not__less0_0) ).
fof(c_0_944,axiom,
! [X1] : ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('<stdin>',cls_gr__implies__not0_0) ).
fof(c_0_945,axiom,
! [X54,X25,X4] :
( X25 = X54
| ~ c_fequal(X25,X54,X4) ),
file('<stdin>',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(c_0_946,axiom,
! [X4] : c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
file('<stdin>',cls_UNIV__not__empty_0) ).
fof(c_0_947,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_948,axiom,
! [X2] : ~ c_HOL_Oord__class_Oless(X2,X2,tc_nat),
file('<stdin>',cls_less__not__refl_0) ).
fof(c_0_949,axiom,
! [X9] : ~ c_HOL_Oord__class_Oless(X9,X9,tc_nat),
file('<stdin>',cls_nat__less__le_1) ).
fof(c_0_950,axiom,
! [X7,X4] : c_Lattices_Olower__semilattice__class_Oinf(X7,X7,tc_fun(X4,tc_bool)) = X7,
file('<stdin>',cls_Int__absorb_0) ).
fof(c_0_951,axiom,
! [X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_double__eq__0__iff_1) ).
fof(c_0_952,axiom,
! [X9,X4] : c_lessequals(X9,X9,tc_fun(X4,tc_bool)),
file('<stdin>',cls_equalityE_0) ).
fof(c_0_953,axiom,
! [X7,X4] : c_lessequals(X7,X7,tc_fun(X4,tc_bool)),
file('<stdin>',cls_subset__refl_0) ).
fof(c_0_954,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_955,axiom,
! [X7,X4] :
( c_Finite__Set_Ocard(X7,X4) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_Finite__Set_Ofinite(X7,X4)
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_card__eq__0__iff_0) ).
fof(c_0_956,axiom,
! [X9,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| X9 = c_HOL_Oplus__class_Oplus(X9,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_class__ringb_Oadd__r0__iff_1) ).
fof(c_0_957,axiom,
c_HOL_Oplus__class_Oplus(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_add__is__1_5) ).
fof(c_0_958,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('<stdin>',cls_one__is__add_4) ).
fof(c_0_959,axiom,
c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
file('<stdin>',cls_add__is__1_4) ).
fof(c_0_960,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
file('<stdin>',cls_one__is__add_5) ).
fof(c_0_961,axiom,
! [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) ),
file('<stdin>',cls_zero__less__one_0) ).
fof(c_0_962,axiom,
! [X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oone__class_Oone(X4),X4) ),
file('<stdin>',cls_zero__le__one_0) ).
fof(c_0_963,axiom,
! [X4] :
( ~ class_Finite__Set_Ofinite_Ofinite(X4)
| c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4) ),
file('<stdin>',cls_finite__UNIV_0) ).
fof(c_0_964,axiom,
! [X9,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| c_HOL_Ominus__class_Ominus(X9,X9,X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_class__ringb_Osubr0__iff_1) ).
fof(c_0_965,axiom,
! [X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(X3,c_HOL_Oone__class_Oone(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_mod__by__1_0) ).
fof(c_0_966,axiom,
! [X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),X9,X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_class__semiring_Omul__0_0) ).
fof(c_0_967,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Omult__zero(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),X3,X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_mult__zero__left_0) ).
fof(c_0_968,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Omult__zero(X4)
| c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_mult__zero__right_0) ).
fof(c_0_969,axiom,
! [X10,X4] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),X10,X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_mult__eq__0__iff_1) ).
fof(c_0_970,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X4)
| c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_mult__eq__0__iff_2) ).
fof(c_0_971,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I10_J_0) ).
fof(c_0_972,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),X3,X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I9_J_0) ).
fof(c_0_973,axiom,
! [X9,X4] :
( ~ class_Lattices_Obounded__lattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X4),X9,X4) = c_Orderings_Obot__class_Obot(X4) ),
file('<stdin>',cls_inf__bot__left_0) ).
fof(c_0_974,axiom,
! [X9,X4] :
( ~ class_Lattices_Obounded__lattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X9,c_Orderings_Obot__class_Obot(X4),X4) = c_Orderings_Obot__class_Obot(X4) ),
file('<stdin>',cls_inf__bot__right_0) ).
fof(c_0_975,axiom,
! [X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X4),X3,X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_mod__0_0) ).
fof(c_0_976,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Ominus__class_Ominus(X3,c_HOL_Ozero__class_Ozero(X4),X4) = X3 ),
file('<stdin>',cls_diff__0__right_0) ).
fof(c_0_977,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X4),X3,X4) = X3 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I5_J_0) ).
fof(c_0_978,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Ozero__class_Ozero(X4),X4) = X3 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(c_0_979,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Omonoid__add(X4)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Ozero__class_Ozero(X4),X4) = X3 ),
file('<stdin>',cls_monoid__add__class_Oadd__0__right_0) ).
fof(c_0_980,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Omonoid__add(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X4),X3,X4) = X3 ),
file('<stdin>',cls_add__0__left_0) ).
fof(c_0_981,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Ozero__class_Ozero(X4),X4) = X3 ),
file('<stdin>',cls_comm__monoid__add_Omult__1__right_0) ).
fof(c_0_982,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X4),X3,X4) = X3 ),
file('<stdin>',cls_comm__monoid__add_Omult__1_0) ).
fof(c_0_983,axiom,
! [X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X4),X9,X4) = X9 ),
file('<stdin>',cls_class__semiring_Oadd__0_0) ).
fof(c_0_984,axiom,
! [X9,X4] :
( ~ class_Lattices_Obounded__lattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(X4),X9,X4) = X9 ),
file('<stdin>',cls_inf__top__left_0) ).
fof(c_0_985,axiom,
! [X9,X4] :
( ~ class_Lattices_Obounded__lattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X9,c_Orderings_Otop__class_Otop(X4),X4) = X9 ),
file('<stdin>',cls_inf__top__right_0) ).
fof(c_0_986,axiom,
! [X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(X3,c_HOL_Ozero__class_Ozero(X4),X4) = X3 ),
file('<stdin>',cls_mod__by__0_0) ).
fof(c_0_987,axiom,
! [X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X4),X9,X4) = X9 ),
file('<stdin>',cls_class__semiring_Omul__1_0) ).
fof(c_0_988,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X4),X3,X4) = X3 ),
file('<stdin>',cls_mult__1_0) ).
fof(c_0_989,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Omonoid__mult(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X4),X3,X4) = X3 ),
file('<stdin>',cls_mult__1__left_0) ).
fof(c_0_990,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Omonoid__mult(X4)
| c_HOL_Otimes__class_Otimes(X3,c_HOL_Oone__class_Oone(X4),X4) = X3 ),
file('<stdin>',cls_mult__1__right_0) ).
fof(c_0_991,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(X3,c_HOL_Oone__class_Oone(X4),X4) = X3 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I12_J_0) ).
fof(c_0_992,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X4),X3,X4) = X3 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I11_J_0) ).
fof(c_0_993,axiom,
! [X4] : c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4) = c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_card__empty_0) ).
fof(c_0_994,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_995,axiom,
! [X9,X4] :
( ~ class_Orderings_Obot(X4)
| c_lessequals(c_Orderings_Obot__class_Obot(X4),X9,X4) ),
file('<stdin>',cls_bot__least_0) ).
fof(c_0_996,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X4),X3,X4) ),
file('<stdin>',cls_one__dvd_0) ).
fof(c_0_997,axiom,
! [X9,X4] :
( ~ class_Orderings_Otop(X4)
| c_lessequals(X9,c_Orderings_Otop__class_Otop(X4),X4) ),
file('<stdin>',cls_top__greatest_0) ).
fof(c_0_998,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_dvd__0__right_0) ).
fof(c_0_999,axiom,
! [X1] : c_Divides_Odiv__class_Omod(X1,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_1000,axiom,
! [X4] : c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),
file('<stdin>',cls_finite_OemptyI_0) ).
fof(c_0_1001,axiom,
! [X9,X4] :
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_HOL_Ominus__class_Ominus(X9,X9,X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_eq__iff__diff__eq__0_0) ).
fof(c_0_1002,axiom,
! [X9,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Ominus__class_Ominus(X9,X9,X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_right__minus__eq_1) ).
fof(c_0_1003,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Ominus__class_Ominus(X3,X3,X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_diff__self_0) ).
fof(c_0_1004,axiom,
! [X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(X3,X3,X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_mod__self_0) ).
fof(c_0_1005,axiom,
! [X2] : c_lessequals(c_Suc(X2),c_Suc(X2),tc_nat),
file('<stdin>',cls_le__Suc__eq_2) ).
fof(c_0_1006,axiom,
! [X5] : c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X5,tc_nat),
file('<stdin>',cls_dvd__1__left_0) ).
fof(c_0_1007,axiom,
! [X2] : c_HOL_Ominus__class_Ominus(c_Suc(X2),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X2,
file('<stdin>',cls_diff__Suc__1_0) ).
fof(c_0_1008,axiom,
! [X9,X4] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X4)
| c_HOL_Otimes__class_Otimes(X9,X9,X4) = X9 ),
file('<stdin>',cls_mult__idem_0) ).
fof(c_0_1009,axiom,
! [X9,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X9,X9,X4) = X9 ),
file('<stdin>',cls_inf__idem_0) ).
fof(c_0_1010,axiom,
! [X9] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X9),tc_nat),
file('<stdin>',cls_gr0__conv__Suc_1) ).
fof(c_0_1011,axiom,
! [X2] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X2),tc_nat),
file('<stdin>',cls_zero__less__Suc_0) ).
fof(c_0_1012,axiom,
! [X9,X4] :
( ~ class_Orderings_Oorder(X4)
| c_lessequals(X9,X9,X4) ),
file('<stdin>',cls_order__eq__iff_0) ).
fof(c_0_1013,axiom,
! [X9,X4] :
( ~ class_Orderings_Opreorder(X4)
| c_lessequals(X9,X9,X4) ),
file('<stdin>',cls_order__eq__refl_0) ).
fof(c_0_1014,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X3,X4) ),
file('<stdin>',cls_dvd__refl_0) ).
fof(c_0_1015,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_1016,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_1017,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_add__is__0_2) ).
fof(c_0_1018,axiom,
! [X2] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_gr0I_0) ).
fof(c_0_1019,axiom,
! [X2] : c_Suc(X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X2,tc_nat),
file('<stdin>',cls_Suc__eq__plus1__left_0) ).
fof(c_0_1020,axiom,
! [X2] : c_Suc(X2) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
file('<stdin>',cls_Suc__eq__plus1_0) ).
fof(c_0_1021,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('<stdin>',cls_le__0__eq_1) ).
fof(c_0_1022,axiom,
! [X2] : c_HOL_Oord__class_Oless(X2,c_Suc(X2),tc_nat),
file('<stdin>',cls_lessI_0) ).
fof(c_0_1023,axiom,
! [X9] : c_HOL_Oord__class_Oless(X9,c_Suc(X9),tc_nat),
file('<stdin>',cls_less__Suc__eq_2) ).
fof(c_0_1024,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_1025,axiom,
! [X2] : c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_diff__0__eq__0_0) ).
fof(c_0_1026,axiom,
! [X1] : c_HOL_Otimes__class_Otimes(X1,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_1027,axiom,
! [X2] : c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_mult__is__0_1) ).
fof(c_0_1028,axiom,
! [X1] : c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
file('<stdin>',cls_minus__nat_Odiff__0_0) ).
fof(c_0_1029,axiom,
! [X1] : c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
file('<stdin>',cls_Nat_Oadd__0__right_0) ).
fof(c_0_1030,axiom,
! [X2] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) = X2,
file('<stdin>',cls_plus__nat_Oadd__0_0) ).
fof(c_0_1031,axiom,
! [X9] : X9 = c_HOL_Oplus__class_Oplus(X9,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('<stdin>',cls_natgb_Oadd__r0__iff_1) ).
fof(c_0_1032,axiom,
! [X2] : c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X2,
file('<stdin>',cls_nat__mult__1__right_0) ).
fof(c_0_1033,axiom,
! [X2] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X2,tc_nat) = X2,
file('<stdin>',cls_nat__mult__1_0) ).
fof(c_0_1034,axiom,
! [X2] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat),
file('<stdin>',cls_le0_0) ).
fof(c_0_1035,axiom,
! [X1] : c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_diff__self__eq__0_0) ).
fof(c_0_1036,axiom,
! [X9,X4] : c_fequal(X9,X9,X4),
file('<stdin>',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
fof(c_0_1037,axiom,
! [X8,X9,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_SetInterval_Oord__class_OatLeast(X9,X4) != c_SetInterval_Oord__class_OatLeast(X8,X4)
| X9 = X8 ),
file('<stdin>',cls_atLeast__eq__iff_0) ).
fof(c_0_1038,axiom,
! [X2,X1,X4] :
( ~ class_Nat_Osemiring__char__0(X4)
| c_Nat_Osemiring__1__class_Oof__nat(X1,X4) != c_Nat_Osemiring__1__class_Oof__nat(X2,X4)
| X1 = X2 ),
file('<stdin>',cls_of__nat__eq__iff_0) ).
fof(c_0_1039,axiom,
! [X2] : c_lessequals(X2,X2,tc_nat),
file('<stdin>',cls_le__refl_0) ).
fof(c_0_1040,axiom,
! [X9] : c_lessequals(X9,X9,tc_nat),
file('<stdin>',cls_eq__imp__le_0) ).
fof(c_0_1041,axiom,
! [X9] : c_Ring__and__Field_Odvd__class_Odvd(X9,X9,tc_nat),
file('<stdin>',cls_dvd_Oeq__iff_0) ).
fof(c_0_1042,axiom,
! [X52,X53] :
( class_Finite__Set_Ofinite_Ofinite(tc_fun(X52,X53))
| ~ class_Finite__Set_Ofinite_Ofinite(X53)
| ~ class_Finite__Set_Ofinite_Ofinite(X52) ),
file('<stdin>',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).
fof(c_0_1043,axiom,
! [X52,X53] :
( class_HOL_Oord(tc_fun(X52,X53))
| ~ class_HOL_Oord(X53) ),
file('<stdin>',clsarity_fun__HOL_Oord) ).
fof(c_0_1044,axiom,
! [X52,X53] :
( class_Orderings_Obot(tc_fun(X52,X53))
| ~ class_Orderings_Obot(X53) ),
file('<stdin>',clsarity_fun__Orderings_Obot) ).
fof(c_0_1045,axiom,
! [X52,X53] :
( class_Orderings_Otop(tc_fun(X52,X53))
| ~ class_Orderings_Otop(X53) ),
file('<stdin>',clsarity_fun__Orderings_Otop) ).
fof(c_0_1046,axiom,
! [X52,X53] :
( class_Orderings_Oorder(tc_fun(X52,X53))
| ~ class_Orderings_Oorder(X53) ),
file('<stdin>',clsarity_fun__Orderings_Oorder) ).
fof(c_0_1047,axiom,
! [X52,X53] :
( class_Lattices_Olattice(tc_fun(X52,X53))
| ~ class_Lattices_Olattice(X53) ),
file('<stdin>',clsarity_fun__Lattices_Olattice) ).
fof(c_0_1048,axiom,
! [X52,X53] :
( class_Orderings_Opreorder(tc_fun(X52,X53))
| ~ class_Orderings_Opreorder(X53) ),
file('<stdin>',clsarity_fun__Orderings_Opreorder) ).
fof(c_0_1049,axiom,
! [X52,X53] :
( class_Lattices_Obounded__lattice(tc_fun(X52,X53))
| ~ class_Lattices_Obounded__lattice(X53) ),
file('<stdin>',clsarity_fun__Lattices_Obounded__lattice) ).
fof(c_0_1050,axiom,
! [X52,X53] :
( class_Lattices_Olower__semilattice(tc_fun(X52,X53))
| ~ class_Lattices_Olattice(X53) ),
file('<stdin>',clsarity_fun__Lattices_Olower__semilattice) ).
fof(c_0_1051,axiom,
! [X52,X53] :
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X52,X53))
| ~ class_Complete__Lattice_Ocomplete__lattice(X53) ),
file('<stdin>',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
fof(c_0_1052,axiom,
! [X7,X4] :
( c_Finite__Set_Ocard(X7,X4) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Finite__Set_Ofinite(X7,X4) ),
file('<stdin>',cls_card__eq__0__iff_2) ).
fof(c_0_1053,axiom,
! [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) ),
file('<stdin>',cls_of__nat__0_0) ).
fof(c_0_1054,axiom,
! [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) ),
file('<stdin>',cls_of__nat__1_0) ).
fof(c_0_1055,axiom,
! [X7,X4] :
( ~ class_Finite__Set_Ofinite_Ofinite(X4)
| c_Finite__Set_Ofinite(X7,X4) ),
file('<stdin>',cls_finite_0) ).
fof(c_0_1056,axiom,
! [X4] :
( ~ class_Ring__and__Field_Ozero__neq__one(X4)
| c_HOL_Oone__class_Oone(X4) != c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_one__neq__zero_0) ).
fof(c_0_1057,axiom,
! [X4] :
( ~ class_Ring__and__Field_Ozero__neq__one(X4)
| c_HOL_Ozero__class_Ozero(X4) != c_HOL_Oone__class_Oone(X4) ),
file('<stdin>',cls_zero__neq__one_0) ).
fof(c_0_1058,axiom,
! [X8,X9] :
( c_Suc(X9) != c_Suc(X8)
| X9 = X8 ),
file('<stdin>',cls_Suc__inject_0) ).
fof(c_0_1059,axiom,
! [X41,X51] :
( c_Suc(X51) != c_Suc(X41)
| X51 = X41 ),
file('<stdin>',cls_nat_Oinject_0) ).
fof(c_0_1060,axiom,
! [X41] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X41),
file('<stdin>',cls_nat_Osimps_I2_J_0) ).
fof(c_0_1061,axiom,
! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
file('<stdin>',cls_Zero__neq__Suc_0) ).
fof(c_0_1062,axiom,
! [X41] : c_Suc(X41) != c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_nat_Osimps_I3_J_0) ).
fof(c_0_1063,axiom,
! [X1] : c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_Suc__neq__Zero_0) ).
fof(c_0_1064,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_1065,axiom,
! [X2] : c_Suc(X2) != X2,
file('<stdin>',cls_Suc__n__not__n_0) ).
fof(c_0_1066,axiom,
! [X2] : X2 != c_Suc(X2),
file('<stdin>',cls_n__not__Suc__n_0) ).
fof(c_0_1067,axiom,
class_HOL_Oord(tc_bool),
file('<stdin>',clsarity_bool__HOL_Oord) ).
fof(c_0_1068,axiom,
class_Orderings_Obot(tc_bool),
file('<stdin>',clsarity_bool__Orderings_Obot) ).
fof(c_0_1069,axiom,
class_Orderings_Otop(tc_bool),
file('<stdin>',clsarity_bool__Orderings_Otop) ).
fof(c_0_1070,axiom,
class_Orderings_Oorder(tc_bool),
file('<stdin>',clsarity_bool__Orderings_Oorder) ).
fof(c_0_1071,axiom,
class_Lattices_Olattice(tc_bool),
file('<stdin>',clsarity_bool__Lattices_Olattice) ).
fof(c_0_1072,axiom,
class_Orderings_Opreorder(tc_bool),
file('<stdin>',clsarity_bool__Orderings_Opreorder) ).
fof(c_0_1073,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
file('<stdin>',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).
fof(c_0_1074,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('<stdin>',clsarity_bool__Lattices_Obounded__lattice) ).
fof(c_0_1075,axiom,
class_Lattices_Olower__semilattice(tc_bool),
file('<stdin>',clsarity_bool__Lattices_Olower__semilattice) ).
fof(c_0_1076,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
file('<stdin>',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
fof(c_0_1077,axiom,
class_HOL_Oord(tc_nat),
file('<stdin>',clsarity_nat__HOL_Oord) ).
fof(c_0_1078,axiom,
class_Orderings_Obot(tc_nat),
file('<stdin>',clsarity_nat__Orderings_Obot) ).
fof(c_0_1079,axiom,
class_Orderings_Oorder(tc_nat),
file('<stdin>',clsarity_nat__Orderings_Oorder) ).
fof(c_0_1080,axiom,
class_Lattices_Olattice(tc_nat),
file('<stdin>',clsarity_nat__Lattices_Olattice) ).
fof(c_0_1081,axiom,
class_Orderings_Olinorder(tc_nat),
file('<stdin>',clsarity_nat__Orderings_Olinorder) ).
fof(c_0_1082,axiom,
class_Orderings_Opreorder(tc_nat),
file('<stdin>',clsarity_nat__Orderings_Opreorder) ).
fof(c_0_1083,axiom,
class_Ring__and__Field_Odvd(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Odvd) ).
fof(c_0_1084,axiom,
class_Nat_Osemiring__char__0(tc_nat),
file('<stdin>',clsarity_nat__Nat_Osemiring__char__0) ).
fof(c_0_1085,axiom,
class_Divides_Osemiring__div(tc_nat),
file('<stdin>',clsarity_nat__Divides_Osemiring__div) ).
fof(c_0_1086,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Omonoid__add) ).
fof(c_0_1087,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Osemiring) ).
fof(c_0_1088,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Omonoid__mult) ).
fof(c_0_1089,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Omult__mono) ).
fof(c_0_1090,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Omult__zero) ).
fof(c_0_1091,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Omult__mono1) ).
fof(c_0_1092,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Osemiring__1) ).
fof(c_0_1093,axiom,
class_Lattices_Olower__semilattice(tc_nat),
file('<stdin>',clsarity_nat__Lattices_Olower__semilattice) ).
fof(c_0_1094,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
fof(c_0_1095,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
fof(c_0_1096,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
fof(c_0_1097,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
fof(c_0_1098,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
fof(c_0_1099,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
fof(c_0_1100,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
fof(c_0_1101,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(c_0_1102,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
fof(c_0_1103,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Oordered__semiring) ).
fof(c_0_1104,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
fof(c_0_1105,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(c_0_1106,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(c_0_1107,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
fof(c_0_1108,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(c_0_1109,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).
fof(c_0_1110,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).
fof(c_0_1111,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_1112,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_1113,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(c_0_1114,plain,
! [X20,X6,X7,X14,X4] :
( c_lessequals(c_Set_Oimage(X20,X7,X4,X14),X6,tc_fun(X14,tc_bool))
| ~ c_in(hAPP(X20,c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1(X7,X6,X20,X4,X14)),X6,X14) ),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_1115,plain,
! [X20,X6,X7,X14,X4] :
( c_lessequals(c_Set_Oimage(X20,X7,X14,X4),X6,tc_fun(X4,tc_bool))
| ~ c_in(hAPP(X20,c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1(X7,X6,X20,X14,X4)),X6,X4) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_1116,axiom,
! [X9,X42,X20,X14,X4] :
( hAPP(X20,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X9,X20,X42,X4,X14)) != hAPP(X42,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X9,X20,X42,X4,X14))
| c_Set_Oimage(X20,X9,X4,X14) = c_Set_Oimage(X42,X9,X4,X14) ),
c_0_2 ).
fof(c_0_1117,axiom,
! [X1,X17,X11,X10,X3,X14,X4] :
( c_Fun_Ofun__upd(c_Fun_Ofun__upd(X1,X3,X10,X4,X14),X11,X17,X4,X14) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X1,X11,X17,X4,X14),X3,X10,X4,X14)
| X3 = X11 ),
c_0_3 ).
fof(c_0_1118,axiom,
! [X15,X8,X9,X20,X14,X4] : c_Fun_Ofun__upd(c_Fun_Ofun__upd(X20,X9,X8,X4,X14),X9,X15,X4,X14) = c_Fun_Ofun__upd(X20,X9,X15,X4,X14),
c_0_4 ).
fof(c_0_1119,plain,
! [X8,X9,X20,X7,X14,X4] :
( c_Set_Oimage(c_Fun_Ofun__upd(X20,X9,X8,X14,X4),X7,X14,X4) = c_Set_Oinsert(X8,c_Set_Oimage(X20,c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool)),X14),tc_fun(X14,tc_bool)),X14,X4),X4)
| ~ c_in(X9,X7,X14) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_1120,plain,
! [X8,X9,X7,X4] :
( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4),c_Finite__Set_Ocard(X7,X4),tc_nat)
| ~ c_in(X8,X7,X4)
| ~ c_in(X9,X7,X4)
| ~ c_Finite__Set_Ofinite(X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_1121,plain,
! [X8,X9,X20,X7,X14,X4] :
( c_Fun_Oinj__on(c_Fun_Ofun__upd(X20,X9,X8,X4,X14),X7,X4,X14)
| c_in(X8,c_Set_Oimage(X20,X7,X4,X14),X14)
| ~ c_Fun_Oinj__on(X20,X7,X4,X14) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_1122,plain,
! [X20,X6,X7,X14,X4] :
( X6 = c_Set_Oimage(X20,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X7,X6,X20,X14,X4),X14,X4)
| ~ c_lessequals(X6,c_Set_Oimage(X20,X7,X14,X4),tc_fun(X4,tc_bool))
| ~ c_Finite__Set_Ofinite(X6,X4) ),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_1123,plain,
! [X20,X6,X7,X14,X4] :
( X6 = c_Set_Oimage(X20,c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(X7,X6,X20,X14,X4),X14,X4)
| ~ c_lessequals(X6,c_Set_Oimage(X20,X7,X14,X4),tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_1124,plain,
! [X20,X6,X7,X14,X4] :
( c_lessequals(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X7,X6,X20,X14,X4),X7,tc_fun(X14,tc_bool))
| ~ c_lessequals(X6,c_Set_Oimage(X20,X7,X14,X4),tc_fun(X4,tc_bool))
| ~ c_Finite__Set_Ofinite(X6,X4) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_1125,plain,
! [X20,X6,X7,X14,X4] :
( c_lessequals(c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(X7,X6,X20,X14,X4),X7,tc_fun(X14,tc_bool))
| ~ c_lessequals(X6,c_Set_Oimage(X20,X7,X14,X4),tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_1126,plain,
! [X20,X6,X7,X14,X4] :
( c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X7,X6,X20,X14,X4),X14)
| ~ c_lessequals(X6,c_Set_Oimage(X20,X7,X14,X4),tc_fun(X4,tc_bool))
| ~ c_Finite__Set_Ofinite(X6,X4) ),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_1127,plain,
! [X15,X20,X7,X14,X4] :
( c_in(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(X7,X20,X15,X14,X4),X7,X14)
| ~ c_in(X15,c_Set_Oimage(X20,X7,X14,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_1128,plain,
! [X20,X10,X7,X14,X4] :
( c_in(c_ATP__Linkup_Osko__Set__XimageE__1__1(X7,X10,X20,X14,X4),X7,X14)
| ~ c_in(X10,c_Set_Oimage(X20,X7,X14,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_1129,plain,
! [X8,X9,X20,X7,X14,X4] :
( hAPP(c_Hilbert__Choice_Oinv__into(X7,X20,X4,X14),X9) != hAPP(c_Hilbert__Choice_Oinv__into(X7,X20,X4,X14),X8)
| X9 = X8
| ~ c_in(X8,c_Set_Oimage(X20,X7,X4,X14),X14)
| ~ c_in(X9,c_Set_Oimage(X20,X7,X4,X14),X14) ),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_1130,plain,
! [X20,X10,X7,X14,X4] :
( X10 = hAPP(X20,c_ATP__Linkup_Osko__Set__XimageE__1__1(X7,X10,X20,X14,X4))
| ~ c_in(X10,c_Set_Oimage(X20,X7,X14,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_1131,plain,
! [X15,X20,X7,X14,X4] :
( X15 = hAPP(X20,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(X7,X20,X15,X14,X4))
| ~ c_in(X15,c_Set_Oimage(X20,X7,X14,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_1132,plain,
! [X20,X3,X7,X14,X4] :
( ~ c_in(hAPP(X20,X3),c_Set_Oimage(X20,c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4,X14),X14)
| ~ c_Fun_Oinj__on(X20,c_Set_Oinsert(X3,X7,X4),X4,X14) ),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_1133,axiom,
! [X20,X6,X7,X14,X4] :
( c_lessequals(c_Set_Oimage(X20,X7,X14,X4),X6,tc_fun(X4,tc_bool))
| c_in(c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1(X7,X6,X20,X14,X4),X7,X14) ),
c_0_19 ).
fof(c_0_1134,axiom,
! [X20,X6,X7,X14,X4] :
( c_lessequals(c_Set_Oimage(X20,X7,X4,X14),X6,tc_fun(X14,tc_bool))
| c_in(c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1(X7,X6,X20,X4,X14),X7,X4) ),
c_0_20 ).
fof(c_0_1135,axiom,
! [X20,X6,X7,X14,X4] : c_lessequals(c_Set_Oimage(X20,c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X14,tc_bool)),X14,X4),c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X20,X7,X14,X4),c_Set_Oimage(X20,X6,X14,X4),tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
c_0_21 ).
fof(c_0_1136,axiom,
! [X20,X6,X7,X14,X4] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(X20,X7,X14,X4),c_Set_Oimage(X20,X6,X14,X4),tc_fun(X4,tc_bool)),c_Set_Oimage(X20,c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X14,tc_bool)),X14,X4),tc_fun(X4,tc_bool)),
c_0_22 ).
fof(c_0_1137,axiom,
! [X8,X9,X20,X7,X14,X4] :
( c_Set_Oimage(c_Fun_Ofun__upd(X20,X9,X8,X14,X4),X7,X14,X4) = c_Set_Oimage(X20,X7,X14,X4)
| c_in(X9,X7,X14) ),
c_0_23 ).
fof(c_0_1138,axiom,
! [X9,X42,X20,X14,X4] :
( c_Set_Oimage(X20,X9,X4,X14) = c_Set_Oimage(X42,X9,X4,X14)
| c_in(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X9,X20,X42,X4,X14),X9,X4) ),
c_0_24 ).
fof(c_0_1139,plain,
! [X42,X20,X3,X25,X14,X4] :
( c_in(hAPP(X42,X3),c_Inductive_Ocomplete__lattice__class_Ogfp(X20,tc_fun(X14,tc_bool)),X14)
| ~ c_lessequals(c_Set_Oimage(X42,X25,X4,X14),hAPP(X20,c_Set_Oimage(X42,X25,X4,X14)),tc_fun(X14,tc_bool))
| ~ c_in(X3,X25,X4) ),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_1140,plain,
! [X42,X20,X6,X7,X14,X4] :
( c_Finite__Set_Ocard(X7,X4) = c_Finite__Set_Ocard(X6,X14)
| ~ c_Finite__Set_Ofinite(X6,X14)
| ~ c_Finite__Set_Ofinite(X7,X4)
| ~ c_lessequals(c_Set_Oimage(X42,X6,X14,X4),X7,tc_fun(X4,tc_bool))
| ~ c_Fun_Oinj__on(X42,X6,X14,X4)
| ~ c_lessequals(c_Set_Oimage(X20,X7,X4,X14),X6,tc_fun(X14,tc_bool))
| ~ c_Fun_Oinj__on(X20,X7,X4,X14) ),
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_1141,plain,
! [X20,X3,X7,X14,X4] :
( c_Fun_Oinj__on(X20,c_Set_Oinsert(X3,X7,X4),X4,X14)
| c_in(hAPP(X20,X3),c_Set_Oimage(X20,c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4,X14),X14)
| ~ c_Fun_Oinj__on(X20,X7,X4,X14) ),
inference(fof_simplification,[status(thm)],[c_0_27]) ).
fof(c_0_1142,plain,
! [X5,X21,X22,X26] :
( ~ c_HOL_Oord__class_Oless(X21,X5,tc_nat)
| X5 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ hBOOL(hAPP(X26,c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X22,tc_nat),X21,tc_nat),X5,tc_nat)))
| hBOOL(hAPP(X26,X21)) ),
inference(fof_simplification,[status(thm)],[c_0_28]) ).
fof(c_0_1143,axiom,
! [X15,X8,X9,X20,X14,X4] :
( hAPP(c_Fun_Ofun__upd(X20,X9,X8,X4,X14),X15) = hAPP(X20,X15)
| X15 = X9 ),
c_0_29 ).
fof(c_0_1144,axiom,
! [X15,X8,X9,X20,X14,X4] :
( hAPP(c_Fun_Ofun__upd(X20,X9,X8,X14,X4),X15) = hAPP(X20,X15)
| X15 = X9 ),
c_0_30 ).
fof(c_0_1145,axiom,
! [X8,X9,X20,X23,X4] : hAPP(c_Fun_Ofun__upd(X20,X9,X8,X4,X23),X9) = X8,
c_0_31 ).
fof(c_0_1146,axiom,
! [X8,X9,X20,X14,X4] : hAPP(c_Fun_Ofun__upd(X20,X9,X8,X14,X4),X9) = X8,
c_0_32 ).
fof(c_0_1147,plain,
! [X20,X6,X7,X14,X4] :
( c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| ~ c_lessequals(c_Set_Oimage(X20,X7,X4,X14),c_Set_Oimage(X20,X6,X4,X14),tc_fun(X14,tc_bool))
| ~ c_Fun_Oinj__on(X20,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X14) ),
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_1148,plain,
! [X20,X16,X6,X7,X14,X4] :
( c_Set_Oimage(X20,c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),X4,X14) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X20,X7,X4,X14),c_Set_Oimage(X20,X6,X4,X14),tc_fun(X14,tc_bool))
| ~ c_lessequals(X6,X16,tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,X16,tc_fun(X4,tc_bool))
| ~ c_Fun_Oinj__on(X20,X16,X4,X14) ),
inference(fof_simplification,[status(thm)],[c_0_34]) ).
fof(c_0_1149,plain,
! [X20,X16,X6,X7,X14,X4] :
( c_Set_Oimage(X20,c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),X4,X14) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X20,X7,X4,X14),c_Set_Oimage(X20,X6,X4,X14),tc_fun(X14,tc_bool))
| ~ c_lessequals(X6,X16,tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,X16,tc_fun(X4,tc_bool))
| ~ c_Fun_Oinj__on(X20,X16,X4,X14) ),
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_1150,plain,
! [X18,X2,X1,X21,X22] :
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),X2,tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X22,X21,tc_nat),X18,tc_nat),X1,tc_nat),X2,tc_nat)
| ~ c_lessequals(X21,X22,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_36]) ).
fof(c_0_1151,plain,
! [X18,X2,X1,X21,X22] :
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X21,X22,tc_nat),X18,tc_nat),X2,tc_nat),tc_nat)
| ~ c_lessequals(X22,X21,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_37]) ).
fof(c_0_1152,plain,
! [X18,X2,X1,X21,X22] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X21,X22,tc_nat),X18,tc_nat),X2,tc_nat),tc_nat)
| ~ c_lessequals(X22,X21,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_38]) ).
fof(c_0_1153,plain,
! [X18,X2,X1,X21,X22] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X22,X21,tc_nat),X18,tc_nat),X1,tc_nat),X2,tc_nat)
| ~ c_lessequals(X21,X22,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_39]) ).
fof(c_0_1154,plain,
! [X19,X17,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X19,X4),X11,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X19,X4),X17,X4),X4)
| ~ c_lessequals(X11,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X3,X4),X19,X4),X17,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_1155,plain,
! [X19,X17,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X19,X4),X11,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X19,X4),X17,X4),X4)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X10,X4),X19,X4),X11,X4),X17,X4) ),
inference(fof_simplification,[status(thm)],[c_0_41]) ).
fof(c_0_1156,plain,
! [X19,X17,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X19,X4),X11,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X19,X4),X17,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X10,X4),X19,X4),X11,X4),X17,X4) ),
inference(fof_simplification,[status(thm)],[c_0_42]) ).
fof(c_0_1157,plain,
! [X19,X17,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X19,X4),X11,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X19,X4),X17,X4),X4)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X3,X4),X19,X4),X17,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_43]) ).
fof(c_0_1158,plain,
! [X20,X6,X7,X14,X4] :
( c_lessequals(c_Set_Ovimage(X20,X6,X4,X14),X7,tc_fun(X4,tc_bool))
| ~ c_lessequals(X6,c_Set_Oimage(X20,X7,X4,X14),tc_fun(X14,tc_bool))
| ~ c_Fun_Oinj__on(X20,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X14) ),
inference(fof_simplification,[status(thm)],[c_0_44]) ).
fof(c_0_1159,plain,
! [X20,X6,X7,X14,X4] :
( c_Set_Oimage(X20,c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),X4,X14) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X20,X7,X4,X14),c_Set_Oimage(X20,X6,X4,X14),tc_fun(X14,tc_bool))
| ~ c_Fun_Oinj__on(X20,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X14) ),
inference(fof_simplification,[status(thm)],[c_0_45]) ).
fof(c_0_1160,plain,
! [X20,X6,X7,X14,X4] :
( c_Set_Oimage(X20,c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),X4,X14) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X20,X7,X4,X14),c_Set_Oimage(X20,X6,X4,X14),tc_fun(X14,tc_bool))
| ~ c_Fun_Oinj__on(X20,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X14) ),
inference(fof_simplification,[status(thm)],[c_0_46]) ).
fof(c_0_1161,plain,
! [X9,X20,X7,X14,X4] :
( c_in(hAPP(c_Hilbert__Choice_Oinv__into(X7,X20,X14,X4),X9),X7,X14)
| ~ c_in(X9,c_Set_Oimage(X20,X7,X14,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_47]) ).
fof(c_0_1162,plain,
! [X18,X2,X1,X21,X22] :
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X22,X21,tc_nat),X18,tc_nat),X1,tc_nat),X2,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),X2,tc_nat),tc_nat)
| ~ c_lessequals(X21,X22,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_48]) ).
fof(c_0_1163,plain,
! [X18,X2,X1,X21,X22] :
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X21,X22,tc_nat),X18,tc_nat),X2,tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),X2,tc_nat),tc_nat)
| ~ c_lessequals(X22,X21,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_49]) ).
fof(c_0_1164,plain,
! [X18,X2,X1,X21,X22] :
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X21,X22,tc_nat),X18,tc_nat),X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),X2,tc_nat),tc_nat)
| ~ c_lessequals(X22,X21,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_50]) ).
fof(c_0_1165,plain,
! [X18,X2,X1,X21,X22] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X22,X21,tc_nat),X18,tc_nat),X1,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),X2,tc_nat),tc_nat)
| ~ c_lessequals(X21,X22,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_51]) ).
fof(c_0_1166,axiom,
! [X8,X9,X20,X14,X4] :
( c_Fun_Ofun__upd(X20,X9,X8,X4,X14) != X20
| hAPP(X20,X9) = X8 ),
c_0_52 ).
fof(c_0_1167,plain,
! [X19,X17,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X4)
| c_lessequals(X11,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X3,X4),X19,X4),X17,X4),X4)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X19,X4),X11,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X19,X4),X17,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_53]) ).
fof(c_0_1168,plain,
! [X19,X17,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X10,X4),X19,X4),X11,X4),X17,X4)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X19,X4),X11,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X19,X4),X17,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_54]) ).
fof(c_0_1169,plain,
! [X19,X17,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X10,X4),X19,X4),X11,X4),X17,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X19,X4),X11,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X19,X4),X17,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_55]) ).
fof(c_0_1170,plain,
! [X19,X17,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X4)
| c_HOL_Oord__class_Oless(X11,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X3,X4),X19,X4),X17,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X19,X4),X11,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X19,X4),X17,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_56]) ).
fof(c_0_1171,plain,
! [X8,X20,X7,X14,X4] :
( hAPP(X20,hAPP(c_Hilbert__Choice_Oinv__into(X7,X20,X14,X4),X8)) = X8
| ~ c_in(X8,c_Set_Oimage(X20,X7,X14,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_57]) ).
fof(c_0_1172,plain,
! [X20,X7,X14,X4] :
( c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X20,X4,X14),c_Set_Oimage(X20,X7,X4,X14),X14,X4) = X7
| ~ c_Fun_Oinj__on(X20,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X14) ),
inference(fof_simplification,[status(thm)],[c_0_58]) ).
fof(c_0_1173,plain,
! [X20,X25,X14,X4] :
( c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X20,X4,X14),c_Set_Oimage(X20,X25,X4,X14),X14,X4) = X25
| ~ c_Fun_Oinj__on(X20,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X14) ),
inference(fof_simplification,[status(thm)],[c_0_59]) ).
fof(c_0_1174,plain,
! [X20,X47,X7,X14,X4] :
( c_Set_Oimage(c_Hilbert__Choice_Oinv__into(X7,X20,X4,X14),c_Set_Oimage(X20,X47,X4,X14),X14,X4) = X47
| ~ c_lessequals(X47,X7,tc_fun(X4,tc_bool))
| ~ c_Fun_Oinj__on(X20,X7,X4,X14) ),
inference(fof_simplification,[status(thm)],[c_0_60]) ).
fof(c_0_1175,plain,
! [X9,X20,X7,X14,X4] :
( hBOOL(hAPP(X7,hAPP(X20,X9)))
| ~ hBOOL(hAPP(c_Set_Ovimage(X20,X7,X4,X14),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_61]) ).
fof(c_0_1176,plain,
! [X20,X6,X7,X14,X4] :
( c_lessequals(c_Set_Oimage(X20,X7,X4,X14),c_Set_Oimage(X20,X6,X4,X14),tc_fun(X14,tc_bool))
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| ~ c_Fun_Oinj__on(X20,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X14) ),
inference(fof_simplification,[status(thm)],[c_0_62]) ).
fof(c_0_1177,plain,
! [X20,X6,X7,X14,X4] :
( c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X7,X20,X14,X4),X6,X4,X14)
| ~ c_lessequals(X6,c_Set_Oimage(X20,X7,X14,X4),tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_63]) ).
fof(c_0_1178,plain,
! [X20,X7,X4] :
( c_Set_Oimage(X20,X7,X4,X4) = X7
| ~ c_Fun_Oinj__on(X20,X7,X4,X4)
| ~ c_lessequals(c_Set_Oimage(X20,X7,X4,X4),X7,tc_fun(X4,tc_bool))
| ~ c_Finite__Set_Ofinite(X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_64]) ).
fof(c_0_1179,axiom,
! [X20,X7,X14,X4] : c_lessequals(c_Set_Oimage(X20,c_Set_Ovimage(X20,X7,X14,X4),X14,X4),X7,tc_fun(X4,tc_bool)),
c_0_65 ).
fof(c_0_1180,plain,
! [X18,X2,X1,X21,X22] :
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),X2,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X22,X21,tc_nat),X18,tc_nat),X1,tc_nat),X2,tc_nat)
| ~ c_lessequals(X21,X22,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_66]) ).
fof(c_0_1181,plain,
! [X18,X2,X1,X21,X22] :
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),X2,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X21,X22,tc_nat),X18,tc_nat),X2,tc_nat),tc_nat)
| ~ c_lessequals(X22,X21,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_67]) ).
fof(c_0_1182,plain,
! [X20,X10,X3,X14,X4] :
( hAPP(X20,X3) = X10
| ~ c_in(X3,c_Set_Ovimage(X20,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool)),X14),X4,X14),X4) ),
inference(fof_simplification,[status(thm)],[c_0_68]) ).
fof(c_0_1183,plain,
! [X9,X43,X5,X17,X44,X4] :
( ~ class_Ring__and__Field_Odvd(X4)
| ~ class_Ring__and__Field_Ocomm__ring(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X17,c_HOL_Oplus__class_Oplus(X9,X43,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X9,c_HOL_Otimes__class_Otimes(X5,X44,X4),X4),X43,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X44,X4) ),
inference(fof_simplification,[status(thm)],[c_0_69]) ).
fof(c_0_1184,axiom,
! [X20,X6,X7,X14,X4] : c_Set_Ovimage(X20,c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X14,tc_bool)),X4,X14) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Ovimage(X20,X7,X4,X14),c_Set_Ovimage(X20,X6,X4,X14),tc_fun(X4,tc_bool)),
c_0_70 ).
fof(c_0_1185,axiom,
! [X20,X6,X7,X14,X4] : c_Set_Ovimage(X20,c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X14,tc_bool)),X4,X14) = c_HOL_Ominus__class_Ominus(c_Set_Ovimage(X20,X7,X4,X14),c_Set_Ovimage(X20,X6,X4,X14),tc_fun(X4,tc_bool)),
c_0_71 ).
fof(c_0_1186,plain,
! [X9,X6,X7,X4] :
( c_HOL_Oord__class_Oless(X7,c_Set_Oinsert(X9,X6,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X6,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(X7,X6,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_72]) ).
fof(c_0_1187,plain,
! [X20,X3,X7,X14,X4] :
( c_in(X3,X7,X4)
| ~ c_in(hAPP(X20,X3),c_Set_Oimage(X20,X7,X4,X14),X14)
| ~ c_Fun_Oinj__on(X20,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X14) ),
inference(fof_simplification,[status(thm)],[c_0_73]) ).
fof(c_0_1188,plain,
! [X9,X6,X7,X4] :
( c_HOL_Oord__class_Oless(X7,c_Set_Oinsert(X9,X6,X4),tc_fun(X4,tc_bool))
| ~ c_in(X9,X7,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X6,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(X7,X6,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_74]) ).
fof(c_0_1189,plain,
! [X20,X6,X7,X14,X4] :
( c_lessequals(c_Finite__Set_Ocard(X7,X4),c_Finite__Set_Ocard(X6,X14),tc_nat)
| ~ c_Finite__Set_Ofinite(X6,X14)
| ~ c_lessequals(c_Set_Oimage(X20,X7,X4,X14),X6,tc_fun(X14,tc_bool))
| ~ c_Fun_Oinj__on(X20,X7,X4,X14) ),
inference(fof_simplification,[status(thm)],[c_0_75]) ).
fof(c_0_1190,axiom,
! [X20,X7,X14,X4] : c_Set_Oimage(X20,c_Set_Ovimage(X20,X7,X14,X4),X14,X4) = c_Lattices_Olower__semilattice__class_Oinf(X7,c_Set_Oimage(X20,c_Orderings_Otop__class_Otop(tc_fun(X14,tc_bool)),X14,X4),tc_fun(X4,tc_bool)),
c_0_76 ).
fof(c_0_1191,plain,
! [X9,X6,X7,X4] :
( c_HOL_Oord__class_Oless(X7,c_Set_Oinsert(X9,X6,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X6,tc_fun(X4,tc_bool))
| c_in(X9,X6,X4) ),
inference(fof_simplification,[status(thm)],[c_0_77]) ).
fof(c_0_1192,plain,
! [X9,X7,X4] :
( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4),c_Finite__Set_Ocard(X7,X4),tc_nat)
| ~ c_in(X9,X7,X4)
| ~ c_Finite__Set_Ofinite(X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_78]) ).
fof(c_0_1193,plain,
! [X9,X6,X7,X4] :
( c_HOL_Oord__class_Oless(X7,c_Set_Oinsert(X9,X6,X4),tc_fun(X4,tc_bool))
| ~ c_in(X9,X7,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X6,tc_fun(X4,tc_bool))
| c_in(X9,X6,X4) ),
inference(fof_simplification,[status(thm)],[c_0_79]) ).
fof(c_0_1194,plain,
! [X9,X6,X7,X4] :
( c_lessequals(X7,c_Set_Oinsert(X9,X6,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X6,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_80]) ).
fof(c_0_1195,plain,
! [X9,X7,X4] :
( c_Finite__Set_Ocard(c_Set_Oinsert(X9,X7,X4),X4) = c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4))
| ~ c_Finite__Set_Ofinite(X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_81]) ).
fof(c_0_1196,plain,
! [X9,X7,X4] :
( c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4)) = c_Finite__Set_Ocard(X7,X4)
| ~ c_in(X9,X7,X4)
| ~ c_Finite__Set_Ofinite(X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_82]) ).
fof(c_0_1197,plain,
! [X9,X6,X7,X4] :
( c_lessequals(X7,c_Set_Oinsert(X9,X6,X4),tc_fun(X4,tc_bool))
| ~ c_in(X9,X7,X4)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X6,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_83]) ).
fof(c_0_1198,plain,
! [X9,X6,X7,X4] :
( c_lessequals(X7,c_Set_Oinsert(X9,X6,X4),tc_fun(X4,tc_bool))
| ~ c_in(X9,X7,X4)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X6,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_84]) ).
fof(c_0_1199,plain,
! [X9,X7,X4] :
( c_lessequals(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4),c_Finite__Set_Ocard(X7,X4),tc_nat)
| ~ c_Finite__Set_Ofinite(X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_85]) ).
fof(c_0_1200,plain,
! [X20,X6,X7,X14,X4] :
( c_Set_Oimage(X20,X7,X4,X14) != c_Set_Oimage(X20,X6,X4,X14)
| ~ c_Fun_Oinj__on(X20,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X14)
| X7 = X6 ),
inference(fof_simplification,[status(thm)],[c_0_86]) ).
fof(c_0_1201,axiom,
! [X9,X20,X23,X4] : c_Fun_Ofun__upd(X20,X9,hAPP(X20,X9),X23,X4) = X20,
c_0_87 ).
fof(c_0_1202,axiom,
! [X9,X20,X14,X4] : c_Fun_Ofun__upd(X20,X9,hAPP(X20,X9),X4,X14) = X20,
c_0_88 ).
fof(c_0_1203,axiom,
! [X9,X20,X14,X4] : c_Fun_Ofun__upd(X20,X9,hAPP(X20,X9),X14,X4) = X20,
c_0_89 ).
fof(c_0_1204,plain,
! [X20,X7,X14,X4] :
( c_Set_Ovimage(X20,c_Set_Oimage(X20,X7,X4,X14),X4,X14) = X7
| ~ c_Fun_Oinj__on(X20,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X14) ),
inference(fof_simplification,[status(thm)],[c_0_90]) ).
fof(c_0_1205,plain,
! [X20,X7,X14,X4] :
( c_Finite__Set_Ofinite(X7,X14)
| ~ c_Fun_Oinj__on(X20,X7,X14,X4)
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(X20,X7,X14,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_91]) ).
fof(c_0_1206,plain,
! [X20,X6,X7,X14,X4] :
( c_lessequals(c_Set_Oimage(X20,X7,X4,X14),c_Set_Oimage(X20,X6,X4,X14),tc_fun(X14,tc_bool))
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_92]) ).
fof(c_0_1207,plain,
! [X9,X20,X7,X14,X4] :
( ~ c_lessequals(X9,X7,tc_fun(X14,tc_bool))
| c_lessequals(c_Set_Oimage(X20,X9,X14,X4),c_Set_Oimage(X20,X7,X14,X4),tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_93]) ).
fof(c_0_1208,plain,
! [X20,X6,X7,X14,X4] :
( c_lessequals(c_Set_Ovimage(X20,X7,X14,X4),c_Set_Ovimage(X20,X6,X14,X4),tc_fun(X14,tc_bool))
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_94]) ).
fof(c_0_1209,plain,
! [X20,X7,X4] :
( c_Fun_Oinj__on(X20,X7,X4,X4)
| ~ c_lessequals(X7,c_Set_Oimage(X20,X7,X4,X4),tc_fun(X4,tc_bool))
| ~ c_Finite__Set_Ofinite(X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_95]) ).
fof(c_0_1210,plain,
! [X9,X43,X5,X17,X44,X4] :
( ~ class_Ring__and__Field_Odvd(X4)
| ~ class_Ring__and__Field_Ocomm__ring(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X17,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X9,c_HOL_Otimes__class_Otimes(X5,X44,X4),X4),X43,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,c_HOL_Oplus__class_Oplus(X9,X43,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X44,X4) ),
inference(fof_simplification,[status(thm)],[c_0_96]) ).
fof(c_0_1211,plain,
! [X9,X20,X7,X14,X4] :
( hBOOL(hAPP(c_Set_Ovimage(X20,X7,X4,X14),X9))
| ~ hBOOL(hAPP(X7,hAPP(X20,X9))) ),
inference(fof_simplification,[status(thm)],[c_0_97]) ).
fof(c_0_1212,plain,
! [X20,X3,X7,X14,X4] :
( c_in(hAPP(X20,X3),c_Set_Oimage(X20,X7,X4,X14),X14)
| ~ c_in(X3,X7,X4)
| ~ c_Fun_Oinj__on(X20,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X14) ),
inference(fof_simplification,[status(thm)],[c_0_98]) ).
fof(c_0_1213,plain,
! [X18,X1,X21,X22] :
( ~ c_lessequals(X21,X22,tc_nat)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),X1,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X22,X21,tc_nat),X18,tc_nat),X1,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_99]) ).
fof(c_0_1214,plain,
! [X18,X2,X21,X22] :
( ~ c_lessequals(X22,X21,tc_nat)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X21,X22,tc_nat),X18,tc_nat),X2,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_100]) ).
fof(c_0_1215,plain,
! [X20,X7,X14,X4] :
( c_lessequals(c_Finite__Set_Ocard(c_Set_Oimage(X20,X7,X4,X14),X14),c_Finite__Set_Ocard(X7,X4),tc_nat)
| ~ c_Finite__Set_Ofinite(X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_101]) ).
fof(c_0_1216,plain,
! [X9,X20,X23,X4] :
( ~ c_Fun_Oinj__on(X20,c_Orderings_Otop__class_Otop(tc_fun(X23,tc_bool)),X23,X4)
| hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X23,tc_bool)),X20,X23,X4),hAPP(X20,X9)) = X9 ),
inference(fof_simplification,[status(thm)],[c_0_102]) ).
fof(c_0_1217,plain,
! [X9,X20,X14,X4] :
( hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X20,X4,X14),hAPP(X20,X9)) = X9
| ~ c_Fun_Oinj__on(X20,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X14) ),
inference(fof_simplification,[status(thm)],[c_0_103]) ).
fof(c_0_1218,plain,
! [X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(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),X4) ),
inference(fof_simplification,[status(thm)],[c_0_104]) ).
fof(c_0_1219,plain,
! [X20,X7,X14,X4] :
( c_Finite__Set_Ocard(c_Set_Oimage(X20,X7,X4,X14),X14) != c_Finite__Set_Ocard(X7,X4)
| ~ c_Finite__Set_Ofinite(X7,X4)
| c_Fun_Oinj__on(X20,X7,X4,X14) ),
inference(fof_simplification,[status(thm)],[c_0_105]) ).
fof(c_0_1220,plain,
! [X9,X6,X7,X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X6,tc_fun(X4,tc_bool))
| ~ c_in(X9,X7,X4)
| c_in(X9,X6,X4)
| ~ c_HOL_Oord__class_Oless(X7,c_Set_Oinsert(X9,X6,X4),tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_106]) ).
fof(c_0_1221,plain,
! [X19,X17,X10,X3,X4] :
( ~ class_Ring__and__Field_Oring(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X19,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X3,X4),X19,X4),X17,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X19,X4),X17,X4) ),
inference(fof_simplification,[status(thm)],[c_0_107]) ).
fof(c_0_1222,plain,
! [X19,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oring(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X19,X4),X11,X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X19,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X10,X4),X19,X4),X11,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_108]) ).
fof(c_0_1223,axiom,
! [X20,X3,X23,X4] : c_in(X3,c_Set_Ovimage(X20,c_Set_Oinsert(hAPP(X20,X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X23,X4),X23),
c_0_109 ).
fof(c_0_1224,plain,
! [X9,X20,X6,X7,X14,X4] :
( c_in(hAPP(X20,X9),X6,X4)
| ~ c_in(X9,X7,X14)
| ~ c_lessequals(c_Set_Oimage(X20,X7,X14,X4),X6,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_110]) ).
fof(c_0_1225,plain,
! [X17,X10,X26] :
( ~ hBOOL(hAPP(X26,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X10,X17,tc_nat),X10,tc_nat)))
| hBOOL(hAPP(X26,X17)) ),
inference(fof_simplification,[status(thm)],[c_0_111]) ).
fof(c_0_1226,plain,
! [X9,X10,X26] :
( ~ hBOOL(hAPP(X26,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X10,X9,tc_nat),X10,tc_nat)))
| hBOOL(hAPP(X26,X9)) ),
inference(fof_simplification,[status(thm)],[c_0_112]) ).
fof(c_0_1227,plain,
! [X36,X37,X11,X10] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,c_Divides_Odiv__class_Omod(X37,X11,tc_nat),tc_nat),X36,tc_nat),c_HOL_Otimes__class_Otimes(X10,X11,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X36,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_113]) ).
fof(c_0_1228,plain,
! [X9,X6,X7,X4] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X6,tc_fun(X4,tc_bool))
| ~ c_in(X9,X7,X4)
| ~ c_lessequals(X7,c_Set_Oinsert(X9,X6,X4),tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_114]) ).
fof(c_0_1229,plain,
! [X9,X20,X7,X23,X4] :
( ~ c_in(X9,X7,X23)
| ~ c_Fun_Oinj__on(X20,X7,X23,X4)
| hAPP(c_Hilbert__Choice_Oinv__into(X7,X20,X23,X4),hAPP(X20,X9)) = X9 ),
inference(fof_simplification,[status(thm)],[c_0_115]) ).
fof(c_0_1230,plain,
! [X9,X20,X7,X14,X4] :
( hAPP(c_Hilbert__Choice_Oinv__into(X7,X20,X4,X14),hAPP(X20,X9)) = X9
| ~ c_in(X9,X7,X4)
| ~ c_Fun_Oinj__on(X20,X7,X4,X14) ),
inference(fof_simplification,[status(thm)],[c_0_116]) ).
fof(c_0_1231,plain,
! [X12,X13,X14,X4] :
( c_Finite__Set_Ofinite(c_Set_Ovimage(X12,X13,X14,X4),X14)
| ~ c_Fun_Oinj__on(X12,c_Orderings_Otop__class_Otop(tc_fun(X14,tc_bool)),X14,X4)
| ~ c_Finite__Set_Ofinite(X13,X4) ),
inference(fof_simplification,[status(thm)],[c_0_117]) ).
fof(c_0_1232,plain,
! [X8,X9,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X9,X4),c_HOL_Otimes__class_Otimes(X8,X8,X4),X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_118]) ).
fof(c_0_1233,plain,
! [X8,X9,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| X9 = c_HOL_Ozero__class_Ozero(X4)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X9,X4),c_HOL_Otimes__class_Otimes(X8,X8,X4),X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_119]) ).
fof(c_0_1234,plain,
! [X8,X9,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X9,X4),c_HOL_Otimes__class_Otimes(X8,X8,X4),X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_120]) ).
fof(c_0_1235,plain,
! [X18,X2,X1,X21,X22] :
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),X1,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),X2,tc_nat)
| ~ c_lessequals(X21,X22,tc_nat)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X22,X21,tc_nat),X18,tc_nat),X1,tc_nat) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_121]) ).
fof(c_0_1236,plain,
! [X18,X2,X1,X21,X22] :
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),X1,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),X2,tc_nat)
| ~ c_lessequals(X22,X21,tc_nat)
| X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X21,X22,tc_nat),X18,tc_nat),X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_122]) ).
fof(c_0_1237,plain,
! [X20,X3,X7,X14,X4] :
( c_in(hAPP(X20,X3),X7,X14)
| ~ c_in(X3,c_Set_Ovimage(X20,X7,X4,X14),X4) ),
inference(fof_simplification,[status(thm)],[c_0_123]) ).
fof(c_0_1238,plain,
! [X20,X3,X6,X14,X4] :
( c_in(hAPP(X20,X3),X6,X14)
| ~ c_in(X3,c_Set_Ovimage(X20,X6,X4,X14),X4) ),
inference(fof_simplification,[status(thm)],[c_0_124]) ).
fof(c_0_1239,plain,
! [X20,X6,X7,X14,X4] :
( c_Finite__Set_Ofinite(X6,X14)
| ~ c_lessequals(X6,c_Set_Oimage(X20,X7,X4,X14),tc_fun(X14,tc_bool))
| ~ c_Finite__Set_Ofinite(X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_125]) ).
fof(c_0_1240,plain,
! [X20,X7,X14,X4] :
( c_Finite__Set_Ocard(c_Set_Oimage(X20,X7,X4,X14),X14) = c_Finite__Set_Ocard(X7,X4)
| ~ c_Fun_Oinj__on(X20,X7,X4,X14)
| ~ c_Finite__Set_Ofinite(X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_126]) ).
fof(c_0_1241,plain,
! [X3,X6,X7,X4] :
( c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X3,X6,X4),tc_fun(X4,tc_bool)),X4) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),X4),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_in(X3,X6,X4)
| ~ c_in(X3,X7,X4)
| ~ c_Finite__Set_Ofinite(X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_127]) ).
fof(c_0_1242,axiom,
! [X20,X3,X6,X14,X4] : c_Set_Oimage(X20,c_Set_Oinsert(X3,X6,X14),X14,X4) = c_Set_Oinsert(hAPP(X20,X3),c_Set_Oimage(X20,X6,X14,X4),X4),
c_0_128 ).
fof(c_0_1243,plain,
! [X20,X7,X14,X4] :
( c_Finite__Set_Ocard(c_Set_Oimage(X20,X7,X4,X14),X14) = c_Finite__Set_Ocard(X7,X4)
| ~ c_Fun_Oinj__on(X20,X7,X4,X14) ),
inference(fof_simplification,[status(thm)],[c_0_129]) ).
fof(c_0_1244,plain,
! [X9,X20,X7,X14,X4] :
( c_Set_Oinsert(hAPP(X20,X9),c_Set_Oimage(X20,X7,X4,X14),X14) = c_Set_Oimage(X20,X7,X4,X14)
| ~ c_in(X9,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_130]) ).
fof(c_0_1245,plain,
! [X19,X17,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oring(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X19,X4),X11,X4) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X19,X4),X17,X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X10,X4),X19,X4),X11,X4) = X17 ),
inference(fof_simplification,[status(thm)],[c_0_131]) ).
fof(c_0_1246,plain,
! [X19,X17,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oring(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X19,X4),X11,X4) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X19,X4),X17,X4)
| X11 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X3,X4),X19,X4),X17,X4) ),
inference(fof_simplification,[status(thm)],[c_0_132]) ).
fof(c_0_1247,plain,
! [X19,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Osemiring(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X19,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X19,X4),X11,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,X10,X4),X19,X4),X11,X4) ),
inference(fof_simplification,[status(thm)],[c_0_133]) ).
fof(c_0_1248,plain,
! [X17,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X17,X4),X4) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X17,X4),c_HOL_Otimes__class_Otimes(X10,X11,X4),X4)
| X11 = X17
| X3 = X10 ),
inference(fof_simplification,[status(thm)],[c_0_134]) ).
fof(c_0_1249,plain,
! [X15,X8,X9,X29,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X29,X8,X4),c_HOL_Otimes__class_Otimes(X9,X15,X4),X4) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X29,X15,X4),c_HOL_Otimes__class_Otimes(X9,X8,X4),X4)
| X8 = X15
| X29 = X9 ),
inference(fof_simplification,[status(thm)],[c_0_135]) ).
fof(c_0_1250,plain,
! [X6,X7,X4] :
( c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),X4) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(X7,X4),c_Finite__Set_Ocard(c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),X4),tc_nat)
| ~ c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),X4) ),
inference(fof_simplification,[status(thm)],[c_0_136]) ).
fof(c_0_1251,axiom,
! [X17,X11,X10,X3,X4] :
( c_Set_Oinsert(X3,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X11,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4)
| X3 = X17
| X3 = X11 ),
c_0_137 ).
fof(c_0_1252,axiom,
! [X17,X11,X10,X3,X4] :
( c_Set_Oinsert(X3,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X11,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4)
| X10 = X11
| X3 = X11 ),
c_0_138 ).
fof(c_0_1253,axiom,
! [X17,X11,X10,X3,X4] :
( c_Set_Oinsert(X3,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X11,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4)
| X3 = X17
| X10 = X17 ),
c_0_139 ).
fof(c_0_1254,axiom,
! [X17,X11,X10,X3,X4] :
( c_Set_Oinsert(X3,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X11,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4)
| X10 = X11
| X10 = X17 ),
c_0_140 ).
fof(c_0_1255,axiom,
! [X3,X6,X7,X4] : c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X3,X6,X4),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X6,tc_fun(X4,tc_bool)),
c_0_141 ).
fof(c_0_1256,axiom,
! [X18,X5,X21,X22] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),X5,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X22,X21,tc_nat),X18,tc_nat),X5,tc_nat),
c_0_142 ).
fof(c_0_1257,axiom,
! [X15,X8,X9,X29] :
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X29,X8,tc_nat),c_HOL_Otimes__class_Otimes(X9,X15,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X29,X15,tc_nat),c_HOL_Otimes__class_Otimes(X9,X8,tc_nat),tc_nat)
| X8 = X15
| X29 = X9 ),
c_0_143 ).
fof(c_0_1258,axiom,
! [X17,X11,X10,X3] :
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X11,tc_nat),c_HOL_Otimes__class_Otimes(X10,X17,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X17,tc_nat),c_HOL_Otimes__class_Otimes(X10,X11,tc_nat),tc_nat)
| X11 = X17
| X3 = X10 ),
c_0_144 ).
fof(c_0_1259,plain,
! [X20,X3,X7,X14,X4] :
( c_Fun_Oinj__on(X20,X7,X4,X14)
| ~ c_Fun_Oinj__on(X20,c_Set_Oinsert(X3,X7,X4),X4,X14) ),
inference(fof_simplification,[status(thm)],[c_0_145]) ).
fof(c_0_1260,plain,
! [X20,X6,X7,X14,X4] :
( c_Fun_Oinj__on(X20,c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),X4,X14)
| ~ c_Fun_Oinj__on(X20,X7,X4,X14) ),
inference(fof_simplification,[status(thm)],[c_0_146]) ).
fof(c_0_1261,plain,
! [X9,X7,X4] :
( c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(X7,X4),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ c_in(X9,X7,X4)
| ~ c_Finite__Set_Ofinite(X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_147]) ).
fof(c_0_1262,plain,
! [X3,X6,X7,X4] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),X4)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X3,X6,X4),tc_fun(X4,tc_bool)),X4) ),
inference(fof_simplification,[status(thm)],[c_0_148]) ).
fof(c_0_1263,plain,
! [X20,X6,X7,X14,X4] :
( c_Fun_Oinj__on(X20,X7,X4,X14)
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| ~ c_Fun_Oinj__on(X20,X6,X4,X14) ),
inference(fof_simplification,[status(thm)],[c_0_149]) ).
fof(c_0_1264,plain,
! [X11,X10,X3,X4] :
( ~ class_Divides_Oring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X3,X10,X4),X11,X4) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X3,X11,X4),c_Divides_Odiv__class_Omod(X10,X11,X4),X4),X11,X4) ),
inference(fof_simplification,[status(thm)],[c_0_150]) ).
fof(c_0_1265,plain,
! [X11,X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X10,X4),X11,X4) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X3,X11,X4),c_Divides_Odiv__class_Omod(X10,X11,X4),X4),X11,X4) ),
inference(fof_simplification,[status(thm)],[c_0_151]) ).
fof(c_0_1266,plain,
! [X11,X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,X10,X4),X11,X4) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X3,X11,X4),c_Divides_Odiv__class_Omod(X10,X11,X4),X4),X11,X4) ),
inference(fof_simplification,[status(thm)],[c_0_152]) ).
fof(c_0_1267,axiom,
! [X2,X1,X5] : c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,tc_nat),X1,tc_nat)),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat),
c_0_153 ).
fof(c_0_1268,plain,
! [X3,X7,X4] :
( c_Set_Oinsert(X3,c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4) = X7
| ~ c_in(X3,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_154]) ).
fof(c_0_1269,plain,
! [X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(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),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_155]) ).
fof(c_0_1270,axiom,
! [X3,X7,X4] : c_Set_Oinsert(X3,c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4) = c_Set_Oinsert(X3,X7,X4),
c_0_156 ).
fof(c_0_1271,plain,
! [X9,X7,X4] :
( c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4) = c_Finite__Set_Ocard(X7,X4)
| c_in(X9,X7,X4)
| ~ c_Finite__Set_Ofinite(X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_157]) ).
fof(c_0_1272,axiom,
! [X9,X20,X14,X4] : c_in(hAPP(X20,X9),c_Set_Oimage(X20,c_Orderings_Otop__class_Otop(tc_fun(X14,tc_bool)),X14,X4),X4),
c_0_158 ).
fof(c_0_1273,plain,
! [X20,X3,X6,X14,X4] :
( c_in(X3,c_Set_Ovimage(X20,X6,X14,X4),X14)
| ~ c_in(hAPP(X20,X3),X6,X4) ),
inference(fof_simplification,[status(thm)],[c_0_159]) ).
fof(c_0_1274,plain,
! [X20,X3,X7,X14,X4] :
( c_in(X3,c_Set_Ovimage(X20,X7,X14,X4),X14)
| ~ c_in(hAPP(X20,X3),X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_160]) ).
fof(c_0_1275,plain,
! [X20,X3,X6,X14,X4] :
( c_in(X3,c_Set_Ovimage(X20,X6,X4,X14),X4)
| ~ c_in(hAPP(X20,X3),X6,X14) ),
inference(fof_simplification,[status(thm)],[c_0_161]) ).
fof(c_0_1276,plain,
! [X11,X27,X10,X28,X3,X4] :
( ~ class_Divides_Oring__div(X4)
| c_Divides_Odiv__class_Omod(X10,X11,X4) != c_Divides_Odiv__class_Omod(X27,X11,X4)
| c_Divides_Odiv__class_Omod(X3,X11,X4) != c_Divides_Odiv__class_Omod(X28,X11,X4)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X3,X10,X4),X11,X4) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X28,X27,X4),X11,X4) ),
inference(fof_simplification,[status(thm)],[c_0_162]) ).
fof(c_0_1277,plain,
! [X11,X27,X10,X28,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(X10,X11,X4) != c_Divides_Odiv__class_Omod(X27,X11,X4)
| c_Divides_Odiv__class_Omod(X3,X11,X4) != c_Divides_Odiv__class_Omod(X28,X11,X4)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X10,X4),X11,X4) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X28,X27,X4),X11,X4) ),
inference(fof_simplification,[status(thm)],[c_0_163]) ).
fof(c_0_1278,plain,
! [X11,X27,X10,X28,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(X10,X11,X4) != c_Divides_Odiv__class_Omod(X27,X11,X4)
| c_Divides_Odiv__class_Omod(X3,X11,X4) != c_Divides_Odiv__class_Omod(X28,X11,X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,X10,X4),X11,X4) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X28,X27,X4),X11,X4) ),
inference(fof_simplification,[status(thm)],[c_0_164]) ).
fof(c_0_1279,plain,
! [X9,X20,X7,X14,X4] :
( c_in(hAPP(X20,X9),c_Set_Oimage(X20,X7,X4,X14),X14)
| ~ c_in(X9,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_165]) ).
fof(c_0_1280,plain,
! [X9,X20,X7,X14,X4] :
( c_in(hAPP(X20,X9),c_Set_Oimage(X20,X7,X14,X4),X4)
| ~ c_in(X9,X7,X14) ),
inference(fof_simplification,[status(thm)],[c_0_166]) ).
fof(c_0_1281,plain,
! [X9,X20,X7,X14,X4] :
( ~ c_in(X9,X7,X14)
| c_in(hAPP(X20,X9),c_Set_Oimage(X20,X7,X14,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_167]) ).
fof(c_0_1282,plain,
! [X9,X20,X7,X23,X4] :
( ~ c_in(X9,X7,X23)
| c_in(hAPP(X20,X9),c_Set_Oimage(X20,X7,X23,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_168]) ).
fof(c_0_1283,plain,
! [X30,X31,X32,X33,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X33,X32,X4),c_HOL_Otimes__class_Otimes(X31,X30,X4),X4) = c_HOL_Otimes__class_Otimes(X31,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X33,X32,X4),X30,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_169]) ).
fof(c_0_1284,plain,
! [X30,X31,X32,X33,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X33,X32,X4),c_HOL_Otimes__class_Otimes(X31,X30,X4),X4) = c_HOL_Otimes__class_Otimes(X33,c_HOL_Otimes__class_Otimes(X32,c_HOL_Otimes__class_Otimes(X31,X30,X4),X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_170]) ).
fof(c_0_1285,plain,
! [X3,X6,X7,X4] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X3,X6,X4),tc_fun(X4,tc_bool)),X4)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),X4) ),
inference(fof_simplification,[status(thm)],[c_0_171]) ).
fof(c_0_1286,plain,
! [X17,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X17,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X11,X17,X4)
| ~ c_HOL_Oord__class_Oless(X3,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_172]) ).
fof(c_0_1287,plain,
! [X17,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X17,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X11,X17,X4)
| ~ c_lessequals(X3,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_173]) ).
fof(c_0_1288,plain,
! [X17,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X17,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(X11,X17,X4)
| ~ c_HOL_Oord__class_Oless(X3,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_174]) ).
fof(c_0_1289,plain,
! [X17,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__semiring(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X17,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(X11,X17,X4)
| ~ c_lessequals(X3,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_175]) ).
fof(c_0_1290,plain,
! [X17,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__semiring(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X17,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X10,X4)
| ~ c_lessequals(X11,X17,X4)
| ~ c_lessequals(X3,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_176]) ).
fof(c_0_1291,plain,
! [X17,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X17,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X10,X4)
| ~ c_HOL_Oord__class_Oless(X11,X17,X4)
| ~ c_HOL_Oord__class_Oless(X3,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_177]) ).
fof(c_0_1292,plain,
! [X2,X1,X5] :
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X5,tc_nat),c_HOL_Ominus__class_Ominus(X2,X5,tc_nat),tc_nat)
| ~ c_lessequals(X5,X2,tc_nat)
| ~ c_lessequals(X5,X1,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_178]) ).
fof(c_0_1293,plain,
! [X2,X1,X5] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X5,tc_nat),c_HOL_Ominus__class_Ominus(X2,X5,tc_nat),tc_nat)
| ~ c_lessequals(X5,X2,tc_nat)
| ~ c_lessequals(X5,X1,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_179]) ).
fof(c_0_1294,plain,
! [X49,X2,X20,X4] :
( ~ class_Orderings_Oorder(X4)
| c_lessequals(hAPP(X20,X2),hAPP(X20,X49),X4)
| ~ c_lessequals(X2,X49,tc_nat)
| ~ c_lessequals(hAPP(X20,c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1(X20,X4)),hAPP(X20,c_Suc(c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1(X20,X4))),X4) ),
inference(fof_simplification,[status(thm)],[c_0_180]) ).
fof(c_0_1295,plain,
! [X44,X16,X6,X7,X4] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),c_HOL_Ominus__class_Ominus(X16,X44,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
| ~ c_lessequals(X44,X6,tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,X16,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_181]) ).
fof(c_0_1296,plain,
! [X44,X16,X6,X7,X4] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X16,X44,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
| ~ c_lessequals(X6,X44,tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,X16,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_182]) ).
fof(c_0_1297,axiom,
! [X3,X6,X7,X4] : c_HOL_Ominus__class_Ominus(X7,c_Set_Oinsert(X3,X6,X4),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),
c_0_183 ).
fof(c_0_1298,axiom,
! [X16,X6,X7,X4] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X7,X16,tc_fun(X4,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X6,X16,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X7,X16,tc_fun(X4,tc_bool)),X6,tc_fun(X4,tc_bool)),
c_0_184 ).
fof(c_0_1299,axiom,
! [X16,X6,X7,X4] : c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),X16,tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X7,X16,tc_fun(X4,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X6,X16,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
c_0_185 ).
fof(c_0_1300,axiom,
! [X16,X6,X7,X4] : c_Lattices_Olower__semilattice__class_Oinf(X16,c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X16,X7,tc_fun(X4,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X16,X6,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
c_0_186 ).
fof(c_0_1301,plain,
! [X8,X9,X20,X7,X14,X4] :
( hAPP(X20,X9) != hAPP(X20,X8)
| ~ c_Fun_Oinj__on(X20,X7,X4,X14)
| X9 = X8
| ~ c_in(X8,X7,X4)
| ~ c_in(X9,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_187]) ).
fof(c_0_1302,plain,
! [X34,X9,X20,X7,X14,X4] :
( hAPP(X20,X9) != hAPP(X20,X34)
| ~ c_in(X34,X7,X4)
| ~ c_in(X9,X7,X4)
| ~ c_Fun_Oinj__on(X20,X7,X4,X14)
| X9 = X34 ),
inference(fof_simplification,[status(thm)],[c_0_188]) ).
fof(c_0_1303,plain,
! [X8,X9,X20,X7,X14,X4] :
( hAPP(X20,X9) != hAPP(X20,X8)
| ~ c_in(X8,X7,X4)
| ~ c_in(X9,X7,X4)
| ~ c_Fun_Oinj__on(X20,X7,X4,X14)
| X9 = X8 ),
inference(fof_simplification,[status(thm)],[c_0_189]) ).
fof(c_0_1304,plain,
! [X8,X9,X20,X7,X14,X4] :
( hAPP(X20,X9) != hAPP(X20,X8)
| ~ c_in(X8,X7,X4)
| ~ c_in(X9,X7,X4)
| X9 = X8
| ~ c_Fun_Oinj__on(X20,X7,X4,X14) ),
inference(fof_simplification,[status(thm)],[c_0_190]) ).
fof(c_0_1305,plain,
! [X8,X9,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X9,X4),c_HOL_Otimes__class_Otimes(X8,X8,X4),X4),X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_191]) ).
fof(c_0_1306,plain,
! [X8,X9,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X9,X4),c_HOL_Otimes__class_Otimes(X8,X8,X4),X4),X4)
| X9 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_192]) ).
fof(c_0_1307,plain,
! [X8,X9,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X9,X4),c_HOL_Otimes__class_Otimes(X8,X8,X4),X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_193]) ).
fof(c_0_1308,axiom,
! [X8,X35,X34,X9,X2] :
( c_HOL_Oplus__class_Oplus(X9,c_HOL_Otimes__class_Otimes(X2,X34,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X8,c_HOL_Otimes__class_Otimes(X2,X35,tc_nat),tc_nat)
| c_Divides_Odiv__class_Omod(X9,X2,tc_nat) = c_Divides_Odiv__class_Omod(X8,X2,tc_nat) ),
c_0_194 ).
fof(c_0_1309,plain,
! [X9,X7,X4] :
( X7 = c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4)
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_195]) ).
fof(c_0_1310,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(X3,X10,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X11,X4) ),
inference(fof_simplification,[status(thm)],[c_0_196]) ).
fof(c_0_1311,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(X10,X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_197]) ).
fof(c_0_1312,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_lessequals(X3,X10,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X11,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_198]) ).
fof(c_0_1313,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_lessequals(X3,X10,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_199]) ).
fof(c_0_1314,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(X3,X10,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X11,X4) ),
inference(fof_simplification,[status(thm)],[c_0_200]) ).
fof(c_0_1315,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(X10,X3,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_201]) ).
fof(c_0_1316,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semiring(X4)
| c_HOL_Oord__class_Oless(X3,X10,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_202]) ).
fof(c_0_1317,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semiring(X4)
| c_HOL_Oord__class_Oless(X3,X10,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X11,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_203]) ).
fof(c_0_1318,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(X3,X10,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_204]) ).
fof(c_0_1319,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(X3,X10,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X11,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_205]) ).
fof(c_0_1320,plain,
! [X9,X6,X7,X4] :
( hBOOL(hAPP(X7,X9))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_206]) ).
fof(c_0_1321,plain,
! [X9,X6,X7,X4] :
( hBOOL(hAPP(X6,X9))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_207]) ).
fof(c_0_1322,plain,
! [X2,X1,X5] :
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ 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,X1,tc_nat),c_HOL_Otimes__class_Otimes(X5,X2,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_208]) ).
fof(c_0_1323,plain,
! [X2,X1,X5] :
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,X1,tc_nat),c_HOL_Otimes__class_Otimes(X5,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_209]) ).
fof(c_0_1324,plain,
! [X2,X1,X5] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X1,tc_nat),c_HOL_Otimes__class_Otimes(X5,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_210]) ).
fof(c_0_1325,plain,
! [X2,X1,X5] :
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X5,X1,tc_nat),c_HOL_Otimes__class_Otimes(X5,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_211]) ).
fof(c_0_1326,plain,
! [X2,X1,X5] :
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X5,X1,tc_nat),c_HOL_Otimes__class_Otimes(X5,X2,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_212]) ).
fof(c_0_1327,plain,
! [X2,X1,X5] :
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X5,tc_nat),c_HOL_Otimes__class_Otimes(X2,X5,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_213]) ).
fof(c_0_1328,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X11,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_214]) ).
fof(c_0_1329,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_215]) ).
fof(c_0_1330,plain,
! [X9,X17,X11,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X11,X4),c_HOL_Otimes__class_Otimes(X9,X17,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X17,X4),c_HOL_Otimes__class_Otimes(X9,X11,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_216]) ).
fof(c_0_1331,plain,
! [X15,X8,X9,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X8,X4),c_HOL_Otimes__class_Otimes(X9,X15,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X15,X4),c_HOL_Otimes__class_Otimes(X9,X8,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_217]) ).
fof(c_0_1332,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(X10,X3,X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_218]) ).
fof(c_0_1333,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X3,X10,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_219]) ).
fof(c_0_1334,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(X10,X3,X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X11,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_220]) ).
fof(c_0_1335,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X3,X10,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X11,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_221]) ).
fof(c_0_1336,plain,
! [X11,X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,c_Divides_Odiv__class_Omod(X10,X11,X4),X4),X11,X4) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,X10,X4),X11,X4) ),
inference(fof_simplification,[status(thm)],[c_0_222]) ).
fof(c_0_1337,plain,
! [X11,X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X3,X11,X4),X10,X4),X11,X4) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,X10,X4),X11,X4) ),
inference(fof_simplification,[status(thm)],[c_0_223]) ).
fof(c_0_1338,plain,
! [X11,X10,X3,X4] :
( ~ class_Divides_Oring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X3,X10,X4),X11,X4) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X3,c_Divides_Odiv__class_Omod(X10,X11,X4),X4),X11,X4) ),
inference(fof_simplification,[status(thm)],[c_0_224]) ).
fof(c_0_1339,plain,
! [X11,X10,X3,X4] :
( ~ class_Divides_Oring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X3,X10,X4),X11,X4) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X3,X11,X4),X10,X4),X11,X4) ),
inference(fof_simplification,[status(thm)],[c_0_225]) ).
fof(c_0_1340,plain,
! [X30,X31,X32,X33,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X33,X32,X4),c_HOL_Otimes__class_Otimes(X31,X30,X4),X4) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X33,X31,X4),c_HOL_Otimes__class_Otimes(X32,X30,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_226]) ).
fof(c_0_1341,plain,
! [X17,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X10,X4),c_HOL_Oplus__class_Oplus(X11,X17,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X11,X4),c_HOL_Oplus__class_Oplus(X10,X17,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_227]) ).
fof(c_0_1342,plain,
! [X11,X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X10,X4),X11,X4) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(X10,X11,X4),X4),X11,X4) ),
inference(fof_simplification,[status(thm)],[c_0_228]) ).
fof(c_0_1343,plain,
! [X11,X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X10,X4),X11,X4) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X3,X11,X4),X10,X4),X11,X4) ),
inference(fof_simplification,[status(thm)],[c_0_229]) ).
fof(c_0_1344,plain,
! [X11,X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X3,X11,X4),X10,X4),X11,X4) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X10,X4),X11,X4) ),
inference(fof_simplification,[status(thm)],[c_0_230]) ).
fof(c_0_1345,plain,
! [X11,X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,X10,X4),X11,X4) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,c_Divides_Odiv__class_Omod(X10,X11,X4),X4),X11,X4) ),
inference(fof_simplification,[status(thm)],[c_0_231]) ).
fof(c_0_1346,plain,
! [X11,X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,X10,X4),X11,X4) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X3,X11,X4),X10,X4),X11,X4) ),
inference(fof_simplification,[status(thm)],[c_0_232]) ).
fof(c_0_1347,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(X10,X3,X4)
| c_HOL_Oord__class_Oless(X3,X10,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X11,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_233]) ).
fof(c_0_1348,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(X10,X3,X4)
| c_HOL_Oord__class_Oless(X3,X10,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_234]) ).
fof(c_0_1349,axiom,
! [X34,X9,X4] : c_Set_Oinsert(X34,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) = c_Set_Oinsert(X9,c_Set_Oinsert(X34,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4),
c_0_235 ).
fof(c_0_1350,plain,
! [X12,X13,X14,X4] :
( c_Finite__Set_Ofinite(c_Set_Oimage(X12,X13,X4,X14),X14)
| ~ c_Finite__Set_Ofinite(X13,X4) ),
inference(fof_simplification,[status(thm)],[c_0_236]) ).
fof(c_0_1351,plain,
! [X9,X36,X17,X11,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| c_HOL_Oplus__class_Oplus(X9,c_HOL_Otimes__class_Otimes(X36,X11,X4),X4) != c_HOL_Oplus__class_Oplus(X9,c_HOL_Otimes__class_Otimes(X36,X17,X4),X4)
| X11 = X17
| X36 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_237]) ).
fof(c_0_1352,axiom,
! [X15,X8,X9] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X8,tc_nat),c_HOL_Otimes__class_Otimes(X9,X15,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X15,tc_nat),c_HOL_Otimes__class_Otimes(X9,X8,tc_nat),tc_nat),
c_0_238 ).
fof(c_0_1353,axiom,
! [X9,X17,X11] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X11,tc_nat),c_HOL_Otimes__class_Otimes(X9,X17,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X17,tc_nat),c_HOL_Otimes__class_Otimes(X9,X11,tc_nat),tc_nat),
c_0_239 ).
fof(c_0_1354,plain,
! [X8,X9,X20,X14,X4] :
( hAPP(X20,X9) != hAPP(X20,X8)
| ~ c_Fun_Oinj__on(X20,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X14)
| X9 = X8 ),
inference(fof_simplification,[status(thm)],[c_0_240]) ).
fof(c_0_1355,plain,
! [X1,X5,X21] :
( c_HOL_Ominus__class_Ominus(X1,c_Suc(c_HOL_Ominus__class_Ominus(X21,X5,tc_nat)),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X5,tc_nat),c_Suc(X21),tc_nat)
| ~ c_lessequals(X5,X21,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_241]) ).
fof(c_0_1356,plain,
! [X1,X5,X21] :
( c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ominus__class_Ominus(X21,X5,tc_nat)),X1,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X21),c_HOL_Oplus__class_Oplus(X5,X1,tc_nat),tc_nat)
| ~ c_lessequals(X5,X21,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_242]) ).
fof(c_0_1357,plain,
! [X2,X1,X5] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X5,tc_nat),c_HOL_Ominus__class_Ominus(X2,X5,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X5,X2,tc_nat)
| ~ c_lessequals(X5,X1,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_243]) ).
fof(c_0_1358,plain,
! [X2,X1,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X5,tc_nat),c_HOL_Ominus__class_Ominus(X2,X5,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(X5,X2,tc_nat)
| ~ c_lessequals(X5,X1,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_244]) ).
fof(c_0_1359,plain,
! [X17,X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_lessequals(X3,c_HOL_Oplus__class_Oplus(X10,X17,X4),X4)
| ~ c_lessequals(X11,X17,X4)
| ~ c_lessequals(X3,c_HOL_Oplus__class_Oplus(X10,X11,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_245]) ).
fof(c_0_1360,plain,
! [X2,X1,X5] :
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X5),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X5),X2,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_246]) ).
fof(c_0_1361,plain,
! [X2,X1,X5] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X5),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X5),X2,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_247]) ).
fof(c_0_1362,axiom,
! [X9,X36,X17,X11] :
( c_HOL_Oplus__class_Oplus(X9,c_HOL_Otimes__class_Otimes(X36,X11,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X9,c_HOL_Otimes__class_Otimes(X36,X17,tc_nat),tc_nat)
| X11 = X17
| X36 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_248 ).
fof(c_0_1363,axiom,
! [X3,X6,X7,X4] : c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X3,X7,X4),c_Set_Oinsert(X3,X6,X4),tc_fun(X4,tc_bool)) = c_Set_Oinsert(X3,c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),X4),
c_0_249 ).
fof(c_0_1364,plain,
! [X10,X3,X26] :
( hBOOL(hAPP(X26,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X3,X10,tc_nat)
| ~ hBOOL(hAPP(X26,c_HOL_Ominus__class_Ominus(X3,X10,tc_nat))) ),
inference(fof_simplification,[status(thm)],[c_0_250]) ).
fof(c_0_1365,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X10,X4)
| X11 = c_HOL_Ozero__class_Ozero(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X11,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_251]) ).
fof(c_0_1366,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X10,X4)
| X11 = c_HOL_Ozero__class_Ozero(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_252]) ).
fof(c_0_1367,plain,
! [X5,X21,X22] :
( c_lessequals(X22,c_HOL_Ominus__class_Ominus(X21,X5,tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X22,X5,tc_nat),X21,tc_nat)
| ~ c_lessequals(X5,X21,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_253]) ).
fof(c_0_1368,plain,
! [X5,X21,X22] :
( c_lessequals(c_HOL_Oplus__class_Oplus(X22,X5,tc_nat),X21,tc_nat)
| ~ c_lessequals(X22,c_HOL_Ominus__class_Ominus(X21,X5,tc_nat),tc_nat)
| ~ c_lessequals(X5,X21,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_254]) ).
fof(c_0_1369,plain,
! [X9,X6,X7,X4] :
( c_HOL_Oord__class_Oless(X7,c_Set_Oinsert(X9,X6,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| c_in(X9,X7,X4)
| ~ c_HOL_Oord__class_Oless(X7,X6,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_255]) ).
fof(c_0_1370,plain,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| c_HOL_Oord__class_Oless(X3,X10,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X3,X4),c_HOL_Oplus__class_Oplus(X11,X10,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_256]) ).
fof(c_0_1371,plain,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| c_HOL_Oord__class_Oless(X3,X10,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X11,X4),c_HOL_Oplus__class_Oplus(X10,X11,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_257]) ).
fof(c_0_1372,plain,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| c_lessequals(X3,X10,X4)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X11,X4),c_HOL_Oplus__class_Oplus(X10,X11,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_258]) ).
fof(c_0_1373,plain,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| c_lessequals(X3,X10,X4)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X11,X3,X4),c_HOL_Oplus__class_Oplus(X11,X10,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_259]) ).
fof(c_0_1374,plain,
! [X2,X1,X5] :
( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X5,tc_nat),c_HOL_Ominus__class_Ominus(X2,X5,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)
| ~ c_lessequals(X5,X2,tc_nat)
| ~ c_lessequals(X5,X1,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_260]) ).
fof(c_0_1375,plain,
! [X9,X6,X7,X4] :
( c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| c_in(X9,X7,X4)
| c_in(X9,X6,X4)
| ~ c_HOL_Oord__class_Oless(X7,c_Set_Oinsert(X9,X6,X4),tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_261]) ).
fof(c_0_1376,plain,
! [X3,X6,X7,X4] :
( c_Lattices_Olower__semilattice__class_Oinf(X7,c_Set_Oinsert(X3,X6,X4),tc_fun(X4,tc_bool)) = c_Set_Oinsert(X3,c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),X4)
| ~ c_in(X3,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_262]) ).
fof(c_0_1377,plain,
! [X3,X16,X6,X4] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X3,X6,X4),X16,tc_fun(X4,tc_bool)) = c_Set_Oinsert(X3,c_Lattices_Olower__semilattice__class_Oinf(X6,X16,tc_fun(X4,tc_bool)),X4)
| ~ c_in(X3,X16,X4) ),
inference(fof_simplification,[status(thm)],[c_0_263]) ).
fof(c_0_1378,plain,
! [X16,X6,X7,X4] :
( c_HOL_Ominus__class_Ominus(X6,c_HOL_Ominus__class_Ominus(X16,X7,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = X7
| ~ c_lessequals(X6,X16,tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_264]) ).
fof(c_0_1379,plain,
! [X16,X6,X7,X4] :
( c_lessequals(X16,c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
| ~ c_lessequals(X16,X6,tc_fun(X4,tc_bool))
| ~ c_lessequals(X16,X7,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_265]) ).
fof(c_0_1380,plain,
! [X16,X6,X7,X4] :
( c_lessequals(X16,c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
| ~ c_lessequals(X16,X6,tc_fun(X4,tc_bool))
| ~ c_lessequals(X16,X7,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_266]) ).
fof(c_0_1381,plain,
! [X2,X1,X5] :
( c_Ring__and__Field_Odvd__class_Odvd(X5,X2,tc_nat)
| ~ c_lessequals(X2,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_267]) ).
fof(c_0_1382,plain,
! [X2,X1,X5] :
( c_Ring__and__Field_Odvd__class_Odvd(X5,X1,tc_nat)
| ~ c_lessequals(X2,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_268]) ).
fof(c_0_1383,plain,
! [X2,X1,X5] :
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| X5 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,X1,tc_nat),c_HOL_Otimes__class_Otimes(X5,X2,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_269]) ).
fof(c_0_1384,plain,
! [X2,X1,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X1,tc_nat),c_HOL_Otimes__class_Otimes(X5,X2,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_270]) ).
fof(c_0_1385,plain,
! [X2,X1,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X5,tc_nat),c_HOL_Otimes__class_Otimes(X2,X5,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_271]) ).
fof(c_0_1386,axiom,
! [X9,X4] :
( c_in(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4)
| c_Finite__Set_Ocard(c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) = c_Suc(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4)) ),
c_0_272 ).
fof(c_0_1387,plain,
! [X2,X1,X5] :
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X5,X1,tc_nat),c_HOL_Oplus__class_Oplus(X5,X2,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_273]) ).
fof(c_0_1388,plain,
! [X2,X1,X5] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X1,tc_nat),c_HOL_Oplus__class_Oplus(X5,X2,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_274]) ).
fof(c_0_1389,plain,
! [X2,X1,X5] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X5,tc_nat),c_HOL_Otimes__class_Otimes(X2,X5,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_275]) ).
fof(c_0_1390,plain,
! [X2,X1,X5] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X1,tc_nat),c_HOL_Otimes__class_Otimes(X5,X2,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_276]) ).
fof(c_0_1391,axiom,
! [X16,X6,X7,X4] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),X16,tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X7,c_HOL_Ominus__class_Ominus(X6,X16,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
c_0_277 ).
fof(c_0_1392,axiom,
! [X16,X6,X7,X4] : c_Lattices_Olower__semilattice__class_Oinf(X7,c_Lattices_Olower__semilattice__class_Oinf(X6,X16,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X16,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
c_0_278 ).
fof(c_0_1393,axiom,
! [X16,X6,X7,X4] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),X16,tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X7,c_Lattices_Olower__semilattice__class_Oinf(X6,X16,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
c_0_279 ).
fof(c_0_1394,axiom,
! [X20,X7,X14,X4] :
( c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) != c_Set_Oimage(X20,X7,X14,X4)
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool)) ),
c_0_280 ).
fof(c_0_1395,axiom,
! [X20,X7,X14,X4] :
( c_Set_Oimage(X20,X7,X14,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool)) ),
c_0_281 ).
fof(c_0_1396,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Omult__mono1(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_lessequals(X3,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_282]) ).
fof(c_0_1397,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Omult__mono(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_lessequals(X3,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_283]) ).
fof(c_0_1398,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Omult__mono(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X11,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_lessequals(X3,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_284]) ).
fof(c_0_1399,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X10,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_285]) ).
fof(c_0_1400,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X11,X4),X4)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X10,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_286]) ).
fof(c_0_1401,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_HOL_Oord__class_Oless(X3,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_287]) ).
fof(c_0_1402,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X11,X4),X4)
| ~ c_HOL_Oord__class_Oless(X10,X3,X4)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_288]) ).
fof(c_0_1403,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X11,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,X10,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X11,X4) ),
inference(fof_simplification,[status(thm)],[c_0_289]) ).
fof(c_0_1404,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X11,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_HOL_Oord__class_Oless(X3,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_290]) ).
fof(c_0_1405,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X11,X4),X4)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X10,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_291]) ).
fof(c_0_1406,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4)
| ~ c_HOL_Oord__class_Oless(X10,X3,X4)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_292]) ).
fof(c_0_1407,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,X10,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X11,X4) ),
inference(fof_simplification,[status(thm)],[c_0_293]) ).
fof(c_0_1408,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X11,X4)
| ~ c_HOL_Oord__class_Oless(X3,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_294]) ).
fof(c_0_1409,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X10,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_295]) ).
fof(c_0_1410,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,X10,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X11,X4) ),
inference(fof_simplification,[status(thm)],[c_0_296]) ).
fof(c_0_1411,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4)
| ~ c_HOL_Oord__class_Oless(X10,X3,X4)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_297]) ).
fof(c_0_1412,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4)
| ~ c_lessequals(X3,X10,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X11,X4) ),
inference(fof_simplification,[status(thm)],[c_0_298]) ).
fof(c_0_1413,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4)
| ~ c_lessequals(X10,X3,X4)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_299]) ).
fof(c_0_1414,plain,
! [X8,X9,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X9,X4),X9,X4)
| ~ c_lessequals(X8,c_HOL_Oone__class_Oone(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X9,X4) ),
inference(fof_simplification,[status(thm)],[c_0_300]) ).
fof(c_0_1415,plain,
! [X8,X9,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X9,X8,X4),X9,X4)
| ~ c_lessequals(X8,c_HOL_Oone__class_Oone(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X9,X4) ),
inference(fof_simplification,[status(thm)],[c_0_301]) ).
fof(c_0_1416,plain,
! [X9,X6,X7,X4] :
( c_HOL_Oord__class_Oless(X7,X6,tc_fun(X4,tc_bool))
| ~ c_in(X9,X6,X4)
| ~ c_HOL_Oord__class_Oless(X7,c_Set_Oinsert(X9,X6,X4),tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_302]) ).
fof(c_0_1417,axiom,
! [X9,X7,X4] :
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X9,X7,X4),c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)) = X7
| c_in(X9,X7,X4) ),
c_0_303 ).
fof(c_0_1418,plain,
! [X2,X1,X5] :
( c_lessequals(X1,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),X5,tc_nat),tc_nat)
| ~ c_lessequals(X5,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_304]) ).
fof(c_0_1419,plain,
! [X17,X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(X3,X11,X4),c_HOL_Oplus__class_Oplus(X10,X17,X4),X4)
| ~ c_lessequals(X11,X17,X4)
| ~ c_lessequals(X3,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_305]) ).
fof(c_0_1420,plain,
! [X17,X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X17,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X17,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_306]) ).
fof(c_0_1421,plain,
! [X17,X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X11,X4),c_HOL_Oplus__class_Oplus(X10,X17,X4),X4)
| ~ c_HOL_Oord__class_Oless(X11,X17,X4)
| ~ c_HOL_Oord__class_Oless(X3,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_307]) ).
fof(c_0_1422,plain,
! [X17,X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X11,X4),c_HOL_Oplus__class_Oplus(X10,X17,X4),X4)
| ~ c_lessequals(X11,X17,X4)
| ~ c_HOL_Oord__class_Oless(X3,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_308]) ).
fof(c_0_1423,plain,
! [X17,X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X11,X4),c_HOL_Oplus__class_Oplus(X10,X17,X4),X4)
| ~ c_HOL_Oord__class_Oless(X11,X17,X4)
| ~ c_lessequals(X3,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_309]) ).
fof(c_0_1424,axiom,
! [X9,X6,X7,X4] :
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X9,X7,X4),X6,tc_fun(X4,tc_bool)) = c_Set_Oinsert(X9,c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),X4)
| c_in(X9,X6,X4) ),
c_0_310 ).
fof(c_0_1425,plain,
! [X8,X9,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X9,X4),c_HOL_Otimes__class_Otimes(X8,X8,X4),X4) != c_HOL_Ozero__class_Ozero(X4)
| X9 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_311]) ).
fof(c_0_1426,plain,
! [X8,X9,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X9,X4),c_HOL_Otimes__class_Otimes(X8,X8,X4),X4) != c_HOL_Ozero__class_Ozero(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_312]) ).
fof(c_0_1427,plain,
! [X16,X6,X7,X4] :
( c_lessequals(X16,X7,tc_fun(X4,tc_bool))
| ~ c_lessequals(X16,c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_313]) ).
fof(c_0_1428,plain,
! [X16,X6,X7,X4] :
( c_lessequals(X16,X6,tc_fun(X4,tc_bool))
| ~ c_lessequals(X16,c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_314]) ).
fof(c_0_1429,plain,
! [X15,X8,X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(X9,c_HOL_Oplus__class_Oplus(X8,X15,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X8,X4),c_HOL_Otimes__class_Otimes(X9,X15,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_315]) ).
fof(c_0_1430,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,X10,X4),X11,X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X11,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_316]) ).
fof(c_0_1431,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,X10,X4),X11,X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X11,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_317]) ).
fof(c_0_1432,plain,
! [X11,X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4) = c_HOL_Otimes__class_Otimes(X11,c_Divides_Odiv__class_Omod(X3,X10,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_318]) ).
fof(c_0_1433,plain,
! [X11,X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X11,X4),X4) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X3,X10,X4),X11,X4) ),
inference(fof_simplification,[status(thm)],[c_0_319]) ).
fof(c_0_1434,plain,
! [X1,X10,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X1,X4),c_HOL_Otimes__class_Otimes(X10,X1,X4),X4) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,X10,X4),X1,X4) ),
inference(fof_simplification,[status(thm)],[c_0_320]) ).
fof(c_0_1435,plain,
! [X11,X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X10,X11,X4),X4),X10,X4) = c_Divides_Odiv__class_Omod(X3,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_321]) ).
fof(c_0_1436,plain,
! [X11,X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X11,X10,X4),X4),X10,X4) = c_Divides_Odiv__class_Omod(X3,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_322]) ).
fof(c_0_1437,plain,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X3,X10,X4),X11,X4) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X3,X11,X4),c_HOL_Oplus__class_Oplus(X10,X11,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_323]) ).
fof(c_0_1438,plain,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_HOL_Oplus__class_Oplus(X3,c_Lattices_Olower__semilattice__class_Oinf(X10,X11,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X3,X10,X4),c_HOL_Oplus__class_Oplus(X3,X11,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_324]) ).
fof(c_0_1439,plain,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(X4)
| c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X3,X10,X4),X11,X4) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X3,X11,X4),c_HOL_Oplus__class_Oplus(X10,X11,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_325]) ).
fof(c_0_1440,plain,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(X4)
| c_HOL_Oplus__class_Oplus(X3,c_Lattices_Olower__semilattice__class_Oinf(X10,X11,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X3,X10,X4),c_HOL_Oplus__class_Oplus(X3,X11,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_326]) ).
fof(c_0_1441,plain,
! [X2,X1,X5] :
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,X1,tc_nat),c_HOL_Otimes__class_Otimes(X5,X2,tc_nat),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_327]) ).
fof(c_0_1442,plain,
! [X2,X1,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X1,tc_nat),c_HOL_Otimes__class_Otimes(X5,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),X5,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_328]) ).
fof(c_0_1443,plain,
! [X5,X21,X22] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X22,X5,tc_nat),c_HOL_Otimes__class_Otimes(X21,X5,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(X22,X21,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_329]) ).
fof(c_0_1444,plain,
! [X5,X21,X22] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X22,tc_nat),c_HOL_Otimes__class_Otimes(X5,X21,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(X22,X21,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_330]) ).
fof(c_0_1445,plain,
! [X2,X1,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X1,tc_nat),c_HOL_Otimes__class_Otimes(X5,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),X5,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_331]) ).
fof(c_0_1446,plain,
! [X2,X1,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X5,tc_nat),c_HOL_Otimes__class_Otimes(X2,X5,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),X5,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_332]) ).
fof(c_0_1447,plain,
! [X2,X1,X5] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X5,X1,tc_nat),c_HOL_Otimes__class_Otimes(X5,X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_333]) ).
fof(c_0_1448,axiom,
! [X2,X1] :
( c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_334 ).
fof(c_0_1449,plain,
! [X9,X6,X7,X4] :
( hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),X9))
| ~ hBOOL(hAPP(X6,X9))
| ~ hBOOL(hAPP(X7,X9)) ),
inference(fof_simplification,[status(thm)],[c_0_335]) ).
fof(c_0_1450,plain,
! [X11,X10,X3] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X11,tc_nat),c_HOL_Ominus__class_Ominus(X10,X11,tc_nat),tc_nat)
| ~ c_lessequals(X11,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X10,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_336]) ).
fof(c_0_1451,plain,
! [X2,X1,X24] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X24,X2,tc_nat),c_HOL_Ominus__class_Ominus(X24,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X24,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_337]) ).
fof(c_0_1452,plain,
! [X24,X5,X21,X22] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X22,X5,tc_nat),c_HOL_Otimes__class_Otimes(X21,X24,tc_nat),tc_nat)
| ~ c_lessequals(X5,X24,tc_nat)
| ~ c_lessequals(X22,X21,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_338]) ).
fof(c_0_1453,plain,
! [X24,X5,X21,X22] :
( c_lessequals(c_HOL_Oplus__class_Oplus(X22,X5,tc_nat),c_HOL_Oplus__class_Oplus(X21,X24,tc_nat),tc_nat)
| ~ c_lessequals(X5,X24,tc_nat)
| ~ c_lessequals(X22,X21,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_339]) ).
fof(c_0_1454,plain,
! [X24,X5,X21,X22] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X22,X5,tc_nat),c_HOL_Oplus__class_Oplus(X21,X24,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X24,tc_nat)
| ~ c_HOL_Oord__class_Oless(X22,X21,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_340]) ).
fof(c_0_1455,plain,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X10,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X3,X10,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_341]) ).
fof(c_0_1456,plain,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X10,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X10,X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_342]) ).
fof(c_0_1457,plain,
! [X2,X26] :
( ~ hBOOL(hAPP(X26,c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
| hBOOL(hAPP(X26,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_343]) ).
fof(c_0_1458,plain,
! [X9,X6,X7,X4] :
( c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,c_Set_Oinsert(X9,X6,X4),tc_fun(X4,tc_bool))
| c_in(X9,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_344]) ).
fof(c_0_1459,plain,
! [X9,X6,X7,X4] :
( c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| c_in(X9,X7,X4)
| ~ c_lessequals(X7,c_Set_Oinsert(X9,X6,X4),tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_345]) ).
fof(c_0_1460,plain,
! [X10,X3,X4] :
( X10 = X3
| ~ c_in(X10,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_346]) ).
fof(c_0_1461,axiom,
! [X2,X1,X5] : c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X5,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X5,tc_nat),c_HOL_Otimes__class_Otimes(X2,X5,tc_nat),tc_nat),
c_0_347 ).
fof(c_0_1462,axiom,
! [X2,X1,X5] : c_HOL_Otimes__class_Otimes(X5,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X5,X1,tc_nat),c_HOL_Otimes__class_Otimes(X5,X2,tc_nat),tc_nat),
c_0_348 ).
fof(c_0_1463,axiom,
! [X2,X1,X5] : c_HOL_Otimes__class_Otimes(X5,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X1,tc_nat),c_HOL_Otimes__class_Otimes(X5,X2,tc_nat),tc_nat),
c_0_349 ).
fof(c_0_1464,axiom,
! [X2,X1,X5] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X5,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X5,tc_nat),c_HOL_Otimes__class_Otimes(X2,X5,tc_nat),tc_nat),
c_0_350 ).
fof(c_0_1465,axiom,
! [X2,X1,X5] : c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,tc_nat),X1,tc_nat),X2,tc_nat) = c_Divides_Odiv__class_Omod(X1,X2,tc_nat),
c_0_351 ).
fof(c_0_1466,axiom,
! [X2,X1,X5] : c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X5,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X5,tc_nat),c_HOL_Otimes__class_Otimes(X2,X5,tc_nat),tc_nat),
c_0_352 ).
fof(c_0_1467,axiom,
! [X2,X1,X5] : c_HOL_Otimes__class_Otimes(X5,c_Divides_Odiv__class_Omod(X1,X2,tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X1,tc_nat),c_HOL_Otimes__class_Otimes(X5,X2,tc_nat),tc_nat),
c_0_353 ).
fof(c_0_1468,plain,
! [X9,X6,X7,X4] :
( c_HOL_Oord__class_Oless(X7,c_Set_Oinsert(X9,X6,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| c_in(X9,X7,X4)
| c_in(X9,X6,X4) ),
inference(fof_simplification,[status(thm)],[c_0_354]) ).
fof(c_0_1469,plain,
! [X6,X7,X4] :
( c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),X4) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(X7,X4),c_Finite__Set_Ocard(X6,X4),tc_nat)
| ~ c_lessequals(X6,X7,tc_fun(X4,tc_bool))
| ~ c_Finite__Set_Ofinite(X6,X4) ),
inference(fof_simplification,[status(thm)],[c_0_355]) ).
fof(c_0_1470,plain,
! [X8,X9,X7,X4] :
( hBOOL(hAPP(X7,X9))
| X8 = X9
| ~ hBOOL(hAPP(c_Set_Oinsert(X8,X7,X4),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_356]) ).
fof(c_0_1471,plain,
! [X3,X44,X16,X4] :
( c_lessequals(c_Set_Oinsert(X3,X16,X4),c_Set_Oinsert(X3,X44,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X16,X44,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_357]) ).
fof(c_0_1472,plain,
! [X11,X6,X7,X4] :
( ~ c_in(X11,X6,X4)
| ~ c_in(X11,c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),X4) ),
inference(fof_simplification,[status(thm)],[c_0_358]) ).
fof(c_0_1473,plain,
! [X5,X22] :
( ~ c_lessequals(X22,c_HOL_Oplus__class_Oplus(X5,X22,tc_nat),tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X5,X22,tc_nat),X22,tc_nat) = X5 ),
inference(fof_simplification,[status(thm)],[c_0_359]) ).
fof(c_0_1474,plain,
! [X5,X21,X22] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X21,X5,tc_nat),X22,tc_nat)
| ~ c_lessequals(X21,c_HOL_Oplus__class_Oplus(X22,X5,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_360]) ).
fof(c_0_1475,plain,
! [X5,X21,X22] :
( c_lessequals(X21,c_HOL_Oplus__class_Oplus(X22,X5,tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X21,X5,tc_nat),X22,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_361]) ).
fof(c_0_1476,plain,
! [X5,X21,X22] :
( c_HOL_Oord__class_Oless(X22,c_HOL_Ominus__class_Ominus(X21,X5,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X22,X5,tc_nat),X21,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_362]) ).
fof(c_0_1477,plain,
! [X5,X21,X22] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X22,X5,tc_nat),X21,tc_nat)
| ~ c_HOL_Oord__class_Oless(X22,c_HOL_Ominus__class_Ominus(X21,X5,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_363]) ).
fof(c_0_1478,plain,
! [X2,X1,X5,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X5,X1,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,c_Divides_Odiv__class_Omod(X1,X2,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_364]) ).
fof(c_0_1479,plain,
! [X2,X1,X5,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X5,X1,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X2,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,c_Divides_Odiv__class_Omod(X1,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_365]) ).
fof(c_0_1480,plain,
! [X15,X8,X9,X18,X4] :
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_HOL_Oplus__class_Oplus(X9,c_HOL_Oplus__class_Oplus(X8,X15,X4),X4) != c_HOL_Oplus__class_Oplus(X8,X18,X4)
| c_HOL_Oplus__class_Oplus(X9,X15,X4) = X18 ),
inference(fof_simplification,[status(thm)],[c_0_366]) ).
fof(c_0_1481,plain,
! [X5,X21,X22] :
( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X21,X5,tc_nat),X22,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X21,X22,tc_nat),X5,tc_nat)
| ~ c_lessequals(X5,X21,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_367]) ).
fof(c_0_1482,plain,
! [X5,X21,X22] :
( c_HOL_Oplus__class_Oplus(X22,c_HOL_Ominus__class_Ominus(X21,X5,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X22,X21,tc_nat),X5,tc_nat)
| ~ c_lessequals(X5,X21,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_368]) ).
fof(c_0_1483,plain,
! [X5,X21,X22] :
( c_HOL_Ominus__class_Ominus(X22,c_HOL_Ominus__class_Ominus(X21,X5,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X22,X5,tc_nat),X21,tc_nat)
| ~ c_lessequals(X5,X21,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_369]) ).
fof(c_0_1484,plain,
! [X5,X21,X22] :
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X21,X22,tc_nat),X5,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X21,X5,tc_nat),X22,tc_nat)
| ~ c_lessequals(X5,X21,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_370]) ).
fof(c_0_1485,plain,
! [X5,X21,X22] :
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X22,X21,tc_nat),X5,tc_nat) = c_HOL_Oplus__class_Oplus(X22,c_HOL_Ominus__class_Ominus(X21,X5,tc_nat),tc_nat)
| ~ c_lessequals(X5,X21,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_371]) ).
fof(c_0_1486,plain,
! [X9,X6,X7,X4] :
( c_lessequals(c_Set_Oinsert(X9,X7,X4),X6,tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| ~ c_in(X9,X6,X4) ),
inference(fof_simplification,[status(thm)],[c_0_372]) ).
fof(c_0_1487,plain,
! [X9,X6,X7,X4] :
( c_HOL_Oord__class_Oless(X7,c_Set_Oinsert(X9,X6,X4),tc_fun(X4,tc_bool))
| ~ c_in(X9,X6,X4)
| ~ c_HOL_Oord__class_Oless(X7,X6,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_373]) ).
fof(c_0_1488,plain,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X10,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_374]) ).
fof(c_0_1489,plain,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X10,X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X10,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_375]) ).
fof(c_0_1490,plain,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(X10,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X10,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_376]) ).
fof(c_0_1491,plain,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X10,X4)
| c_lessequals(X10,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X10,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_377]) ).
fof(c_0_1492,plain,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(X10,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X10,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X3,X10,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_378]) ).
fof(c_0_1493,plain,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X10,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X3,X10,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_379]) ).
fof(c_0_1494,plain,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(X10,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X3,X10,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_380]) ).
fof(c_0_1495,plain,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X3,X10,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_381]) ).
fof(c_0_1496,plain,
! [X6,X7,X4] :
( c_HOL_Oord__class_Oless(X7,X6,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(X7,X4),c_Finite__Set_Ocard(X6,X4),tc_nat)
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| ~ c_Finite__Set_Ofinite(X6,X4) ),
inference(fof_simplification,[status(thm)],[c_0_382]) ).
fof(c_0_1497,axiom,
! [X2,X1] :
( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_383 ).
fof(c_0_1498,plain,
! [X11,X6,X7,X4] :
( c_in(X11,X7,X4)
| ~ c_in(X11,c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),X4) ),
inference(fof_simplification,[status(thm)],[c_0_384]) ).
fof(c_0_1499,plain,
! [X11,X6,X7,X4] :
( c_in(X11,X6,X4)
| ~ c_in(X11,c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),X4) ),
inference(fof_simplification,[status(thm)],[c_0_385]) ).
fof(c_0_1500,plain,
! [X11,X6,X7,X4] :
( c_in(X11,X7,X4)
| ~ c_in(X11,c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),X4) ),
inference(fof_simplification,[status(thm)],[c_0_386]) ).
fof(c_0_1501,plain,
! [X11,X6,X7,X4] :
( c_in(X11,c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),X4)
| ~ c_in(X11,X6,X4)
| ~ c_in(X11,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_387]) ).
fof(c_0_1502,plain,
! [X11,X6,X7,X4] :
( c_in(X11,c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),X4)
| ~ c_in(X11,X6,X4)
| ~ c_in(X11,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_388]) ).
fof(c_0_1503,plain,
! [X20,X3,X25,X4] :
( c_in(X3,c_Inductive_Ocomplete__lattice__class_Ogfp(X20,tc_fun(X4,tc_bool)),X4)
| ~ c_lessequals(X25,hAPP(X20,X25),tc_fun(X4,tc_bool))
| ~ c_in(X3,X25,X4) ),
inference(fof_simplification,[status(thm)],[c_0_389]) ).
fof(c_0_1504,plain,
! [X2,X1] :
( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_390]) ).
fof(c_0_1505,plain,
! [X2,X1] :
( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),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(fof_simplification,[status(thm)],[c_0_391]) ).
fof(c_0_1506,plain,
! [X2,X1,X5] :
( c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X5),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X5),X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_392]) ).
fof(c_0_1507,plain,
! [X2,X1,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X5),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X5),X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_393]) ).
fof(c_0_1508,plain,
! [X9,X6,X7,X4] :
( c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X9,X7,X4),X6,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_394]) ).
fof(c_0_1509,plain,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X3,X10,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X10,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_395]) ).
fof(c_0_1510,plain,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X3,X10,X4),X4)
| ~ c_lessequals(X10,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_396]) ).
fof(c_0_1511,plain,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X3,X10,X4),X4)
| ~ c_lessequals(X10,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_397]) ).
fof(c_0_1512,plain,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X3,X10,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X10,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_398]) ).
fof(c_0_1513,plain,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X3,X10,X4),X4)
| ~ c_lessequals(X10,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_399]) ).
fof(c_0_1514,plain,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X3,X10,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X10,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_400]) ).
fof(c_0_1515,plain,
! [X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(X3,X10,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X10,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_401]) ).
fof(c_0_1516,plain,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X10,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X10,X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_402]) ).
fof(c_0_1517,plain,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X10,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_403]) ).
fof(c_0_1518,plain,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_404]) ).
fof(c_0_1519,plain,
! [X2,X1,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),c_HOL_Otimes__class_Otimes(X1,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),X1,X4) ),
inference(fof_simplification,[status(thm)],[c_0_405]) ).
fof(c_0_1520,plain,
! [X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(X3,X10,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X10,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_406]) ).
fof(c_0_1521,plain,
! [X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X10,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X10,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_407]) ).
fof(c_0_1522,plain,
! [X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X10,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_408]) ).
fof(c_0_1523,plain,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X3,X10,X4),X4)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_409]) ).
fof(c_0_1524,plain,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X3,X10,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X10,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_410]) ).
fof(c_0_1525,plain,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X10,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X10,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_411]) ).
fof(c_0_1526,plain,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X10,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X10,X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_412]) ).
fof(c_0_1527,plain,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X10,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X10,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_413]) ).
fof(c_0_1528,plain,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X10,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X10,X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_414]) ).
fof(c_0_1529,plain,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X10,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X10,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_415]) ).
fof(c_0_1530,plain,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X10,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X10,X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_416]) ).
fof(c_0_1531,plain,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X10,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X10,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_417]) ).
fof(c_0_1532,plain,
! [X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(X3,X10,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X10,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_418]) ).
fof(c_0_1533,plain,
! [X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(X3,X10,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X10,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_419]) ).
fof(c_0_1534,plain,
! [X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X10,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_420]) ).
fof(c_0_1535,plain,
! [X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(X3,X10,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X10,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_421]) ).
fof(c_0_1536,axiom,
! [X1] : c_lessequals(X1,c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X1,X1,tc_nat),tc_nat),tc_nat),
c_0_422 ).
fof(c_0_1537,plain,
! [X2,X1] :
( 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_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_423]) ).
fof(c_0_1538,plain,
! [X2,X1] :
( c_HOL_Oord__class_Oless(X2,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(fof_simplification,[status(thm)],[c_0_424]) ).
fof(c_0_1539,plain,
! [X2,X1] :
( c_HOL_Oord__class_Oless(X2,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(fof_simplification,[status(thm)],[c_0_425]) ).
fof(c_0_1540,plain,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X3,X4),c_HOL_Oplus__class_Oplus(X11,X10,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_426]) ).
fof(c_0_1541,plain,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X3,X4),c_HOL_Oplus__class_Oplus(X11,X10,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_427]) ).
fof(c_0_1542,plain,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X11,X4),c_HOL_Oplus__class_Oplus(X10,X11,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_428]) ).
fof(c_0_1543,plain,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X11,X4),c_HOL_Oplus__class_Oplus(X10,X11,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_429]) ).
fof(c_0_1544,plain,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(X3,X11,X4),c_HOL_Oplus__class_Oplus(X10,X11,X4),X4)
| ~ c_lessequals(X3,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_430]) ).
fof(c_0_1545,plain,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(X11,X3,X4),c_HOL_Oplus__class_Oplus(X11,X10,X4),X4)
| ~ c_lessequals(X3,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_431]) ).
fof(c_0_1546,plain,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(X3,X11,X4),c_HOL_Oplus__class_Oplus(X10,X11,X4),X4)
| ~ c_lessequals(X3,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_432]) ).
fof(c_0_1547,plain,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(X11,X3,X4),c_HOL_Oplus__class_Oplus(X11,X10,X4),X4)
| ~ c_lessequals(X3,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_433]) ).
fof(c_0_1548,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X11,X3,X4),c_HOL_Otimes__class_Otimes(X11,X10,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_434]) ).
fof(c_0_1549,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X11,X4),c_HOL_Otimes__class_Otimes(X10,X11,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_435]) ).
fof(c_0_1550,plain,
! [X9,X6,X7,X4] :
( c_lessequals(X7,c_Set_Oinsert(X9,X6,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| c_in(X9,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_436]) ).
fof(c_0_1551,plain,
! [X9,X6,X7,X4] :
( c_lessequals(X7,c_Set_Oinsert(X9,X6,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| c_in(X9,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_437]) ).
fof(c_0_1552,plain,
! [X15,X8,X9] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X9,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X15,X8,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X15,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X8,X9,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X8,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_438]) ).
fof(c_0_1553,plain,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_lessequals(X10,c_HOL_Oplus__class_Oplus(X3,X11,X4),X4)
| ~ c_lessequals(X10,X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X11,X4) ),
inference(fof_simplification,[status(thm)],[c_0_439]) ).
fof(c_0_1554,plain,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_lessequals(X10,c_HOL_Oplus__class_Oplus(X3,X11,X4),X4)
| ~ c_lessequals(X10,X11,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_440]) ).
fof(c_0_1555,plain,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_HOL_Oord__class_Oless(X10,c_HOL_Oplus__class_Oplus(X3,X11,X4),X4)
| ~ c_lessequals(X10,X11,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_441]) ).
fof(c_0_1556,plain,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_HOL_Oord__class_Oless(X10,c_HOL_Oplus__class_Oplus(X3,X11,X4),X4)
| ~ c_HOL_Oord__class_Oless(X10,X11,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_442]) ).
fof(c_0_1557,plain,
! [X1,X5] :
( c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Otimes__class_Otimes(X5,X1,tc_nat)),X5,tc_nat) = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X5,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_443]) ).
fof(c_0_1558,plain,
! [X2,X48,X26] :
( hBOOL(hAPP(X26,X48))
| ~ hBOOL(hAPP(X26,c_Suc(c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1(X26,X2))))
| ~ c_lessequals(c_Suc(X2),X48,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_444]) ).
fof(c_0_1559,plain,
! [X5,X22,X26] :
( hBOOL(hAPP(X26,c_HOL_Ominus__class_Ominus(X5,X22,tc_nat)))
| hBOOL(hAPP(X26,c_Suc(c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1(X26))))
| ~ hBOOL(hAPP(X26,X5)) ),
inference(fof_simplification,[status(thm)],[c_0_445]) ).
fof(c_0_1560,plain,
! [X5,X22,X26] :
( hBOOL(hAPP(X26,c_HOL_Ominus__class_Ominus(X5,X22,tc_nat)))
| ~ hBOOL(hAPP(X26,c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1(X26)))
| ~ hBOOL(hAPP(X26,X5)) ),
inference(fof_simplification,[status(thm)],[c_0_446]) ).
fof(c_0_1561,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(X10,c_HOL_Oplus__class_Oplus(X3,X11,X4),X4)
| ~ c_HOL_Oord__class_Oless(X10,X11,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_447]) ).
fof(c_0_1562,plain,
! [X11,X6,X7,X4] :
( c_in(X11,c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),X4)
| c_in(X11,X6,X4)
| ~ c_in(X11,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_448]) ).
fof(c_0_1563,plain,
! [X11,X6,X7,X4] :
( c_in(X11,c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),X4)
| c_in(X11,X6,X4)
| ~ c_in(X11,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_449]) ).
fof(c_0_1564,plain,
! [X9,X6,X7,X4] :
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X9,X7,X4),X6,tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool))
| ~ c_in(X9,X6,X4) ),
inference(fof_simplification,[status(thm)],[c_0_450]) ).
fof(c_0_1565,plain,
! [X9,X6,X7,X4] :
( c_in(X9,X6,X4)
| ~ c_lessequals(c_Set_Oinsert(X9,X7,X4),X6,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_451]) ).
fof(c_0_1566,plain,
! [X2,X1,X24] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X24,tc_nat),c_HOL_Ominus__class_Ominus(X2,X24,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_452]) ).
fof(c_0_1567,plain,
! [X2,X1,X24] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X24,X2,tc_nat),c_HOL_Ominus__class_Ominus(X24,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_453]) ).
fof(c_0_1568,plain,
! [X5,X21,X22] :
( c_lessequals(c_HOL_Oplus__class_Oplus(X22,X5,tc_nat),c_HOL_Oplus__class_Oplus(X21,X5,tc_nat),tc_nat)
| ~ c_lessequals(X22,X21,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_454]) ).
fof(c_0_1569,plain,
! [X2,X1,X5] :
( c_lessequals(c_HOL_Oplus__class_Oplus(X5,X1,tc_nat),c_HOL_Oplus__class_Oplus(X5,X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_455]) ).
fof(c_0_1570,plain,
! [X5,X21,X22] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X22,X5,tc_nat),c_HOL_Otimes__class_Otimes(X21,X5,tc_nat),tc_nat)
| ~ c_lessequals(X22,X21,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_456]) ).
fof(c_0_1571,plain,
! [X5,X21,X22] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X5,X22,tc_nat),c_HOL_Otimes__class_Otimes(X5,X21,tc_nat),tc_nat)
| ~ c_lessequals(X22,X21,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_457]) ).
fof(c_0_1572,plain,
! [X2,X1,X5] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X5,X1,tc_nat),c_HOL_Otimes__class_Otimes(X5,X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_458]) ).
fof(c_0_1573,plain,
! [X2,X1,X5] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X5,tc_nat),c_HOL_Otimes__class_Otimes(X2,X5,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_459]) ).
fof(c_0_1574,plain,
! [X2,X1,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X1,tc_nat),c_HOL_Oplus__class_Oplus(X5,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_460]) ).
fof(c_0_1575,plain,
! [X5,X21,X22] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X22,X5,tc_nat),c_HOL_Oplus__class_Oplus(X21,X5,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X22,X21,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_461]) ).
fof(c_0_1576,plain,
! [X2,X1,X5] :
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,X1,tc_nat),c_HOL_Otimes__class_Otimes(X5,X2,tc_nat),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_462]) ).
fof(c_0_1577,plain,
! [X1,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X3,X1,X4),X4) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(X4),X4),X1,X4) ),
inference(fof_simplification,[status(thm)],[c_0_463]) ).
fof(c_0_1578,plain,
! [X1,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X1,X4),X1,X4) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(X4),X4),X1,X4) ),
inference(fof_simplification,[status(thm)],[c_0_464]) ).
fof(c_0_1579,plain,
! [X9,X7,X4] :
( c_lessequals(c_Finite__Set_Ocard(X7,X4),c_Finite__Set_Ocard(c_Set_Oinsert(X9,X7,X4),X4),tc_nat)
| ~ c_Finite__Set_Ofinite(X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_465]) ).
fof(c_0_1580,plain,
! [X15,X8,X9,X4] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X9,c_HOL_Ominus__class_Ominus(X8,X15,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X15,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_466]) ).
fof(c_0_1581,plain,
! [X15,X8,X9,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(X9,c_Lattices_Olower__semilattice__class_Oinf(X8,X15,X4),X4)
| ~ c_lessequals(X9,X15,X4)
| ~ c_lessequals(X9,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_467]) ).
fof(c_0_1582,plain,
! [X15,X8,X9,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(X9,c_Lattices_Olower__semilattice__class_Oinf(X8,X15,X4),X4)
| ~ c_lessequals(X9,X15,X4)
| ~ c_lessequals(X9,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_468]) ).
fof(c_0_1583,plain,
! [X9,X10,X3,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(X9,c_Lattices_Olower__semilattice__class_Oinf(X3,X10,X4),X4)
| ~ c_lessequals(X9,X10,X4)
| ~ c_lessequals(X9,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_469]) ).
fof(c_0_1584,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Oplus__class_Oplus(X10,X11,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X11,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_470]) ).
fof(c_0_1585,plain,
! [X2,X1,X5,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X5,c_Divides_Odiv__class_Omod(X1,X2,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X2,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X1,X4) ),
inference(fof_simplification,[status(thm)],[c_0_471]) ).
fof(c_0_1586,plain,
! [X2,X1,X5,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X5,c_Divides_Odiv__class_Omod(X1,X2,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X1,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_472]) ).
fof(c_0_1587,plain,
! [X2,X1] :
( 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)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_473]) ).
fof(c_0_1588,plain,
! [X2,X1] :
( 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)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_474]) ).
fof(c_0_1589,plain,
! [X2,X1] :
( 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)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_475]) ).
fof(c_0_1590,plain,
! [X9,X6,X7,X4] :
( ~ c_in(X9,X6,X4)
| ~ c_in(X9,X7,X4)
| c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_476]) ).
fof(c_0_1591,plain,
! [X2,X1,X5] :
( c_HOL_Ominus__class_Ominus(X1,X5,tc_nat) != c_HOL_Ominus__class_Ominus(X2,X5,tc_nat)
| ~ c_lessequals(X5,X2,tc_nat)
| ~ c_lessequals(X5,X1,tc_nat)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[c_0_477]) ).
fof(c_0_1592,axiom,
! [X10,X3,X4] :
( c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4) != c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4)
| X3 = X10 ),
c_0_478 ).
fof(c_0_1593,plain,
! [X2,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X1,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(fof_simplification,[status(thm)],[c_0_479]) ).
fof(c_0_1594,plain,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_480]) ).
fof(c_0_1595,plain,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(X3,X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_481]) ).
fof(c_0_1596,plain,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_482]) ).
fof(c_0_1597,plain,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_483]) ).
fof(c_0_1598,plain,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(X3,X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_484]) ).
fof(c_0_1599,axiom,
! [X2,X1,X5] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X1),X2,tc_nat),c_Suc(X5),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X5,tc_nat),
c_0_485 ).
fof(c_0_1600,plain,
! [X2,X1] :
( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_486]) ).
fof(c_0_1601,plain,
! [X2,X1] :
( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_487]) ).
fof(c_0_1602,plain,
! [X15,X8,X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(X9,c_HOL_Otimes__class_Otimes(X8,X15,X4),X4) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X9,X8,X4),X15,X4) ),
inference(fof_simplification,[status(thm)],[c_0_488]) ).
fof(c_0_1603,plain,
! [X30,X31,X33,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(X33,c_HOL_Otimes__class_Otimes(X31,X30,X4),X4) = c_HOL_Otimes__class_Otimes(X31,c_HOL_Otimes__class_Otimes(X33,X30,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_489]) ).
fof(c_0_1604,plain,
! [X30,X31,X33,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(X33,c_HOL_Otimes__class_Otimes(X31,X30,X4),X4) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X33,X31,X4),X30,X4) ),
inference(fof_simplification,[status(thm)],[c_0_490]) ).
fof(c_0_1605,plain,
! [X31,X32,X33,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X33,X32,X4),X31,X4) = c_HOL_Otimes__class_Otimes(X33,c_HOL_Otimes__class_Otimes(X32,X31,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_491]) ).
fof(c_0_1606,plain,
! [X31,X32,X33,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X33,X32,X4),X31,X4) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X33,X31,X4),X32,X4) ),
inference(fof_simplification,[status(thm)],[c_0_492]) ).
fof(c_0_1607,plain,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X3,X10,X4),X11,X4) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X10,X11,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_493]) ).
fof(c_0_1608,plain,
! [X15,X8,X9,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X9,X8,X4),X15,X4) = c_Lattices_Olower__semilattice__class_Oinf(X9,c_Lattices_Olower__semilattice__class_Oinf(X8,X15,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_494]) ).
fof(c_0_1609,plain,
! [X15,X8,X9,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X9,c_Lattices_Olower__semilattice__class_Oinf(X8,X15,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X8,c_Lattices_Olower__semilattice__class_Oinf(X9,X15,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_495]) ).
fof(c_0_1610,plain,
! [X15,X8,X9,X4] :
( ~ class_Lattices_Olattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X9,c_Lattices_Olower__semilattice__class_Oinf(X8,X15,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X8,c_Lattices_Olower__semilattice__class_Oinf(X9,X15,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_496]) ).
fof(c_0_1611,plain,
! [X15,X8,X9,X4] :
( ~ class_Lattices_Olattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X9,X8,X4),X15,X4) = c_Lattices_Olower__semilattice__class_Oinf(X9,c_Lattices_Olower__semilattice__class_Oinf(X8,X15,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_497]) ).
fof(c_0_1612,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X10,X4),X11,X4) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X10,X11,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_498]) ).
fof(c_0_1613,plain,
! [X17,X11,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X11,X17,X4),X4) = c_HOL_Oplus__class_Oplus(X11,c_HOL_Oplus__class_Oplus(X3,X17,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_499]) ).
fof(c_0_1614,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X10,X4),X11,X4) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X11,X4),X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_500]) ).
fof(c_0_1615,plain,
! [X17,X11,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X11,X17,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X11,X4),X17,X4) ),
inference(fof_simplification,[status(thm)],[c_0_501]) ).
fof(c_0_1616,plain,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Oab__semigroup__add(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X10,X4),X11,X4) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X10,X11,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_502]) ).
fof(c_0_1617,plain,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X10,X11,X4),X4) = c_HOL_Oplus__class_Oplus(X10,c_HOL_Oplus__class_Oplus(X3,X11,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_503]) ).
fof(c_0_1618,plain,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X10,X4),X11,X4) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X10,X11,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_504]) ).
fof(c_0_1619,plain,
! [X15,X8,X9,X4] :
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_HOL_Oplus__class_Oplus(X9,c_HOL_Oplus__class_Oplus(X8,X15,X4),X4) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X9,X15,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_505]) ).
fof(c_0_1620,plain,
! [X15,X8,X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(X9,c_HOL_Oplus__class_Oplus(X8,X15,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X9,X8,X4),X15,X4) ),
inference(fof_simplification,[status(thm)],[c_0_506]) ).
fof(c_0_1621,plain,
! [X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oplus__class_Oplus(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) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_507]) ).
fof(c_0_1622,plain,
! [X15,X8,X9] :
( c_Ring__and__Field_Odvd__class_Odvd(X9,X15,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X15,X8,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X15,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X8,X9,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X8,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_508]) ).
fof(c_0_1623,axiom,
! [X20,X14,X4] : c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) = c_Set_Oimage(X20,c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool)),X14,X4),
c_0_509 ).
fof(c_0_1624,axiom,
! [X20,X14,X4] : c_Set_Oimage(X20,c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool)),X14,X4) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
c_0_510 ).
fof(c_0_1625,axiom,
! [X20,X14,X4] : c_Set_Ovimage(X20,c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool)),X4,X14) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
c_0_511 ).
fof(c_0_1626,axiom,
! [X20,X14,X4] : c_Set_Ovimage(X20,c_Orderings_Otop__class_Otop(tc_fun(X14,tc_bool)),X4,X14) = c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),
c_0_512 ).
fof(c_0_1627,plain,
! [X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_lessequals(X3,X10,X4)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X3,X10,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_513]) ).
fof(c_0_1628,plain,
! [X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(X3,X10,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X10,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_514]) ).
fof(c_0_1629,axiom,
! [X2,X1] : 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),
c_0_515 ).
fof(c_0_1630,plain,
! [X2,X1,X5] :
( c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X1,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_516]) ).
fof(c_0_1631,axiom,
! [X8,X9,X7,X4] : c_Set_Oinsert(X9,c_Set_Oinsert(X8,X7,X4),X4) = c_Set_Oinsert(X8,c_Set_Oinsert(X9,X7,X4),X4),
c_0_517 ).
fof(c_0_1632,plain,
! [X16,X6,X7,X4] :
( c_lessequals(X7,X16,tc_fun(X4,tc_bool))
| ~ c_lessequals(X6,X16,tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_518]) ).
fof(c_0_1633,plain,
! [X16,X6,X7,X4] :
( c_HOL_Oord__class_Oless(X7,X16,tc_fun(X4,tc_bool))
| ~ c_lessequals(X6,X16,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(X7,X6,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_519]) ).
fof(c_0_1634,plain,
! [X16,X6,X7,X4] :
( c_HOL_Oord__class_Oless(X7,X16,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(X6,X16,tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_520]) ).
fof(c_0_1635,plain,
! [X16,X6,X7,X4] :
( c_HOL_Oord__class_Oless(X7,X16,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(X6,X16,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(X7,X6,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_521]) ).
fof(c_0_1636,plain,
! [X38,X8,X39,X9,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_HOL_Ominus__class_Ominus(X9,X8,X4) != c_HOL_Ominus__class_Ominus(X39,X38,X4)
| c_lessequals(X38,X39,X4)
| ~ c_lessequals(X8,X9,X4) ),
inference(fof_simplification,[status(thm)],[c_0_522]) ).
fof(c_0_1637,plain,
! [X38,X8,X39,X9,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_HOL_Ominus__class_Ominus(X9,X8,X4) != c_HOL_Ominus__class_Ominus(X39,X38,X4)
| c_lessequals(X8,X9,X4)
| ~ c_lessequals(X38,X39,X4) ),
inference(fof_simplification,[status(thm)],[c_0_523]) ).
fof(c_0_1638,plain,
! [X38,X8,X39,X9,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_HOL_Ominus__class_Ominus(X9,X8,X4) != c_HOL_Ominus__class_Ominus(X39,X38,X4)
| c_HOL_Oord__class_Oless(X39,X38,X4)
| ~ c_HOL_Oord__class_Oless(X9,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_524]) ).
fof(c_0_1639,plain,
! [X38,X8,X39,X9,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_HOL_Ominus__class_Ominus(X9,X8,X4) != c_HOL_Ominus__class_Ominus(X39,X38,X4)
| c_HOL_Oord__class_Oless(X9,X8,X4)
| ~ c_HOL_Oord__class_Oless(X39,X38,X4) ),
inference(fof_simplification,[status(thm)],[c_0_525]) ).
fof(c_0_1640,axiom,
! [X2,X1,X5] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X5,X1,tc_nat),c_HOL_Otimes__class_Otimes(X5,X2,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
c_0_526 ).
fof(c_0_1641,axiom,
! [X2,X1,X5] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X5,tc_nat),c_HOL_Otimes__class_Otimes(X2,X5,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
c_0_527 ).
fof(c_0_1642,axiom,
! [X3,X6,X7,X4] :
( c_Lattices_Olower__semilattice__class_Oinf(X7,c_Set_Oinsert(X3,X6,X4),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool))
| c_in(X3,X7,X4) ),
c_0_528 ).
fof(c_0_1643,axiom,
! [X3,X16,X6,X4] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X3,X6,X4),X16,tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,X16,tc_fun(X4,tc_bool))
| c_in(X3,X16,X4) ),
c_0_529 ).
fof(c_0_1644,plain,
! [X15,X8,X9,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(X9,X15,X4)
| ~ c_lessequals(X9,c_Lattices_Olower__semilattice__class_Oinf(X8,X15,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_530]) ).
fof(c_0_1645,plain,
! [X15,X8,X9,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(X9,X8,X4)
| ~ c_lessequals(X9,c_Lattices_Olower__semilattice__class_Oinf(X8,X15,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_531]) ).
fof(c_0_1646,plain,
! [X9,X10,X3,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(X9,X10,X4)
| ~ c_lessequals(X9,c_Lattices_Olower__semilattice__class_Oinf(X3,X10,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_532]) ).
fof(c_0_1647,plain,
! [X9,X10,X3,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(X9,X3,X4)
| ~ c_lessequals(X9,c_Lattices_Olower__semilattice__class_Oinf(X3,X10,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_533]) ).
fof(c_0_1648,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X11,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X10,X4),X11,X4) ),
inference(fof_simplification,[status(thm)],[c_0_534]) ).
fof(c_0_1649,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X10,X11,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X10,X4),X11,X4) ),
inference(fof_simplification,[status(thm)],[c_0_535]) ).
fof(c_0_1650,plain,
! [X2,X1,X4] :
( ~ class_Ring__and__Field_Oring__1(X4)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X4) = c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(X1,X4),c_Nat_Osemiring__1__class_Oof__nat(X2,X4),X4)
| ~ c_lessequals(X2,X1,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_536]) ).
fof(c_0_1651,axiom,
! [X5,X21,X22] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X22,X21,tc_nat),X5,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X22,X5,tc_nat),X21,tc_nat),
c_0_537 ).
fof(c_0_1652,axiom,
! [X2,X1,X5] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X5,X1,tc_nat),c_HOL_Oplus__class_Oplus(X5,X2,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),
c_0_538 ).
fof(c_0_1653,axiom,
! [X2,X1,X5] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X5,tc_nat),c_HOL_Oplus__class_Oplus(X2,X5,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),
c_0_539 ).
fof(c_0_1654,axiom,
! [X5,X21,X22] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X22,X21,tc_nat),X5,tc_nat) = c_HOL_Ominus__class_Ominus(X22,c_HOL_Oplus__class_Oplus(X21,X5,tc_nat),tc_nat),
c_0_540 ).
fof(c_0_1655,axiom,
! [X2,X1,X5] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X5,tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X5,tc_nat),tc_nat),
c_0_541 ).
fof(c_0_1656,axiom,
! [X2,X1,X5] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X5,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X5,tc_nat),tc_nat),
c_0_542 ).
fof(c_0_1657,axiom,
! [X15,X8,X9] : c_HOL_Oplus__class_Oplus(X9,c_HOL_Oplus__class_Oplus(X8,X15,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X9,X15,tc_nat),tc_nat),
c_0_543 ).
fof(c_0_1658,plain,
! [X6,X7,X4] :
( X7 = X6
| ~ c_lessequals(c_Finite__Set_Ocard(X6,X4),c_Finite__Set_Ocard(X7,X4),tc_nat)
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| ~ c_Finite__Set_Ofinite(X6,X4) ),
inference(fof_simplification,[status(thm)],[c_0_544]) ).
fof(c_0_1659,plain,
! [X10,X3,X7,X4] :
( c_in(X3,X7,X4)
| X3 = X10
| ~ c_in(X3,c_Set_Oinsert(X10,X7,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_545]) ).
fof(c_0_1660,plain,
! [X11,X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X3,X10,X4),X11,X4) = c_Divides_Odiv__class_Omod(X3,X11,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_546]) ).
fof(c_0_1661,plain,
! [X21,X22,X26] :
( hBOOL(hAPP(X26,X22))
| hBOOL(hAPP(X26,c_Suc(c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X26,X21))))
| ~ hBOOL(hAPP(X26,X21))
| ~ c_lessequals(X22,X21,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_547]) ).
fof(c_0_1662,plain,
! [X2,X1] :
( 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(fof_simplification,[status(thm)],[c_0_548]) ).
fof(c_0_1663,plain,
! [X2,X1] :
( 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(fof_simplification,[status(thm)],[c_0_549]) ).
fof(c_0_1664,axiom,
! [X6,X7,X4] : c_Lattices_Olower__semilattice__class_Oinf(X7,c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),
c_0_550 ).
fof(c_0_1665,axiom,
! [X6,X7,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),X6,tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),
c_0_551 ).
fof(c_0_1666,plain,
! [X10,X6,X7,X4] :
( c_lessequals(X7,c_Set_Oinsert(X10,X6,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_552]) ).
fof(c_0_1667,plain,
! [X2,X1] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_553]) ).
fof(c_0_1668,plain,
! [X15,X8,X9] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X9,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X15,X8,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X15,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X8,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_554]) ).
fof(c_0_1669,plain,
! [X15,X8,X9] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X9,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X15,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X8,X9,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X8,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_555]) ).
fof(c_0_1670,plain,
! [X2,X1,X24,X5] :
( c_HOL_Oplus__class_Oplus(X1,X24,tc_nat) != c_HOL_Oplus__class_Oplus(X5,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X24,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_556]) ).
fof(c_0_1671,plain,
! [X2,X1,X5] :
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X5,tc_nat),X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_557]) ).
fof(c_0_1672,plain,
! [X2,X1,X5] :
( c_lessequals(X5,X2,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X5,tc_nat),X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_558]) ).
fof(c_0_1673,plain,
! [X2,X5] :
( c_Ring__and__Field_Odvd__class_Odvd(X5,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Oplus__class_Oplus(X2,X5,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_559]) ).
fof(c_0_1674,plain,
! [X5,X21,X22] :
( c_HOL_Oord__class_Oless(X22,X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X22,X21,tc_nat),X5,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_560]) ).
fof(c_0_1675,plain,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),X3,X4),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),X10,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_561]) ).
fof(c_0_1676,plain,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X4),X4),c_HOL_Otimes__class_Otimes(X10,c_HOL_Ozero__class_Ozero(X4),X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_562]) ).
fof(c_0_1677,plain,
! [X6,X7,X4] :
( c_Finite__Set_Ofinite(X7,X4)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),X4)
| ~ c_Finite__Set_Ofinite(X6,X4) ),
inference(fof_simplification,[status(thm)],[c_0_563]) ).
fof(c_0_1678,axiom,
! [X20,X14,X4] : c_Fun_Oinj__on(X20,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4,X14),
c_0_564 ).
fof(c_0_1679,plain,
! [X2,X26] :
( ~ hBOOL(hAPP(X26,X2))
| hBOOL(hAPP(X26,c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
inference(fof_simplification,[status(thm)],[c_0_565]) ).
fof(c_0_1680,plain,
! [X8,X9,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_HOL_Oplus__class_Oplus(X9,X8,X4) != c_HOL_Ozero__class_Ozero(X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X9,X4)
| X9 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_566]) ).
fof(c_0_1681,plain,
! [X8,X9,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_HOL_Oplus__class_Oplus(X9,X8,X4) != c_HOL_Ozero__class_Ozero(X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X9,X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_567]) ).
fof(c_0_1682,plain,
! [X42,X20,X14,X4] :
( ~ class_HOL_Oord(X14)
| c_HOL_Oord__class_Oless(X20,X42,tc_fun(X4,X14))
| c_lessequals(X42,X20,tc_fun(X4,X14))
| ~ c_lessequals(X20,X42,tc_fun(X4,X14)) ),
inference(fof_simplification,[status(thm)],[c_0_568]) ).
fof(c_0_1683,plain,
! [X2,X1] :
( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat)
| ~ c_lessequals(X2,X1,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_569]) ).
fof(c_0_1684,plain,
! [X4] : ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_nat),
inference(fof_simplification,[status(thm)],[c_0_570]) ).
fof(c_0_1685,plain,
! [X8,X9,X7,X4] :
( hBOOL(hAPP(c_Set_Oinsert(X8,X7,X4),X9))
| ~ hBOOL(hAPP(X7,X9)) ),
inference(fof_simplification,[status(thm)],[c_0_571]) ).
fof(c_0_1686,plain,
! [X21,X22,X26] :
( hBOOL(hAPP(X26,X22))
| ~ hBOOL(hAPP(X26,c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X26,X21)))
| ~ hBOOL(hAPP(X26,X21))
| ~ c_lessequals(X22,X21,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_572]) ).
fof(c_0_1687,plain,
! [X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4),tc_nat)
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4) ),
inference(fof_simplification,[status(thm)],[c_0_573]) ).
fof(c_0_1688,plain,
! [X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_574]) ).
fof(c_0_1689,plain,
! [X45,X46,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X45,X4),c_Finite__Set_Olinorder__class_OMin(X46,X4),X4)
| ~ c_Finite__Set_Ofinite(X45,X4)
| X46 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ c_lessequals(X46,X45,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_575]) ).
fof(c_0_1690,plain,
! [X45,X46,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_lessequals(c_Finite__Set_Olinorder__class_OMax(X46,X4),c_Finite__Set_Olinorder__class_OMax(X45,X4),X4)
| ~ c_Finite__Set_Ofinite(X45,X4)
| X46 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ c_lessequals(X46,X45,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_576]) ).
fof(c_0_1691,axiom,
! [X9,X6,X7,X4] :
( c_Set_Oinsert(X9,X7,X4) != c_Set_Oinsert(X9,X6,X4)
| c_in(X9,X6,X4)
| c_in(X9,X7,X4)
| X7 = X6 ),
c_0_577 ).
fof(c_0_1692,axiom,
! [X2,X1] :
( c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat))
| c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) = X2 ),
c_0_578 ).
fof(c_0_1693,plain,
! [X15,X8,X9] :
( c_Ring__and__Field_Odvd__class_Odvd(X9,X15,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X15,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X8,X9,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X8,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_579]) ).
fof(c_0_1694,plain,
! [X15,X8,X9] :
( c_Ring__and__Field_Odvd__class_Odvd(X9,X15,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X15,X8,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X15,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X8,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_580]) ).
fof(c_0_1695,axiom,
! [X2,X1] : 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_581 ).
fof(c_0_1696,plain,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(X3,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_582]) ).
fof(c_0_1697,plain,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(X3,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_583]) ).
fof(c_0_1698,plain,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_584]) ).
fof(c_0_1699,plain,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_585]) ).
fof(c_0_1700,plain,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_586]) ).
fof(c_0_1701,plain,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(X3,X3,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_587]) ).
fof(c_0_1702,axiom,
! [X9,X1] : c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X1,X9,tc_nat)),tc_nat),
c_0_588 ).
fof(c_0_1703,axiom,
! [X1,X22] : c_HOL_Oord__class_Oless(X22,c_Suc(c_HOL_Oplus__class_Oplus(X1,X22,tc_nat)),tc_nat),
c_0_589 ).
fof(c_0_1704,axiom,
! [X1,X22] : c_HOL_Oord__class_Oless(X22,c_Suc(c_HOL_Oplus__class_Oplus(X22,X1,tc_nat)),tc_nat),
c_0_590 ).
fof(c_0_1705,plain,
! [X8,X9,X4] :
( ~ class_Orderings_Oorder(X4)
| c_lessequals(X8,X9,X4)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeast(X9,X4),c_SetInterval_Oord__class_OatLeast(X8,X4),tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_591]) ).
fof(c_0_1706,axiom,
! [X9,X4] : c_in(X9,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4),
c_0_592 ).
fof(c_0_1707,plain,
! [X9,X6,X7,X4] :
( c_in(X9,X6,X4)
| ~ c_in(X9,X7,X4)
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_593]) ).
fof(c_0_1708,plain,
! [X11,X6,X7,X4] :
( c_in(X11,X6,X4)
| ~ c_in(X11,X7,X4)
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_594]) ).
fof(c_0_1709,plain,
! [X9,X6,X7,X4] :
( c_in(X9,X6,X4)
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| ~ c_in(X9,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_595]) ).
fof(c_0_1710,plain,
! [X43,X6,X7,X4] :
( c_in(X43,X6,X4)
| ~ c_in(X43,X7,X4)
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_596]) ).
fof(c_0_1711,plain,
! [X11,X6,X7,X4] :
( c_in(X11,X6,X4)
| ~ c_in(X11,X7,X4)
| ~ c_HOL_Oord__class_Oless(X7,X6,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_597]) ).
fof(c_0_1712,axiom,
! [X2,X1] :
( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_598 ).
fof(c_0_1713,plain,
! [X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_lessequals(c_HOL_Ominus__class_Ominus(X3,X10,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_599]) ).
fof(c_0_1714,plain,
! [X42,X20,X14,X4] :
( ~ class_HOL_Oord(X14)
| ~ c_lessequals(X42,X20,tc_fun(X4,X14))
| ~ c_HOL_Oord__class_Oless(X20,X42,tc_fun(X4,X14)) ),
inference(fof_simplification,[status(thm)],[c_0_600]) ).
fof(c_0_1715,plain,
! [X10,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X10,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_601]) ).
fof(c_0_1716,plain,
! [X7,X4] :
( c_Finite__Set_Ocard(X7,X4) != c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4)
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4)
| X7 = c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_602]) ).
fof(c_0_1717,plain,
! [X2,X22] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,c_Suc(X22),tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_603]) ).
fof(c_0_1718,plain,
! [X2,X1,X5] :
( c_HOL_Otimes__class_Otimes(X5,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X5,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[c_0_604]) ).
fof(c_0_1719,axiom,
! [X6,X7,X4] : c_Lattices_Olower__semilattice__class_Oinf(X7,c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
c_0_605 ).
fof(c_0_1720,plain,
! [X2,X1] :
( ~ 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(fof_simplification,[status(thm)],[c_0_606]) ).
fof(c_0_1721,plain,
! [X9,X10,X3,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X10,X4),X9,X4)
| ~ c_lessequals(X10,X9,X4) ),
inference(fof_simplification,[status(thm)],[c_0_607]) ).
fof(c_0_1722,plain,
! [X9,X10,X3,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X10,X4),X9,X4)
| ~ c_lessequals(X3,X9,X4) ),
inference(fof_simplification,[status(thm)],[c_0_608]) ).
fof(c_0_1723,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Otimes__class_Otimes(X10,X11,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X11,X4) ),
inference(fof_simplification,[status(thm)],[c_0_609]) ).
fof(c_0_1724,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Otimes__class_Otimes(X10,X11,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_610]) ).
fof(c_0_1725,plain,
! [X9,X10,X3,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X3,X10,X4),X9,X4)
| ~ c_HOL_Oord__class_Oless(X3,X9,X4) ),
inference(fof_simplification,[status(thm)],[c_0_611]) ).
fof(c_0_1726,plain,
! [X9,X10,X3,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X3,X10,X4),X9,X4)
| ~ c_HOL_Oord__class_Oless(X10,X9,X4) ),
inference(fof_simplification,[status(thm)],[c_0_612]) ).
fof(c_0_1727,plain,
! [X1] :
( ~ 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(fof_simplification,[status(thm)],[c_0_613]) ).
fof(c_0_1728,plain,
! [X1] :
( ~ 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(fof_simplification,[status(thm)],[c_0_614]) ).
fof(c_0_1729,plain,
! [X2,X1] :
( c_HOL_Ominus__class_Ominus(c_Suc(X1),X2,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat))
| ~ c_lessequals(X2,X1,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_615]) ).
fof(c_0_1730,plain,
! [X6,X7,X4] :
( c_lessequals(c_Finite__Set_Ocard(X7,X4),c_Finite__Set_Ocard(X6,X4),tc_nat)
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| ~ c_Finite__Set_Ofinite(X6,X4) ),
inference(fof_simplification,[status(thm)],[c_0_616]) ).
fof(c_0_1731,plain,
! [X6,X7,X4] :
( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(X7,X4),c_Finite__Set_Ocard(X6,X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,X6,tc_fun(X4,tc_bool))
| ~ c_Finite__Set_Ofinite(X6,X4) ),
inference(fof_simplification,[status(thm)],[c_0_617]) ).
fof(c_0_1732,plain,
! [X2,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_618]) ).
fof(c_0_1733,plain,
! [X2,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_619]) ).
fof(c_0_1734,plain,
! [X10,X3,X6,X4] :
( c_in(X3,c_Set_Oinsert(X10,X6,X4),X4)
| ~ c_in(X3,X6,X4) ),
inference(fof_simplification,[status(thm)],[c_0_620]) ).
fof(c_0_1735,plain,
! [X10,X3,X7,X4] :
( c_in(X3,c_Set_Oinsert(X10,X7,X4),X4)
| ~ c_in(X3,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_621]) ).
fof(c_0_1736,plain,
! [X1,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(X1,X1,X4) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X4),c_HOL_Oone__class_Oone(X4),X4),X1,X4) ),
inference(fof_simplification,[status(thm)],[c_0_622]) ).
fof(c_0_1737,plain,
! [X21,X22] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X21,X22,tc_nat),X22,tc_nat),
inference(fof_simplification,[status(thm)],[c_0_623]) ).
fof(c_0_1738,plain,
! [X21,X22] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X22,X21,tc_nat),X22,tc_nat),
inference(fof_simplification,[status(thm)],[c_0_624]) ).
fof(c_0_1739,plain,
! [X6,X7,X4] :
( X7 = X6
| ~ c_lessequals(X6,X7,tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_625]) ).
fof(c_0_1740,plain,
! [X6,X7,X4] :
( X7 = X6
| ~ c_lessequals(X6,X7,tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_626]) ).
fof(c_0_1741,plain,
! [X2,X1] :
( c_lessequals(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_627]) ).
fof(c_0_1742,plain,
! [X2,X1] :
( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_628]) ).
fof(c_0_1743,plain,
! [X9,X7,X4] :
( c_Finite__Set_Ocard(c_Set_Oinsert(X9,X7,X4),X4) = c_Finite__Set_Ocard(X7,X4)
| ~ c_in(X9,X7,X4)
| ~ c_Finite__Set_Ofinite(X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_629]) ).
fof(c_0_1744,axiom,
! [X9,X7,X4] : hBOOL(hAPP(c_Set_Oinsert(X9,X7,X4),X9)),
c_0_630 ).
fof(c_0_1745,plain,
! [X2,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_631]) ).
fof(c_0_1746,axiom,
! [X6,X7,X4] :
( c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)) = X7 ),
c_0_632 ).
fof(c_0_1747,plain,
! [X2,X22] :
( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X2,X22,tc_nat),tc_nat) = X22
| ~ c_lessequals(X22,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_633]) ).
fof(c_0_1748,plain,
! [X2,X1] :
( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat) = X1
| ~ c_lessequals(X2,X1,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_634]) ).
fof(c_0_1749,plain,
! [X2,X1] :
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) = X1
| ~ c_lessequals(X2,X1,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_635]) ).
fof(c_0_1750,plain,
! [X21,X22] :
( ~ c_lessequals(X22,X21,tc_nat)
| X21 = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X21,X22,tc_nat),X22,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_636]) ).
fof(c_0_1751,plain,
! [X21,X22,X26] :
( hBOOL(hAPP(X26,X22))
| c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X26,X21),X21,tc_nat)
| ~ hBOOL(hAPP(X26,X21))
| ~ c_lessequals(X22,X21,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_637]) ).
fof(c_0_1752,plain,
! [X9,X42,X20,X14,X4] :
( ~ class_HOL_Oord(X14)
| c_lessequals(hAPP(X20,X9),hAPP(X42,X9),X14)
| ~ c_lessequals(X20,X42,tc_fun(X4,X14)) ),
inference(fof_simplification,[status(thm)],[c_0_638]) ).
fof(c_0_1753,plain,
! [X2,X5,X21] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X21,X2,tc_nat),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(X21,X5,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_639]) ).
fof(c_0_1754,plain,
! [X15,X8,X9] :
( c_lessequals(X9,c_HOL_Oplus__class_Oplus(X8,X15,tc_nat),tc_nat)
| ~ c_lessequals(X9,X8,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_640]) ).
fof(c_0_1755,plain,
! [X15,X8,X9] :
( c_lessequals(X9,c_HOL_Oplus__class_Oplus(X8,X15,tc_nat),tc_nat)
| ~ c_lessequals(X9,X15,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_641]) ).
fof(c_0_1756,plain,
! [X1,X21,X22] :
( c_lessequals(X22,c_HOL_Oplus__class_Oplus(X21,X1,tc_nat),tc_nat)
| ~ c_lessequals(X22,X21,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_642]) ).
fof(c_0_1757,plain,
! [X1,X21,X22] :
( c_lessequals(X22,c_HOL_Oplus__class_Oplus(X1,X21,tc_nat),tc_nat)
| ~ c_lessequals(X22,X21,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_643]) ).
fof(c_0_1758,plain,
! [X2,X5] :
( c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Oplus__class_Oplus(X2,X5,tc_nat),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_644]) ).
fof(c_0_1759,plain,
! [X1,X21,X22] :
( c_HOL_Oord__class_Oless(X22,c_HOL_Oplus__class_Oplus(X1,X21,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X22,X21,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_645]) ).
fof(c_0_1760,plain,
! [X1,X21,X22] :
( c_HOL_Oord__class_Oless(X22,c_HOL_Oplus__class_Oplus(X21,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X22,X21,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_646]) ).
fof(c_0_1761,plain,
! [X15,X8,X9] :
( c_HOL_Oord__class_Oless(X9,c_HOL_Oplus__class_Oplus(X8,X15,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X9,X15,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_647]) ).
fof(c_0_1762,plain,
! [X15,X8,X9] :
( c_HOL_Oord__class_Oless(X9,c_HOL_Oplus__class_Oplus(X8,X15,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X9,X8,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_648]) ).
fof(c_0_1763,plain,
! [X15,X8,X9,X4] :
( ~ class_Orderings_Oorder(X4)
| c_lessequals(X15,X9,X4)
| ~ c_lessequals(X15,X8,X4)
| ~ c_lessequals(X8,X9,X4) ),
inference(fof_simplification,[status(thm)],[c_0_649]) ).
fof(c_0_1764,plain,
! [X15,X8,X9,X4] :
( ~ class_Orderings_Opreorder(X4)
| c_lessequals(X9,X15,X4)
| ~ c_lessequals(X8,X15,X4)
| ~ c_lessequals(X9,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_650]) ).
fof(c_0_1765,plain,
! [X11,X10,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X11,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X11,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_651]) ).
fof(c_0_1766,plain,
! [X15,X8,X9,X4] :
( ~ class_Orderings_Oorder(X4)
| c_HOL_Oord__class_Oless(X15,X9,X4)
| ~ c_lessequals(X15,X8,X4)
| ~ c_HOL_Oord__class_Oless(X8,X9,X4) ),
inference(fof_simplification,[status(thm)],[c_0_652]) ).
fof(c_0_1767,plain,
! [X15,X8,X9,X4] :
( ~ class_Orderings_Oorder(X4)
| c_HOL_Oord__class_Oless(X15,X9,X4)
| ~ c_HOL_Oord__class_Oless(X15,X8,X4)
| ~ c_lessequals(X8,X9,X4) ),
inference(fof_simplification,[status(thm)],[c_0_653]) ).
fof(c_0_1768,plain,
! [X15,X8,X9,X4] :
( ~ class_Orderings_Opreorder(X4)
| c_HOL_Oord__class_Oless(X9,X15,X4)
| ~ c_HOL_Oord__class_Oless(X8,X15,X4)
| ~ c_lessequals(X9,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_654]) ).
fof(c_0_1769,plain,
! [X15,X8,X9,X4] :
( ~ class_Orderings_Opreorder(X4)
| c_HOL_Oord__class_Oless(X9,X15,X4)
| ~ c_lessequals(X8,X15,X4)
| ~ c_HOL_Oord__class_Oless(X9,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_655]) ).
fof(c_0_1770,plain,
! [X15,X8,X9,X4] :
( ~ class_Orderings_Oorder(X4)
| c_HOL_Oord__class_Oless(X15,X9,X4)
| ~ c_HOL_Oord__class_Oless(X15,X8,X4)
| ~ c_HOL_Oord__class_Oless(X8,X9,X4) ),
inference(fof_simplification,[status(thm)],[c_0_656]) ).
fof(c_0_1771,plain,
! [X15,X8,X9,X4] :
( ~ class_Orderings_Opreorder(X4)
| c_HOL_Oord__class_Oless(X9,X15,X4)
| ~ c_HOL_Oord__class_Oless(X8,X15,X4)
| ~ c_HOL_Oord__class_Oless(X9,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_657]) ).
fof(c_0_1772,axiom,
! [X2,X1] :
( 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) ),
c_0_658 ).
fof(c_0_1773,plain,
! [X3,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) = X3 ),
inference(fof_simplification,[status(thm)],[c_0_659]) ).
fof(c_0_1774,plain,
! [X3,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) = X3 ),
inference(fof_simplification,[status(thm)],[c_0_660]) ).
fof(c_0_1775,plain,
! [X7,X4] :
( X7 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_661]) ).
fof(c_0_1776,plain,
! [X2,X1,X4] :
( ~ class_Ring__and__Field_Osemiring__1(X4)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X4) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(X1,X4),c_Nat_Osemiring__1__class_Oof__nat(X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_662]) ).
fof(c_0_1777,plain,
! [X2,X1,X4] :
( ~ class_Ring__and__Field_Osemiring__1(X4)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X4) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(X1,X4),c_Nat_Osemiring__1__class_Oof__nat(X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_663]) ).
fof(c_0_1778,axiom,
! [X6,X7,X4] : c_lessequals(c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),X7,tc_fun(X4,tc_bool)),
c_0_664 ).
fof(c_0_1779,axiom,
! [X6,X7,X4] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),X7,tc_fun(X4,tc_bool)),
c_0_665 ).
fof(c_0_1780,axiom,
! [X6,X7,X4] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)),X6,tc_fun(X4,tc_bool)),
c_0_666 ).
fof(c_0_1781,plain,
! [X9,X7,X4] :
( c_Finite__Set_Ocard(c_Set_Oinsert(X9,X7,X4),X4) = c_Suc(c_Finite__Set_Ocard(X7,X4))
| c_in(X9,X7,X4)
| ~ c_Finite__Set_Ofinite(X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_667]) ).
fof(c_0_1782,plain,
! [X2,X1,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X4),c_Nat_Osemiring__1__class_Oof__nat(X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_668]) ).
fof(c_0_1783,plain,
! [X2,X1,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X4),c_Nat_Osemiring__1__class_Oof__nat(X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_669]) ).
fof(c_0_1784,plain,
! [X5,X21,X22] :
( c_HOL_Oord__class_Oless(c_Suc(X22),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(X21,X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(X22,X21,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_670]) ).
fof(c_0_1785,plain,
! [X2,X5] :
( c_lessequals(X5,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_671]) ).
fof(c_0_1786,plain,
! [X8,X9,X4] :
( ~ class_Orderings_Oorder(X4)
| c_lessequals(c_SetInterval_Oord__class_OatLeast(X9,X4),c_SetInterval_Oord__class_OatLeast(X8,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X8,X9,X4) ),
inference(fof_simplification,[status(thm)],[c_0_672]) ).
fof(c_0_1787,plain,
! [X8,X9,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X9,c_Lattices_Olower__semilattice__class_Oinf(X9,X8,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X9,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_673]) ).
fof(c_0_1788,plain,
! [X8,X9,X4] :
( ~ class_Lattices_Olattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X9,c_Lattices_Olower__semilattice__class_Oinf(X9,X8,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X9,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_674]) ).
fof(c_0_1789,plain,
! [X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X10,X3,X4),X10,X4) = c_Divides_Odiv__class_Omod(X3,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_675]) ).
fof(c_0_1790,plain,
! [X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,X10,X4),X10,X4) = c_Divides_Odiv__class_Omod(X3,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_676]) ).
fof(c_0_1791,plain,
! [X8,X9,X4] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X4)
| c_HOL_Otimes__class_Otimes(X9,c_HOL_Otimes__class_Otimes(X9,X8,X4),X4) = c_HOL_Otimes__class_Otimes(X9,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_677]) ).
fof(c_0_1792,plain,
! [X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X3,X10,X4),X10,X4) = c_Divides_Odiv__class_Omod(X3,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_678]) ).
fof(c_0_1793,axiom,
! [X34,X9,X4] :
( c_in(X9,X34,X4)
| c_Finite__Set_Ocard(c_Set_Oinsert(X9,X34,X4),X4) = c_Suc(c_Finite__Set_Ocard(X34,X4))
| c_Finite__Set_Ocard(X34,X4) = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_679 ).
fof(c_0_1794,plain,
! [X2] :
( c_Suc(c_HOL_Ominus__class_Ominus(X2,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_680]) ).
fof(c_0_1795,axiom,
! [X2,X1] : c_HOL_Ominus__class_Ominus(X1,c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),
c_0_681 ).
fof(c_0_1796,plain,
! [X5,X21,X22] :
( c_lessequals(X22,X5,tc_nat)
| ~ c_lessequals(X21,X5,tc_nat)
| ~ c_lessequals(X22,X21,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_682]) ).
fof(c_0_1797,plain,
! [X15,X8,X9] :
( c_Ring__and__Field_Odvd__class_Odvd(X9,X15,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X15,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X8,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_683]) ).
fof(c_0_1798,axiom,
! [X9,X7,X4] : c_Set_Oinsert(X9,c_Set_Oinsert(X9,X7,X4),X4) = c_Set_Oinsert(X9,X7,X4),
c_0_684 ).
fof(c_0_1799,axiom,
! [X2,X1] : c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
c_0_685 ).
fof(c_0_1800,axiom,
! [X2,X1] : c_HOL_Otimes__class_Otimes(X1,c_Suc(X2),tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
c_0_686 ).
fof(c_0_1801,plain,
! [X9,X26,X4] :
( ~ hBOOL(hAPP(X26,X9))
| ~ c_in(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4) ),
inference(fof_simplification,[status(thm)],[c_0_687]) ).
fof(c_0_1802,plain,
! [X42,X20,X14,X4] :
( ~ class_HOL_Oord(X14)
| c_lessequals(X20,X42,tc_fun(X4,X14))
| ~ c_HOL_Oord__class_Oless(X20,X42,tc_fun(X4,X14)) ),
inference(fof_simplification,[status(thm)],[c_0_688]) ).
fof(c_0_1803,plain,
! [X20,X25,X4] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X4)
| c_lessequals(X25,c_Inductive_Ocomplete__lattice__class_Ogfp(X20,X4),X4)
| ~ c_lessequals(X25,hAPP(X20,X25),X4) ),
inference(fof_simplification,[status(thm)],[c_0_689]) ).
fof(c_0_1804,plain,
! [X6,X7,X4] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),X4)
| ~ c_Finite__Set_Ofinite(X7,X4)
| ~ c_Finite__Set_Ofinite(X6,X4) ),
inference(fof_simplification,[status(thm)],[c_0_690]) ).
fof(c_0_1805,axiom,
! [X2,X1] :
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) = X1
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_691 ).
fof(c_0_1806,plain,
! [X9,X4] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X9)),
inference(fof_simplification,[status(thm)],[c_0_692]) ).
fof(c_0_1807,plain,
! [X3,X7,X4] :
( c_Finite__Set_Ofinite(X7,X4)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X3,X7,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_693]) ).
fof(c_0_1808,plain,
! [X2] :
( X2 = c_Suc(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_694]) ).
fof(c_0_1809,plain,
! [X2] :
( c_Suc(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_695]) ).
fof(c_0_1810,plain,
! [X7,X4] : ~ c_HOL_Oord__class_Oless(X7,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(fof_simplification,[status(thm)],[c_0_696]) ).
fof(c_0_1811,plain,
! [X2,X48,X26] :
( hBOOL(hAPP(X26,X48))
| c_lessequals(X2,c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1(X26,X2),tc_nat)
| ~ c_lessequals(c_Suc(X2),X48,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_697]) ).
fof(c_0_1812,plain,
! [X8,X9,X4] :
( ~ class_Orderings_Opreorder(X4)
| c_HOL_Oord__class_Oless(X9,X8,X4)
| c_lessequals(X8,X9,X4)
| ~ c_lessequals(X9,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_698]) ).
fof(c_0_1813,plain,
! [X6,X7,X4] :
( c_HOL_Oord__class_Oless(X7,X6,tc_fun(X4,tc_bool))
| X7 = X6
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_699]) ).
fof(c_0_1814,plain,
! [X6,X7,X4] :
( X7 = X6
| c_HOL_Oord__class_Oless(X7,X6,tc_fun(X4,tc_bool))
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_700]) ).
fof(c_0_1815,plain,
! [X6,X7,X4] :
( c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)) = X6
| ~ c_lessequals(X6,X7,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_701]) ).
fof(c_0_1816,plain,
! [X6,X7,X4] :
( c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)) = X7
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_702]) ).
fof(c_0_1817,plain,
! [X9,X50,X26,X4] :
( hBOOL(hAPP(X50,X9))
| ~ hBOOL(hAPP(X26,X9))
| ~ c_lessequals(X26,X50,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_703]) ).
fof(c_0_1818,plain,
! [X9,X50,X26,X4] :
( hBOOL(hAPP(X50,X9))
| ~ c_lessequals(X26,X50,tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(X26,X9)) ),
inference(fof_simplification,[status(thm)],[c_0_704]) ).
fof(c_0_1819,plain,
! [X2,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| 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(X4),c_Nat_Osemiring__1__class_Oof__nat(X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_705]) ).
fof(c_0_1820,plain,
! [X6,X7,X4] :
( c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(X7,X6,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_706]) ).
fof(c_0_1821,plain,
! [X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X4),c_HOL_Oone__class_Oone(X4),X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_707]) ).
fof(c_0_1822,plain,
! [X9,X26,X4] :
( hBOOL(hAPP(X26,X9))
| ~ c_in(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4) ),
inference(fof_simplification,[status(thm)],[c_0_708]) ).
fof(c_0_1823,plain,
! [X2,X1,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X4),c_Nat_Osemiring__1__class_Oof__nat(X2,X4),X4)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_709]) ).
fof(c_0_1824,plain,
! [X2,X1,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X4),c_Nat_Osemiring__1__class_Oof__nat(X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_710]) ).
fof(c_0_1825,plain,
! [X9,X7,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_lessequals(X9,c_Finite__Set_Olinorder__class_OMax(X7,X4),X4)
| ~ c_in(X9,X7,X4)
| ~ c_Finite__Set_Ofinite(X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_711]) ).
fof(c_0_1826,plain,
! [X9,X7,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X7,X4),X9,X4)
| ~ c_in(X9,X7,X4)
| ~ c_Finite__Set_Ofinite(X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_712]) ).
fof(c_0_1827,axiom,
! [X2,X1,X26] :
( hBOOL(hAPP(hAPP(X26,X2),X1))
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_713 ).
fof(c_0_1828,plain,
! [X40,X13,X4] :
( c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X13,X40,tc_fun(X4,tc_bool)),X4)
| ~ c_Finite__Set_Ofinite(X13,X4) ),
inference(fof_simplification,[status(thm)],[c_0_714]) ).
fof(c_0_1829,plain,
! [X40,X13,X4] :
( c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X13,X40,tc_fun(X4,tc_bool)),X4)
| ~ c_Finite__Set_Ofinite(X40,X4) ),
inference(fof_simplification,[status(thm)],[c_0_715]) ).
fof(c_0_1830,plain,
! [X6,X7,X4] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X4,tc_bool)),X4)
| ~ c_Finite__Set_Ofinite(X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_716]) ).
fof(c_0_1831,plain,
! [X5,X22,X4] :
( ~ class_HOL_Oord(X4)
| c_lessequals(X5,X22,X4)
| ~ c_in(X22,c_SetInterval_Oord__class_OatLeast(X5,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_717]) ).
fof(c_0_1832,axiom,
! [X2,X1,X5] :
( c_HOL_Otimes__class_Otimes(c_Suc(X5),X1,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X5),X2,tc_nat)
| X1 = X2 ),
c_0_718 ).
fof(c_0_1833,plain,
! [X15,X8,X9,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| c_HOL_Oplus__class_Oplus(X9,X8,X4) != c_HOL_Oplus__class_Oplus(X9,X15,X4)
| X8 = X15 ),
inference(fof_simplification,[status(thm)],[c_0_719]) ).
fof(c_0_1834,axiom,
! [X3,X6,X4] : c_lessequals(X6,c_Set_Oinsert(X3,X6,X4),tc_fun(X4,tc_bool)),
c_0_720 ).
fof(c_0_1835,axiom,
! [X34,X9,X4] :
( c_Set_Oinsert(X9,X34,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| c_in(X9,X34,X4) ),
c_0_721 ).
fof(c_0_1836,plain,
! [X2,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Nat_Osemiring__1__class_Oof__nat(X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_722]) ).
fof(c_0_1837,plain,
! [X8,X9,X4] :
( ~ class_Orderings_Oorder(X4)
| X9 = X8
| ~ c_lessequals(X8,X9,X4)
| ~ c_lessequals(X9,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_723]) ).
fof(c_0_1838,plain,
! [X8,X9,X4] :
( ~ class_Orderings_Oorder(X4)
| X9 = X8
| ~ c_lessequals(X8,X9,X4)
| ~ c_lessequals(X9,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_724]) ).
fof(c_0_1839,plain,
! [X8,X9,X4] :
( ~ class_Orderings_Oorder(X4)
| X9 = X8
| ~ c_lessequals(X9,X8,X4)
| ~ c_lessequals(X8,X9,X4) ),
inference(fof_simplification,[status(thm)],[c_0_725]) ).
fof(c_0_1840,axiom,
! [X4] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
c_0_726 ).
fof(c_0_1841,plain,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(X4),X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_727]) ).
fof(c_0_1842,plain,
! [X38,X39,X9,X4] :
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_HOL_Ominus__class_Ominus(X9,X9,X4) != c_HOL_Ominus__class_Ominus(X39,X38,X4)
| X39 = X38 ),
inference(fof_simplification,[status(thm)],[c_0_728]) ).
fof(c_0_1843,plain,
! [X8,X34,X9,X4] :
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_HOL_Ominus__class_Ominus(X34,X8,X4) != c_HOL_Ominus__class_Ominus(X9,X9,X4)
| X34 = X8 ),
inference(fof_simplification,[status(thm)],[c_0_729]) ).
fof(c_0_1844,plain,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X4)
| c_HOL_Oplus__class_Oplus(X10,X3,X4) != c_HOL_Oplus__class_Oplus(X11,X3,X4)
| X10 = X11 ),
inference(fof_simplification,[status(thm)],[c_0_730]) ).
fof(c_0_1845,plain,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X4)
| c_HOL_Oplus__class_Oplus(X3,X10,X4) != c_HOL_Oplus__class_Oplus(X3,X11,X4)
| X10 = X11 ),
inference(fof_simplification,[status(thm)],[c_0_731]) ).
fof(c_0_1846,plain,
! [X11,X10,X3,X4] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X4)
| c_HOL_Oplus__class_Oplus(X3,X10,X4) != c_HOL_Oplus__class_Oplus(X3,X11,X4)
| X10 = X11 ),
inference(fof_simplification,[status(thm)],[c_0_732]) ).
fof(c_0_1847,plain,
! [X10,X3,X4] :
( ~ class_Orderings_Opreorder(X4)
| ~ c_HOL_Oord__class_Oless(X10,X3,X4)
| ~ c_HOL_Oord__class_Oless(X3,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_733]) ).
fof(c_0_1848,plain,
! [X8,X9,X4] :
( ~ class_Orderings_Opreorder(X4)
| ~ c_HOL_Oord__class_Oless(X8,X9,X4)
| ~ c_HOL_Oord__class_Oless(X9,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_734]) ).
fof(c_0_1849,plain,
! [X8,X9,X4] :
( ~ class_Orderings_Olinorder(X4)
| ~ c_HOL_Oord__class_Oless(X9,X8,X4)
| ~ c_HOL_Oord__class_Oless(X8,X9,X4) ),
inference(fof_simplification,[status(thm)],[c_0_735]) ).
fof(c_0_1850,plain,
! [X10,X3,X4] :
( ~ class_Orderings_Oorder(X4)
| ~ c_HOL_Oord__class_Oless(X3,X10,X4)
| ~ c_HOL_Oord__class_Oless(X10,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_736]) ).
fof(c_0_1851,plain,
! [X8,X9,X4] :
( ~ class_Orderings_Opreorder(X4)
| ~ c_lessequals(X8,X9,X4)
| ~ c_HOL_Oord__class_Oless(X9,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_737]) ).
fof(c_0_1852,plain,
! [X8,X9,X4] :
( ~ class_Orderings_Olinorder(X4)
| ~ c_lessequals(X9,X8,X4)
| ~ c_HOL_Oord__class_Oless(X8,X9,X4) ),
inference(fof_simplification,[status(thm)],[c_0_738]) ).
fof(c_0_1853,plain,
! [X8,X9,X4] :
( ~ class_Orderings_Olinorder(X4)
| ~ c_HOL_Oord__class_Oless(X9,X8,X4)
| ~ c_lessequals(X8,X9,X4) ),
inference(fof_simplification,[status(thm)],[c_0_739]) ).
fof(c_0_1854,plain,
! [X9,X4] :
( ~ class_Orderings_Olinorder(X4)
| ~ c_lessequals(X9,X9,X4)
| ~ c_HOL_Oord__class_Oless(X9,X9,X4) ),
inference(fof_simplification,[status(thm)],[c_0_740]) ).
fof(c_0_1855,plain,
! [X2,X1] :
( X2 = X1
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_741]) ).
fof(c_0_1856,plain,
! [X2,X1] :
( ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_Suc(X2),X1,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_742]) ).
fof(c_0_1857,plain,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_743]) ).
fof(c_0_1858,axiom,
! [X2,X1] :
( c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = X2 ),
c_0_744 ).
fof(c_0_1859,plain,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X3,X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_745]) ).
fof(c_0_1860,plain,
! [X5,X22,X4] :
( ~ class_HOL_Oord(X4)
| c_in(X22,c_SetInterval_Oord__class_OatLeast(X5,X4),X4)
| ~ c_lessequals(X5,X22,X4) ),
inference(fof_simplification,[status(thm)],[c_0_746]) ).
fof(c_0_1861,plain,
! [X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X10,X3,X4),X10,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_747]) ).
fof(c_0_1862,plain,
! [X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X10,X4),X10,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_748]) ).
fof(c_0_1863,axiom,
! [X2,X1,X5] :
( c_HOL_Otimes__class_Otimes(X1,X5,tc_nat) != c_HOL_Otimes__class_Otimes(X2,X5,tc_nat)
| X5 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = X2 ),
c_0_749 ).
fof(c_0_1864,axiom,
! [X2,X1,X5] :
( c_HOL_Otimes__class_Otimes(X5,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X5,X2,tc_nat)
| X5 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = X2 ),
c_0_750 ).
fof(c_0_1865,axiom,
! [X2,X1,X5] :
( c_HOL_Otimes__class_Otimes(X5,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X5,X2,tc_nat)
| X1 = X2
| X5 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_751 ).
fof(c_0_1866,plain,
! [X2,X1] :
( X1 = X2
| ~ c_lessequals(X2,X1,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_752]) ).
fof(c_0_1867,plain,
! [X10,X3] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X10,tc_nat)
| X3 = X10 ),
inference(fof_simplification,[status(thm)],[c_0_753]) ).
fof(c_0_1868,plain,
! [X10,X3] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X3,tc_nat)
| X3 = X10
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X10,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_754]) ).
fof(c_0_1869,plain,
! [X8,X9] :
( X9 = X8
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X8,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X9,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_755]) ).
fof(c_0_1870,plain,
! [X2,X1] :
( X1 = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_756]) ).
fof(c_0_1871,plain,
! [X8,X9] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X9,tc_nat)
| X9 = X8
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X8,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_757]) ).
fof(c_0_1872,plain,
! [X8,X9] :
( X9 = X8
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X9,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X8,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_758]) ).
fof(c_0_1873,plain,
! [X8,X9] :
( X9 = X8
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X9,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X8,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_759]) ).
fof(c_0_1874,plain,
! [X10,X3,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X10,X4),X10,X4) = X3 ),
inference(fof_simplification,[status(thm)],[c_0_760]) ).
fof(c_0_1875,plain,
! [X10,X3,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X3,X10,X4),X10,X4) = X3 ),
inference(fof_simplification,[status(thm)],[c_0_761]) ).
fof(c_0_1876,plain,
! [X8,X9,X4] :
( ~ class_Lattices_Olattice(X4)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X9,X8,X4),X9,X4) ),
inference(fof_simplification,[status(thm)],[c_0_762]) ).
fof(c_0_1877,plain,
! [X8,X9,X4] :
( ~ class_Lattices_Olattice(X4)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X9,X8,X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_763]) ).
fof(c_0_1878,plain,
! [X8,X9,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X9,X8,X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_764]) ).
fof(c_0_1879,plain,
! [X8,X9,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X9,X8,X4),X9,X4) ),
inference(fof_simplification,[status(thm)],[c_0_765]) ).
fof(c_0_1880,axiom,
! [X2,X1,X5] :
( c_HOL_Oplus__class_Oplus(X5,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X5,X2,tc_nat)
| X1 = X2 ),
c_0_766 ).
fof(c_0_1881,axiom,
! [X2,X1,X5] :
( c_HOL_Oplus__class_Oplus(X1,X5,tc_nat) != c_HOL_Oplus__class_Oplus(X2,X5,tc_nat)
| X1 = X2 ),
c_0_767 ).
fof(c_0_1882,axiom,
! [X15,X8,X9] :
( c_HOL_Oplus__class_Oplus(X9,X8,tc_nat) != c_HOL_Oplus__class_Oplus(X9,X15,tc_nat)
| X8 = X15 ),
c_0_768 ).
fof(c_0_1883,plain,
! [X5,X10,X4] :
( ~ class_Ring__and__Field_Odvd(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X10,c_HOL_Otimes__class_Otimes(X10,X5,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_769]) ).
fof(c_0_1884,plain,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Otimes__class_Otimes(X3,X10,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_770]) ).
fof(c_0_1885,plain,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Otimes__class_Otimes(X10,X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_771]) ).
fof(c_0_1886,plain,
! [X3,X4] : ~ c_in(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),
inference(fof_simplification,[status(thm)],[c_0_772]) ).
fof(c_0_1887,plain,
! [X11,X4] : ~ c_in(X11,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),
inference(fof_simplification,[status(thm)],[c_0_773]) ).
fof(c_0_1888,plain,
! [X9,X4] : ~ c_in(X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),
inference(fof_simplification,[status(thm)],[c_0_774]) ).
fof(c_0_1889,axiom,
! [X2,X1] : c_HOL_Oplus__class_Oplus(X1,c_Suc(X2),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),
c_0_775 ).
fof(c_0_1890,axiom,
! [X2,X1] : c_HOL_Oplus__class_Oplus(c_Suc(X1),X2,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),
c_0_776 ).
fof(c_0_1891,plain,
! [X2,X1,X26] :
( hBOOL(hAPP(X26,X2))
| hBOOL(hAPP(X26,X1))
| ~ c_lessequals(c_Suc(X1),c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1(X26),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_777]) ).
fof(c_0_1892,axiom,
! [X2,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_Suc(X1),tc_nat),
c_0_778 ).
fof(c_0_1893,axiom,
! [X9,X6,X4] : c_in(X9,c_Set_Oinsert(X9,X6,X4),X4),
c_0_779 ).
fof(c_0_1894,axiom,
! [X3,X6,X4] : c_in(X3,c_Set_Oinsert(X3,X6,X4),X4),
c_0_780 ).
fof(c_0_1895,axiom,
! [X9,X7,X4] : c_in(X9,c_Set_Oinsert(X9,X7,X4),X4),
c_0_781 ).
fof(c_0_1896,plain,
! [X6,X7,X4] :
( c_Finite__Set_Ofinite(X7,X4)
| ~ c_Finite__Set_Ofinite(X6,X4)
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_782]) ).
fof(c_0_1897,plain,
! [X6,X7,X4] :
( c_Finite__Set_Ofinite(X7,X4)
| ~ c_lessequals(X7,X6,tc_fun(X4,tc_bool))
| ~ c_Finite__Set_Ofinite(X6,X4) ),
inference(fof_simplification,[status(thm)],[c_0_783]) ).
fof(c_0_1898,axiom,
! [X9,X17] : c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X17,X9,tc_nat),X17,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_784 ).
fof(c_0_1899,axiom,
! [X2,X1] : c_HOL_Ominus__class_Ominus(X2,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_785 ).
fof(c_0_1900,axiom,
! [X2,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),X2,tc_nat) = X1,
c_0_786 ).
fof(c_0_1901,axiom,
! [X2,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat) = X1,
c_0_787 ).
fof(c_0_1902,axiom,
! [X2,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X1,tc_nat),
c_0_788 ).
fof(c_0_1903,axiom,
! [X1] : c_lessequals(X1,c_HOL_Otimes__class_Otimes(X1,X1,tc_nat),tc_nat),
c_0_789 ).
fof(c_0_1904,axiom,
! [X2,X1] : c_lessequals(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X1,tc_nat),
c_0_790 ).
fof(c_0_1905,axiom,
! [X2,X1] : c_lessequals(X2,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat),
c_0_791 ).
fof(c_0_1906,axiom,
! [X2,X1] : c_lessequals(X2,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),
c_0_792 ).
fof(c_0_1907,axiom,
! [X9,X1] : c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,X9,tc_nat),tc_nat),
c_0_793 ).
fof(c_0_1908,plain,
! [X2,X1] :
( c_lessequals(X2,X1,tc_nat)
| ~ c_lessequals(c_Suc(X2),c_Suc(X1),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_794]) ).
fof(c_0_1909,plain,
! [X2,X1] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_795]) ).
fof(c_0_1910,axiom,
! [X7,X4] : c_HOL_Ominus__class_Ominus(X7,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
c_0_796 ).
fof(c_0_1911,axiom,
! [X7,X4] : c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X7,tc_fun(X4,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
c_0_797 ).
fof(c_0_1912,axiom,
! [X7,X4] : c_Lattices_Olower__semilattice__class_Oinf(X7,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
c_0_798 ).
fof(c_0_1913,axiom,
! [X6,X4] : c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X6,tc_fun(X4,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
c_0_799 ).
fof(c_0_1914,axiom,
! [X6,X7,X4] : c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X4,tc_bool)),
c_0_800 ).
fof(c_0_1915,plain,
! [X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(X10,X3,X4) != c_HOL_Ozero__class_Ozero(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_801]) ).
fof(c_0_1916,plain,
! [X2,X1] :
( X1 = c_Suc(X2)
| c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X1,c_Suc(X2),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_802]) ).
fof(c_0_1917,plain,
! [X10,X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(X10,X3,X4) = c_HOL_Ozero__class_Ozero(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_803]) ).
fof(c_0_1918,axiom,
! [X5,X7,X4] :
( c_Finite__Set_Ocard(X7,X4) != c_Suc(X5)
| c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(X7,X5,X4),X4) = X5 ),
c_0_804 ).
fof(c_0_1919,axiom,
! [X5,X7,X4] :
( c_Finite__Set_Ocard(X7,X4) != c_Suc(X5)
| c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(X7,X5,X4),X4) = X5 ),
c_0_805 ).
fof(c_0_1920,plain,
! [X10,X3,X4] :
( ~ class_Orderings_Oorder(X4)
| c_HOL_Oord__class_Oless(X10,X3,X4)
| X3 = X10
| ~ c_lessequals(X10,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_806]) ).
fof(c_0_1921,plain,
! [X10,X3,X4] :
( ~ class_Orderings_Oorder(X4)
| c_HOL_Oord__class_Oless(X10,X3,X4)
| ~ c_lessequals(X10,X3,X4)
| X3 = X10 ),
inference(fof_simplification,[status(thm)],[c_0_807]) ).
fof(c_0_1922,plain,
! [X8,X9,X4] :
( ~ class_Orderings_Oorder(X4)
| X9 = X8
| c_HOL_Oord__class_Oless(X9,X8,X4)
| ~ c_lessequals(X9,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_808]) ).
fof(c_0_1923,plain,
! [X8,X9,X4] :
( ~ class_Orderings_Oorder(X4)
| c_HOL_Oord__class_Oless(X9,X8,X4)
| X9 = X8
| ~ c_lessequals(X9,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_809]) ).
fof(c_0_1924,plain,
! [X10,X3,X4] :
( ~ class_Orderings_Oorder(X4)
| c_HOL_Oord__class_Oless(X3,X10,X4)
| X3 = X10
| ~ c_lessequals(X3,X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_810]) ).
fof(c_0_1925,plain,
! [X10,X3,X4] :
( ~ class_Orderings_Oorder(X4)
| c_HOL_Oord__class_Oless(X3,X10,X4)
| ~ c_lessequals(X3,X10,X4)
| X3 = X10 ),
inference(fof_simplification,[status(thm)],[c_0_811]) ).
fof(c_0_1926,plain,
! [X8,X9,X4] :
( ~ class_Orderings_Olinorder(X4)
| X9 = X8
| ~ c_lessequals(X9,X8,X4)
| c_HOL_Oord__class_Oless(X9,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_812]) ).
fof(c_0_1927,plain,
! [X8,X9,X4] :
( ~ class_Orderings_Olinorder(X4)
| X9 = X8
| c_HOL_Oord__class_Oless(X9,X8,X4)
| ~ c_lessequals(X9,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_813]) ).
fof(c_0_1928,plain,
! [X8,X9,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X9,X8,X4) != X9
| c_lessequals(X9,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_814]) ).
fof(c_0_1929,plain,
! [X2,X1] :
( c_lessequals(c_Suc(X2),c_Suc(X1),tc_nat)
| ~ c_lessequals(X2,X1,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_815]) ).
fof(c_0_1930,plain,
! [X2,X1] :
( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_816]) ).
fof(c_0_1931,plain,
! [X9,X2] :
( c_HOL_Oord__class_Oless(c_Suc(X9),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X9,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_817]) ).
fof(c_0_1932,plain,
! [X2,X1] :
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_818]) ).
fof(c_0_1933,plain,
! [X2,X1] :
( X1 = X2
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_819]) ).
fof(c_0_1934,plain,
! [X2,X1] :
( X2 = X1
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_820]) ).
fof(c_0_1935,plain,
! [X8,X9,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X9,X8,X4) = X8
| ~ c_lessequals(X8,X9,X4) ),
inference(fof_simplification,[status(thm)],[c_0_821]) ).
fof(c_0_1936,plain,
! [X8,X9,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X9,X8,X4) = X9
| ~ c_lessequals(X9,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_822]) ).
fof(c_0_1937,plain,
! [X2,X1] :
( 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(fof_simplification,[status(thm)],[c_0_823]) ).
fof(c_0_1938,plain,
! [X8,X9,X4] :
( ~ class_Orderings_Oorder(X4)
| c_lessequals(X9,X8,X4)
| ~ c_HOL_Oord__class_Oless(X9,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_824]) ).
fof(c_0_1939,plain,
! [X8,X9,X4] :
( ~ class_Orderings_Opreorder(X4)
| c_lessequals(X9,X8,X4)
| ~ c_HOL_Oord__class_Oless(X9,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_825]) ).
fof(c_0_1940,plain,
! [X2,X1] :
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_826]) ).
fof(c_0_1941,plain,
! [X2,X1] :
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_lessequals(c_Suc(X2),X1,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_827]) ).
fof(c_0_1942,plain,
! [X2,X1] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_828]) ).
fof(c_0_1943,plain,
! [X2,X1] :
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_829]) ).
fof(c_0_1944,plain,
! [X2,X1] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_830]) ).
fof(c_0_1945,plain,
! [X3,X7,X4] :
( c_Finite__Set_Ofinite(c_Set_Oinsert(X3,X7,X4),X4)
| ~ c_Finite__Set_Ofinite(X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_831]) ).
fof(c_0_1946,plain,
! [X7,X4] :
( c_Finite__Set_Ofinite(X7,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(X7,X4),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_832]) ).
fof(c_0_1947,plain,
! [X1,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_833]) ).
fof(c_0_1948,plain,
! [X2,X1] :
( c_lessequals(X1,c_Suc(X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_834]) ).
fof(c_0_1949,plain,
! [X2,X1] :
( c_lessequals(c_Suc(X2),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_835]) ).
fof(c_0_1950,plain,
! [X2,X1] :
( c_lessequals(c_Suc(X1),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_836]) ).
fof(c_0_1951,plain,
! [X2,X1] :
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_837]) ).
fof(c_0_1952,plain,
! [X9] :
( ~ c_lessequals(X9,X9,tc_nat)
| c_HOL_Oord__class_Oless(X9,c_Suc(X9),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_838]) ).
fof(c_0_1953,plain,
! [X2,X1] :
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_839]) ).
fof(c_0_1954,plain,
! [X3,X7,X4] :
( c_Set_Oinsert(X3,X7,X4) = X7
| ~ c_in(X3,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_840]) ).
fof(c_0_1955,axiom,
! [X2,X1] :
( c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_lessequals(X1,X2,tc_nat) ),
c_0_841 ).
fof(c_0_1956,plain,
! [X2,X1] :
( c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_842]) ).
fof(c_0_1957,plain,
! [X2,X1] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_843]) ).
fof(c_0_1958,plain,
! [X2,X1] :
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_844]) ).
fof(c_0_1959,plain,
! [X2,X1] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_845]) ).
fof(c_0_1960,plain,
! [X7,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_in(c_Finite__Set_Olinorder__class_OMax(X7,X4),X7,X4)
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ c_Finite__Set_Ofinite(X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_846]) ).
fof(c_0_1961,plain,
! [X7,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_in(c_Finite__Set_Olinorder__class_OMin(X7,X4),X7,X4)
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ c_Finite__Set_Ofinite(X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_847]) ).
fof(c_0_1962,plain,
! [X2,X1] :
( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = X1
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_848]) ).
fof(c_0_1963,plain,
! [X8,X9] :
( c_lessequals(X9,X8,tc_nat)
| ~ c_HOL_Oord__class_Oless(X9,X8,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_849]) ).
fof(c_0_1964,plain,
! [X2,X1] :
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_850]) ).
fof(c_0_1965,axiom,
! [X9,X4] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X9)),
c_0_851 ).
fof(c_0_1966,plain,
! [X7,X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(X7,X4),tc_nat)
| ~ c_Finite__Set_Ofinite(X7,X4)
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_852]) ).
fof(c_0_1967,axiom,
! [X7,X4] : c_Lattices_Olower__semilattice__class_Oinf(X7,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = X7,
c_0_853 ).
fof(c_0_1968,axiom,
! [X6,X4] : c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X6,tc_fun(X4,tc_bool)) = X6,
c_0_854 ).
fof(c_0_1969,axiom,
! [X7,X4] : c_HOL_Ominus__class_Ominus(X7,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = X7,
c_0_855 ).
fof(c_0_1970,axiom,
! [X7,X4] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X7,tc_fun(X4,tc_bool)),
c_0_856 ).
fof(c_0_1971,axiom,
! [X7,X4] : c_lessequals(X7,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
c_0_857 ).
fof(c_0_1972,axiom,
! [X3,X7,X4] : c_Set_Oinsert(X3,X7,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
c_0_858 ).
fof(c_0_1973,axiom,
! [X3,X7,X4] : c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) != c_Set_Oinsert(X3,X7,X4),
c_0_859 ).
fof(c_0_1974,plain,
! [X9,X4] : ~ c_HOL_Oord__class_Oless(X9,X9,tc_fun(X4,tc_bool)),
inference(fof_simplification,[status(thm)],[c_0_860]) ).
fof(c_0_1975,plain,
! [X8,X9,X4] :
( ~ class_Orderings_Olinorder(X4)
| X9 = X8
| c_HOL_Oord__class_Oless(X9,X8,X4)
| c_HOL_Oord__class_Oless(X8,X9,X4) ),
inference(fof_simplification,[status(thm)],[c_0_861]) ).
fof(c_0_1976,plain,
! [X8,X9,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_HOL_Oord__class_Oless(X8,X9,X4)
| X9 = X8
| c_HOL_Oord__class_Oless(X9,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_862]) ).
fof(c_0_1977,plain,
! [X8,X9,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_HOL_Oord__class_Oless(X8,X9,X4)
| c_HOL_Oord__class_Oless(X9,X8,X4)
| X9 = X8 ),
inference(fof_simplification,[status(thm)],[c_0_863]) ).
fof(c_0_1978,plain,
! [X8,X9,X4] :
( ~ class_Orderings_Olinorder(X4)
| X9 = X8
| c_HOL_Oord__class_Oless(X8,X9,X4)
| c_HOL_Oord__class_Oless(X9,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_864]) ).
fof(c_0_1979,plain,
! [X8,X9,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_HOL_Oord__class_Oless(X8,X9,X4)
| c_HOL_Oord__class_Oless(X9,X8,X4)
| X9 = X8 ),
inference(fof_simplification,[status(thm)],[c_0_865]) ).
fof(c_0_1980,axiom,
! [X2,X1] : c_HOL_Ominus__class_Ominus(c_Suc(X1),c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),
c_0_866 ).
fof(c_0_1981,axiom,
! [X2,X1] : c_HOL_Oplus__class_Oplus(c_Suc(X1),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_Suc(X2),tc_nat),
c_0_867 ).
fof(c_0_1982,axiom,
! [X7,X4] :
( c_Finite__Set_Ocard(X7,X4) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(X7,c_HOL_Ozero__class_Ozero(tc_nat),X4) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
c_0_868 ).
fof(c_0_1983,axiom,
! [X7,X4] :
( c_Finite__Set_Ocard(X7,X4) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(X7,c_HOL_Ozero__class_Ozero(tc_nat),X4) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
c_0_869 ).
fof(c_0_1984,plain,
! [X8,X9,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_lessequals(X8,X9,X4)
| c_lessequals(X9,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_870]) ).
fof(c_0_1985,plain,
! [X8,X9,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_HOL_Oord__class_Oless(X8,X9,X4)
| c_lessequals(X9,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_871]) ).
fof(c_0_1986,plain,
! [X8,X9,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_lessequals(X8,X9,X4)
| c_HOL_Oord__class_Oless(X9,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_872]) ).
fof(c_0_1987,plain,
! [X9,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_HOL_Oord__class_Oless(X9,X9,X4)
| c_lessequals(X9,X9,X4) ),
inference(fof_simplification,[status(thm)],[c_0_873]) ).
fof(c_0_1988,plain,
! [X8,X9,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_HOL_Oord__class_Oless(X9,X8,X4)
| c_lessequals(X8,X9,X4) ),
inference(fof_simplification,[status(thm)],[c_0_874]) ).
fof(c_0_1989,plain,
! [X9,X47,X4] :
( hBOOL(hAPP(X47,X9))
| ~ c_in(X9,X47,X4) ),
inference(fof_simplification,[status(thm)],[c_0_875]) ).
fof(c_0_1990,plain,
! [X8,X9,X4] :
( ~ class_Lattices_Olattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X9,X8,X4) = c_Lattices_Olower__semilattice__class_Oinf(X8,X9,X4) ),
inference(fof_simplification,[status(thm)],[c_0_876]) ).
fof(c_0_1991,plain,
! [X8,X9,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X9,X8,X4) = c_Lattices_Olower__semilattice__class_Oinf(X8,X9,X4) ),
inference(fof_simplification,[status(thm)],[c_0_877]) ).
fof(c_0_1992,plain,
! [X8,X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(X9,X8,X4) = c_HOL_Oplus__class_Oplus(X8,X9,X4) ),
inference(fof_simplification,[status(thm)],[c_0_878]) ).
fof(c_0_1993,plain,
! [X10,X3,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_HOL_Oplus__class_Oplus(X3,X10,X4) = c_HOL_Oplus__class_Oplus(X10,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_879]) ).
fof(c_0_1994,plain,
! [X11,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(X3,X11,X4) = c_HOL_Oplus__class_Oplus(X11,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_880]) ).
fof(c_0_1995,plain,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(X3,X10,X4) = c_HOL_Otimes__class_Otimes(X10,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_881]) ).
fof(c_0_1996,plain,
! [X8,X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(X9,X8,X4) = c_HOL_Otimes__class_Otimes(X8,X9,X4) ),
inference(fof_simplification,[status(thm)],[c_0_882]) ).
fof(c_0_1997,plain,
! [X1,X4] :
( ~ class_Ring__and__Field_Osemiring__1(X4)
| c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X1),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X4),c_Nat_Osemiring__1__class_Oof__nat(X1,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_883]) ).
fof(c_0_1998,axiom,
! [X2,X1] :
( c_lessequals(c_Suc(X2),X1,tc_nat)
| c_lessequals(X1,X2,tc_nat) ),
c_0_884 ).
fof(c_0_1999,axiom,
! [X2,X1] :
( c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_885 ).
fof(c_0_2000,axiom,
! [X9] :
( c_HOL_Oord__class_Oless(X9,X9,tc_nat)
| c_HOL_Oord__class_Oless(X9,c_Suc(X9),tc_nat) ),
c_0_886 ).
fof(c_0_2001,plain,
! [X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_887]) ).
fof(c_0_2002,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(fof_simplification,[status(thm)],[c_0_888]) ).
fof(c_0_2003,axiom,
! [X2,X1] : 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_889 ).
fof(c_0_2004,axiom,
! [X2,X1] : 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_890 ).
fof(c_0_2005,axiom,
! [X2,X1] :
( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != 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)) ),
c_0_891 ).
fof(c_0_2006,axiom,
! [X2,X1] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_892 ).
fof(c_0_2007,plain,
! [X1] :
( 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(fof_simplification,[status(thm)],[c_0_893]) ).
fof(c_0_2008,plain,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X4)
| c_HOL_Otimes__class_Otimes(X3,X10,X4) != c_HOL_Ozero__class_Ozero(X4)
| X3 = c_HOL_Ozero__class_Ozero(X4)
| X10 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_894]) ).
fof(c_0_2009,plain,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X4)
| c_HOL_Otimes__class_Otimes(X3,X10,X4) != c_HOL_Ozero__class_Ozero(X4)
| X10 = c_HOL_Ozero__class_Ozero(X4)
| X3 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_895]) ).
fof(c_0_2010,plain,
! [X10,X3,X4] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X4)
| c_HOL_Otimes__class_Otimes(X3,X10,X4) != c_HOL_Ozero__class_Ozero(X4)
| X10 = c_HOL_Ozero__class_Ozero(X4)
| X3 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_896]) ).
fof(c_0_2011,axiom,
! [X8,X9] :
( c_HOL_Oord__class_Oless(X8,X9,tc_nat)
| c_HOL_Oord__class_Oless(X9,X8,tc_nat)
| X9 = X8 ),
c_0_897 ).
fof(c_0_2012,axiom,
! [X2,X1] :
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2 ),
c_0_898 ).
fof(c_0_2013,plain,
! [X8,X9,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| c_HOL_Ominus__class_Ominus(X9,X8,X4) != c_HOL_Ozero__class_Ozero(X4)
| X9 = X8 ),
inference(fof_simplification,[status(thm)],[c_0_899]) ).
fof(c_0_2014,plain,
! [X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| X3 = c_HOL_Ozero__class_Ozero(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_900]) ).
fof(c_0_2015,plain,
! [X9,X3,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| X9 != c_HOL_Oplus__class_Oplus(X9,X3,X4)
| X3 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_901]) ).
fof(c_0_2016,axiom,
! [X2,X1] :
( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != 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)) ),
c_0_902 ).
fof(c_0_2017,axiom,
! [X2,X1] :
( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_903 ).
fof(c_0_2018,axiom,
! [X2,X1] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_904 ).
fof(c_0_2019,axiom,
! [X2,X1] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_905 ).
fof(c_0_2020,plain,
! [X2] :
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_906]) ).
fof(c_0_2021,axiom,
! [X2,X1] :
( c_lessequals(X2,X1,tc_nat)
| c_lessequals(X1,X2,tc_nat) ),
c_0_907 ).
fof(c_0_2022,axiom,
! [X9,X4] : c_in(X9,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4),
c_0_908 ).
fof(c_0_2023,axiom,
! [X2,X1] : c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),
c_0_909 ).
fof(c_0_2024,axiom,
! [X2,X1] : c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) = c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),
c_0_910 ).
fof(c_0_2025,plain,
! [X2,X48] :
( X48 = c_Suc(c_ATP__Linkup_Osko__Nat__XSuc__le__D__1__1(X48))
| ~ c_lessequals(c_Suc(X2),X48,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_911]) ).
fof(c_0_2026,plain,
! [X6,X7,X4] :
( ~ class_Lattices_Obounded__lattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X7,X6,X4) != c_Orderings_Otop__class_Otop(X4)
| X7 = c_Orderings_Otop__class_Otop(X4) ),
inference(fof_simplification,[status(thm)],[c_0_912]) ).
fof(c_0_2027,plain,
! [X6,X7,X4] :
( ~ class_Lattices_Obounded__lattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X7,X6,X4) != c_Orderings_Otop__class_Otop(X4)
| X6 = c_Orderings_Otop__class_Otop(X4) ),
inference(fof_simplification,[status(thm)],[c_0_913]) ).
fof(c_0_2028,plain,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_HOL_Oplus__class_Oplus(X3,X3,X4) != c_HOL_Ozero__class_Ozero(X4)
| X3 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_914]) ).
fof(c_0_2029,axiom,
! [X7,X4] : c_HOL_Ominus__class_Ominus(X7,X7,tc_fun(X4,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
c_0_915 ).
fof(c_0_2030,axiom,
! [X2,X1] :
( c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_916 ).
fof(c_0_2031,axiom,
! [X2,X1] :
( 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)) ),
c_0_917 ).
fof(c_0_2032,plain,
! [X9,X47,X4] :
( c_in(X9,X47,X4)
| ~ hBOOL(hAPP(X47,X9)) ),
inference(fof_simplification,[status(thm)],[c_0_918]) ).
fof(c_0_2033,axiom,
! [X2,X1] :
( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_919 ).
fof(c_0_2034,axiom,
! [X2,X1] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_920 ).
fof(c_0_2035,plain,
! [X10,X3,X4] :
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_HOL_Ominus__class_Ominus(X3,X10,X4) != c_HOL_Ozero__class_Ozero(X4)
| X3 = X10 ),
inference(fof_simplification,[status(thm)],[c_0_921]) ).
fof(c_0_2036,plain,
! [X10,X3,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Ominus__class_Ominus(X3,X10,X4) != c_HOL_Ozero__class_Ozero(X4)
| X3 = X10 ),
inference(fof_simplification,[status(thm)],[c_0_922]) ).
fof(c_0_2037,plain,
! [X2,X26] :
( hBOOL(hAPP(X26,X2))
| ~ hBOOL(hAPP(X26,c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1(X26))) ),
inference(fof_simplification,[status(thm)],[c_0_923]) ).
fof(c_0_2038,axiom,
! [X2,X1] :
( 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) ),
c_0_924 ).
fof(c_0_2039,plain,
! [X1,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_Nat_Osemiring__1__class_Oof__nat(X1,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_925]) ).
fof(c_0_2040,plain,
! [X2,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_Nat_Osemiring__1__class_Oof__nat(X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_926]) ).
fof(c_0_2041,plain,
! [X2] : ~ c_lessequals(c_Suc(X2),X2,tc_nat),
inference(fof_simplification,[status(thm)],[c_0_927]) ).
fof(c_0_2042,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_928]) ).
fof(c_0_2043,plain,
! [X9,X4] :
( ~ class_Orderings_Opreorder(X4)
| ~ c_HOL_Oord__class_Oless(X9,X9,X4) ),
inference(fof_simplification,[status(thm)],[c_0_929]) ).
fof(c_0_2044,plain,
! [X9,X4] :
( ~ class_Orderings_Olinorder(X4)
| ~ c_HOL_Oord__class_Oless(X9,X9,X4) ),
inference(fof_simplification,[status(thm)],[c_0_930]) ).
fof(c_0_2045,plain,
! [X9,X4] :
( ~ class_Orderings_Oorder(X4)
| ~ c_HOL_Oord__class_Oless(X9,X9,X4) ),
inference(fof_simplification,[status(thm)],[c_0_931]) ).
fof(c_0_2046,axiom,
! [X2,X1] :
( X1 != c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Oone__class_Oone(tc_nat) ),
c_0_932 ).
fof(c_0_2047,plain,
! [X2] :
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_933]) ).
fof(c_0_2048,plain,
! [X1] :
( 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(fof_simplification,[status(thm)],[c_0_934]) ).
fof(c_0_2049,axiom,
! [X2,X1] :
( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)
| X2 = c_HOL_Oone__class_Oone(tc_nat) ),
c_0_935 ).
fof(c_0_2050,axiom,
! [X2,X1] :
( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)
| X1 = c_HOL_Oone__class_Oone(tc_nat) ),
c_0_936 ).
fof(c_0_2051,axiom,
! [X2,X1] :
( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_937 ).
fof(c_0_2052,axiom,
! [X2,X1] :
( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_938 ).
fof(c_0_2053,axiom,
! [X2,X1] :
( c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
| X1 = c_HOL_Oone__class_Oone(tc_nat) ),
c_0_939 ).
fof(c_0_2054,axiom,
! [X2,X1] :
( c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
| X2 = c_HOL_Oone__class_Oone(tc_nat) ),
c_0_940 ).
fof(c_0_2055,axiom,
! [X9,X3] :
( X9 != c_HOL_Oplus__class_Oplus(X9,X3,tc_nat)
| X3 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_941 ).
fof(c_0_2056,axiom,
! [X2,X1] :
( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != X1
| X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_942 ).
fof(c_0_2057,plain,
! [X2] : ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(fof_simplification,[status(thm)],[c_0_943]) ).
fof(c_0_2058,plain,
! [X1] : ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(fof_simplification,[status(thm)],[c_0_944]) ).
fof(c_0_2059,plain,
! [X54,X25,X4] :
( X25 = X54
| ~ c_fequal(X25,X54,X4) ),
inference(fof_simplification,[status(thm)],[c_0_945]) ).
fof(c_0_2060,axiom,
! [X4] : c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
c_0_946 ).
fof(c_0_2061,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_947 ).
fof(c_0_2062,plain,
! [X2] : ~ c_HOL_Oord__class_Oless(X2,X2,tc_nat),
inference(fof_simplification,[status(thm)],[c_0_948]) ).
fof(c_0_2063,plain,
! [X9] : ~ c_HOL_Oord__class_Oless(X9,X9,tc_nat),
inference(fof_simplification,[status(thm)],[c_0_949]) ).
fof(c_0_2064,axiom,
! [X7,X4] : c_Lattices_Olower__semilattice__class_Oinf(X7,X7,tc_fun(X4,tc_bool)) = X7,
c_0_950 ).
fof(c_0_2065,plain,
! [X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_951]) ).
fof(c_0_2066,axiom,
! [X9,X4] : c_lessequals(X9,X9,tc_fun(X4,tc_bool)),
c_0_952 ).
fof(c_0_2067,axiom,
! [X7,X4] : c_lessequals(X7,X7,tc_fun(X4,tc_bool)),
c_0_953 ).
fof(c_0_2068,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_954 ).
fof(c_0_2069,plain,
! [X7,X4] :
( c_Finite__Set_Ocard(X7,X4) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_Finite__Set_Ofinite(X7,X4)
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_955]) ).
fof(c_0_2070,plain,
! [X9,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| X9 = c_HOL_Oplus__class_Oplus(X9,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_956]) ).
fof(c_0_2071,axiom,
c_HOL_Oplus__class_Oplus(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_957 ).
fof(c_0_2072,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_958 ).
fof(c_0_2073,axiom,
c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_959 ).
fof(c_0_2074,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
c_0_960 ).
fof(c_0_2075,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(fof_simplification,[status(thm)],[c_0_961]) ).
fof(c_0_2076,plain,
! [X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oone__class_Oone(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_962]) ).
fof(c_0_2077,plain,
! [X4] :
( ~ class_Finite__Set_Ofinite_Ofinite(X4)
| c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4) ),
inference(fof_simplification,[status(thm)],[c_0_963]) ).
fof(c_0_2078,plain,
! [X9,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| c_HOL_Ominus__class_Ominus(X9,X9,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_964]) ).
fof(c_0_2079,plain,
! [X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(X3,c_HOL_Oone__class_Oone(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_965]) ).
fof(c_0_2080,plain,
! [X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),X9,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_966]) ).
fof(c_0_2081,plain,
! [X3,X4] :
( ~ class_Ring__and__Field_Omult__zero(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),X3,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_967]) ).
fof(c_0_2082,plain,
! [X3,X4] :
( ~ class_Ring__and__Field_Omult__zero(X4)
| c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_968]) ).
fof(c_0_2083,plain,
! [X10,X4] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),X10,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_969]) ).
fof(c_0_2084,plain,
! [X3,X4] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X4)
| c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_970]) ).
fof(c_0_2085,plain,
! [X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_971]) ).
fof(c_0_2086,plain,
! [X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),X3,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_972]) ).
fof(c_0_2087,plain,
! [X9,X4] :
( ~ class_Lattices_Obounded__lattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X4),X9,X4) = c_Orderings_Obot__class_Obot(X4) ),
inference(fof_simplification,[status(thm)],[c_0_973]) ).
fof(c_0_2088,plain,
! [X9,X4] :
( ~ class_Lattices_Obounded__lattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X9,c_Orderings_Obot__class_Obot(X4),X4) = c_Orderings_Obot__class_Obot(X4) ),
inference(fof_simplification,[status(thm)],[c_0_974]) ).
fof(c_0_2089,plain,
! [X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X4),X3,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_975]) ).
fof(c_0_2090,plain,
! [X3,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Ominus__class_Ominus(X3,c_HOL_Ozero__class_Ozero(X4),X4) = X3 ),
inference(fof_simplification,[status(thm)],[c_0_976]) ).
fof(c_0_2091,plain,
! [X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X4),X3,X4) = X3 ),
inference(fof_simplification,[status(thm)],[c_0_977]) ).
fof(c_0_2092,plain,
! [X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Ozero__class_Ozero(X4),X4) = X3 ),
inference(fof_simplification,[status(thm)],[c_0_978]) ).
fof(c_0_2093,plain,
! [X3,X4] :
( ~ class_OrderedGroup_Omonoid__add(X4)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Ozero__class_Ozero(X4),X4) = X3 ),
inference(fof_simplification,[status(thm)],[c_0_979]) ).
fof(c_0_2094,plain,
! [X3,X4] :
( ~ class_OrderedGroup_Omonoid__add(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X4),X3,X4) = X3 ),
inference(fof_simplification,[status(thm)],[c_0_980]) ).
fof(c_0_2095,plain,
! [X3,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Ozero__class_Ozero(X4),X4) = X3 ),
inference(fof_simplification,[status(thm)],[c_0_981]) ).
fof(c_0_2096,plain,
! [X3,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X4),X3,X4) = X3 ),
inference(fof_simplification,[status(thm)],[c_0_982]) ).
fof(c_0_2097,plain,
! [X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X4),X9,X4) = X9 ),
inference(fof_simplification,[status(thm)],[c_0_983]) ).
fof(c_0_2098,plain,
! [X9,X4] :
( ~ class_Lattices_Obounded__lattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(X4),X9,X4) = X9 ),
inference(fof_simplification,[status(thm)],[c_0_984]) ).
fof(c_0_2099,plain,
! [X9,X4] :
( ~ class_Lattices_Obounded__lattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X9,c_Orderings_Otop__class_Otop(X4),X4) = X9 ),
inference(fof_simplification,[status(thm)],[c_0_985]) ).
fof(c_0_2100,plain,
! [X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(X3,c_HOL_Ozero__class_Ozero(X4),X4) = X3 ),
inference(fof_simplification,[status(thm)],[c_0_986]) ).
fof(c_0_2101,plain,
! [X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X4),X9,X4) = X9 ),
inference(fof_simplification,[status(thm)],[c_0_987]) ).
fof(c_0_2102,plain,
! [X3,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X4),X3,X4) = X3 ),
inference(fof_simplification,[status(thm)],[c_0_988]) ).
fof(c_0_2103,plain,
! [X3,X4] :
( ~ class_OrderedGroup_Omonoid__mult(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X4),X3,X4) = X3 ),
inference(fof_simplification,[status(thm)],[c_0_989]) ).
fof(c_0_2104,plain,
! [X3,X4] :
( ~ class_OrderedGroup_Omonoid__mult(X4)
| c_HOL_Otimes__class_Otimes(X3,c_HOL_Oone__class_Oone(X4),X4) = X3 ),
inference(fof_simplification,[status(thm)],[c_0_990]) ).
fof(c_0_2105,plain,
! [X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(X3,c_HOL_Oone__class_Oone(X4),X4) = X3 ),
inference(fof_simplification,[status(thm)],[c_0_991]) ).
fof(c_0_2106,plain,
! [X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X4),X3,X4) = X3 ),
inference(fof_simplification,[status(thm)],[c_0_992]) ).
fof(c_0_2107,axiom,
! [X4] : c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_993 ).
fof(c_0_2108,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_994 ).
fof(c_0_2109,plain,
! [X9,X4] :
( ~ class_Orderings_Obot(X4)
| c_lessequals(c_Orderings_Obot__class_Obot(X4),X9,X4) ),
inference(fof_simplification,[status(thm)],[c_0_995]) ).
fof(c_0_2110,plain,
! [X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_996]) ).
fof(c_0_2111,plain,
! [X9,X4] :
( ~ class_Orderings_Otop(X4)
| c_lessequals(X9,c_Orderings_Otop__class_Otop(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_997]) ).
fof(c_0_2112,plain,
! [X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_998]) ).
fof(c_0_2113,axiom,
! [X1] : 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_999 ).
fof(c_0_2114,axiom,
! [X4] : c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),
c_0_1000 ).
fof(c_0_2115,plain,
! [X9,X4] :
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_HOL_Ominus__class_Ominus(X9,X9,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1001]) ).
fof(c_0_2116,plain,
! [X9,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Ominus__class_Ominus(X9,X9,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1002]) ).
fof(c_0_2117,plain,
! [X3,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Ominus__class_Ominus(X3,X3,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1003]) ).
fof(c_0_2118,plain,
! [X3,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(X3,X3,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1004]) ).
fof(c_0_2119,axiom,
! [X2] : c_lessequals(c_Suc(X2),c_Suc(X2),tc_nat),
c_0_1005 ).
fof(c_0_2120,axiom,
! [X5] : c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X5,tc_nat),
c_0_1006 ).
fof(c_0_2121,axiom,
! [X2] : c_HOL_Ominus__class_Ominus(c_Suc(X2),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X2,
c_0_1007 ).
fof(c_0_2122,plain,
! [X9,X4] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X4)
| c_HOL_Otimes__class_Otimes(X9,X9,X4) = X9 ),
inference(fof_simplification,[status(thm)],[c_0_1008]) ).
fof(c_0_2123,plain,
! [X9,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X9,X9,X4) = X9 ),
inference(fof_simplification,[status(thm)],[c_0_1009]) ).
fof(c_0_2124,axiom,
! [X9] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X9),tc_nat),
c_0_1010 ).
fof(c_0_2125,axiom,
! [X2] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X2),tc_nat),
c_0_1011 ).
fof(c_0_2126,plain,
! [X9,X4] :
( ~ class_Orderings_Oorder(X4)
| c_lessequals(X9,X9,X4) ),
inference(fof_simplification,[status(thm)],[c_0_1012]) ).
fof(c_0_2127,plain,
! [X9,X4] :
( ~ class_Orderings_Opreorder(X4)
| c_lessequals(X9,X9,X4) ),
inference(fof_simplification,[status(thm)],[c_0_1013]) ).
fof(c_0_2128,plain,
! [X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_1014]) ).
fof(c_0_2129,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_1015 ).
fof(c_0_2130,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_1016 ).
fof(c_0_2131,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1017 ).
fof(c_0_2132,axiom,
! [X2] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_1018 ).
fof(c_0_2133,axiom,
! [X2] : c_Suc(X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X2,tc_nat),
c_0_1019 ).
fof(c_0_2134,axiom,
! [X2] : c_Suc(X2) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
c_0_1020 ).
fof(c_0_2135,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_1021 ).
fof(c_0_2136,axiom,
! [X2] : c_HOL_Oord__class_Oless(X2,c_Suc(X2),tc_nat),
c_0_1022 ).
fof(c_0_2137,axiom,
! [X9] : c_HOL_Oord__class_Oless(X9,c_Suc(X9),tc_nat),
c_0_1023 ).
fof(c_0_2138,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_1024 ).
fof(c_0_2139,axiom,
! [X2] : c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1025 ).
fof(c_0_2140,axiom,
! [X1] : c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1026 ).
fof(c_0_2141,axiom,
! [X2] : c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1027 ).
fof(c_0_2142,axiom,
! [X1] : c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
c_0_1028 ).
fof(c_0_2143,axiom,
! [X1] : c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
c_0_1029 ).
fof(c_0_2144,axiom,
! [X2] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) = X2,
c_0_1030 ).
fof(c_0_2145,axiom,
! [X9] : X9 = c_HOL_Oplus__class_Oplus(X9,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_1031 ).
fof(c_0_2146,axiom,
! [X2] : c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X2,
c_0_1032 ).
fof(c_0_2147,axiom,
! [X2] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X2,tc_nat) = X2,
c_0_1033 ).
fof(c_0_2148,axiom,
! [X2] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat),
c_0_1034 ).
fof(c_0_2149,axiom,
! [X1] : c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1035 ).
fof(c_0_2150,axiom,
! [X9,X4] : c_fequal(X9,X9,X4),
c_0_1036 ).
fof(c_0_2151,plain,
! [X8,X9,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_SetInterval_Oord__class_OatLeast(X9,X4) != c_SetInterval_Oord__class_OatLeast(X8,X4)
| X9 = X8 ),
inference(fof_simplification,[status(thm)],[c_0_1037]) ).
fof(c_0_2152,plain,
! [X2,X1,X4] :
( ~ class_Nat_Osemiring__char__0(X4)
| c_Nat_Osemiring__1__class_Oof__nat(X1,X4) != c_Nat_Osemiring__1__class_Oof__nat(X2,X4)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[c_0_1038]) ).
fof(c_0_2153,axiom,
! [X2] : c_lessequals(X2,X2,tc_nat),
c_0_1039 ).
fof(c_0_2154,axiom,
! [X9] : c_lessequals(X9,X9,tc_nat),
c_0_1040 ).
fof(c_0_2155,axiom,
! [X9] : c_Ring__and__Field_Odvd__class_Odvd(X9,X9,tc_nat),
c_0_1041 ).
fof(c_0_2156,plain,
! [X52,X53] :
( class_Finite__Set_Ofinite_Ofinite(tc_fun(X52,X53))
| ~ class_Finite__Set_Ofinite_Ofinite(X53)
| ~ class_Finite__Set_Ofinite_Ofinite(X52) ),
inference(fof_simplification,[status(thm)],[c_0_1042]) ).
fof(c_0_2157,plain,
! [X52,X53] :
( class_HOL_Oord(tc_fun(X52,X53))
| ~ class_HOL_Oord(X53) ),
inference(fof_simplification,[status(thm)],[c_0_1043]) ).
fof(c_0_2158,plain,
! [X52,X53] :
( class_Orderings_Obot(tc_fun(X52,X53))
| ~ class_Orderings_Obot(X53) ),
inference(fof_simplification,[status(thm)],[c_0_1044]) ).
fof(c_0_2159,plain,
! [X52,X53] :
( class_Orderings_Otop(tc_fun(X52,X53))
| ~ class_Orderings_Otop(X53) ),
inference(fof_simplification,[status(thm)],[c_0_1045]) ).
fof(c_0_2160,plain,
! [X52,X53] :
( class_Orderings_Oorder(tc_fun(X52,X53))
| ~ class_Orderings_Oorder(X53) ),
inference(fof_simplification,[status(thm)],[c_0_1046]) ).
fof(c_0_2161,plain,
! [X52,X53] :
( class_Lattices_Olattice(tc_fun(X52,X53))
| ~ class_Lattices_Olattice(X53) ),
inference(fof_simplification,[status(thm)],[c_0_1047]) ).
fof(c_0_2162,plain,
! [X52,X53] :
( class_Orderings_Opreorder(tc_fun(X52,X53))
| ~ class_Orderings_Opreorder(X53) ),
inference(fof_simplification,[status(thm)],[c_0_1048]) ).
fof(c_0_2163,plain,
! [X52,X53] :
( class_Lattices_Obounded__lattice(tc_fun(X52,X53))
| ~ class_Lattices_Obounded__lattice(X53) ),
inference(fof_simplification,[status(thm)],[c_0_1049]) ).
fof(c_0_2164,plain,
! [X52,X53] :
( class_Lattices_Olower__semilattice(tc_fun(X52,X53))
| ~ class_Lattices_Olattice(X53) ),
inference(fof_simplification,[status(thm)],[c_0_1050]) ).
fof(c_0_2165,plain,
! [X52,X53] :
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X52,X53))
| ~ class_Complete__Lattice_Ocomplete__lattice(X53) ),
inference(fof_simplification,[status(thm)],[c_0_1051]) ).
fof(c_0_2166,axiom,
! [X7,X4] :
( c_Finite__Set_Ocard(X7,X4) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Finite__Set_Ofinite(X7,X4) ),
c_0_1052 ).
fof(c_0_2167,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(fof_simplification,[status(thm)],[c_0_1053]) ).
fof(c_0_2168,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(fof_simplification,[status(thm)],[c_0_1054]) ).
fof(c_0_2169,plain,
! [X7,X4] :
( ~ class_Finite__Set_Ofinite_Ofinite(X4)
| c_Finite__Set_Ofinite(X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_1055]) ).
fof(c_0_2170,plain,
! [X4] :
( ~ class_Ring__and__Field_Ozero__neq__one(X4)
| c_HOL_Oone__class_Oone(X4) != c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1056]) ).
fof(c_0_2171,plain,
! [X4] :
( ~ class_Ring__and__Field_Ozero__neq__one(X4)
| c_HOL_Ozero__class_Ozero(X4) != c_HOL_Oone__class_Oone(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1057]) ).
fof(c_0_2172,axiom,
! [X8,X9] :
( c_Suc(X9) != c_Suc(X8)
| X9 = X8 ),
c_0_1058 ).
fof(c_0_2173,axiom,
! [X41,X51] :
( c_Suc(X51) != c_Suc(X41)
| X51 = X41 ),
c_0_1059 ).
fof(c_0_2174,axiom,
! [X41] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X41),
c_0_1060 ).
fof(c_0_2175,axiom,
! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
c_0_1061 ).
fof(c_0_2176,axiom,
! [X41] : c_Suc(X41) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1062 ).
fof(c_0_2177,axiom,
! [X1] : c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1063 ).
fof(c_0_2178,axiom,
c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_1064 ).
fof(c_0_2179,axiom,
! [X2] : c_Suc(X2) != X2,
c_0_1065 ).
fof(c_0_2180,axiom,
! [X2] : X2 != c_Suc(X2),
c_0_1066 ).
fof(c_0_2181,axiom,
class_HOL_Oord(tc_bool),
c_0_1067 ).
fof(c_0_2182,axiom,
class_Orderings_Obot(tc_bool),
c_0_1068 ).
fof(c_0_2183,axiom,
class_Orderings_Otop(tc_bool),
c_0_1069 ).
fof(c_0_2184,axiom,
class_Orderings_Oorder(tc_bool),
c_0_1070 ).
fof(c_0_2185,axiom,
class_Lattices_Olattice(tc_bool),
c_0_1071 ).
fof(c_0_2186,axiom,
class_Orderings_Opreorder(tc_bool),
c_0_1072 ).
fof(c_0_2187,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
c_0_1073 ).
fof(c_0_2188,axiom,
class_Lattices_Obounded__lattice(tc_bool),
c_0_1074 ).
fof(c_0_2189,axiom,
class_Lattices_Olower__semilattice(tc_bool),
c_0_1075 ).
fof(c_0_2190,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
c_0_1076 ).
fof(c_0_2191,axiom,
class_HOL_Oord(tc_nat),
c_0_1077 ).
fof(c_0_2192,axiom,
class_Orderings_Obot(tc_nat),
c_0_1078 ).
fof(c_0_2193,axiom,
class_Orderings_Oorder(tc_nat),
c_0_1079 ).
fof(c_0_2194,axiom,
class_Lattices_Olattice(tc_nat),
c_0_1080 ).
fof(c_0_2195,axiom,
class_Orderings_Olinorder(tc_nat),
c_0_1081 ).
fof(c_0_2196,axiom,
class_Orderings_Opreorder(tc_nat),
c_0_1082 ).
fof(c_0_2197,axiom,
class_Ring__and__Field_Odvd(tc_nat),
c_0_1083 ).
fof(c_0_2198,axiom,
class_Nat_Osemiring__char__0(tc_nat),
c_0_1084 ).
fof(c_0_2199,axiom,
class_Divides_Osemiring__div(tc_nat),
c_0_1085 ).
fof(c_0_2200,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
c_0_1086 ).
fof(c_0_2201,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
c_0_1087 ).
fof(c_0_2202,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
c_0_1088 ).
fof(c_0_2203,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
c_0_1089 ).
fof(c_0_2204,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
c_0_1090 ).
fof(c_0_2205,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
c_0_1091 ).
fof(c_0_2206,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
c_0_1092 ).
fof(c_0_2207,axiom,
class_Lattices_Olower__semilattice(tc_nat),
c_0_1093 ).
fof(c_0_2208,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
c_0_1094 ).
fof(c_0_2209,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
c_0_1095 ).
fof(c_0_2210,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
c_0_1096 ).
fof(c_0_2211,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
c_0_1097 ).
fof(c_0_2212,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
c_0_1098 ).
fof(c_0_2213,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
c_0_1099 ).
fof(c_0_2214,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
c_0_1100 ).
fof(c_0_2215,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
c_0_1101 ).
fof(c_0_2216,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
c_0_1102 ).
fof(c_0_2217,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
c_0_1103 ).
fof(c_0_2218,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
c_0_1104 ).
fof(c_0_2219,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
c_0_1105 ).
fof(c_0_2220,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
c_0_1106 ).
fof(c_0_2221,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
c_0_1107 ).
fof(c_0_2222,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
c_0_1108 ).
fof(c_0_2223,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
c_0_1109 ).
fof(c_0_2224,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
c_0_1110 ).
fof(c_0_2225,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
c_0_1111 ).
fof(c_0_2226,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
c_0_1112 ).
fof(c_0_2227,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
c_0_1113 ).
fof(c_0_2228,plain,
! [X21,X22,X23,X24,X25] :
( c_lessequals(c_Set_Oimage(X21,X23,X25,X24),X22,tc_fun(X24,tc_bool))
| ~ c_in(hAPP(X21,c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1(X23,X22,X21,X25,X24)),X22,X24) ),
inference(variable_rename,[status(thm)],[c_0_1114]) ).
fof(c_0_2229,plain,
! [X21,X22,X23,X24,X25] :
( c_lessequals(c_Set_Oimage(X21,X23,X24,X25),X22,tc_fun(X25,tc_bool))
| ~ c_in(hAPP(X21,c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1(X23,X22,X21,X24,X25)),X22,X25) ),
inference(variable_rename,[status(thm)],[c_0_1115]) ).
fof(c_0_2230,plain,
! [X43,X44,X45,X46,X47] :
( hAPP(X45,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X43,X45,X44,X47,X46)) != hAPP(X44,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X43,X45,X44,X47,X46))
| c_Set_Oimage(X45,X43,X47,X46) = c_Set_Oimage(X44,X43,X47,X46) ),
inference(variable_rename,[status(thm)],[c_0_1116]) ).
fof(c_0_2231,plain,
! [X18,X19,X20,X21,X22,X23,X24] :
( c_Fun_Ofun__upd(c_Fun_Ofun__upd(X18,X22,X21,X24,X23),X20,X19,X24,X23) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X18,X20,X19,X24,X23),X22,X21,X24,X23)
| X22 = X20 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1117])])]) ).
fof(c_0_2232,plain,
! [X21,X22,X23,X24,X25,X26] : c_Fun_Ofun__upd(c_Fun_Ofun__upd(X24,X23,X22,X26,X25),X23,X21,X26,X25) = c_Fun_Ofun__upd(X24,X23,X21,X26,X25),
inference(variable_rename,[status(thm)],[c_0_1118]) ).
fof(c_0_2233,plain,
! [X21,X22,X23,X24,X25,X26] :
( c_Set_Oimage(c_Fun_Ofun__upd(X23,X22,X21,X25,X26),X24,X25,X26) = c_Set_Oinsert(X21,c_Set_Oimage(X23,c_HOL_Ominus__class_Ominus(X24,c_Set_Oinsert(X22,c_Orderings_Obot__class_Obot(tc_fun(X25,tc_bool)),X25),tc_fun(X25,tc_bool)),X25,X26),X26)
| ~ c_in(X22,X24,X25) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1119])])]) ).
fof(c_0_2234,plain,
! [X10,X11,X12,X13] :
( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X11,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X13),tc_fun(X13,tc_bool)),c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X13),tc_fun(X13,tc_bool)),X13),c_Finite__Set_Ocard(X12,X13),tc_nat)
| ~ c_in(X10,X12,X13)
| ~ c_in(X11,X12,X13)
| ~ c_Finite__Set_Ofinite(X12,X13) ),
inference(variable_rename,[status(thm)],[c_0_1120]) ).
fof(c_0_2235,plain,
! [X21,X22,X23,X24,X25,X26] :
( c_Fun_Oinj__on(c_Fun_Ofun__upd(X23,X22,X21,X26,X25),X24,X26,X25)
| c_in(X21,c_Set_Oimage(X23,X24,X26,X25),X25)
| ~ c_Fun_Oinj__on(X23,X24,X26,X25) ),
inference(variable_rename,[status(thm)],[c_0_1121]) ).
fof(c_0_2236,plain,
! [X21,X22,X23,X24,X25] :
( X22 = c_Set_Oimage(X21,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X23,X22,X21,X24,X25),X24,X25)
| ~ c_lessequals(X22,c_Set_Oimage(X21,X23,X24,X25),tc_fun(X25,tc_bool))
| ~ c_Finite__Set_Ofinite(X22,X25) ),
inference(variable_rename,[status(thm)],[c_0_1122]) ).
fof(c_0_2237,plain,
! [X21,X22,X23,X24,X25] :
( X22 = c_Set_Oimage(X21,c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(X23,X22,X21,X24,X25),X24,X25)
| ~ c_lessequals(X22,c_Set_Oimage(X21,X23,X24,X25),tc_fun(X25,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1123]) ).
fof(c_0_2238,plain,
! [X21,X22,X23,X24,X25] :
( c_lessequals(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X23,X22,X21,X24,X25),X23,tc_fun(X24,tc_bool))
| ~ c_lessequals(X22,c_Set_Oimage(X21,X23,X24,X25),tc_fun(X25,tc_bool))
| ~ c_Finite__Set_Ofinite(X22,X25) ),
inference(variable_rename,[status(thm)],[c_0_1124]) ).
fof(c_0_2239,plain,
! [X21,X22,X23,X24,X25] :
( c_lessequals(c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(X23,X22,X21,X24,X25),X23,tc_fun(X24,tc_bool))
| ~ c_lessequals(X22,c_Set_Oimage(X21,X23,X24,X25),tc_fun(X25,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1125]) ).
fof(c_0_2240,plain,
! [X21,X22,X23,X24,X25] :
( c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X23,X22,X21,X24,X25),X24)
| ~ c_lessequals(X22,c_Set_Oimage(X21,X23,X24,X25),tc_fun(X25,tc_bool))
| ~ c_Finite__Set_Ofinite(X22,X25) ),
inference(variable_rename,[status(thm)],[c_0_1126]) ).
fof(c_0_2241,plain,
! [X21,X22,X23,X24,X25] :
( c_in(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(X23,X22,X21,X24,X25),X23,X24)
| ~ c_in(X21,c_Set_Oimage(X22,X23,X24,X25),X25) ),
inference(variable_rename,[status(thm)],[c_0_1127]) ).
fof(c_0_2242,plain,
! [X21,X22,X23,X24,X25] :
( c_in(c_ATP__Linkup_Osko__Set__XimageE__1__1(X23,X22,X21,X24,X25),X23,X24)
| ~ c_in(X22,c_Set_Oimage(X21,X23,X24,X25),X25) ),
inference(variable_rename,[status(thm)],[c_0_1128]) ).
fof(c_0_2243,plain,
! [X21,X22,X23,X24,X25,X26] :
( hAPP(c_Hilbert__Choice_Oinv__into(X24,X23,X26,X25),X22) != hAPP(c_Hilbert__Choice_Oinv__into(X24,X23,X26,X25),X21)
| X22 = X21
| ~ c_in(X21,c_Set_Oimage(X23,X24,X26,X25),X25)
| ~ c_in(X22,c_Set_Oimage(X23,X24,X26,X25),X25) ),
inference(variable_rename,[status(thm)],[c_0_1129]) ).
fof(c_0_2244,plain,
! [X21,X22,X23,X24,X25] :
( X22 = hAPP(X21,c_ATP__Linkup_Osko__Set__XimageE__1__1(X23,X22,X21,X24,X25))
| ~ c_in(X22,c_Set_Oimage(X21,X23,X24,X25),X25) ),
inference(variable_rename,[status(thm)],[c_0_1130]) ).
fof(c_0_2245,plain,
! [X21,X22,X23,X24,X25] :
( X21 = hAPP(X22,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(X23,X22,X21,X24,X25))
| ~ c_in(X21,c_Set_Oimage(X22,X23,X24,X25),X25) ),
inference(variable_rename,[status(thm)],[c_0_1131]) ).
fof(c_0_2246,plain,
! [X21,X22,X23,X24,X25] :
( ~ c_in(hAPP(X21,X22),c_Set_Oimage(X21,c_HOL_Ominus__class_Ominus(X23,c_Set_Oinsert(X22,c_Orderings_Obot__class_Obot(tc_fun(X25,tc_bool)),X25),tc_fun(X25,tc_bool)),X25,X24),X24)
| ~ c_Fun_Oinj__on(X21,c_Set_Oinsert(X22,X23,X25),X25,X24) ),
inference(variable_rename,[status(thm)],[c_0_1132]) ).
fof(c_0_2247,plain,
! [X21,X22,X23,X24,X25] :
( c_lessequals(c_Set_Oimage(X21,X23,X24,X25),X22,tc_fun(X25,tc_bool))
| c_in(c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1(X23,X22,X21,X24,X25),X23,X24) ),
inference(variable_rename,[status(thm)],[c_0_1133]) ).
fof(c_0_2248,plain,
! [X21,X22,X23,X24,X25] :
( c_lessequals(c_Set_Oimage(X21,X23,X25,X24),X22,tc_fun(X24,tc_bool))
| c_in(c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1(X23,X22,X21,X25,X24),X23,X25) ),
inference(variable_rename,[status(thm)],[c_0_1134]) ).
fof(c_0_2249,plain,
! [X21,X22,X23,X24,X25] : c_lessequals(c_Set_Oimage(X21,c_Lattices_Olower__semilattice__class_Oinf(X23,X22,tc_fun(X24,tc_bool)),X24,X25),c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X21,X23,X24,X25),c_Set_Oimage(X21,X22,X24,X25),tc_fun(X25,tc_bool)),tc_fun(X25,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1135]) ).
fof(c_0_2250,plain,
! [X21,X22,X23,X24,X25] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(X21,X23,X24,X25),c_Set_Oimage(X21,X22,X24,X25),tc_fun(X25,tc_bool)),c_Set_Oimage(X21,c_HOL_Ominus__class_Ominus(X23,X22,tc_fun(X24,tc_bool)),X24,X25),tc_fun(X25,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1136]) ).
fof(c_0_2251,plain,
! [X21,X22,X23,X24,X25,X26] :
( c_Set_Oimage(c_Fun_Ofun__upd(X23,X22,X21,X25,X26),X24,X25,X26) = c_Set_Oimage(X23,X24,X25,X26)
| c_in(X22,X24,X25) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1137])])]) ).
fof(c_0_2252,plain,
! [X43,X44,X45,X46,X47] :
( c_Set_Oimage(X45,X43,X47,X46) = c_Set_Oimage(X44,X43,X47,X46)
| c_in(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X43,X45,X44,X47,X46),X43,X47) ),
inference(variable_rename,[status(thm)],[c_0_1138]) ).
fof(c_0_2253,plain,
! [X43,X44,X45,X46,X47,X48] :
( c_in(hAPP(X43,X45),c_Inductive_Ocomplete__lattice__class_Ogfp(X44,tc_fun(X47,tc_bool)),X47)
| ~ c_lessequals(c_Set_Oimage(X43,X46,X48,X47),hAPP(X44,c_Set_Oimage(X43,X46,X48,X47)),tc_fun(X47,tc_bool))
| ~ c_in(X45,X46,X48) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1139])])]) ).
fof(c_0_2254,plain,
! [X43,X44,X45,X46,X47,X48] :
( c_Finite__Set_Ocard(X46,X48) = c_Finite__Set_Ocard(X45,X47)
| ~ c_Finite__Set_Ofinite(X45,X47)
| ~ c_Finite__Set_Ofinite(X46,X48)
| ~ c_lessequals(c_Set_Oimage(X43,X45,X47,X48),X46,tc_fun(X48,tc_bool))
| ~ c_Fun_Oinj__on(X43,X45,X47,X48)
| ~ c_lessequals(c_Set_Oimage(X44,X46,X48,X47),X45,tc_fun(X47,tc_bool))
| ~ c_Fun_Oinj__on(X44,X46,X48,X47) ),
inference(variable_rename,[status(thm)],[c_0_1140]) ).
fof(c_0_2255,plain,
! [X21,X22,X23,X24,X25] :
( c_Fun_Oinj__on(X21,c_Set_Oinsert(X22,X23,X25),X25,X24)
| c_in(hAPP(X21,X22),c_Set_Oimage(X21,c_HOL_Ominus__class_Ominus(X23,c_Set_Oinsert(X22,c_Orderings_Obot__class_Obot(tc_fun(X25,tc_bool)),X25),tc_fun(X25,tc_bool)),X25,X24),X24)
| ~ c_Fun_Oinj__on(X21,X23,X25,X24) ),
inference(variable_rename,[status(thm)],[c_0_1141]) ).
fof(c_0_2256,plain,
! [X27,X28,X29,X30] :
( ~ c_HOL_Oord__class_Oless(X28,X27,tc_nat)
| X27 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ hBOOL(hAPP(X30,c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X27,X29,tc_nat),X28,tc_nat),X27,tc_nat)))
| hBOOL(hAPP(X30,X28)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1142])])]) ).
fof(c_0_2257,plain,
! [X21,X22,X23,X24,X25,X26] :
( hAPP(c_Fun_Ofun__upd(X24,X23,X22,X26,X25),X21) = hAPP(X24,X21)
| X21 = X23 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1143])])]) ).
fof(c_0_2258,plain,
! [X21,X22,X23,X24,X25,X26] :
( hAPP(c_Fun_Ofun__upd(X24,X23,X22,X25,X26),X21) = hAPP(X24,X21)
| X21 = X23 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1144])])]) ).
fof(c_0_2259,plain,
! [X24,X25,X26,X27,X28] : hAPP(c_Fun_Ofun__upd(X26,X25,X24,X28,X27),X25) = X24,
inference(variable_rename,[status(thm)],[c_0_1145]) ).
fof(c_0_2260,plain,
! [X21,X22,X23,X24,X25] : hAPP(c_Fun_Ofun__upd(X23,X22,X21,X24,X25),X22) = X21,
inference(variable_rename,[status(thm)],[c_0_1146]) ).
fof(c_0_2261,plain,
! [X21,X22,X23,X24,X25] :
( c_lessequals(X23,X22,tc_fun(X25,tc_bool))
| ~ c_lessequals(c_Set_Oimage(X21,X23,X25,X24),c_Set_Oimage(X21,X22,X25,X24),tc_fun(X24,tc_bool))
| ~ c_Fun_Oinj__on(X21,c_Orderings_Otop__class_Otop(tc_fun(X25,tc_bool)),X25,X24) ),
inference(variable_rename,[status(thm)],[c_0_1147]) ).
fof(c_0_2262,plain,
! [X21,X22,X23,X24,X25,X26] :
( c_Set_Oimage(X21,c_Lattices_Olower__semilattice__class_Oinf(X24,X23,tc_fun(X26,tc_bool)),X26,X25) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X21,X24,X26,X25),c_Set_Oimage(X21,X23,X26,X25),tc_fun(X25,tc_bool))
| ~ c_lessequals(X23,X22,tc_fun(X26,tc_bool))
| ~ c_lessequals(X24,X22,tc_fun(X26,tc_bool))
| ~ c_Fun_Oinj__on(X21,X22,X26,X25) ),
inference(variable_rename,[status(thm)],[c_0_1148]) ).
fof(c_0_2263,plain,
! [X21,X22,X23,X24,X25,X26] :
( c_Set_Oimage(X21,c_HOL_Ominus__class_Ominus(X24,X23,tc_fun(X26,tc_bool)),X26,X25) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X21,X24,X26,X25),c_Set_Oimage(X21,X23,X26,X25),tc_fun(X25,tc_bool))
| ~ c_lessequals(X23,X22,tc_fun(X26,tc_bool))
| ~ c_lessequals(X24,X22,tc_fun(X26,tc_bool))
| ~ c_Fun_Oinj__on(X21,X22,X26,X25) ),
inference(variable_rename,[status(thm)],[c_0_1149]) ).
fof(c_0_2264,plain,
! [X23,X24,X25,X26,X27] :
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X27,X23,tc_nat),X25,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X26,X23,tc_nat),X24,tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X27,X26,tc_nat),X23,tc_nat),X25,tc_nat),X24,tc_nat)
| ~ c_lessequals(X26,X27,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1150]) ).
fof(c_0_2265,plain,
! [X23,X24,X25,X26,X27] :
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X27,X23,tc_nat),X25,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X26,X23,tc_nat),X24,tc_nat),tc_nat)
| ~ c_lessequals(X25,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X26,X27,tc_nat),X23,tc_nat),X24,tc_nat),tc_nat)
| ~ c_lessequals(X27,X26,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1151]) ).
fof(c_0_2266,plain,
! [X23,X24,X25,X26,X27] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X27,X23,tc_nat),X25,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X26,X23,tc_nat),X24,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X25,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X26,X27,tc_nat),X23,tc_nat),X24,tc_nat),tc_nat)
| ~ c_lessequals(X27,X26,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1152]) ).
fof(c_0_2267,plain,
! [X23,X24,X25,X26,X27] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X27,X23,tc_nat),X25,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X26,X23,tc_nat),X24,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X27,X26,tc_nat),X23,tc_nat),X25,tc_nat),X24,tc_nat)
| ~ c_lessequals(X26,X27,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1153]) ).
fof(c_0_2268,plain,
! [X20,X21,X22,X23,X24,X25] :
( ~ class_Ring__and__Field_Opordered__ring(X25)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X24,X20,X25),X22,X25),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X23,X20,X25),X21,X25),X25)
| ~ c_lessequals(X22,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X23,X24,X25),X20,X25),X21,X25),X25) ),
inference(variable_rename,[status(thm)],[c_0_1154]) ).
fof(c_0_2269,plain,
! [X20,X21,X22,X23,X24,X25] :
( ~ class_Ring__and__Field_Opordered__ring(X25)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X24,X20,X25),X22,X25),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X23,X20,X25),X21,X25),X25)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X24,X23,X25),X20,X25),X22,X25),X21,X25) ),
inference(variable_rename,[status(thm)],[c_0_1155]) ).
fof(c_0_2270,plain,
! [X20,X21,X22,X23,X24,X25] :
( ~ class_Ring__and__Field_Opordered__ring(X25)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X24,X20,X25),X22,X25),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X23,X20,X25),X21,X25),X25)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X24,X23,X25),X20,X25),X22,X25),X21,X25) ),
inference(variable_rename,[status(thm)],[c_0_1156]) ).
fof(c_0_2271,plain,
! [X20,X21,X22,X23,X24,X25] :
( ~ class_Ring__and__Field_Opordered__ring(X25)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X24,X20,X25),X22,X25),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X23,X20,X25),X21,X25),X25)
| ~ c_HOL_Oord__class_Oless(X22,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X23,X24,X25),X20,X25),X21,X25),X25) ),
inference(variable_rename,[status(thm)],[c_0_1157]) ).
fof(c_0_2272,plain,
! [X21,X22,X23,X24,X25] :
( c_lessequals(c_Set_Ovimage(X21,X22,X25,X24),X23,tc_fun(X25,tc_bool))
| ~ c_lessequals(X22,c_Set_Oimage(X21,X23,X25,X24),tc_fun(X24,tc_bool))
| ~ c_Fun_Oinj__on(X21,c_Orderings_Otop__class_Otop(tc_fun(X25,tc_bool)),X25,X24) ),
inference(variable_rename,[status(thm)],[c_0_1158]) ).
fof(c_0_2273,plain,
! [X21,X22,X23,X24,X25] :
( c_Set_Oimage(X21,c_HOL_Ominus__class_Ominus(X23,X22,tc_fun(X25,tc_bool)),X25,X24) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X21,X23,X25,X24),c_Set_Oimage(X21,X22,X25,X24),tc_fun(X24,tc_bool))
| ~ c_Fun_Oinj__on(X21,c_Orderings_Otop__class_Otop(tc_fun(X25,tc_bool)),X25,X24) ),
inference(variable_rename,[status(thm)],[c_0_1159]) ).
fof(c_0_2274,plain,
! [X21,X22,X23,X24,X25] :
( c_Set_Oimage(X21,c_Lattices_Olower__semilattice__class_Oinf(X23,X22,tc_fun(X25,tc_bool)),X25,X24) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X21,X23,X25,X24),c_Set_Oimage(X21,X22,X25,X24),tc_fun(X24,tc_bool))
| ~ c_Fun_Oinj__on(X21,c_Orderings_Otop__class_Otop(tc_fun(X25,tc_bool)),X25,X24) ),
inference(variable_rename,[status(thm)],[c_0_1160]) ).
fof(c_0_2275,plain,
! [X21,X22,X23,X24,X25] :
( c_in(hAPP(c_Hilbert__Choice_Oinv__into(X23,X22,X24,X25),X21),X23,X24)
| ~ c_in(X21,c_Set_Oimage(X22,X23,X24,X25),X25) ),
inference(variable_rename,[status(thm)],[c_0_1161]) ).
fof(c_0_2276,plain,
! [X23,X24,X25,X26,X27] :
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X27,X26,tc_nat),X23,tc_nat),X25,tc_nat),X24,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X27,X23,tc_nat),X25,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X26,X23,tc_nat),X24,tc_nat),tc_nat)
| ~ c_lessequals(X26,X27,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1162]) ).
fof(c_0_2277,plain,
! [X23,X24,X25,X26,X27] :
( c_lessequals(X25,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X26,X27,tc_nat),X23,tc_nat),X24,tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X27,X23,tc_nat),X25,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X26,X23,tc_nat),X24,tc_nat),tc_nat)
| ~ c_lessequals(X27,X26,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1163]) ).
fof(c_0_2278,plain,
! [X23,X24,X25,X26,X27] :
( c_HOL_Oord__class_Oless(X25,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X26,X27,tc_nat),X23,tc_nat),X24,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X27,X23,tc_nat),X25,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X26,X23,tc_nat),X24,tc_nat),tc_nat)
| ~ c_lessequals(X27,X26,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1164]) ).
fof(c_0_2279,plain,
! [X23,X24,X25,X26,X27] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X27,X26,tc_nat),X23,tc_nat),X25,tc_nat),X24,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X27,X23,tc_nat),X25,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X26,X23,tc_nat),X24,tc_nat),tc_nat)
| ~ c_lessequals(X26,X27,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1165]) ).
fof(c_0_2280,plain,
! [X21,X22,X23,X24,X25] :
( c_Fun_Ofun__upd(X23,X22,X21,X25,X24) != X23
| hAPP(X23,X22) = X21 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1166])])]) ).
fof(c_0_2281,plain,
! [X20,X21,X22,X23,X24,X25] :
( ~ class_Ring__and__Field_Opordered__ring(X25)
| c_lessequals(X22,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X23,X24,X25),X20,X25),X21,X25),X25)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X24,X20,X25),X22,X25),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X23,X20,X25),X21,X25),X25) ),
inference(variable_rename,[status(thm)],[c_0_1167]) ).
fof(c_0_2282,plain,
! [X20,X21,X22,X23,X24,X25] :
( ~ class_Ring__and__Field_Opordered__ring(X25)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X24,X23,X25),X20,X25),X22,X25),X21,X25)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X24,X20,X25),X22,X25),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X23,X20,X25),X21,X25),X25) ),
inference(variable_rename,[status(thm)],[c_0_1168]) ).
fof(c_0_2283,plain,
! [X20,X21,X22,X23,X24,X25] :
( ~ class_Ring__and__Field_Opordered__ring(X25)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X24,X23,X25),X20,X25),X22,X25),X21,X25)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X24,X20,X25),X22,X25),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X23,X20,X25),X21,X25),X25) ),
inference(variable_rename,[status(thm)],[c_0_1169]) ).
fof(c_0_2284,plain,
! [X20,X21,X22,X23,X24,X25] :
( ~ class_Ring__and__Field_Opordered__ring(X25)
| c_HOL_Oord__class_Oless(X22,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X23,X24,X25),X20,X25),X21,X25),X25)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X24,X20,X25),X22,X25),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X23,X20,X25),X21,X25),X25) ),
inference(variable_rename,[status(thm)],[c_0_1170]) ).
fof(c_0_2285,plain,
! [X21,X22,X23,X24,X25] :
( hAPP(X22,hAPP(c_Hilbert__Choice_Oinv__into(X23,X22,X24,X25),X21)) = X21
| ~ c_in(X21,c_Set_Oimage(X22,X23,X24,X25),X25) ),
inference(variable_rename,[status(thm)],[c_0_1171]) ).
fof(c_0_2286,plain,
! [X21,X22,X23,X24] :
( c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X24,tc_bool)),X21,X24,X23),c_Set_Oimage(X21,X22,X24,X23),X23,X24) = X22
| ~ c_Fun_Oinj__on(X21,c_Orderings_Otop__class_Otop(tc_fun(X24,tc_bool)),X24,X23) ),
inference(variable_rename,[status(thm)],[c_0_1172]) ).
fof(c_0_2287,plain,
! [X26,X27,X28,X29] :
( c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X29,tc_bool)),X26,X29,X28),c_Set_Oimage(X26,X27,X29,X28),X28,X29) = X27
| ~ c_Fun_Oinj__on(X26,c_Orderings_Otop__class_Otop(tc_fun(X29,tc_bool)),X29,X28) ),
inference(variable_rename,[status(thm)],[c_0_1173]) ).
fof(c_0_2288,plain,
! [X48,X49,X50,X51,X52] :
( c_Set_Oimage(c_Hilbert__Choice_Oinv__into(X50,X48,X52,X51),c_Set_Oimage(X48,X49,X52,X51),X51,X52) = X49
| ~ c_lessequals(X49,X50,tc_fun(X52,tc_bool))
| ~ c_Fun_Oinj__on(X48,X50,X52,X51) ),
inference(variable_rename,[status(thm)],[c_0_1174]) ).
fof(c_0_2289,plain,
! [X21,X22,X23,X24,X25] :
( hBOOL(hAPP(X23,hAPP(X22,X21)))
| ~ hBOOL(hAPP(c_Set_Ovimage(X22,X23,X25,X24),X21)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1175])])]) ).
fof(c_0_2290,plain,
! [X21,X22,X23,X24,X25] :
( c_lessequals(c_Set_Oimage(X21,X23,X25,X24),c_Set_Oimage(X21,X22,X25,X24),tc_fun(X24,tc_bool))
| ~ c_lessequals(X23,X22,tc_fun(X25,tc_bool))
| ~ c_Fun_Oinj__on(X21,c_Orderings_Otop__class_Otop(tc_fun(X25,tc_bool)),X25,X24) ),
inference(variable_rename,[status(thm)],[c_0_1176]) ).
fof(c_0_2291,plain,
! [X21,X22,X23,X24,X25] :
( c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X23,X21,X24,X25),X22,X25,X24)
| ~ c_lessequals(X22,c_Set_Oimage(X21,X23,X24,X25),tc_fun(X25,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1177]) ).
fof(c_0_2292,plain,
! [X21,X22,X23] :
( c_Set_Oimage(X21,X22,X23,X23) = X22
| ~ c_Fun_Oinj__on(X21,X22,X23,X23)
| ~ c_lessequals(c_Set_Oimage(X21,X22,X23,X23),X22,tc_fun(X23,tc_bool))
| ~ c_Finite__Set_Ofinite(X22,X23) ),
inference(variable_rename,[status(thm)],[c_0_1178]) ).
fof(c_0_2293,plain,
! [X21,X22,X23,X24] : c_lessequals(c_Set_Oimage(X21,c_Set_Ovimage(X21,X22,X23,X24),X23,X24),X22,tc_fun(X24,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1179]) ).
fof(c_0_2294,plain,
! [X23,X24,X25,X26,X27] :
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X27,X23,tc_nat),X25,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X26,X23,tc_nat),X24,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X27,X26,tc_nat),X23,tc_nat),X25,tc_nat),X24,tc_nat)
| ~ c_lessequals(X26,X27,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1180]) ).
fof(c_0_2295,plain,
! [X23,X24,X25,X26,X27] :
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X27,X23,tc_nat),X25,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X26,X23,tc_nat),X24,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X25,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X26,X27,tc_nat),X23,tc_nat),X24,tc_nat),tc_nat)
| ~ c_lessequals(X27,X26,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1181]) ).
fof(c_0_2296,plain,
! [X21,X22,X23,X24,X25] :
( hAPP(X21,X23) = X22
| ~ c_in(X23,c_Set_Ovimage(X21,c_Set_Oinsert(X22,c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)),X24),X25,X24),X25) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1182])])]) ).
fof(c_0_2297,plain,
! [X45,X46,X47,X48,X49,X50] :
( ~ class_Ring__and__Field_Odvd(X50)
| ~ class_Ring__and__Field_Ocomm__ring(X50)
| c_Ring__and__Field_Odvd__class_Odvd(X48,c_HOL_Oplus__class_Oplus(X45,X46,X50),X50)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X48,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X45,c_HOL_Otimes__class_Otimes(X47,X49,X50),X50),X46,X50),X50)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X48,X49,X50) ),
inference(variable_rename,[status(thm)],[c_0_1183]) ).
fof(c_0_2298,plain,
! [X21,X22,X23,X24,X25] : c_Set_Ovimage(X21,c_Lattices_Olower__semilattice__class_Oinf(X23,X22,tc_fun(X24,tc_bool)),X25,X24) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Ovimage(X21,X23,X25,X24),c_Set_Ovimage(X21,X22,X25,X24),tc_fun(X25,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1184]) ).
fof(c_0_2299,plain,
! [X21,X22,X23,X24,X25] : c_Set_Ovimage(X21,c_HOL_Ominus__class_Ominus(X23,X22,tc_fun(X24,tc_bool)),X25,X24) = c_HOL_Ominus__class_Ominus(c_Set_Ovimage(X21,X23,X25,X24),c_Set_Ovimage(X21,X22,X25,X24),tc_fun(X25,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1185]) ).
fof(c_0_2300,plain,
! [X10,X11,X12,X13] :
( c_HOL_Oord__class_Oless(X12,c_Set_Oinsert(X10,X11,X13),tc_fun(X13,tc_bool))
| ~ c_lessequals(X12,X11,tc_fun(X13,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X13),tc_fun(X13,tc_bool)),X11,tc_fun(X13,tc_bool))
| ~ c_HOL_Oord__class_Oless(X12,X11,tc_fun(X13,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1186]) ).
fof(c_0_2301,plain,
! [X21,X22,X23,X24,X25] :
( c_in(X22,X23,X25)
| ~ c_in(hAPP(X21,X22),c_Set_Oimage(X21,X23,X25,X24),X24)
| ~ c_Fun_Oinj__on(X21,c_Orderings_Otop__class_Otop(tc_fun(X25,tc_bool)),X25,X24) ),
inference(variable_rename,[status(thm)],[c_0_1187]) ).
fof(c_0_2302,plain,
! [X10,X11,X12,X13] :
( c_HOL_Oord__class_Oless(X12,c_Set_Oinsert(X10,X11,X13),tc_fun(X13,tc_bool))
| ~ c_in(X10,X12,X13)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X13),tc_fun(X13,tc_bool)),X11,tc_fun(X13,tc_bool))
| ~ c_HOL_Oord__class_Oless(X12,X11,tc_fun(X13,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1188]) ).
fof(c_0_2303,plain,
! [X21,X22,X23,X24,X25] :
( c_lessequals(c_Finite__Set_Ocard(X23,X25),c_Finite__Set_Ocard(X22,X24),tc_nat)
| ~ c_Finite__Set_Ofinite(X22,X24)
| ~ c_lessequals(c_Set_Oimage(X21,X23,X25,X24),X22,tc_fun(X24,tc_bool))
| ~ c_Fun_Oinj__on(X21,X23,X25,X24) ),
inference(variable_rename,[status(thm)],[c_0_1189]) ).
fof(c_0_2304,plain,
! [X21,X22,X23,X24] : c_Set_Oimage(X21,c_Set_Ovimage(X21,X22,X23,X24),X23,X24) = c_Lattices_Olower__semilattice__class_Oinf(X22,c_Set_Oimage(X21,c_Orderings_Otop__class_Otop(tc_fun(X23,tc_bool)),X23,X24),tc_fun(X24,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1190]) ).
fof(c_0_2305,plain,
! [X10,X11,X12,X13] :
( c_HOL_Oord__class_Oless(X12,c_Set_Oinsert(X10,X11,X13),tc_fun(X13,tc_bool))
| ~ c_lessequals(X12,X11,tc_fun(X13,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X13),tc_fun(X13,tc_bool)),X11,tc_fun(X13,tc_bool))
| c_in(X10,X11,X13) ),
inference(variable_rename,[status(thm)],[c_0_1191]) ).
fof(c_0_2306,plain,
! [X10,X11,X12] :
( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X11,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),X12),tc_fun(X12,tc_bool)),X12),c_Finite__Set_Ocard(X11,X12),tc_nat)
| ~ c_in(X10,X11,X12)
| ~ c_Finite__Set_Ofinite(X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1192]) ).
fof(c_0_2307,plain,
! [X10,X11,X12,X13] :
( c_HOL_Oord__class_Oless(X12,c_Set_Oinsert(X10,X11,X13),tc_fun(X13,tc_bool))
| ~ c_in(X10,X12,X13)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X13),tc_fun(X13,tc_bool)),X11,tc_fun(X13,tc_bool))
| c_in(X10,X11,X13) ),
inference(variable_rename,[status(thm)],[c_0_1193]) ).
fof(c_0_2308,plain,
! [X10,X11,X12,X13] :
( c_lessequals(X12,c_Set_Oinsert(X10,X11,X13),tc_fun(X13,tc_bool))
| ~ c_lessequals(X12,X11,tc_fun(X13,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X13),tc_fun(X13,tc_bool)),X11,tc_fun(X13,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1194]) ).
fof(c_0_2309,plain,
! [X10,X11,X12] :
( c_Finite__Set_Ocard(c_Set_Oinsert(X10,X11,X12),X12) = c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X11,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),X12),tc_fun(X12,tc_bool)),X12))
| ~ c_Finite__Set_Ofinite(X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1195]) ).
fof(c_0_2310,plain,
! [X10,X11,X12] :
( c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X11,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),X12),tc_fun(X12,tc_bool)),X12)) = c_Finite__Set_Ocard(X11,X12)
| ~ c_in(X10,X11,X12)
| ~ c_Finite__Set_Ofinite(X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1196]) ).
fof(c_0_2311,plain,
! [X10,X11,X12,X13] :
( c_lessequals(X12,c_Set_Oinsert(X10,X11,X13),tc_fun(X13,tc_bool))
| ~ c_in(X10,X12,X13)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X13),tc_fun(X13,tc_bool)),X11,tc_fun(X13,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1197]) ).
fof(c_0_2312,plain,
! [X10,X11,X12,X13] :
( c_lessequals(X12,c_Set_Oinsert(X10,X11,X13),tc_fun(X13,tc_bool))
| ~ c_in(X10,X12,X13)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X13),tc_fun(X13,tc_bool)),X11,tc_fun(X13,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1198]) ).
fof(c_0_2313,plain,
! [X10,X11,X12] :
( c_lessequals(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X11,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),X12),tc_fun(X12,tc_bool)),X12),c_Finite__Set_Ocard(X11,X12),tc_nat)
| ~ c_Finite__Set_Ofinite(X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1199]) ).
fof(c_0_2314,plain,
! [X21,X22,X23,X24,X25] :
( c_Set_Oimage(X21,X23,X25,X24) != c_Set_Oimage(X21,X22,X25,X24)
| ~ c_Fun_Oinj__on(X21,c_Orderings_Otop__class_Otop(tc_fun(X25,tc_bool)),X25,X24)
| X23 = X22 ),
inference(variable_rename,[status(thm)],[c_0_1200]) ).
fof(c_0_2315,plain,
! [X24,X25,X26,X27] : c_Fun_Ofun__upd(X25,X24,hAPP(X25,X24),X26,X27) = X25,
inference(variable_rename,[status(thm)],[c_0_1201]) ).
fof(c_0_2316,plain,
! [X21,X22,X23,X24] : c_Fun_Ofun__upd(X22,X21,hAPP(X22,X21),X24,X23) = X22,
inference(variable_rename,[status(thm)],[c_0_1202]) ).
fof(c_0_2317,plain,
! [X21,X22,X23,X24] : c_Fun_Ofun__upd(X22,X21,hAPP(X22,X21),X23,X24) = X22,
inference(variable_rename,[status(thm)],[c_0_1203]) ).
fof(c_0_2318,plain,
! [X21,X22,X23,X24] :
( c_Set_Ovimage(X21,c_Set_Oimage(X21,X22,X24,X23),X24,X23) = X22
| ~ c_Fun_Oinj__on(X21,c_Orderings_Otop__class_Otop(tc_fun(X24,tc_bool)),X24,X23) ),
inference(variable_rename,[status(thm)],[c_0_1204]) ).
fof(c_0_2319,plain,
! [X21,X22,X23,X24] :
( c_Finite__Set_Ofinite(X22,X23)
| ~ c_Fun_Oinj__on(X21,X22,X23,X24)
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(X21,X22,X23,X24),X24) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1205])])]) ).
fof(c_0_2320,plain,
! [X21,X22,X23,X24,X25] :
( c_lessequals(c_Set_Oimage(X21,X23,X25,X24),c_Set_Oimage(X21,X22,X25,X24),tc_fun(X24,tc_bool))
| ~ c_lessequals(X23,X22,tc_fun(X25,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1206]) ).
fof(c_0_2321,plain,
! [X21,X22,X23,X24,X25] :
( ~ c_lessequals(X21,X23,tc_fun(X24,tc_bool))
| c_lessequals(c_Set_Oimage(X22,X21,X24,X25),c_Set_Oimage(X22,X23,X24,X25),tc_fun(X25,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1207])])]) ).
fof(c_0_2322,plain,
! [X21,X22,X23,X24,X25] :
( c_lessequals(c_Set_Ovimage(X21,X23,X24,X25),c_Set_Ovimage(X21,X22,X24,X25),tc_fun(X24,tc_bool))
| ~ c_lessequals(X23,X22,tc_fun(X25,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1208]) ).
fof(c_0_2323,plain,
! [X21,X22,X23] :
( c_Fun_Oinj__on(X21,X22,X23,X23)
| ~ c_lessequals(X22,c_Set_Oimage(X21,X22,X23,X23),tc_fun(X23,tc_bool))
| ~ c_Finite__Set_Ofinite(X22,X23) ),
inference(variable_rename,[status(thm)],[c_0_1209]) ).
fof(c_0_2324,plain,
! [X45,X46,X47,X48,X49,X50] :
( ~ class_Ring__and__Field_Odvd(X50)
| ~ class_Ring__and__Field_Ocomm__ring(X50)
| c_Ring__and__Field_Odvd__class_Odvd(X48,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X45,c_HOL_Otimes__class_Otimes(X47,X49,X50),X50),X46,X50),X50)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X48,c_HOL_Oplus__class_Oplus(X45,X46,X50),X50)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X48,X49,X50) ),
inference(variable_rename,[status(thm)],[c_0_1210]) ).
fof(c_0_2325,plain,
! [X21,X22,X23,X24,X25] :
( hBOOL(hAPP(c_Set_Ovimage(X22,X23,X25,X24),X21))
| ~ hBOOL(hAPP(X23,hAPP(X22,X21))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1211])])]) ).
fof(c_0_2326,plain,
! [X21,X22,X23,X24,X25] :
( c_in(hAPP(X21,X22),c_Set_Oimage(X21,X23,X25,X24),X24)
| ~ c_in(X22,X23,X25)
| ~ c_Fun_Oinj__on(X21,c_Orderings_Otop__class_Otop(tc_fun(X25,tc_bool)),X25,X24) ),
inference(variable_rename,[status(thm)],[c_0_1212]) ).
fof(c_0_2327,plain,
! [X23,X24,X25,X26] :
( ~ c_lessequals(X25,X26,tc_nat)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X26,X23,tc_nat),X24,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X25,X23,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X26,X25,tc_nat),X23,tc_nat),X24,tc_nat),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1213]) ).
fof(c_0_2328,plain,
! [X23,X24,X25,X26] :
( ~ c_lessequals(X26,X25,tc_nat)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X26,X23,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X25,X26,tc_nat),X23,tc_nat),X24,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X25,X23,tc_nat),X24,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1214]) ).
fof(c_0_2329,plain,
! [X21,X22,X23,X24] :
( c_lessequals(c_Finite__Set_Ocard(c_Set_Oimage(X21,X22,X24,X23),X23),c_Finite__Set_Ocard(X22,X24),tc_nat)
| ~ c_Finite__Set_Ofinite(X22,X24) ),
inference(variable_rename,[status(thm)],[c_0_1215]) ).
fof(c_0_2330,plain,
! [X24,X25,X26,X27] :
( ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X26,tc_bool)),X26,X27)
| hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X26,tc_bool)),X25,X26,X27),hAPP(X25,X24)) = X24 ),
inference(variable_rename,[status(thm)],[c_0_1216]) ).
fof(c_0_2331,plain,
! [X21,X22,X23,X24] :
( hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X24,tc_bool)),X22,X24,X23),hAPP(X22,X21)) = X21
| ~ c_Fun_Oinj__on(X22,c_Orderings_Otop__class_Otop(tc_fun(X24,tc_bool)),X24,X23) ),
inference(variable_rename,[status(thm)],[c_0_1217]) ).
fof(c_0_2332,plain,
! [X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),c_HOL_Ozero__class_Ozero(X5),X5),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),c_HOL_Ozero__class_Ozero(X5),X5),X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1218]) ).
fof(c_0_2333,plain,
! [X21,X22,X23,X24] :
( c_Finite__Set_Ocard(c_Set_Oimage(X21,X22,X24,X23),X23) != c_Finite__Set_Ocard(X22,X24)
| ~ c_Finite__Set_Ofinite(X22,X24)
| c_Fun_Oinj__on(X21,X22,X24,X23) ),
inference(variable_rename,[status(thm)],[c_0_1219]) ).
fof(c_0_2334,plain,
! [X10,X11,X12,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X13),tc_fun(X13,tc_bool)),X11,tc_fun(X13,tc_bool))
| ~ c_in(X10,X12,X13)
| c_in(X10,X11,X13)
| ~ c_HOL_Oord__class_Oless(X12,c_Set_Oinsert(X10,X11,X13),tc_fun(X13,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1220]) ).
fof(c_0_2335,plain,
! [X20,X21,X22,X23,X24] :
( ~ class_Ring__and__Field_Oring(X24)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X23,X20,X24),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X22,X23,X24),X20,X24),X21,X24),X24) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X20,X24),X21,X24) ),
inference(variable_rename,[status(thm)],[c_0_1221]) ).
fof(c_0_2336,plain,
! [X20,X21,X22,X23,X24] :
( ~ class_Ring__and__Field_Oring(X24)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X23,X20,X24),X21,X24) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X20,X24),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X23,X22,X24),X20,X24),X21,X24),X24) ),
inference(variable_rename,[status(thm)],[c_0_1222]) ).
fof(c_0_2337,plain,
! [X24,X25,X26,X27] : c_in(X25,c_Set_Ovimage(X24,c_Set_Oinsert(hAPP(X24,X25),c_Orderings_Obot__class_Obot(tc_fun(X27,tc_bool)),X27),X26,X27),X26),
inference(variable_rename,[status(thm)],[c_0_1223]) ).
fof(c_0_2338,plain,
! [X21,X22,X23,X24,X25,X26] :
( c_in(hAPP(X22,X21),X23,X26)
| ~ c_in(X21,X24,X25)
| ~ c_lessequals(c_Set_Oimage(X22,X24,X25,X26),X23,tc_fun(X26,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1224]) ).
fof(c_0_2339,plain,
! [X27,X28,X29] :
( ~ hBOOL(hAPP(X29,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X28,X27,tc_nat),X28,tc_nat)))
| hBOOL(hAPP(X29,X27)) ),
inference(variable_rename,[status(thm)],[c_0_1225]) ).
fof(c_0_2340,plain,
! [X27,X28,X29] :
( ~ hBOOL(hAPP(X29,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X28,X27,tc_nat),X28,tc_nat)))
| hBOOL(hAPP(X29,X27)) ),
inference(variable_rename,[status(thm)],[c_0_1226]) ).
fof(c_0_2341,plain,
! [X38,X39,X40,X41] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X41,c_Divides_Odiv__class_Omod(X39,X40,tc_nat),tc_nat),X38,tc_nat),c_HOL_Otimes__class_Otimes(X41,X40,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X38,X41,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X40,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1227]) ).
fof(c_0_2342,plain,
! [X10,X11,X12,X13] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X13),tc_fun(X13,tc_bool)),X11,tc_fun(X13,tc_bool))
| ~ c_in(X10,X12,X13)
| ~ c_lessequals(X12,c_Set_Oinsert(X10,X11,X13),tc_fun(X13,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1228]) ).
fof(c_0_2343,plain,
! [X24,X25,X26,X27,X28] :
( ~ c_in(X24,X26,X27)
| ~ c_Fun_Oinj__on(X25,X26,X27,X28)
| hAPP(c_Hilbert__Choice_Oinv__into(X26,X25,X27,X28),hAPP(X25,X24)) = X24 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1229])])]) ).
fof(c_0_2344,plain,
! [X21,X22,X23,X24,X25] :
( hAPP(c_Hilbert__Choice_Oinv__into(X23,X22,X25,X24),hAPP(X22,X21)) = X21
| ~ c_in(X21,X23,X25)
| ~ c_Fun_Oinj__on(X22,X23,X25,X24) ),
inference(variable_rename,[status(thm)],[c_0_1230]) ).
fof(c_0_2345,plain,
! [X15,X16,X17,X18] :
( c_Finite__Set_Ofinite(c_Set_Ovimage(X15,X16,X17,X18),X17)
| ~ c_Fun_Oinj__on(X15,c_Orderings_Otop__class_Otop(tc_fun(X17,tc_bool)),X17,X18)
| ~ c_Finite__Set_Ofinite(X16,X18) ),
inference(variable_rename,[status(thm)],[c_0_1231]) ).
fof(c_0_2346,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| X10 = c_HOL_Ozero__class_Ozero(X12)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X11,X11,X12),c_HOL_Otimes__class_Otimes(X10,X10,X12),X12),c_HOL_Ozero__class_Ozero(X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1232]) ).
fof(c_0_2347,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| X11 = c_HOL_Ozero__class_Ozero(X12)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X11,X11,X12),c_HOL_Otimes__class_Otimes(X10,X10,X12),X12),c_HOL_Ozero__class_Ozero(X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1233]) ).
fof(c_0_2348,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X11,X11,X12),c_HOL_Otimes__class_Otimes(X10,X10,X12),X12),c_HOL_Ozero__class_Ozero(X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1234]) ).
fof(c_0_2349,plain,
! [X23,X24,X25,X26,X27] :
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X27,X23,tc_nat),X25,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X26,X23,tc_nat),X24,tc_nat)
| ~ c_lessequals(X26,X27,tc_nat)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X27,X26,tc_nat),X23,tc_nat),X25,tc_nat) = X24 ),
inference(variable_rename,[status(thm)],[c_0_1235]) ).
fof(c_0_2350,plain,
! [X23,X24,X25,X26,X27] :
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X27,X23,tc_nat),X25,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X26,X23,tc_nat),X24,tc_nat)
| ~ c_lessequals(X27,X26,tc_nat)
| X25 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X26,X27,tc_nat),X23,tc_nat),X24,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1236]) ).
fof(c_0_2351,plain,
! [X21,X22,X23,X24,X25] :
( c_in(hAPP(X21,X22),X23,X24)
| ~ c_in(X22,c_Set_Ovimage(X21,X23,X25,X24),X25) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1237])])]) ).
fof(c_0_2352,plain,
! [X21,X22,X23,X24,X25] :
( c_in(hAPP(X21,X22),X23,X24)
| ~ c_in(X22,c_Set_Ovimage(X21,X23,X25,X24),X25) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1238])])]) ).
fof(c_0_2353,plain,
! [X21,X22,X23,X24,X25] :
( c_Finite__Set_Ofinite(X22,X24)
| ~ c_lessequals(X22,c_Set_Oimage(X21,X23,X25,X24),tc_fun(X24,tc_bool))
| ~ c_Finite__Set_Ofinite(X23,X25) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1239])])]) ).
fof(c_0_2354,plain,
! [X21,X22,X23,X24] :
( c_Finite__Set_Ocard(c_Set_Oimage(X21,X22,X24,X23),X23) = c_Finite__Set_Ocard(X22,X24)
| ~ c_Fun_Oinj__on(X21,X22,X24,X23)
| ~ c_Finite__Set_Ofinite(X22,X24) ),
inference(variable_rename,[status(thm)],[c_0_1240]) ).
fof(c_0_2355,plain,
! [X8,X9,X10,X11] :
( c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X10,c_Set_Oinsert(X8,X9,X11),tc_fun(X11,tc_bool)),X11) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X10,X9,tc_fun(X11,tc_bool)),X11),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_in(X8,X9,X11)
| ~ c_in(X8,X10,X11)
| ~ c_Finite__Set_Ofinite(X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_1241]) ).
fof(c_0_2356,plain,
! [X21,X22,X23,X24,X25] : c_Set_Oimage(X21,c_Set_Oinsert(X22,X23,X24),X24,X25) = c_Set_Oinsert(hAPP(X21,X22),c_Set_Oimage(X21,X23,X24,X25),X25),
inference(variable_rename,[status(thm)],[c_0_1242]) ).
fof(c_0_2357,plain,
! [X21,X22,X23,X24] :
( c_Finite__Set_Ocard(c_Set_Oimage(X21,X22,X24,X23),X23) = c_Finite__Set_Ocard(X22,X24)
| ~ c_Fun_Oinj__on(X21,X22,X24,X23) ),
inference(variable_rename,[status(thm)],[c_0_1243]) ).
fof(c_0_2358,plain,
! [X21,X22,X23,X24,X25] :
( c_Set_Oinsert(hAPP(X22,X21),c_Set_Oimage(X22,X23,X25,X24),X24) = c_Set_Oimage(X22,X23,X25,X24)
| ~ c_in(X21,X23,X25) ),
inference(variable_rename,[status(thm)],[c_0_1244]) ).
fof(c_0_2359,plain,
! [X20,X21,X22,X23,X24,X25] :
( ~ class_Ring__and__Field_Oring(X25)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X24,X20,X25),X22,X25) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X23,X20,X25),X21,X25)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X24,X23,X25),X20,X25),X22,X25) = X21 ),
inference(variable_rename,[status(thm)],[c_0_1245]) ).
fof(c_0_2360,plain,
! [X20,X21,X22,X23,X24,X25] :
( ~ class_Ring__and__Field_Oring(X25)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X24,X20,X25),X22,X25) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X23,X20,X25),X21,X25)
| X22 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X23,X24,X25),X20,X25),X21,X25) ),
inference(variable_rename,[status(thm)],[c_0_1246]) ).
fof(c_0_2361,plain,
! [X20,X21,X22,X23,X24] :
( ~ class_Ring__and__Field_Osemiring(X24)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X23,X20,X24),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X20,X24),X21,X24),X24) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X23,X22,X24),X20,X24),X21,X24) ),
inference(variable_rename,[status(thm)],[c_0_1247]) ).
fof(c_0_2362,plain,
! [X18,X19,X20,X21,X22] :
( ~ class_Ring__and__Field_Oidom(X22)
| ~ class_Int_Onumber__ring(X22)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X19,X22),c_HOL_Otimes__class_Otimes(X20,X18,X22),X22) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,X22),c_HOL_Otimes__class_Otimes(X20,X19,X22),X22)
| X19 = X18
| X21 = X20 ),
inference(variable_rename,[status(thm)],[c_0_1248]) ).
fof(c_0_2363,plain,
! [X30,X31,X32,X33,X34] :
( ~ class_Ring__and__Field_Oidom(X34)
| ~ class_Int_Onumber__ring(X34)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X33,X31,X34),c_HOL_Otimes__class_Otimes(X32,X30,X34),X34) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X33,X30,X34),c_HOL_Otimes__class_Otimes(X32,X31,X34),X34)
| X31 = X30
| X33 = X32 ),
inference(variable_rename,[status(thm)],[c_0_1249]) ).
fof(c_0_2364,plain,
! [X8,X9,X10] :
( c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X9,X8,tc_fun(X10,tc_bool)),X10) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(X9,X10),c_Finite__Set_Ocard(c_Lattices_Olower__semilattice__class_Oinf(X9,X8,tc_fun(X10,tc_bool)),X10),tc_nat)
| ~ c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X9,X8,tc_fun(X10,tc_bool)),X10) ),
inference(variable_rename,[status(thm)],[c_0_1250]) ).
fof(c_0_2365,plain,
! [X18,X19,X20,X21,X22] :
( c_Set_Oinsert(X21,c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X22,tc_bool)),X22),X22) != c_Set_Oinsert(X19,c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X22,tc_bool)),X22),X22)
| X21 = X18
| X21 = X19 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1251])])]) ).
fof(c_0_2366,plain,
! [X18,X19,X20,X21,X22] :
( c_Set_Oinsert(X21,c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X22,tc_bool)),X22),X22) != c_Set_Oinsert(X19,c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X22,tc_bool)),X22),X22)
| X20 = X19
| X21 = X19 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1252])])]) ).
fof(c_0_2367,plain,
! [X18,X19,X20,X21,X22] :
( c_Set_Oinsert(X21,c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X22,tc_bool)),X22),X22) != c_Set_Oinsert(X19,c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X22,tc_bool)),X22),X22)
| X21 = X18
| X20 = X18 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1253])])]) ).
fof(c_0_2368,plain,
! [X18,X19,X20,X21,X22] :
( c_Set_Oinsert(X21,c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X22,tc_bool)),X22),X22) != c_Set_Oinsert(X19,c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X22,tc_bool)),X22),X22)
| X20 = X19
| X20 = X18 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1254])])]) ).
fof(c_0_2369,plain,
! [X8,X9,X10,X11] : c_HOL_Ominus__class_Ominus(X10,c_Set_Oinsert(X8,X9,X11),tc_fun(X11,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X10,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)),X11),tc_fun(X11,tc_bool)),X9,tc_fun(X11,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1255]) ).
fof(c_0_2370,plain,
! [X23,X24,X25,X26] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X26,X23,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X25,X23,tc_nat),X24,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X26,X25,tc_nat),X23,tc_nat),X24,tc_nat),
inference(variable_rename,[status(thm)],[c_0_1256]) ).
fof(c_0_2371,plain,
! [X30,X31,X32,X33] :
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X33,X31,tc_nat),c_HOL_Otimes__class_Otimes(X32,X30,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X33,X30,tc_nat),c_HOL_Otimes__class_Otimes(X32,X31,tc_nat),tc_nat)
| X31 = X30
| X33 = X32 ),
inference(variable_rename,[status(thm)],[c_0_1257]) ).
fof(c_0_2372,plain,
! [X18,X19,X20,X21] :
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X19,tc_nat),c_HOL_Otimes__class_Otimes(X20,X18,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),c_HOL_Otimes__class_Otimes(X20,X19,tc_nat),tc_nat)
| X19 = X18
| X21 = X20 ),
inference(variable_rename,[status(thm)],[c_0_1258]) ).
fof(c_0_2373,plain,
! [X21,X22,X23,X24,X25] :
( c_Fun_Oinj__on(X21,X23,X25,X24)
| ~ c_Fun_Oinj__on(X21,c_Set_Oinsert(X22,X23,X25),X25,X24) ),
inference(variable_rename,[status(thm)],[c_0_1259]) ).
fof(c_0_2374,plain,
! [X21,X22,X23,X24,X25] :
( c_Fun_Oinj__on(X21,c_HOL_Ominus__class_Ominus(X23,X22,tc_fun(X25,tc_bool)),X25,X24)
| ~ c_Fun_Oinj__on(X21,X23,X25,X24) ),
inference(variable_rename,[status(thm)],[c_0_1260]) ).
fof(c_0_2375,plain,
! [X10,X11,X12] :
( c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X11,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),X12),tc_fun(X12,tc_bool)),X12) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(X11,X12),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ c_in(X10,X11,X12)
| ~ c_Finite__Set_Ofinite(X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1261]) ).
fof(c_0_2376,plain,
! [X8,X9,X10,X11] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X10,X9,tc_fun(X11,tc_bool)),X11)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X10,c_Set_Oinsert(X8,X9,X11),tc_fun(X11,tc_bool)),X11) ),
inference(variable_rename,[status(thm)],[c_0_1262]) ).
fof(c_0_2377,plain,
! [X21,X22,X23,X24,X25] :
( c_Fun_Oinj__on(X21,X23,X25,X24)
| ~ c_lessequals(X23,X22,tc_fun(X25,tc_bool))
| ~ c_Fun_Oinj__on(X21,X22,X25,X24) ),
inference(variable_rename,[status(thm)],[c_0_1263]) ).
fof(c_0_2378,plain,
! [X12,X13,X14,X15] :
( ~ class_Divides_Oring__div(X15)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X14,X13,X15),X12,X15) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(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_1264]) ).
fof(c_0_2379,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_1265]) ).
fof(c_0_2380,plain,
! [X12,X13,X14,X15] :
( ~ class_Divides_Osemiring__div(X15)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X14,X13,X15),X12,X15) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(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_1266]) ).
fof(c_0_2381,plain,
! [X6,X7,X8] : c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X6,tc_nat),X7,tc_nat)),X6,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X7),X6,tc_nat),
inference(variable_rename,[status(thm)],[c_0_1267]) ).
fof(c_0_2382,plain,
! [X8,X9,X10] :
( c_Set_Oinsert(X8,c_HOL_Ominus__class_Ominus(X9,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)),X10),tc_fun(X10,tc_bool)),X10) = X9
| ~ c_in(X8,X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_1268]) ).
fof(c_0_2383,plain,
! [X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),c_HOL_Ozero__class_Ozero(X5),X5),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),c_HOL_Ozero__class_Ozero(X5),X5),X5),c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1269]) ).
fof(c_0_2384,plain,
! [X8,X9,X10] : c_Set_Oinsert(X8,c_HOL_Ominus__class_Ominus(X9,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)),X10),tc_fun(X10,tc_bool)),X10) = c_Set_Oinsert(X8,X9,X10),
inference(variable_rename,[status(thm)],[c_0_1270]) ).
fof(c_0_2385,plain,
! [X10,X11,X12] :
( c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X11,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),X12),tc_fun(X12,tc_bool)),X12) = c_Finite__Set_Ocard(X11,X12)
| c_in(X10,X11,X12)
| ~ c_Finite__Set_Ofinite(X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1271]) ).
fof(c_0_2386,plain,
! [X21,X22,X23,X24] : c_in(hAPP(X22,X21),c_Set_Oimage(X22,c_Orderings_Otop__class_Otop(tc_fun(X23,tc_bool)),X23,X24),X24),
inference(variable_rename,[status(thm)],[c_0_1272]) ).
fof(c_0_2387,plain,
! [X21,X22,X23,X24,X25] :
( c_in(X22,c_Set_Ovimage(X21,X23,X24,X25),X24)
| ~ c_in(hAPP(X21,X22),X23,X25) ),
inference(variable_rename,[status(thm)],[c_0_1273]) ).
fof(c_0_2388,plain,
! [X21,X22,X23,X24,X25] :
( c_in(X22,c_Set_Ovimage(X21,X23,X24,X25),X24)
| ~ c_in(hAPP(X21,X22),X23,X25) ),
inference(variable_rename,[status(thm)],[c_0_1274]) ).
fof(c_0_2389,plain,
! [X21,X22,X23,X24,X25] :
( c_in(X22,c_Set_Ovimage(X21,X23,X25,X24),X25)
| ~ c_in(hAPP(X21,X22),X23,X24) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1275])])]) ).
fof(c_0_2390,plain,
! [X29,X30,X31,X32,X33,X34] :
( ~ class_Divides_Oring__div(X34)
| c_Divides_Odiv__class_Omod(X31,X29,X34) != c_Divides_Odiv__class_Omod(X30,X29,X34)
| c_Divides_Odiv__class_Omod(X33,X29,X34) != c_Divides_Odiv__class_Omod(X32,X29,X34)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X33,X31,X34),X29,X34) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X32,X30,X34),X29,X34) ),
inference(variable_rename,[status(thm)],[c_0_1276]) ).
fof(c_0_2391,plain,
! [X29,X30,X31,X32,X33,X34] :
( ~ class_Divides_Osemiring__div(X34)
| c_Divides_Odiv__class_Omod(X31,X29,X34) != c_Divides_Odiv__class_Omod(X30,X29,X34)
| c_Divides_Odiv__class_Omod(X33,X29,X34) != c_Divides_Odiv__class_Omod(X32,X29,X34)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X33,X31,X34),X29,X34) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X32,X30,X34),X29,X34) ),
inference(variable_rename,[status(thm)],[c_0_1277]) ).
fof(c_0_2392,plain,
! [X29,X30,X31,X32,X33,X34] :
( ~ class_Divides_Osemiring__div(X34)
| c_Divides_Odiv__class_Omod(X31,X29,X34) != c_Divides_Odiv__class_Omod(X30,X29,X34)
| c_Divides_Odiv__class_Omod(X33,X29,X34) != c_Divides_Odiv__class_Omod(X32,X29,X34)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X33,X31,X34),X29,X34) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X32,X30,X34),X29,X34) ),
inference(variable_rename,[status(thm)],[c_0_1278]) ).
fof(c_0_2393,plain,
! [X21,X22,X23,X24,X25] :
( c_in(hAPP(X22,X21),c_Set_Oimage(X22,X23,X25,X24),X24)
| ~ c_in(X21,X23,X25) ),
inference(variable_rename,[status(thm)],[c_0_1279]) ).
fof(c_0_2394,plain,
! [X21,X22,X23,X24,X25] :
( c_in(hAPP(X22,X21),c_Set_Oimage(X22,X23,X24,X25),X25)
| ~ c_in(X21,X23,X24) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1280])])]) ).
fof(c_0_2395,plain,
! [X21,X22,X23,X24,X25] :
( ~ c_in(X21,X23,X24)
| c_in(hAPP(X22,X21),c_Set_Oimage(X22,X23,X24,X25),X25) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1281])])]) ).
fof(c_0_2396,plain,
! [X24,X25,X26,X27,X28] :
( ~ c_in(X24,X26,X27)
| c_in(hAPP(X25,X24),c_Set_Oimage(X25,X26,X27,X28),X28) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1282])])]) ).
fof(c_0_2397,plain,
! [X34,X35,X36,X37,X38] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X38)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X37,X36,X38),c_HOL_Otimes__class_Otimes(X35,X34,X38),X38) = c_HOL_Otimes__class_Otimes(X35,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X37,X36,X38),X34,X38),X38) ),
inference(variable_rename,[status(thm)],[c_0_1283]) ).
fof(c_0_2398,plain,
! [X34,X35,X36,X37,X38] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X38)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X37,X36,X38),c_HOL_Otimes__class_Otimes(X35,X34,X38),X38) = c_HOL_Otimes__class_Otimes(X37,c_HOL_Otimes__class_Otimes(X36,c_HOL_Otimes__class_Otimes(X35,X34,X38),X38),X38) ),
inference(variable_rename,[status(thm)],[c_0_1284]) ).
fof(c_0_2399,plain,
! [X8,X9,X10,X11] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X10,c_Set_Oinsert(X8,X9,X11),tc_fun(X11,tc_bool)),X11)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X10,X9,tc_fun(X11,tc_bool)),X11) ),
inference(variable_rename,[status(thm)],[c_0_1285]) ).
fof(c_0_2400,plain,
! [X18,X19,X20,X21,X22] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X22)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X21,X19,X22),c_HOL_Otimes__class_Otimes(X20,X18,X22),X22)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X22),X19,X22)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X22),X21,X22)
| ~ c_HOL_Oord__class_Oless(X19,X18,X22)
| ~ c_HOL_Oord__class_Oless(X21,X20,X22) ),
inference(variable_rename,[status(thm)],[c_0_1286]) ).
fof(c_0_2401,plain,
! [X18,X19,X20,X21,X22] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X22)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X21,X19,X22),c_HOL_Otimes__class_Otimes(X20,X18,X22),X22)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X22),X19,X22)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X22),X21,X22)
| ~ c_HOL_Oord__class_Oless(X19,X18,X22)
| ~ c_lessequals(X21,X20,X22) ),
inference(variable_rename,[status(thm)],[c_0_1287]) ).
fof(c_0_2402,plain,
! [X18,X19,X20,X21,X22] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X22)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X21,X19,X22),c_HOL_Otimes__class_Otimes(X20,X18,X22),X22)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X22),X19,X22)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X22),X21,X22)
| ~ c_lessequals(X19,X18,X22)
| ~ c_HOL_Oord__class_Oless(X21,X20,X22) ),
inference(variable_rename,[status(thm)],[c_0_1288]) ).
fof(c_0_2403,plain,
! [X18,X19,X20,X21,X22] :
( ~ class_Ring__and__Field_Opordered__semiring(X22)
| c_lessequals(c_HOL_Otimes__class_Otimes(X21,X19,X22),c_HOL_Otimes__class_Otimes(X20,X18,X22),X22)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X22),X19,X22)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X22),X21,X22)
| ~ c_lessequals(X19,X18,X22)
| ~ c_lessequals(X21,X20,X22) ),
inference(variable_rename,[status(thm)],[c_0_1289]) ).
fof(c_0_2404,plain,
! [X18,X19,X20,X21,X22] :
( ~ class_Ring__and__Field_Opordered__semiring(X22)
| c_lessequals(c_HOL_Otimes__class_Otimes(X21,X19,X22),c_HOL_Otimes__class_Otimes(X20,X18,X22),X22)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X22),X19,X22)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X22),X20,X22)
| ~ c_lessequals(X19,X18,X22)
| ~ c_lessequals(X21,X20,X22) ),
inference(variable_rename,[status(thm)],[c_0_1290]) ).
fof(c_0_2405,plain,
! [X18,X19,X20,X21,X22] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X22)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X21,X19,X22),c_HOL_Otimes__class_Otimes(X20,X18,X22),X22)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X22),X19,X22)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X22),X20,X22)
| ~ c_HOL_Oord__class_Oless(X19,X18,X22)
| ~ c_HOL_Oord__class_Oless(X21,X20,X22) ),
inference(variable_rename,[status(thm)],[c_0_1291]) ).
fof(c_0_2406,plain,
! [X6,X7,X8] :
( c_lessequals(X7,X6,tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X7,X8,tc_nat),c_HOL_Ominus__class_Ominus(X6,X8,tc_nat),tc_nat)
| ~ c_lessequals(X8,X6,tc_nat)
| ~ c_lessequals(X8,X7,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1292])])]) ).
fof(c_0_2407,plain,
! [X6,X7,X8] :
( c_HOL_Oord__class_Oless(X7,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X7,X8,tc_nat),c_HOL_Ominus__class_Ominus(X6,X8,tc_nat),tc_nat)
| ~ c_lessequals(X8,X6,tc_nat)
| ~ c_lessequals(X8,X7,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1293])])]) ).
fof(c_0_2408,plain,
! [X50,X51,X52,X53] :
( ~ class_Orderings_Oorder(X53)
| c_lessequals(hAPP(X52,X51),hAPP(X52,X50),X53)
| ~ c_lessequals(X51,X50,tc_nat)
| ~ c_lessequals(hAPP(X52,c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1(X52,X53)),hAPP(X52,c_Suc(c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1(X52,X53))),X53) ),
inference(variable_rename,[status(thm)],[c_0_1294]) ).
fof(c_0_2409,plain,
! [X45,X46,X47,X48,X49] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X48,X47,tc_fun(X49,tc_bool)),c_HOL_Ominus__class_Ominus(X46,X45,tc_fun(X49,tc_bool)),tc_fun(X49,tc_bool))
| ~ c_lessequals(X45,X47,tc_fun(X49,tc_bool))
| ~ c_lessequals(X48,X46,tc_fun(X49,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1295]) ).
fof(c_0_2410,plain,
! [X45,X46,X47,X48,X49] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X48,X47,tc_fun(X49,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X46,X45,tc_fun(X49,tc_bool)),tc_fun(X49,tc_bool))
| ~ c_lessequals(X47,X45,tc_fun(X49,tc_bool))
| ~ c_lessequals(X48,X46,tc_fun(X49,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1296]) ).
fof(c_0_2411,plain,
! [X8,X9,X10,X11] : c_HOL_Ominus__class_Ominus(X10,c_Set_Oinsert(X8,X9,X11),tc_fun(X11,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X10,X9,tc_fun(X11,tc_bool)),c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)),X11),tc_fun(X11,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1297]) ).
fof(c_0_2412,plain,
! [X17,X18,X19,X20] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X19,X17,tc_fun(X20,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X18,X17,tc_fun(X20,tc_bool)),tc_fun(X20,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X19,X17,tc_fun(X20,tc_bool)),X18,tc_fun(X20,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1298]) ).
fof(c_0_2413,plain,
! [X17,X18,X19,X20] : c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X19,X18,tc_fun(X20,tc_bool)),X17,tc_fun(X20,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X19,X17,tc_fun(X20,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X18,X17,tc_fun(X20,tc_bool)),tc_fun(X20,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1299]) ).
fof(c_0_2414,plain,
! [X17,X18,X19,X20] : c_Lattices_Olower__semilattice__class_Oinf(X17,c_HOL_Ominus__class_Ominus(X19,X18,tc_fun(X20,tc_bool)),tc_fun(X20,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X17,X19,tc_fun(X20,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X17,X18,tc_fun(X20,tc_bool)),tc_fun(X20,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1300]) ).
fof(c_0_2415,plain,
! [X21,X22,X23,X24,X25,X26] :
( hAPP(X23,X22) != hAPP(X23,X21)
| ~ c_Fun_Oinj__on(X23,X24,X26,X25)
| X22 = X21
| ~ c_in(X21,X24,X26)
| ~ c_in(X22,X24,X26) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1301])])]) ).
fof(c_0_2416,plain,
! [X35,X36,X37,X38,X39,X40] :
( hAPP(X37,X36) != hAPP(X37,X35)
| ~ c_in(X35,X38,X40)
| ~ c_in(X36,X38,X40)
| ~ c_Fun_Oinj__on(X37,X38,X40,X39)
| X36 = X35 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1302])])]) ).
fof(c_0_2417,plain,
! [X21,X22,X23,X24,X25,X26] :
( hAPP(X23,X22) != hAPP(X23,X21)
| ~ c_in(X21,X24,X26)
| ~ c_in(X22,X24,X26)
| ~ c_Fun_Oinj__on(X23,X24,X26,X25)
| X22 = X21 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1303])])]) ).
fof(c_0_2418,plain,
! [X21,X22,X23,X24,X25,X26] :
( hAPP(X23,X22) != hAPP(X23,X21)
| ~ c_in(X21,X24,X26)
| ~ c_in(X22,X24,X26)
| X22 = X21
| ~ c_Fun_Oinj__on(X23,X24,X26,X25) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1304])])]) ).
fof(c_0_2419,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X11,X11,X12),c_HOL_Otimes__class_Otimes(X10,X10,X12),X12),X12)
| X10 = c_HOL_Ozero__class_Ozero(X12) ),
inference(variable_rename,[status(thm)],[c_0_1305]) ).
fof(c_0_2420,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X11,X11,X12),c_HOL_Otimes__class_Otimes(X10,X10,X12),X12),X12)
| X11 = c_HOL_Ozero__class_Ozero(X12) ),
inference(variable_rename,[status(thm)],[c_0_1306]) ).
fof(c_0_2421,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| c_lessequals(c_HOL_Ozero__class_Ozero(X12),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X11,X11,X12),c_HOL_Otimes__class_Otimes(X10,X10,X12),X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1307]) ).
fof(c_0_2422,plain,
! [X36,X37,X38,X39,X40] :
( c_HOL_Oplus__class_Oplus(X39,c_HOL_Otimes__class_Otimes(X40,X38,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X36,c_HOL_Otimes__class_Otimes(X40,X37,tc_nat),tc_nat)
| c_Divides_Odiv__class_Omod(X39,X40,tc_nat) = c_Divides_Odiv__class_Omod(X36,X40,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1308]) ).
fof(c_0_2423,plain,
! [X10,X11,X12] :
( X11 = c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),X12)
| X11 = c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool))
| ~ c_lessequals(X11,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),X12),tc_fun(X12,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1309]) ).
fof(c_0_2424,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_1310]) ).
fof(c_0_2425,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_1311]) ).
fof(c_0_2426,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X15)
| c_lessequals(X14,X13,X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X15),X12,X15)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X14,X12,X15),c_HOL_Otimes__class_Otimes(X13,X12,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_1312]) ).
fof(c_0_2427,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X15)
| c_lessequals(X14,X13,X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X15),X12,X15)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X12,X14,X15),c_HOL_Otimes__class_Otimes(X12,X13,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_1313]) ).
fof(c_0_2428,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X15)
| c_lessequals(X14,X13,X15)
| ~ c_lessequals(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_1314]) ).
fof(c_0_2429,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X15)
| c_lessequals(X13,X14,X15)
| ~ c_lessequals(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_1315]) ).
fof(c_0_2430,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__semiring(X15)
| c_HOL_Oord__class_Oless(X14,X13,X15)
| ~ c_lessequals(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_1316]) ).
fof(c_0_2431,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__semiring(X15)
| c_HOL_Oord__class_Oless(X14,X13,X15)
| ~ c_lessequals(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_1317]) ).
fof(c_0_2432,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X15)
| c_HOL_Oord__class_Oless(X14,X13,X15)
| ~ c_lessequals(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_1318]) ).
fof(c_0_2433,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X15)
| c_HOL_Oord__class_Oless(X14,X13,X15)
| ~ c_lessequals(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_1319]) ).
fof(c_0_2434,plain,
! [X10,X11,X12,X13] :
( hBOOL(hAPP(X12,X10))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X12,X11,tc_fun(X13,tc_bool)),X10)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1320])])]) ).
fof(c_0_2435,plain,
! [X10,X11,X12,X13] :
( hBOOL(hAPP(X11,X10))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X12,X11,tc_fun(X13,tc_bool)),X10)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1321])])]) ).
fof(c_0_2436,plain,
! [X6,X7,X8] :
( c_Ring__and__Field_Odvd__class_Odvd(X7,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X8,X7,tc_nat),c_HOL_Otimes__class_Otimes(X8,X6,tc_nat),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1322])])]) ).
fof(c_0_2437,plain,
! [X6,X7,X8] :
( c_Ring__and__Field_Odvd__class_Odvd(X7,X6,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X8,X7,tc_nat),c_HOL_Otimes__class_Otimes(X8,X6,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1323])])]) ).
fof(c_0_2438,plain,
! [X6,X7,X8] :
( c_HOL_Oord__class_Oless(X7,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X7,tc_nat),c_HOL_Otimes__class_Otimes(X8,X6,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1324])])]) ).
fof(c_0_2439,plain,
! [X6,X7,X8] :
( c_lessequals(X7,X6,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X7,tc_nat),c_HOL_Otimes__class_Otimes(X8,X6,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1325])])]) ).
fof(c_0_2440,plain,
! [X6,X7,X8] :
( c_lessequals(X7,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X7,tc_nat),c_HOL_Otimes__class_Otimes(X8,X6,tc_nat),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1326])])]) ).
fof(c_0_2441,plain,
! [X6,X7,X8] :
( c_lessequals(X7,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X7,X8,tc_nat),c_HOL_Otimes__class_Otimes(X6,X8,tc_nat),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1327])])]) ).
fof(c_0_2442,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_1328]) ).
fof(c_0_2443,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_1329]) ).
fof(c_0_2444,plain,
! [X18,X19,X20,X21] :
( ~ class_Ring__and__Field_Oidom(X21)
| ~ class_Int_Onumber__ring(X21)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X18,X20,X21),c_HOL_Otimes__class_Otimes(X18,X19,X21),X21) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X18,X19,X21),c_HOL_Otimes__class_Otimes(X18,X20,X21),X21) ),
inference(variable_rename,[status(thm)],[c_0_1330]) ).
fof(c_0_2445,plain,
! [X16,X17,X18,X19] :
( ~ class_Ring__and__Field_Oidom(X19)
| ~ class_Int_Onumber__ring(X19)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X18,X17,X19),c_HOL_Otimes__class_Otimes(X18,X16,X19),X19) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X18,X16,X19),c_HOL_Otimes__class_Otimes(X18,X17,X19),X19) ),
inference(variable_rename,[status(thm)],[c_0_1331]) ).
fof(c_0_2446,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_1332]) ).
fof(c_0_2447,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_1333]) ).
fof(c_0_2448,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_1334]) ).
fof(c_0_2449,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_1335]) ).
fof(c_0_2450,plain,
! [X12,X13,X14,X15] :
( ~ class_Divides_Osemiring__div(X15)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X14,c_Divides_Odiv__class_Omod(X13,X12,X15),X15),X12,X15) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X14,X13,X15),X12,X15) ),
inference(variable_rename,[status(thm)],[c_0_1336]) ).
fof(c_0_2451,plain,
! [X12,X13,X14,X15] :
( ~ class_Divides_Osemiring__div(X15)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X14,X12,X15),X13,X15),X12,X15) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X14,X13,X15),X12,X15) ),
inference(variable_rename,[status(thm)],[c_0_1337]) ).
fof(c_0_2452,plain,
! [X12,X13,X14,X15] :
( ~ class_Divides_Oring__div(X15)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X14,X13,X15),X12,X15) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X14,c_Divides_Odiv__class_Omod(X13,X12,X15),X15),X12,X15) ),
inference(variable_rename,[status(thm)],[c_0_1338]) ).
fof(c_0_2453,plain,
! [X12,X13,X14,X15] :
( ~ class_Divides_Oring__div(X15)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X14,X13,X15),X12,X15) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X14,X12,X15),X13,X15),X12,X15) ),
inference(variable_rename,[status(thm)],[c_0_1339]) ).
fof(c_0_2454,plain,
! [X34,X35,X36,X37,X38] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X38)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X37,X36,X38),c_HOL_Otimes__class_Otimes(X35,X34,X38),X38) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X37,X35,X38),c_HOL_Otimes__class_Otimes(X36,X34,X38),X38) ),
inference(variable_rename,[status(thm)],[c_0_1340]) ).
fof(c_0_2455,plain,
! [X18,X19,X20,X21,X22] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X22)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X21,X20,X22),c_HOL_Oplus__class_Oplus(X19,X18,X22),X22) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X21,X19,X22),c_HOL_Oplus__class_Oplus(X20,X18,X22),X22) ),
inference(variable_rename,[status(thm)],[c_0_1341]) ).
fof(c_0_2456,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_1342]) ).
fof(c_0_2457,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_1343]) ).
fof(c_0_2458,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_1344]) ).
fof(c_0_2459,plain,
! [X12,X13,X14,X15] :
( ~ class_Divides_Osemiring__div(X15)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X14,X13,X15),X12,X15) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X14,c_Divides_Odiv__class_Omod(X13,X12,X15),X15),X12,X15) ),
inference(variable_rename,[status(thm)],[c_0_1345]) ).
fof(c_0_2460,plain,
! [X12,X13,X14,X15] :
( ~ class_Divides_Osemiring__div(X15)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X14,X13,X15),X12,X15) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X14,X12,X15),X13,X15),X12,X15) ),
inference(variable_rename,[status(thm)],[c_0_1346]) ).
fof(c_0_2461,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_1347]) ).
fof(c_0_2462,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_1348]) ).
fof(c_0_2463,plain,
! [X35,X36,X37] : c_Set_Oinsert(X35,c_Set_Oinsert(X36,c_Orderings_Obot__class_Obot(tc_fun(X37,tc_bool)),X37),X37) = c_Set_Oinsert(X36,c_Set_Oinsert(X35,c_Orderings_Obot__class_Obot(tc_fun(X37,tc_bool)),X37),X37),
inference(variable_rename,[status(thm)],[c_0_1349]) ).
fof(c_0_2464,plain,
! [X15,X16,X17,X18] :
( c_Finite__Set_Ofinite(c_Set_Oimage(X15,X16,X18,X17),X17)
| ~ c_Finite__Set_Ofinite(X16,X18) ),
inference(variable_rename,[status(thm)],[c_0_1350]) ).
fof(c_0_2465,plain,
! [X37,X38,X39,X40,X41] :
( ~ class_Ring__and__Field_Oidom(X41)
| ~ class_Int_Onumber__ring(X41)
| c_HOL_Oplus__class_Oplus(X37,c_HOL_Otimes__class_Otimes(X38,X40,X41),X41) != c_HOL_Oplus__class_Oplus(X37,c_HOL_Otimes__class_Otimes(X38,X39,X41),X41)
| X40 = X39
| X38 = c_HOL_Ozero__class_Ozero(X41) ),
inference(variable_rename,[status(thm)],[c_0_1351]) ).
fof(c_0_2466,plain,
! [X16,X17,X18] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X18,X17,tc_nat),c_HOL_Otimes__class_Otimes(X18,X16,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X18,X16,tc_nat),c_HOL_Otimes__class_Otimes(X18,X17,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1352]) ).
fof(c_0_2467,plain,
! [X18,X19,X20] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X18,X20,tc_nat),c_HOL_Otimes__class_Otimes(X18,X19,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X18,X19,tc_nat),c_HOL_Otimes__class_Otimes(X18,X20,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1353]) ).
fof(c_0_2468,plain,
! [X21,X22,X23,X24,X25] :
( hAPP(X23,X22) != hAPP(X23,X21)
| ~ c_Fun_Oinj__on(X23,c_Orderings_Otop__class_Otop(tc_fun(X25,tc_bool)),X25,X24)
| X22 = X21 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1354])])]) ).
fof(c_0_2469,plain,
! [X22,X23,X24] :
( c_HOL_Ominus__class_Ominus(X22,c_Suc(c_HOL_Ominus__class_Ominus(X24,X23,tc_nat)),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X22,X23,tc_nat),c_Suc(X24),tc_nat)
| ~ c_lessequals(X23,X24,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1355]) ).
fof(c_0_2470,plain,
! [X22,X23,X24] :
( c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ominus__class_Ominus(X24,X23,tc_nat)),X22,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X24),c_HOL_Oplus__class_Oplus(X23,X22,tc_nat),tc_nat)
| ~ c_lessequals(X23,X24,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1356]) ).
fof(c_0_2471,plain,
! [X6,X7,X8] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X7,X8,tc_nat),c_HOL_Ominus__class_Ominus(X6,X8,tc_nat),tc_nat)
| ~ c_lessequals(X7,X6,tc_nat)
| ~ c_lessequals(X8,X6,tc_nat)
| ~ c_lessequals(X8,X7,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1357]) ).
fof(c_0_2472,plain,
! [X6,X7,X8] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X7,X8,tc_nat),c_HOL_Ominus__class_Ominus(X6,X8,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,X6,tc_nat)
| ~ c_lessequals(X8,X6,tc_nat)
| ~ c_lessequals(X8,X7,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1358]) ).
fof(c_0_2473,plain,
! [X18,X19,X20,X21,X22] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X22)
| c_lessequals(X21,c_HOL_Oplus__class_Oplus(X20,X18,X22),X22)
| ~ c_lessequals(X19,X18,X22)
| ~ c_lessequals(X21,c_HOL_Oplus__class_Oplus(X20,X19,X22),X22) ),
inference(variable_rename,[status(thm)],[c_0_1359]) ).
fof(c_0_2474,plain,
! [X6,X7,X8] :
( c_lessequals(X7,X6,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X8),X7,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X8),X6,tc_nat),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1360])])]) ).
fof(c_0_2475,plain,
! [X6,X7,X8] :
( c_HOL_Oord__class_Oless(X7,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X8),X7,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X8),X6,tc_nat),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1361])])]) ).
fof(c_0_2476,plain,
! [X37,X38,X39,X40] :
( c_HOL_Oplus__class_Oplus(X37,c_HOL_Otimes__class_Otimes(X38,X40,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X37,c_HOL_Otimes__class_Otimes(X38,X39,tc_nat),tc_nat)
| X40 = X39
| X38 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1362]) ).
fof(c_0_2477,plain,
! [X8,X9,X10,X11] : c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X8,X10,X11),c_Set_Oinsert(X8,X9,X11),tc_fun(X11,tc_bool)) = c_Set_Oinsert(X8,c_Lattices_Olower__semilattice__class_Oinf(X10,X9,tc_fun(X11,tc_bool)),X11),
inference(variable_rename,[status(thm)],[c_0_1363]) ).
fof(c_0_2478,plain,
! [X27,X28,X29] :
( hBOOL(hAPP(X29,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X28,X27,tc_nat)
| ~ hBOOL(hAPP(X29,c_HOL_Ominus__class_Ominus(X28,X27,tc_nat))) ),
inference(variable_rename,[status(thm)],[c_0_1364]) ).
fof(c_0_2479,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_1365]) ).
fof(c_0_2480,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_1366]) ).
fof(c_0_2481,plain,
! [X23,X24,X25] :
( c_lessequals(X25,c_HOL_Ominus__class_Ominus(X24,X23,tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X25,X23,tc_nat),X24,tc_nat)
| ~ c_lessequals(X23,X24,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1367]) ).
fof(c_0_2482,plain,
! [X23,X24,X25] :
( c_lessequals(c_HOL_Oplus__class_Oplus(X25,X23,tc_nat),X24,tc_nat)
| ~ c_lessequals(X25,c_HOL_Ominus__class_Ominus(X24,X23,tc_nat),tc_nat)
| ~ c_lessequals(X23,X24,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1368]) ).
fof(c_0_2483,plain,
! [X10,X11,X12,X13] :
( c_HOL_Oord__class_Oless(X12,c_Set_Oinsert(X10,X11,X13),tc_fun(X13,tc_bool))
| ~ c_lessequals(X12,X11,tc_fun(X13,tc_bool))
| c_in(X10,X12,X13)
| ~ c_HOL_Oord__class_Oless(X12,X11,tc_fun(X13,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1369]) ).
fof(c_0_2484,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(c_HOL_Oplus__class_Oplus(X12,X14,X15),c_HOL_Oplus__class_Oplus(X12,X13,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_1370]) ).
fof(c_0_2485,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(c_HOL_Oplus__class_Oplus(X14,X12,X15),c_HOL_Oplus__class_Oplus(X13,X12,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_1371]) ).
fof(c_0_2486,plain,
! [X12,X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X15)
| c_lessequals(X14,X13,X15)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X14,X12,X15),c_HOL_Oplus__class_Oplus(X13,X12,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_1372]) ).
fof(c_0_2487,plain,
! [X12,X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X15)
| c_lessequals(X14,X13,X15)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X12,X14,X15),c_HOL_Oplus__class_Oplus(X12,X13,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_1373]) ).
fof(c_0_2488,plain,
! [X6,X7,X8] :
( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X7,X8,tc_nat),c_HOL_Ominus__class_Ominus(X6,X8,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X7,X6,tc_nat)
| ~ c_lessequals(X8,X6,tc_nat)
| ~ c_lessequals(X8,X7,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1374]) ).
fof(c_0_2489,plain,
! [X10,X11,X12,X13] :
( c_lessequals(X12,X11,tc_fun(X13,tc_bool))
| c_in(X10,X12,X13)
| c_in(X10,X11,X13)
| ~ c_HOL_Oord__class_Oless(X12,c_Set_Oinsert(X10,X11,X13),tc_fun(X13,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1375]) ).
fof(c_0_2490,plain,
! [X8,X9,X10,X11] :
( c_Lattices_Olower__semilattice__class_Oinf(X10,c_Set_Oinsert(X8,X9,X11),tc_fun(X11,tc_bool)) = c_Set_Oinsert(X8,c_Lattices_Olower__semilattice__class_Oinf(X10,X9,tc_fun(X11,tc_bool)),X11)
| ~ c_in(X8,X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_1376]) ).
fof(c_0_2491,plain,
! [X17,X18,X19,X20] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X17,X19,X20),X18,tc_fun(X20,tc_bool)) = c_Set_Oinsert(X17,c_Lattices_Olower__semilattice__class_Oinf(X19,X18,tc_fun(X20,tc_bool)),X20)
| ~ c_in(X17,X18,X20) ),
inference(variable_rename,[status(thm)],[c_0_1377]) ).
fof(c_0_2492,plain,
! [X17,X18,X19,X20] :
( c_HOL_Ominus__class_Ominus(X18,c_HOL_Ominus__class_Ominus(X17,X19,tc_fun(X20,tc_bool)),tc_fun(X20,tc_bool)) = X19
| ~ c_lessequals(X18,X17,tc_fun(X20,tc_bool))
| ~ c_lessequals(X19,X18,tc_fun(X20,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1378]) ).
fof(c_0_2493,plain,
! [X17,X18,X19,X20] :
( c_lessequals(X17,c_Lattices_Olower__semilattice__class_Oinf(X19,X18,tc_fun(X20,tc_bool)),tc_fun(X20,tc_bool))
| ~ c_lessequals(X17,X18,tc_fun(X20,tc_bool))
| ~ c_lessequals(X17,X19,tc_fun(X20,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1379]) ).
fof(c_0_2494,plain,
! [X17,X18,X19,X20] :
( c_lessequals(X17,c_Lattices_Olower__semilattice__class_Oinf(X19,X18,tc_fun(X20,tc_bool)),tc_fun(X20,tc_bool))
| ~ c_lessequals(X17,X18,tc_fun(X20,tc_bool))
| ~ c_lessequals(X17,X19,tc_fun(X20,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1380]) ).
fof(c_0_2495,plain,
! [X6,X7,X8] :
( c_Ring__and__Field_Odvd__class_Odvd(X8,X6,tc_nat)
| ~ c_lessequals(X6,X7,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X7,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1381]) ).
fof(c_0_2496,plain,
! [X6,X7,X8] :
( c_Ring__and__Field_Odvd__class_Odvd(X8,X7,tc_nat)
| ~ c_lessequals(X6,X7,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X6,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1382]) ).
fof(c_0_2497,plain,
! [X6,X7,X8] :
( c_Ring__and__Field_Odvd__class_Odvd(X7,X6,tc_nat)
| X8 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X8,X7,tc_nat),c_HOL_Otimes__class_Otimes(X8,X6,tc_nat),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1383])])]) ).
fof(c_0_2498,plain,
! [X6,X7,X8] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X7,tc_nat),c_HOL_Otimes__class_Otimes(X8,X6,tc_nat),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1384]) ).
fof(c_0_2499,plain,
! [X6,X7,X8] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X8,tc_nat),c_HOL_Otimes__class_Otimes(X6,X8,tc_nat),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1385]) ).
fof(c_0_2500,plain,
! [X10,X11] :
( c_in(X10,c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)),X11)
| c_Finite__Set_Ocard(c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)),X11),X11) = c_Suc(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)),X11)) ),
inference(variable_rename,[status(thm)],[c_0_1386]) ).
fof(c_0_2501,plain,
! [X6,X7,X8] :
( c_lessequals(X7,X6,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),c_HOL_Oplus__class_Oplus(X8,X6,tc_nat),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1387])])]) ).
fof(c_0_2502,plain,
! [X6,X7,X8] :
( c_HOL_Oord__class_Oless(X7,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),c_HOL_Oplus__class_Oplus(X8,X6,tc_nat),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1388])])]) ).
fof(c_0_2503,plain,
! [X6,X7,X8] :
( c_HOL_Oord__class_Oless(X7,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X8,tc_nat),c_HOL_Otimes__class_Otimes(X6,X8,tc_nat),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1389])])]) ).
fof(c_0_2504,plain,
! [X6,X7,X8] :
( c_HOL_Oord__class_Oless(X7,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X7,tc_nat),c_HOL_Otimes__class_Otimes(X8,X6,tc_nat),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1390])])]) ).
fof(c_0_2505,plain,
! [X17,X18,X19,X20] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X19,X18,tc_fun(X20,tc_bool)),X17,tc_fun(X20,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X19,c_HOL_Ominus__class_Ominus(X18,X17,tc_fun(X20,tc_bool)),tc_fun(X20,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1391]) ).
fof(c_0_2506,plain,
! [X17,X18,X19,X20] : c_Lattices_Olower__semilattice__class_Oinf(X19,c_Lattices_Olower__semilattice__class_Oinf(X18,X17,tc_fun(X20,tc_bool)),tc_fun(X20,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X18,c_Lattices_Olower__semilattice__class_Oinf(X19,X17,tc_fun(X20,tc_bool)),tc_fun(X20,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1392]) ).
fof(c_0_2507,plain,
! [X17,X18,X19,X20] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X19,X18,tc_fun(X20,tc_bool)),X17,tc_fun(X20,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X19,c_Lattices_Olower__semilattice__class_Oinf(X18,X17,tc_fun(X20,tc_bool)),tc_fun(X20,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1393]) ).
fof(c_0_2508,plain,
! [X21,X22,X23,X24] :
( c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)) != c_Set_Oimage(X21,X22,X23,X24)
| X22 = c_Orderings_Obot__class_Obot(tc_fun(X23,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1394])])]) ).
fof(c_0_2509,plain,
! [X21,X22,X23,X24] :
( c_Set_Oimage(X21,X22,X23,X24) != c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool))
| X22 = c_Orderings_Obot__class_Obot(tc_fun(X23,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1395])])]) ).
fof(c_0_2510,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Omult__mono1(X15)
| c_lessequals(c_HOL_Otimes__class_Otimes(X12,X14,X15),c_HOL_Otimes__class_Otimes(X12,X13,X15),X15)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X15),X12,X15)
| ~ c_lessequals(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_1396]) ).
fof(c_0_2511,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Omult__mono(X15)
| c_lessequals(c_HOL_Otimes__class_Otimes(X12,X14,X15),c_HOL_Otimes__class_Otimes(X12,X13,X15),X15)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X15),X12,X15)
| ~ c_lessequals(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_1397]) ).
fof(c_0_2512,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Omult__mono(X15)
| c_lessequals(c_HOL_Otimes__class_Otimes(X14,X12,X15),c_HOL_Otimes__class_Otimes(X13,X12,X15),X15)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X15),X12,X15)
| ~ c_lessequals(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_1398]) ).
fof(c_0_2513,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Opordered__ring(X15)
| c_lessequals(c_HOL_Otimes__class_Otimes(X12,X14,X15),c_HOL_Otimes__class_Otimes(X12,X13,X15),X15)
| ~ c_lessequals(X12,c_HOL_Ozero__class_Ozero(X15),X15)
| ~ c_lessequals(X13,X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_1399]) ).
fof(c_0_2514,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Opordered__ring(X15)
| c_lessequals(c_HOL_Otimes__class_Otimes(X14,X12,X15),c_HOL_Otimes__class_Otimes(X13,X12,X15),X15)
| ~ c_lessequals(X12,c_HOL_Ozero__class_Ozero(X15),X15)
| ~ c_lessequals(X13,X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_1400]) ).
fof(c_0_2515,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_1401]) ).
fof(c_0_2516,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_1402]) ).
fof(c_0_2517,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_1403]) ).
fof(c_0_2518,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_1404]) ).
fof(c_0_2519,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_1405]) ).
fof(c_0_2520,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_1406]) ).
fof(c_0_2521,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_1407]) ).
fof(c_0_2522,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_1408]) ).
fof(c_0_2523,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_1409]) ).
fof(c_0_2524,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_1410]) ).
fof(c_0_2525,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_1411]) ).
fof(c_0_2526,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X15)
| c_lessequals(c_HOL_Otimes__class_Otimes(X12,X14,X15),c_HOL_Otimes__class_Otimes(X12,X13,X15),X15)
| ~ c_lessequals(X14,X13,X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X15),X12,X15) ),
inference(variable_rename,[status(thm)],[c_0_1412]) ).
fof(c_0_2527,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X15)
| c_lessequals(c_HOL_Otimes__class_Otimes(X12,X14,X15),c_HOL_Otimes__class_Otimes(X12,X13,X15),X15)
| ~ c_lessequals(X13,X14,X15)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_1413]) ).
fof(c_0_2528,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__idom(X12)
| c_lessequals(c_HOL_Otimes__class_Otimes(X10,X11,X12),X11,X12)
| ~ c_lessequals(X10,c_HOL_Oone__class_Oone(X12),X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X10,X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1414]) ).
fof(c_0_2529,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__idom(X12)
| c_lessequals(c_HOL_Otimes__class_Otimes(X11,X10,X12),X11,X12)
| ~ c_lessequals(X10,c_HOL_Oone__class_Oone(X12),X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X10,X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1415]) ).
fof(c_0_2530,plain,
! [X10,X11,X12,X13] :
( c_HOL_Oord__class_Oless(X12,X11,tc_fun(X13,tc_bool))
| ~ c_in(X10,X11,X13)
| ~ c_HOL_Oord__class_Oless(X12,c_Set_Oinsert(X10,X11,X13),tc_fun(X13,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1416]) ).
fof(c_0_2531,plain,
! [X10,X11,X12] :
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X10,X11,X12),c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),X12),tc_fun(X12,tc_bool)) = X11
| c_in(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1417]) ).
fof(c_0_2532,plain,
! [X6,X7,X8] :
( c_lessequals(X7,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X6,X7,tc_nat),X8,tc_nat),tc_nat)
| ~ c_lessequals(X8,X6,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1418]) ).
fof(c_0_2533,plain,
! [X18,X19,X20,X21,X22] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X22)
| c_lessequals(c_HOL_Oplus__class_Oplus(X21,X19,X22),c_HOL_Oplus__class_Oplus(X20,X18,X22),X22)
| ~ c_lessequals(X19,X18,X22)
| ~ c_lessequals(X21,X20,X22) ),
inference(variable_rename,[status(thm)],[c_0_1419]) ).
fof(c_0_2534,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_1420]) ).
fof(c_0_2535,plain,
! [X18,X19,X20,X21,X22] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X22)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X21,X19,X22),c_HOL_Oplus__class_Oplus(X20,X18,X22),X22)
| ~ c_HOL_Oord__class_Oless(X19,X18,X22)
| ~ c_HOL_Oord__class_Oless(X21,X20,X22) ),
inference(variable_rename,[status(thm)],[c_0_1421]) ).
fof(c_0_2536,plain,
! [X18,X19,X20,X21,X22] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X22)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X21,X19,X22),c_HOL_Oplus__class_Oplus(X20,X18,X22),X22)
| ~ c_lessequals(X19,X18,X22)
| ~ c_HOL_Oord__class_Oless(X21,X20,X22) ),
inference(variable_rename,[status(thm)],[c_0_1422]) ).
fof(c_0_2537,plain,
! [X18,X19,X20,X21,X22] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X22)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X21,X19,X22),c_HOL_Oplus__class_Oplus(X20,X18,X22),X22)
| ~ c_HOL_Oord__class_Oless(X19,X18,X22)
| ~ c_lessequals(X21,X20,X22) ),
inference(variable_rename,[status(thm)],[c_0_1423]) ).
fof(c_0_2538,plain,
! [X10,X11,X12,X13] :
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X10,X12,X13),X11,tc_fun(X13,tc_bool)) = c_Set_Oinsert(X10,c_HOL_Ominus__class_Ominus(X12,X11,tc_fun(X13,tc_bool)),X13)
| c_in(X10,X11,X13) ),
inference(variable_rename,[status(thm)],[c_0_1424]) ).
fof(c_0_2539,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X11,X11,X12),c_HOL_Otimes__class_Otimes(X10,X10,X12),X12) != c_HOL_Ozero__class_Ozero(X12)
| X11 = c_HOL_Ozero__class_Ozero(X12) ),
inference(variable_rename,[status(thm)],[c_0_1425]) ).
fof(c_0_2540,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X11,X11,X12),c_HOL_Otimes__class_Otimes(X10,X10,X12),X12) != c_HOL_Ozero__class_Ozero(X12)
| X10 = c_HOL_Ozero__class_Ozero(X12) ),
inference(variable_rename,[status(thm)],[c_0_1426]) ).
fof(c_0_2541,plain,
! [X17,X18,X19,X20] :
( c_lessequals(X17,X19,tc_fun(X20,tc_bool))
| ~ c_lessequals(X17,c_Lattices_Olower__semilattice__class_Oinf(X19,X18,tc_fun(X20,tc_bool)),tc_fun(X20,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1427]) ).
fof(c_0_2542,plain,
! [X17,X18,X19,X20] :
( c_lessequals(X17,X18,tc_fun(X20,tc_bool))
| ~ c_lessequals(X17,c_Lattices_Olower__semilattice__class_Oinf(X19,X18,tc_fun(X20,tc_bool)),tc_fun(X20,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1428]) ).
fof(c_0_2543,plain,
! [X16,X17,X18,X19] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X19)
| c_HOL_Otimes__class_Otimes(X18,c_HOL_Oplus__class_Oplus(X17,X16,X19),X19) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X18,X17,X19),c_HOL_Otimes__class_Otimes(X18,X16,X19),X19) ),
inference(variable_rename,[status(thm)],[c_0_1429]) ).
fof(c_0_2544,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring(X15)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X14,X13,X15),X12,X15) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X12,X15),c_HOL_Otimes__class_Otimes(X13,X12,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_1430]) ).
fof(c_0_2545,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X15)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X14,X13,X15),X12,X15) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X12,X15),c_HOL_Otimes__class_Otimes(X13,X12,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_1431]) ).
fof(c_0_2546,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_1432]) ).
fof(c_0_2547,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_1433]) ).
fof(c_0_2548,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X14)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X13,X11,X14),c_HOL_Otimes__class_Otimes(X12,X11,X14),X14) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X13,X12,X14),X11,X14) ),
inference(variable_rename,[status(thm)],[c_0_1434]) ).
fof(c_0_2549,plain,
! [X12,X13,X14,X15] :
( ~ class_Divides_Osemiring__div(X15)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X14,c_HOL_Otimes__class_Otimes(X13,X12,X15),X15),X13,X15) = c_Divides_Odiv__class_Omod(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_1435]) ).
fof(c_0_2550,plain,
! [X12,X13,X14,X15] :
( ~ class_Divides_Osemiring__div(X15)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X14,c_HOL_Otimes__class_Otimes(X12,X13,X15),X15),X13,X15) = c_Divides_Odiv__class_Omod(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_1436]) ).
fof(c_0_2551,plain,
! [X12,X13,X14,X15] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X15)
| c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X14,X13,X15),X12,X15) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X14,X12,X15),c_HOL_Oplus__class_Oplus(X13,X12,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_1437]) ).
fof(c_0_2552,plain,
! [X12,X13,X14,X15] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X15)
| c_HOL_Oplus__class_Oplus(X14,c_Lattices_Olower__semilattice__class_Oinf(X13,X12,X15),X15) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X14,X13,X15),c_HOL_Oplus__class_Oplus(X14,X12,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_1438]) ).
fof(c_0_2553,plain,
! [X12,X13,X14,X15] :
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(X15)
| c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X14,X13,X15),X12,X15) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X14,X12,X15),c_HOL_Oplus__class_Oplus(X13,X12,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_1439]) ).
fof(c_0_2554,plain,
! [X12,X13,X14,X15] :
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(X15)
| c_HOL_Oplus__class_Oplus(X14,c_Lattices_Olower__semilattice__class_Oinf(X13,X12,X15),X15) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X14,X13,X15),c_HOL_Oplus__class_Oplus(X14,X12,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_1440]) ).
fof(c_0_2555,plain,
! [X6,X7,X8] :
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X8,X7,tc_nat),c_HOL_Otimes__class_Otimes(X8,X6,tc_nat),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1441]) ).
fof(c_0_2556,plain,
! [X6,X7,X8] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X7,tc_nat),c_HOL_Otimes__class_Otimes(X8,X6,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1442]) ).
fof(c_0_2557,plain,
! [X23,X24,X25] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X25,X23,tc_nat),c_HOL_Otimes__class_Otimes(X24,X23,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X23,tc_nat)
| ~ c_HOL_Oord__class_Oless(X25,X24,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1443]) ).
fof(c_0_2558,plain,
! [X23,X24,X25] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X23,X25,tc_nat),c_HOL_Otimes__class_Otimes(X23,X24,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X23,tc_nat)
| ~ c_HOL_Oord__class_Oless(X25,X24,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1444]) ).
fof(c_0_2559,plain,
! [X6,X7,X8] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X7,tc_nat),c_HOL_Otimes__class_Otimes(X8,X6,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1445]) ).
fof(c_0_2560,plain,
! [X6,X7,X8] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X8,tc_nat),c_HOL_Otimes__class_Otimes(X6,X8,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1446]) ).
fof(c_0_2561,plain,
! [X6,X7,X8] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X8,X7,tc_nat),c_HOL_Otimes__class_Otimes(X8,X6,tc_nat),tc_nat)
| ~ c_lessequals(X7,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1447]) ).
fof(c_0_2562,plain,
! [X3,X4] :
( c_HOL_Otimes__class_Otimes(X4,X3,tc_nat) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,tc_nat),tc_nat)
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1448]) ).
fof(c_0_2563,plain,
! [X10,X11,X12,X13] :
( hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X12,X11,tc_fun(X13,tc_bool)),X10))
| ~ hBOOL(hAPP(X11,X10))
| ~ hBOOL(hAPP(X12,X10)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1449])])]) ).
fof(c_0_2564,plain,
! [X12,X13,X14] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X14,X12,tc_nat),c_HOL_Ominus__class_Ominus(X13,X12,tc_nat),tc_nat)
| ~ c_lessequals(X12,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(X14,X13,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1450]) ).
fof(c_0_2565,plain,
! [X25,X26,X27] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X27,X25,tc_nat),c_HOL_Ominus__class_Ominus(X27,X26,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X26,X27,tc_nat)
| ~ c_HOL_Oord__class_Oless(X26,X25,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1451]) ).
fof(c_0_2566,plain,
! [X25,X26,X27,X28] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X28,X26,tc_nat),c_HOL_Otimes__class_Otimes(X27,X25,tc_nat),tc_nat)
| ~ c_lessequals(X26,X25,tc_nat)
| ~ c_lessequals(X28,X27,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1452]) ).
fof(c_0_2567,plain,
! [X25,X26,X27,X28] :
( c_lessequals(c_HOL_Oplus__class_Oplus(X28,X26,tc_nat),c_HOL_Oplus__class_Oplus(X27,X25,tc_nat),tc_nat)
| ~ c_lessequals(X26,X25,tc_nat)
| ~ c_lessequals(X28,X27,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1453]) ).
fof(c_0_2568,plain,
! [X25,X26,X27,X28] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X28,X26,tc_nat),c_HOL_Oplus__class_Oplus(X27,X25,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X26,X25,tc_nat)
| ~ c_HOL_Oord__class_Oless(X28,X27,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1454]) ).
fof(c_0_2569,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X13)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X13),X11,X13)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X13),X12,X13)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X13),c_HOL_Otimes__class_Otimes(X12,X11,X13),X13) ),
inference(variable_rename,[status(thm)],[c_0_1455]) ).
fof(c_0_2570,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X13)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X13),X11,X13)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X13),X12,X13)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X13),c_HOL_Otimes__class_Otimes(X11,X12,X13),X13) ),
inference(variable_rename,[status(thm)],[c_0_1456]) ).
fof(c_0_2571,plain,
! [X27,X28] :
( ~ hBOOL(hAPP(X28,c_Divides_Odiv__class_Omod(X27,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
| hBOOL(hAPP(X28,X27)) ),
inference(variable_rename,[status(thm)],[c_0_1457]) ).
fof(c_0_2572,plain,
! [X10,X11,X12,X13] :
( c_lessequals(X12,X11,tc_fun(X13,tc_bool))
| ~ c_lessequals(X12,c_Set_Oinsert(X10,X11,X13),tc_fun(X13,tc_bool))
| c_in(X10,X12,X13) ),
inference(variable_rename,[status(thm)],[c_0_1458]) ).
fof(c_0_2573,plain,
! [X10,X11,X12,X13] :
( c_lessequals(X12,X11,tc_fun(X13,tc_bool))
| c_in(X10,X12,X13)
| ~ c_lessequals(X12,c_Set_Oinsert(X10,X11,X13),tc_fun(X13,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1459]) ).
fof(c_0_2574,plain,
! [X11,X12,X13] :
( X11 = X12
| ~ c_in(X11,c_Set_Oinsert(X12,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X13),X13) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1460])])]) ).
fof(c_0_2575,plain,
! [X6,X7,X8] : c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),X8,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X7,X8,tc_nat),c_HOL_Otimes__class_Otimes(X6,X8,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1461]) ).
fof(c_0_2576,plain,
! [X6,X7,X8] : c_HOL_Otimes__class_Otimes(X8,c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X8,X7,tc_nat),c_HOL_Otimes__class_Otimes(X8,X6,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1462]) ).
fof(c_0_2577,plain,
! [X6,X7,X8] : c_HOL_Otimes__class_Otimes(X8,c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X7,tc_nat),c_HOL_Otimes__class_Otimes(X8,X6,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1463]) ).
fof(c_0_2578,plain,
! [X6,X7,X8] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),X8,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X8,tc_nat),c_HOL_Otimes__class_Otimes(X6,X8,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1464]) ).
fof(c_0_2579,plain,
! [X6,X7,X8] : c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X6,tc_nat),X7,tc_nat),X6,tc_nat) = c_Divides_Odiv__class_Omod(X7,X6,tc_nat),
inference(variable_rename,[status(thm)],[c_0_1465]) ).
fof(c_0_2580,plain,
! [X6,X7,X8] : c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X7,X6,tc_nat),X8,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X7,X8,tc_nat),c_HOL_Otimes__class_Otimes(X6,X8,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1466]) ).
fof(c_0_2581,plain,
! [X6,X7,X8] : c_HOL_Otimes__class_Otimes(X8,c_Divides_Odiv__class_Omod(X7,X6,tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X8,X7,tc_nat),c_HOL_Otimes__class_Otimes(X8,X6,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1467]) ).
fof(c_0_2582,plain,
! [X10,X11,X12,X13] :
( c_HOL_Oord__class_Oless(X12,c_Set_Oinsert(X10,X11,X13),tc_fun(X13,tc_bool))
| ~ c_lessequals(X12,X11,tc_fun(X13,tc_bool))
| c_in(X10,X12,X13)
| c_in(X10,X11,X13) ),
inference(variable_rename,[status(thm)],[c_0_1468]) ).
fof(c_0_2583,plain,
! [X8,X9,X10] :
( c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X9,X8,tc_fun(X10,tc_bool)),X10) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(X9,X10),c_Finite__Set_Ocard(X8,X10),tc_nat)
| ~ c_lessequals(X8,X9,tc_fun(X10,tc_bool))
| ~ c_Finite__Set_Ofinite(X8,X10) ),
inference(variable_rename,[status(thm)],[c_0_1469]) ).
fof(c_0_2584,plain,
! [X10,X11,X12,X13] :
( hBOOL(hAPP(X12,X11))
| X10 = X11
| ~ hBOOL(hAPP(c_Set_Oinsert(X10,X12,X13),X11)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1470])])]) ).
fof(c_0_2585,plain,
! [X45,X46,X47,X48] :
( c_lessequals(c_Set_Oinsert(X45,X47,X48),c_Set_Oinsert(X45,X46,X48),tc_fun(X48,tc_bool))
| ~ c_lessequals(X47,X46,tc_fun(X48,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1471]) ).
fof(c_0_2586,plain,
! [X12,X13,X14,X15] :
( ~ c_in(X12,X13,X15)
| ~ c_in(X12,c_HOL_Ominus__class_Ominus(X14,X13,tc_fun(X15,tc_bool)),X15) ),
inference(variable_rename,[status(thm)],[c_0_1472]) ).
fof(c_0_2587,plain,
! [X23,X24] :
( ~ c_lessequals(X24,c_HOL_Oplus__class_Oplus(X23,X24,tc_nat),tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X23,X24,tc_nat),X24,tc_nat) = X23 ),
inference(variable_rename,[status(thm)],[c_0_1473]) ).
fof(c_0_2588,plain,
! [X23,X24,X25] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X24,X23,tc_nat),X25,tc_nat)
| ~ c_lessequals(X24,c_HOL_Oplus__class_Oplus(X25,X23,tc_nat),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1474]) ).
fof(c_0_2589,plain,
! [X23,X24,X25] :
( c_lessequals(X24,c_HOL_Oplus__class_Oplus(X25,X23,tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X24,X23,tc_nat),X25,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1475]) ).
fof(c_0_2590,plain,
! [X23,X24,X25] :
( c_HOL_Oord__class_Oless(X25,c_HOL_Ominus__class_Ominus(X24,X23,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X25,X23,tc_nat),X24,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1476]) ).
fof(c_0_2591,plain,
! [X23,X24,X25] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X25,X23,tc_nat),X24,tc_nat)
| ~ c_HOL_Oord__class_Oless(X25,c_HOL_Ominus__class_Ominus(X24,X23,tc_nat),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1477]) ).
fof(c_0_2592,plain,
! [X6,X7,X8,X9] :
( ~ class_Divides_Osemiring__div(X9)
| c_Ring__and__Field_Odvd__class_Odvd(X8,X7,X9)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,c_Divides_Odiv__class_Omod(X7,X6,X9),X9)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X6,X9) ),
inference(variable_rename,[status(thm)],[c_0_1478]) ).
fof(c_0_2593,plain,
! [X6,X7,X8,X9] :
( ~ class_Divides_Osemiring__div(X9)
| c_Ring__and__Field_Odvd__class_Odvd(X8,X7,X9)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X6,X9)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,c_Divides_Odiv__class_Omod(X7,X6,X9),X9) ),
inference(variable_rename,[status(thm)],[c_0_1479]) ).
fof(c_0_2594,plain,
! [X19,X20,X21,X22,X23] :
( ~ class_OrderedGroup_Oab__group__add(X23)
| c_HOL_Oplus__class_Oplus(X21,c_HOL_Oplus__class_Oplus(X20,X19,X23),X23) != c_HOL_Oplus__class_Oplus(X20,X22,X23)
| c_HOL_Oplus__class_Oplus(X21,X19,X23) = X22 ),
inference(variable_rename,[status(thm)],[c_0_1480]) ).
fof(c_0_2595,plain,
! [X23,X24,X25] :
( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X24,X23,tc_nat),X25,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X24,X25,tc_nat),X23,tc_nat)
| ~ c_lessequals(X23,X24,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1481])])]) ).
fof(c_0_2596,plain,
! [X23,X24,X25] :
( c_HOL_Oplus__class_Oplus(X25,c_HOL_Ominus__class_Ominus(X24,X23,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X25,X24,tc_nat),X23,tc_nat)
| ~ c_lessequals(X23,X24,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1482])])]) ).
fof(c_0_2597,plain,
! [X23,X24,X25] :
( c_HOL_Ominus__class_Ominus(X25,c_HOL_Ominus__class_Ominus(X24,X23,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X25,X23,tc_nat),X24,tc_nat)
| ~ c_lessequals(X23,X24,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1483])])]) ).
fof(c_0_2598,plain,
! [X23,X24,X25] :
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X24,X25,tc_nat),X23,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X24,X23,tc_nat),X25,tc_nat)
| ~ c_lessequals(X23,X24,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1484])])]) ).
fof(c_0_2599,plain,
! [X23,X24,X25] :
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X25,X24,tc_nat),X23,tc_nat) = c_HOL_Oplus__class_Oplus(X25,c_HOL_Ominus__class_Ominus(X24,X23,tc_nat),tc_nat)
| ~ c_lessequals(X23,X24,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1485])])]) ).
fof(c_0_2600,plain,
! [X10,X11,X12,X13] :
( c_lessequals(c_Set_Oinsert(X10,X12,X13),X11,tc_fun(X13,tc_bool))
| ~ c_lessequals(X12,X11,tc_fun(X13,tc_bool))
| ~ c_in(X10,X11,X13) ),
inference(variable_rename,[status(thm)],[c_0_1486]) ).
fof(c_0_2601,plain,
! [X10,X11,X12,X13] :
( c_HOL_Oord__class_Oless(X12,c_Set_Oinsert(X10,X11,X13),tc_fun(X13,tc_bool))
| ~ c_in(X10,X11,X13)
| ~ c_HOL_Oord__class_Oless(X12,X11,tc_fun(X13,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1487]) ).
fof(c_0_2602,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X13)
| c_lessequals(X12,c_HOL_Ozero__class_Ozero(X13),X13)
| c_lessequals(c_HOL_Ozero__class_Ozero(X13),X12,X13)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X12,X11,X13),c_HOL_Ozero__class_Ozero(X13),X13) ),
inference(variable_rename,[status(thm)],[c_0_1488]) ).
fof(c_0_2603,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X13)
| c_lessequals(c_HOL_Ozero__class_Ozero(X13),X11,X13)
| c_lessequals(c_HOL_Ozero__class_Ozero(X13),X12,X13)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X12,X11,X13),c_HOL_Ozero__class_Ozero(X13),X13) ),
inference(variable_rename,[status(thm)],[c_0_1489]) ).
fof(c_0_2604,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X13)
| c_lessequals(X12,c_HOL_Ozero__class_Ozero(X13),X13)
| c_lessequals(X11,c_HOL_Ozero__class_Ozero(X13),X13)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X12,X11,X13),c_HOL_Ozero__class_Ozero(X13),X13) ),
inference(variable_rename,[status(thm)],[c_0_1490]) ).
fof(c_0_2605,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X13)
| c_lessequals(c_HOL_Ozero__class_Ozero(X13),X11,X13)
| c_lessequals(X11,c_HOL_Ozero__class_Ozero(X13),X13)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X12,X11,X13),c_HOL_Ozero__class_Ozero(X13),X13) ),
inference(variable_rename,[status(thm)],[c_0_1491]) ).
fof(c_0_2606,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X13)
| c_lessequals(X11,c_HOL_Ozero__class_Ozero(X13),X13)
| c_lessequals(c_HOL_Ozero__class_Ozero(X13),X11,X13)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X13),c_HOL_Otimes__class_Otimes(X12,X11,X13),X13) ),
inference(variable_rename,[status(thm)],[c_0_1492]) ).
fof(c_0_2607,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X13)
| c_lessequals(X12,c_HOL_Ozero__class_Ozero(X13),X13)
| c_lessequals(c_HOL_Ozero__class_Ozero(X13),X11,X13)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X13),c_HOL_Otimes__class_Otimes(X12,X11,X13),X13) ),
inference(variable_rename,[status(thm)],[c_0_1493]) ).
fof(c_0_2608,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X13)
| c_lessequals(X11,c_HOL_Ozero__class_Ozero(X13),X13)
| c_lessequals(c_HOL_Ozero__class_Ozero(X13),X12,X13)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X13),c_HOL_Otimes__class_Otimes(X12,X11,X13),X13) ),
inference(variable_rename,[status(thm)],[c_0_1494]) ).
fof(c_0_2609,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X13)
| c_lessequals(X12,c_HOL_Ozero__class_Ozero(X13),X13)
| c_lessequals(c_HOL_Ozero__class_Ozero(X13),X12,X13)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X13),c_HOL_Otimes__class_Otimes(X12,X11,X13),X13) ),
inference(variable_rename,[status(thm)],[c_0_1495]) ).
fof(c_0_2610,plain,
! [X8,X9,X10] :
( c_HOL_Oord__class_Oless(X9,X8,tc_fun(X10,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(X9,X10),c_Finite__Set_Ocard(X8,X10),tc_nat)
| ~ c_lessequals(X9,X8,tc_fun(X10,tc_bool))
| ~ c_Finite__Set_Ofinite(X8,X10) ),
inference(variable_rename,[status(thm)],[c_0_1496]) ).
fof(c_0_2611,plain,
! [X3,X4] :
( c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,tc_nat))
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1497]) ).
fof(c_0_2612,plain,
! [X12,X13,X14,X15] :
( c_in(X12,X14,X15)
| ~ c_in(X12,c_Lattices_Olower__semilattice__class_Oinf(X14,X13,tc_fun(X15,tc_bool)),X15) ),
inference(variable_rename,[status(thm)],[c_0_1498]) ).
fof(c_0_2613,plain,
! [X12,X13,X14,X15] :
( c_in(X12,X13,X15)
| ~ c_in(X12,c_Lattices_Olower__semilattice__class_Oinf(X14,X13,tc_fun(X15,tc_bool)),X15) ),
inference(variable_rename,[status(thm)],[c_0_1499]) ).
fof(c_0_2614,plain,
! [X12,X13,X14,X15] :
( c_in(X12,X14,X15)
| ~ c_in(X12,c_HOL_Ominus__class_Ominus(X14,X13,tc_fun(X15,tc_bool)),X15) ),
inference(variable_rename,[status(thm)],[c_0_1500]) ).
fof(c_0_2615,plain,
! [X12,X13,X14,X15] :
( c_in(X12,c_Lattices_Olower__semilattice__class_Oinf(X14,X13,tc_fun(X15,tc_bool)),X15)
| ~ c_in(X12,X13,X15)
| ~ c_in(X12,X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_1501]) ).
fof(c_0_2616,plain,
! [X12,X13,X14,X15] :
( c_in(X12,c_Lattices_Olower__semilattice__class_Oinf(X14,X13,tc_fun(X15,tc_bool)),X15)
| ~ c_in(X12,X13,X15)
| ~ c_in(X12,X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_1502]) ).
fof(c_0_2617,plain,
! [X26,X27,X28,X29] :
( c_in(X27,c_Inductive_Ocomplete__lattice__class_Ogfp(X26,tc_fun(X29,tc_bool)),X29)
| ~ c_lessequals(X28,hAPP(X26,X28),tc_fun(X29,tc_bool))
| ~ c_in(X27,X28,X29) ),
inference(variable_rename,[status(thm)],[c_0_1503]) ).
fof(c_0_2618,plain,
! [X3,X4] :
( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X4,X3,tc_nat),tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1504]) ).
fof(c_0_2619,plain,
! [X3,X4] :
( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X4,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1505]) ).
fof(c_0_2620,plain,
! [X6,X7,X8] :
( c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X8),X7,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X8),X6,tc_nat),tc_nat)
| ~ c_lessequals(X7,X6,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1506])])]) ).
fof(c_0_2621,plain,
! [X6,X7,X8] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X8),X7,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X8),X6,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,X6,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1507])])]) ).
fof(c_0_2622,plain,
! [X10,X11,X12,X13] :
( c_lessequals(X12,X11,tc_fun(X13,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X10,X12,X13),X11,tc_fun(X13,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1508]) ).
fof(c_0_2623,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Opordered__ring(X13)
| c_lessequals(c_HOL_Ozero__class_Ozero(X13),c_HOL_Otimes__class_Otimes(X12,X11,X13),X13)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X13),X11,X13)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X13),X12,X13) ),
inference(variable_rename,[status(thm)],[c_0_1509]) ).
fof(c_0_2624,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Opordered__ring(X13)
| c_lessequals(c_HOL_Ozero__class_Ozero(X13),c_HOL_Otimes__class_Otimes(X12,X11,X13),X13)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X13),X13)
| ~ c_lessequals(X12,c_HOL_Ozero__class_Ozero(X13),X13) ),
inference(variable_rename,[status(thm)],[c_0_1510]) ).
fof(c_0_2625,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Opordered__ring(X13)
| c_lessequals(c_HOL_Ozero__class_Ozero(X13),c_HOL_Otimes__class_Otimes(X12,X11,X13),X13)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X13),X13)
| ~ c_lessequals(X12,c_HOL_Ozero__class_Ozero(X13),X13) ),
inference(variable_rename,[status(thm)],[c_0_1511]) ).
fof(c_0_2626,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X13)
| c_lessequals(c_HOL_Ozero__class_Ozero(X13),c_HOL_Otimes__class_Otimes(X12,X11,X13),X13)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X13),X11,X13)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X13),X12,X13) ),
inference(variable_rename,[status(thm)],[c_0_1512]) ).
fof(c_0_2627,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X13)
| c_lessequals(c_HOL_Ozero__class_Ozero(X13),c_HOL_Otimes__class_Otimes(X12,X11,X13),X13)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X13),X13)
| ~ c_lessequals(X12,c_HOL_Ozero__class_Ozero(X13),X13) ),
inference(variable_rename,[status(thm)],[c_0_1513]) ).
fof(c_0_2628,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X13)
| c_lessequals(c_HOL_Ozero__class_Ozero(X13),c_HOL_Otimes__class_Otimes(X12,X11,X13),X13)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X13),X11,X13)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X13),X12,X13) ),
inference(variable_rename,[status(thm)],[c_0_1514]) ).
fof(c_0_2629,plain,
! [X11,X12,X13] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X13)
| c_lessequals(c_HOL_Oplus__class_Oplus(X12,X11,X13),c_HOL_Ozero__class_Ozero(X13),X13)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X13),X13)
| ~ c_lessequals(X12,c_HOL_Ozero__class_Ozero(X13),X13) ),
inference(variable_rename,[status(thm)],[c_0_1515]) ).
fof(c_0_2630,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X13)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X12,X11,X13),c_HOL_Ozero__class_Ozero(X13),X13)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X13),X11,X13)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X13),X13) ),
inference(variable_rename,[status(thm)],[c_0_1516]) ).
fof(c_0_2631,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X13)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X12,X11,X13),c_HOL_Ozero__class_Ozero(X13),X13)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X13),X13)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X13),X12,X13) ),
inference(variable_rename,[status(thm)],[c_0_1517]) ).
fof(c_0_2632,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X13)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X12,X13),c_HOL_Ozero__class_Ozero(X13),X13)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X13),X13)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X13),X12,X13) ),
inference(variable_rename,[status(thm)],[c_0_1518]) ).
fof(c_0_2633,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,X5,X7),X7)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X7),X5,X7)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X7),X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_1519]) ).
fof(c_0_2634,plain,
! [X11,X12,X13] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X13)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X13),c_HOL_Oplus__class_Oplus(X12,X11,X13),X13)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X13),X11,X13)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X13),X12,X13) ),
inference(variable_rename,[status(thm)],[c_0_1520]) ).
fof(c_0_2635,plain,
! [X11,X12,X13] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X13)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X12,X11,X13),c_HOL_Ozero__class_Ozero(X13),X13)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X13),X13)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X13),X13) ),
inference(variable_rename,[status(thm)],[c_0_1521]) ).
fof(c_0_2636,plain,
! [X11,X12,X13] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X13)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X12,X11,X13),c_HOL_Ozero__class_Ozero(X13),X13)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X13),X13)
| ~ c_lessequals(X12,c_HOL_Ozero__class_Ozero(X13),X13) ),
inference(variable_rename,[status(thm)],[c_0_1522]) ).
fof(c_0_2637,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X13)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X13),c_HOL_Otimes__class_Otimes(X12,X11,X13),X13)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X13),X13)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X13),X13) ),
inference(variable_rename,[status(thm)],[c_0_1523]) ).
fof(c_0_2638,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X13)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X13),c_HOL_Otimes__class_Otimes(X12,X11,X13),X13)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X13),X11,X13)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X13),X12,X13) ),
inference(variable_rename,[status(thm)],[c_0_1524]) ).
fof(c_0_2639,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X13)
| c_lessequals(c_HOL_Otimes__class_Otimes(X11,X12,X13),c_HOL_Ozero__class_Ozero(X13),X13)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X13),X13)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X13),X12,X13) ),
inference(variable_rename,[status(thm)],[c_0_1525]) ).
fof(c_0_2640,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X13)
| c_lessequals(c_HOL_Otimes__class_Otimes(X12,X11,X13),c_HOL_Ozero__class_Ozero(X13),X13)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X13),X11,X13)
| ~ c_lessequals(X12,c_HOL_Ozero__class_Ozero(X13),X13) ),
inference(variable_rename,[status(thm)],[c_0_1526]) ).
fof(c_0_2641,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X13)
| c_lessequals(c_HOL_Otimes__class_Otimes(X12,X11,X13),c_HOL_Ozero__class_Ozero(X13),X13)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X13),X13)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X13),X12,X13) ),
inference(variable_rename,[status(thm)],[c_0_1527]) ).
fof(c_0_2642,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X13)
| c_lessequals(c_HOL_Otimes__class_Otimes(X12,X11,X13),c_HOL_Ozero__class_Ozero(X13),X13)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X13),X11,X13)
| ~ c_lessequals(X12,c_HOL_Ozero__class_Ozero(X13),X13) ),
inference(variable_rename,[status(thm)],[c_0_1528]) ).
fof(c_0_2643,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X13)
| c_lessequals(c_HOL_Otimes__class_Otimes(X12,X11,X13),c_HOL_Ozero__class_Ozero(X13),X13)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X13),X13)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X13),X12,X13) ),
inference(variable_rename,[status(thm)],[c_0_1529]) ).
fof(c_0_2644,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X13)
| c_lessequals(c_HOL_Otimes__class_Otimes(X12,X11,X13),c_HOL_Ozero__class_Ozero(X13),X13)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X13),X11,X13)
| ~ c_lessequals(X12,c_HOL_Ozero__class_Ozero(X13),X13) ),
inference(variable_rename,[status(thm)],[c_0_1530]) ).
fof(c_0_2645,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X13)
| c_lessequals(c_HOL_Otimes__class_Otimes(X12,X11,X13),c_HOL_Ozero__class_Ozero(X13),X13)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X13),X13)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X13),X12,X13) ),
inference(variable_rename,[status(thm)],[c_0_1531]) ).
fof(c_0_2646,plain,
! [X11,X12,X13] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X13)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X13),c_HOL_Oplus__class_Oplus(X12,X11,X13),X13)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X13),X11,X13)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X13),X12,X13) ),
inference(variable_rename,[status(thm)],[c_0_1532]) ).
fof(c_0_2647,plain,
! [X11,X12,X13] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X13)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X13),c_HOL_Oplus__class_Oplus(X12,X11,X13),X13)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X13),X11,X13)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X13),X12,X13) ),
inference(variable_rename,[status(thm)],[c_0_1533]) ).
fof(c_0_2648,plain,
! [X11,X12,X13] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X13)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X12,X11,X13),c_HOL_Ozero__class_Ozero(X13),X13)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X13),X13)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X13),X13) ),
inference(variable_rename,[status(thm)],[c_0_1534]) ).
fof(c_0_2649,plain,
! [X11,X12,X13] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X13)
| c_lessequals(c_HOL_Ozero__class_Ozero(X13),c_HOL_Oplus__class_Oplus(X12,X11,X13),X13)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X13),X11,X13)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X13),X12,X13) ),
inference(variable_rename,[status(thm)],[c_0_1535]) ).
fof(c_0_2650,plain,
! [X2] : c_lessequals(X2,c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X2,X2,tc_nat),tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1536]) ).
fof(c_0_2651,plain,
! [X3,X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,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),c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1537])])]) ).
fof(c_0_2652,plain,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1538]) ).
fof(c_0_2653,plain,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1539]) ).
fof(c_0_2654,plain,
! [X12,X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X15)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X12,X14,X15),c_HOL_Oplus__class_Oplus(X12,X13,X15),X15)
| ~ c_HOL_Oord__class_Oless(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_1540]) ).
fof(c_0_2655,plain,
! [X12,X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X15)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X12,X14,X15),c_HOL_Oplus__class_Oplus(X12,X13,X15),X15)
| ~ c_HOL_Oord__class_Oless(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_1541]) ).
fof(c_0_2656,plain,
! [X12,X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X15)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X14,X12,X15),c_HOL_Oplus__class_Oplus(X13,X12,X15),X15)
| ~ c_HOL_Oord__class_Oless(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_1542]) ).
fof(c_0_2657,plain,
! [X12,X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X15)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X14,X12,X15),c_HOL_Oplus__class_Oplus(X13,X12,X15),X15)
| ~ c_HOL_Oord__class_Oless(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_1543]) ).
fof(c_0_2658,plain,
! [X12,X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X15)
| c_lessequals(c_HOL_Oplus__class_Oplus(X14,X12,X15),c_HOL_Oplus__class_Oplus(X13,X12,X15),X15)
| ~ c_lessequals(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_1544]) ).
fof(c_0_2659,plain,
! [X12,X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X15)
| c_lessequals(c_HOL_Oplus__class_Oplus(X12,X14,X15),c_HOL_Oplus__class_Oplus(X12,X13,X15),X15)
| ~ c_lessequals(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_1545]) ).
fof(c_0_2660,plain,
! [X12,X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X15)
| c_lessequals(c_HOL_Oplus__class_Oplus(X14,X12,X15),c_HOL_Oplus__class_Oplus(X13,X12,X15),X15)
| ~ c_lessequals(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_1546]) ).
fof(c_0_2661,plain,
! [X12,X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X15)
| c_lessequals(c_HOL_Oplus__class_Oplus(X12,X14,X15),c_HOL_Oplus__class_Oplus(X12,X13,X15),X15)
| ~ c_lessequals(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_1547]) ).
fof(c_0_2662,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_1548]) ).
fof(c_0_2663,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_1549]) ).
fof(c_0_2664,plain,
! [X10,X11,X12,X13] :
( c_lessequals(X12,c_Set_Oinsert(X10,X11,X13),tc_fun(X13,tc_bool))
| ~ c_lessequals(X12,X11,tc_fun(X13,tc_bool))
| c_in(X10,X12,X13) ),
inference(variable_rename,[status(thm)],[c_0_1550]) ).
fof(c_0_2665,plain,
! [X10,X11,X12,X13] :
( c_lessequals(X12,c_Set_Oinsert(X10,X11,X13),tc_fun(X13,tc_bool))
| ~ c_lessequals(X12,X11,tc_fun(X13,tc_bool))
| c_in(X10,X12,X13) ),
inference(variable_rename,[status(thm)],[c_0_1551]) ).
fof(c_0_2666,plain,
! [X16,X17,X18] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X18,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X16,X17,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X16,tc_nat)
| 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_1552]) ).
fof(c_0_2667,plain,
! [X12,X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X15)
| ~ class_OrderedGroup_Ocomm__monoid__add(X15)
| c_lessequals(X13,c_HOL_Oplus__class_Oplus(X14,X12,X15),X15)
| ~ c_lessequals(X13,X14,X15)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X15),X12,X15) ),
inference(variable_rename,[status(thm)],[c_0_1553]) ).
fof(c_0_2668,plain,
! [X12,X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X15)
| ~ class_OrderedGroup_Ocomm__monoid__add(X15)
| c_lessequals(X13,c_HOL_Oplus__class_Oplus(X14,X12,X15),X15)
| ~ c_lessequals(X13,X12,X15)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X15),X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_1554]) ).
fof(c_0_2669,plain,
! [X12,X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X15)
| ~ class_OrderedGroup_Ocomm__monoid__add(X15)
| c_HOL_Oord__class_Oless(X13,c_HOL_Oplus__class_Oplus(X14,X12,X15),X15)
| ~ c_lessequals(X13,X12,X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X15),X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_1555]) ).
fof(c_0_2670,plain,
! [X12,X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X15)
| ~ class_OrderedGroup_Ocomm__monoid__add(X15)
| c_HOL_Oord__class_Oless(X13,c_HOL_Oplus__class_Oplus(X14,X12,X15),X15)
| ~ c_HOL_Oord__class_Oless(X13,X12,X15)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X15),X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_1556]) ).
fof(c_0_2671,plain,
! [X6,X7] :
( c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Otimes__class_Otimes(X7,X6,tc_nat)),X7,tc_nat) = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X7,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1557]) ).
fof(c_0_2672,plain,
! [X49,X50,X51] :
( hBOOL(hAPP(X51,X50))
| ~ hBOOL(hAPP(X51,c_Suc(c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1(X51,X49))))
| ~ c_lessequals(c_Suc(X49),X50,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1558]) ).
fof(c_0_2673,plain,
! [X27,X28,X29] :
( hBOOL(hAPP(X29,c_HOL_Ominus__class_Ominus(X27,X28,tc_nat)))
| hBOOL(hAPP(X29,c_Suc(c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1(X29))))
| ~ hBOOL(hAPP(X29,X27)) ),
inference(variable_rename,[status(thm)],[c_0_1559]) ).
fof(c_0_2674,plain,
! [X27,X28,X29] :
( hBOOL(hAPP(X29,c_HOL_Ominus__class_Ominus(X27,X28,tc_nat)))
| ~ hBOOL(hAPP(X29,c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1(X29)))
| ~ hBOOL(hAPP(X29,X27)) ),
inference(variable_rename,[status(thm)],[c_0_1560]) ).
fof(c_0_2675,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X15)
| c_HOL_Oord__class_Oless(X13,c_HOL_Oplus__class_Oplus(X14,X12,X15),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_1561]) ).
fof(c_0_2676,plain,
! [X12,X13,X14,X15] :
( c_in(X12,c_HOL_Ominus__class_Ominus(X14,X13,tc_fun(X15,tc_bool)),X15)
| c_in(X12,X13,X15)
| ~ c_in(X12,X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_1562]) ).
fof(c_0_2677,plain,
! [X12,X13,X14,X15] :
( c_in(X12,c_HOL_Ominus__class_Ominus(X14,X13,tc_fun(X15,tc_bool)),X15)
| c_in(X12,X13,X15)
| ~ c_in(X12,X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_1563]) ).
fof(c_0_2678,plain,
! [X10,X11,X12,X13] :
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X10,X12,X13),X11,tc_fun(X13,tc_bool)) = c_HOL_Ominus__class_Ominus(X12,X11,tc_fun(X13,tc_bool))
| ~ c_in(X10,X11,X13) ),
inference(variable_rename,[status(thm)],[c_0_1564]) ).
fof(c_0_2679,plain,
! [X10,X11,X12,X13] :
( c_in(X10,X11,X13)
| ~ c_lessequals(c_Set_Oinsert(X10,X12,X13),X11,tc_fun(X13,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1565]) ).
fof(c_0_2680,plain,
! [X25,X26,X27] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X26,X27,tc_nat),c_HOL_Ominus__class_Ominus(X25,X27,tc_nat),tc_nat)
| ~ c_lessequals(X26,X25,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1566])])]) ).
fof(c_0_2681,plain,
! [X25,X26,X27] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X27,X25,tc_nat),c_HOL_Ominus__class_Ominus(X27,X26,tc_nat),tc_nat)
| ~ c_lessequals(X26,X25,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1567])])]) ).
fof(c_0_2682,plain,
! [X23,X24,X25] :
( c_lessequals(c_HOL_Oplus__class_Oplus(X25,X23,tc_nat),c_HOL_Oplus__class_Oplus(X24,X23,tc_nat),tc_nat)
| ~ c_lessequals(X25,X24,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1568]) ).
fof(c_0_2683,plain,
! [X6,X7,X8] :
( c_lessequals(c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),c_HOL_Oplus__class_Oplus(X8,X6,tc_nat),tc_nat)
| ~ c_lessequals(X7,X6,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1569])])]) ).
fof(c_0_2684,plain,
! [X23,X24,X25] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X25,X23,tc_nat),c_HOL_Otimes__class_Otimes(X24,X23,tc_nat),tc_nat)
| ~ c_lessequals(X25,X24,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1570]) ).
fof(c_0_2685,plain,
! [X23,X24,X25] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X23,X25,tc_nat),c_HOL_Otimes__class_Otimes(X23,X24,tc_nat),tc_nat)
| ~ c_lessequals(X25,X24,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1571]) ).
fof(c_0_2686,plain,
! [X6,X7,X8] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X8,X7,tc_nat),c_HOL_Otimes__class_Otimes(X8,X6,tc_nat),tc_nat)
| ~ c_lessequals(X7,X6,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1572])])]) ).
fof(c_0_2687,plain,
! [X6,X7,X8] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X7,X8,tc_nat),c_HOL_Otimes__class_Otimes(X6,X8,tc_nat),tc_nat)
| ~ c_lessequals(X7,X6,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1573])])]) ).
fof(c_0_2688,plain,
! [X6,X7,X8] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),c_HOL_Oplus__class_Oplus(X8,X6,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,X6,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1574])])]) ).
fof(c_0_2689,plain,
! [X23,X24,X25] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X25,X23,tc_nat),c_HOL_Oplus__class_Oplus(X24,X23,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X25,X24,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1575]) ).
fof(c_0_2690,plain,
! [X6,X7,X8] :
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X8,X7,tc_nat),c_HOL_Otimes__class_Otimes(X8,X6,tc_nat),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1576])])]) ).
fof(c_0_2691,plain,
! [X5,X6,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X7)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X6,X5,X7),X7) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X6,c_HOL_Oone__class_Oone(X7),X7),X5,X7) ),
inference(variable_rename,[status(thm)],[c_0_1577]) ).
fof(c_0_2692,plain,
! [X5,X6,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X7)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X6,X5,X7),X5,X7) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X6,c_HOL_Oone__class_Oone(X7),X7),X5,X7) ),
inference(variable_rename,[status(thm)],[c_0_1578]) ).
fof(c_0_2693,plain,
! [X10,X11,X12] :
( c_lessequals(c_Finite__Set_Ocard(X11,X12),c_Finite__Set_Ocard(c_Set_Oinsert(X10,X11,X12),X12),tc_nat)
| ~ c_Finite__Set_Ofinite(X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1579]) ).
fof(c_0_2694,plain,
! [X16,X17,X18,X19] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X19)
| c_Ring__and__Field_Odvd__class_Odvd(X18,c_HOL_Ominus__class_Ominus(X17,X16,X19),X19)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X16,X19)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_1580]) ).
fof(c_0_2695,plain,
! [X16,X17,X18,X19] :
( ~ class_Lattices_Olower__semilattice(X19)
| c_lessequals(X18,c_Lattices_Olower__semilattice__class_Oinf(X17,X16,X19),X19)
| ~ c_lessequals(X18,X16,X19)
| ~ c_lessequals(X18,X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_1581]) ).
fof(c_0_2696,plain,
! [X16,X17,X18,X19] :
( ~ class_Lattices_Olower__semilattice(X19)
| c_lessequals(X18,c_Lattices_Olower__semilattice__class_Oinf(X17,X16,X19),X19)
| ~ c_lessequals(X18,X16,X19)
| ~ c_lessequals(X18,X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_1582]) ).
fof(c_0_2697,plain,
! [X11,X12,X13,X14] :
( ~ class_Lattices_Olower__semilattice(X14)
| c_lessequals(X11,c_Lattices_Olower__semilattice__class_Oinf(X13,X12,X14),X14)
| ~ c_lessequals(X11,X12,X14)
| ~ c_lessequals(X11,X13,X14) ),
inference(variable_rename,[status(thm)],[c_0_1583]) ).
fof(c_0_2698,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X15)
| c_Ring__and__Field_Odvd__class_Odvd(X14,c_HOL_Oplus__class_Oplus(X13,X12,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_1584]) ).
fof(c_0_2699,plain,
! [X6,X7,X8,X9] :
( ~ class_Divides_Osemiring__div(X9)
| c_Ring__and__Field_Odvd__class_Odvd(X8,c_Divides_Odiv__class_Omod(X7,X6,X9),X9)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X6,X9)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X7,X9) ),
inference(variable_rename,[status(thm)],[c_0_1585]) ).
fof(c_0_2700,plain,
! [X6,X7,X8,X9] :
( ~ class_Divides_Osemiring__div(X9)
| c_Ring__and__Field_Odvd__class_Odvd(X8,c_Divides_Odiv__class_Omod(X7,X6,X9),X9)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X7,X9)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X6,X9) ),
inference(variable_rename,[status(thm)],[c_0_1586]) ).
fof(c_0_2701,plain,
! [X3,X4] :
( X3 = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1587])])]) ).
fof(c_0_2702,plain,
! [X3,X4] :
( X3 = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X3,tc_nat),X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1588])])]) ).
fof(c_0_2703,plain,
! [X3,X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X4,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1589]) ).
fof(c_0_2704,plain,
! [X10,X11,X12,X13] :
( ~ c_in(X10,X11,X13)
| ~ c_in(X10,X12,X13)
| c_Lattices_Olower__semilattice__class_Oinf(X12,X11,tc_fun(X13,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1590]) ).
fof(c_0_2705,plain,
! [X6,X7,X8] :
( c_HOL_Ominus__class_Ominus(X7,X8,tc_nat) != c_HOL_Ominus__class_Ominus(X6,X8,tc_nat)
| ~ c_lessequals(X8,X6,tc_nat)
| ~ c_lessequals(X8,X7,tc_nat)
| X7 = X6 ),
inference(variable_rename,[status(thm)],[c_0_1591]) ).
fof(c_0_2706,plain,
! [X11,X12,X13] :
( c_Set_Oinsert(X12,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X13) != c_Set_Oinsert(X11,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X13)
| X12 = X11 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1592])])]) ).
fof(c_0_2707,plain,
! [X3,X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),X4,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),X3,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1593]) ).
fof(c_0_2708,plain,
! [X5,X6] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X6)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X5,X5,X6),c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1594]) ).
fof(c_0_2709,plain,
! [X5,X6] :
( ~ class_OrderedGroup_Olordered__ab__group__add(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_Oplus__class_Oplus(X5,X5,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1595]) ).
fof(c_0_2710,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Oordered__idom(X6)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X5,X6),c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1596]) ).
fof(c_0_2711,plain,
! [X5,X6] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X6)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X5,X6),c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1597]) ).
fof(c_0_2712,plain,
! [X5,X6] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X6)
| c_lessequals(c_HOL_Ozero__class_Ozero(X6),X5,X6)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),c_HOL_Oplus__class_Oplus(X5,X5,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1598]) ).
fof(c_0_2713,plain,
! [X6,X7,X8] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X7),X6,tc_nat),c_Suc(X8),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),X8,tc_nat),
inference(variable_rename,[status(thm)],[c_0_1599]) ).
fof(c_0_2714,plain,
! [X3,X4] :
( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X4,X3,tc_nat),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1600]) ).
fof(c_0_2715,plain,
! [X3,X4] :
( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X4,X3,tc_nat),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1601])])]) ).
fof(c_0_2716,plain,
! [X16,X17,X18,X19] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X19)
| c_HOL_Otimes__class_Otimes(X18,c_HOL_Otimes__class_Otimes(X17,X16,X19),X19) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X18,X17,X19),X16,X19) ),
inference(variable_rename,[status(thm)],[c_0_1602]) ).
fof(c_0_2717,plain,
! [X34,X35,X36,X37] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X37)
| c_HOL_Otimes__class_Otimes(X36,c_HOL_Otimes__class_Otimes(X35,X34,X37),X37) = c_HOL_Otimes__class_Otimes(X35,c_HOL_Otimes__class_Otimes(X36,X34,X37),X37) ),
inference(variable_rename,[status(thm)],[c_0_1603]) ).
fof(c_0_2718,plain,
! [X34,X35,X36,X37] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X37)
| c_HOL_Otimes__class_Otimes(X36,c_HOL_Otimes__class_Otimes(X35,X34,X37),X37) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X36,X35,X37),X34,X37) ),
inference(variable_rename,[status(thm)],[c_0_1604]) ).
fof(c_0_2719,plain,
! [X34,X35,X36,X37] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X37)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X36,X35,X37),X34,X37) = c_HOL_Otimes__class_Otimes(X36,c_HOL_Otimes__class_Otimes(X35,X34,X37),X37) ),
inference(variable_rename,[status(thm)],[c_0_1605]) ).
fof(c_0_2720,plain,
! [X34,X35,X36,X37] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X37)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X36,X35,X37),X34,X37) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X36,X34,X37),X35,X37) ),
inference(variable_rename,[status(thm)],[c_0_1606]) ).
fof(c_0_2721,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_1607]) ).
fof(c_0_2722,plain,
! [X16,X17,X18,X19] :
( ~ class_Lattices_Olower__semilattice(X19)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X18,X17,X19),X16,X19) = c_Lattices_Olower__semilattice__class_Oinf(X18,c_Lattices_Olower__semilattice__class_Oinf(X17,X16,X19),X19) ),
inference(variable_rename,[status(thm)],[c_0_1608]) ).
fof(c_0_2723,plain,
! [X16,X17,X18,X19] :
( ~ class_Lattices_Olower__semilattice(X19)
| c_Lattices_Olower__semilattice__class_Oinf(X18,c_Lattices_Olower__semilattice__class_Oinf(X17,X16,X19),X19) = c_Lattices_Olower__semilattice__class_Oinf(X17,c_Lattices_Olower__semilattice__class_Oinf(X18,X16,X19),X19) ),
inference(variable_rename,[status(thm)],[c_0_1609]) ).
fof(c_0_2724,plain,
! [X16,X17,X18,X19] :
( ~ class_Lattices_Olattice(X19)
| c_Lattices_Olower__semilattice__class_Oinf(X18,c_Lattices_Olower__semilattice__class_Oinf(X17,X16,X19),X19) = c_Lattices_Olower__semilattice__class_Oinf(X17,c_Lattices_Olower__semilattice__class_Oinf(X18,X16,X19),X19) ),
inference(variable_rename,[status(thm)],[c_0_1610]) ).
fof(c_0_2725,plain,
! [X16,X17,X18,X19] :
( ~ class_Lattices_Olattice(X19)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X18,X17,X19),X16,X19) = c_Lattices_Olower__semilattice__class_Oinf(X18,c_Lattices_Olower__semilattice__class_Oinf(X17,X16,X19),X19) ),
inference(variable_rename,[status(thm)],[c_0_1611]) ).
fof(c_0_2726,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X15)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X14,X13,X15),X12,X15) = c_HOL_Oplus__class_Oplus(X14,c_HOL_Oplus__class_Oplus(X13,X12,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_1612]) ).
fof(c_0_2727,plain,
! [X18,X19,X20,X21] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X21)
| c_HOL_Oplus__class_Oplus(X20,c_HOL_Oplus__class_Oplus(X19,X18,X21),X21) = c_HOL_Oplus__class_Oplus(X19,c_HOL_Oplus__class_Oplus(X20,X18,X21),X21) ),
inference(variable_rename,[status(thm)],[c_0_1613]) ).
fof(c_0_2728,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X15)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X14,X13,X15),X12,X15) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X14,X12,X15),X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_1614]) ).
fof(c_0_2729,plain,
! [X18,X19,X20,X21] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X21)
| c_HOL_Oplus__class_Oplus(X20,c_HOL_Oplus__class_Oplus(X19,X18,X21),X21) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X20,X19,X21),X18,X21) ),
inference(variable_rename,[status(thm)],[c_0_1615]) ).
fof(c_0_2730,plain,
! [X12,X13,X14,X15] :
( ~ class_OrderedGroup_Oab__semigroup__add(X15)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X14,X13,X15),X12,X15) = c_HOL_Oplus__class_Oplus(X14,c_HOL_Oplus__class_Oplus(X13,X12,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_1616]) ).
fof(c_0_2731,plain,
! [X12,X13,X14,X15] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X15)
| c_HOL_Oplus__class_Oplus(X14,c_HOL_Oplus__class_Oplus(X13,X12,X15),X15) = c_HOL_Oplus__class_Oplus(X13,c_HOL_Oplus__class_Oplus(X14,X12,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_1617]) ).
fof(c_0_2732,plain,
! [X12,X13,X14,X15] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X15)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X14,X13,X15),X12,X15) = c_HOL_Oplus__class_Oplus(X14,c_HOL_Oplus__class_Oplus(X13,X12,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_1618]) ).
fof(c_0_2733,plain,
! [X16,X17,X18,X19] :
( ~ class_OrderedGroup_Oab__group__add(X19)
| c_HOL_Oplus__class_Oplus(X18,c_HOL_Oplus__class_Oplus(X17,X16,X19),X19) = c_HOL_Oplus__class_Oplus(X17,c_HOL_Oplus__class_Oplus(X18,X16,X19),X19) ),
inference(variable_rename,[status(thm)],[c_0_1619]) ).
fof(c_0_2734,plain,
! [X16,X17,X18,X19] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X19)
| c_HOL_Oplus__class_Oplus(X18,c_HOL_Oplus__class_Oplus(X17,X16,X19),X19) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X18,X17,X19),X16,X19) ),
inference(variable_rename,[status(thm)],[c_0_1620]) ).
fof(c_0_2735,plain,
! [X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),c_HOL_Ozero__class_Ozero(X5),X5),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),c_HOL_Ozero__class_Ozero(X5),X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1621]) ).
fof(c_0_2736,plain,
! [X16,X17,X18] :
( c_Ring__and__Field_Odvd__class_Odvd(X18,X16,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X16,X17,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X16,tc_nat)
| 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_1622]) ).
fof(c_0_2737,plain,
! [X21,X22,X23] : c_Orderings_Obot__class_Obot(tc_fun(X23,tc_bool)) = c_Set_Oimage(X21,c_Orderings_Obot__class_Obot(tc_fun(X22,tc_bool)),X22,X23),
inference(variable_rename,[status(thm)],[c_0_1623]) ).
fof(c_0_2738,plain,
! [X21,X22,X23] : c_Set_Oimage(X21,c_Orderings_Obot__class_Obot(tc_fun(X22,tc_bool)),X22,X23) = c_Orderings_Obot__class_Obot(tc_fun(X23,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1624]) ).
fof(c_0_2739,plain,
! [X21,X22,X23] : c_Set_Ovimage(X21,c_Orderings_Obot__class_Obot(tc_fun(X22,tc_bool)),X23,X22) = c_Orderings_Obot__class_Obot(tc_fun(X23,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1625]) ).
fof(c_0_2740,plain,
! [X21,X22,X23] : c_Set_Ovimage(X21,c_Orderings_Otop__class_Otop(tc_fun(X22,tc_bool)),X23,X22) = c_Orderings_Otop__class_Otop(tc_fun(X23,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1626]) ).
fof(c_0_2741,plain,
! [X11,X12,X13] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X13)
| c_lessequals(X12,X11,X13)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X12,X11,X13),c_HOL_Ozero__class_Ozero(X13),X13) ),
inference(variable_rename,[status(thm)],[c_0_1627]) ).
fof(c_0_2742,plain,
! [X11,X12,X13] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X13)
| c_HOL_Oord__class_Oless(X12,X11,X13)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X12,X11,X13),c_HOL_Ozero__class_Ozero(X13),X13) ),
inference(variable_rename,[status(thm)],[c_0_1628]) ).
fof(c_0_2743,plain,
! [X3,X4] : c_Divides_Odiv__class_Omod(c_Suc(X4),X3,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(X4,X3,tc_nat)),X3,tc_nat),
inference(variable_rename,[status(thm)],[c_0_1629]) ).
fof(c_0_2744,plain,
! [X6,X7,X8] :
( c_Ring__and__Field_Odvd__class_Odvd(X8,c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X6,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X7,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1630]) ).
fof(c_0_2745,plain,
! [X10,X11,X12,X13] : c_Set_Oinsert(X11,c_Set_Oinsert(X10,X12,X13),X13) = c_Set_Oinsert(X10,c_Set_Oinsert(X11,X12,X13),X13),
inference(variable_rename,[status(thm)],[c_0_1631]) ).
fof(c_0_2746,plain,
! [X17,X18,X19,X20] :
( c_lessequals(X19,X17,tc_fun(X20,tc_bool))
| ~ c_lessequals(X18,X17,tc_fun(X20,tc_bool))
| ~ c_lessequals(X19,X18,tc_fun(X20,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1632]) ).
fof(c_0_2747,plain,
! [X17,X18,X19,X20] :
( c_HOL_Oord__class_Oless(X19,X17,tc_fun(X20,tc_bool))
| ~ c_lessequals(X18,X17,tc_fun(X20,tc_bool))
| ~ c_HOL_Oord__class_Oless(X19,X18,tc_fun(X20,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1633]) ).
fof(c_0_2748,plain,
! [X17,X18,X19,X20] :
( c_HOL_Oord__class_Oless(X19,X17,tc_fun(X20,tc_bool))
| ~ c_HOL_Oord__class_Oless(X18,X17,tc_fun(X20,tc_bool))
| ~ c_lessequals(X19,X18,tc_fun(X20,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1634]) ).
fof(c_0_2749,plain,
! [X17,X18,X19,X20] :
( c_HOL_Oord__class_Oless(X19,X17,tc_fun(X20,tc_bool))
| ~ c_HOL_Oord__class_Oless(X18,X17,tc_fun(X20,tc_bool))
| ~ c_HOL_Oord__class_Oless(X19,X18,tc_fun(X20,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1635]) ).
fof(c_0_2750,plain,
! [X40,X41,X42,X43,X44] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X44)
| c_HOL_Ominus__class_Ominus(X43,X41,X44) != c_HOL_Ominus__class_Ominus(X42,X40,X44)
| c_lessequals(X40,X42,X44)
| ~ c_lessequals(X41,X43,X44) ),
inference(variable_rename,[status(thm)],[c_0_1636]) ).
fof(c_0_2751,plain,
! [X40,X41,X42,X43,X44] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X44)
| c_HOL_Ominus__class_Ominus(X43,X41,X44) != c_HOL_Ominus__class_Ominus(X42,X40,X44)
| c_lessequals(X41,X43,X44)
| ~ c_lessequals(X40,X42,X44) ),
inference(variable_rename,[status(thm)],[c_0_1637]) ).
fof(c_0_2752,plain,
! [X40,X41,X42,X43,X44] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X44)
| c_HOL_Ominus__class_Ominus(X43,X41,X44) != c_HOL_Ominus__class_Ominus(X42,X40,X44)
| c_HOL_Oord__class_Oless(X42,X40,X44)
| ~ c_HOL_Oord__class_Oless(X43,X41,X44) ),
inference(variable_rename,[status(thm)],[c_0_1638]) ).
fof(c_0_2753,plain,
! [X40,X41,X42,X43,X44] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X44)
| c_HOL_Ominus__class_Ominus(X43,X41,X44) != c_HOL_Ominus__class_Ominus(X42,X40,X44)
| c_HOL_Oord__class_Oless(X43,X41,X44)
| ~ c_HOL_Oord__class_Oless(X42,X40,X44) ),
inference(variable_rename,[status(thm)],[c_0_1639]) ).
fof(c_0_2754,plain,
! [X6,X7,X8] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X8,X7,tc_nat),c_HOL_Otimes__class_Otimes(X8,X6,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1640]) ).
fof(c_0_2755,plain,
! [X6,X7,X8] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X7,X8,tc_nat),c_HOL_Otimes__class_Otimes(X6,X8,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1641]) ).
fof(c_0_2756,plain,
! [X8,X9,X10,X11] :
( c_Lattices_Olower__semilattice__class_Oinf(X10,c_Set_Oinsert(X8,X9,X11),tc_fun(X11,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X10,X9,tc_fun(X11,tc_bool))
| c_in(X8,X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_1642]) ).
fof(c_0_2757,plain,
! [X17,X18,X19,X20] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X17,X19,X20),X18,tc_fun(X20,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X19,X18,tc_fun(X20,tc_bool))
| c_in(X17,X18,X20) ),
inference(variable_rename,[status(thm)],[c_0_1643]) ).
fof(c_0_2758,plain,
! [X16,X17,X18,X19] :
( ~ class_Lattices_Olower__semilattice(X19)
| c_lessequals(X18,X16,X19)
| ~ c_lessequals(X18,c_Lattices_Olower__semilattice__class_Oinf(X17,X16,X19),X19) ),
inference(variable_rename,[status(thm)],[c_0_1644]) ).
fof(c_0_2759,plain,
! [X16,X17,X18,X19] :
( ~ class_Lattices_Olower__semilattice(X19)
| c_lessequals(X18,X17,X19)
| ~ c_lessequals(X18,c_Lattices_Olower__semilattice__class_Oinf(X17,X16,X19),X19) ),
inference(variable_rename,[status(thm)],[c_0_1645]) ).
fof(c_0_2760,plain,
! [X11,X12,X13,X14] :
( ~ class_Lattices_Olower__semilattice(X14)
| c_lessequals(X11,X12,X14)
| ~ c_lessequals(X11,c_Lattices_Olower__semilattice__class_Oinf(X13,X12,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_1646]) ).
fof(c_0_2761,plain,
! [X11,X12,X13,X14] :
( ~ class_Lattices_Olower__semilattice(X14)
| c_lessequals(X11,X13,X14)
| ~ c_lessequals(X11,c_Lattices_Olower__semilattice__class_Oinf(X13,X12,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_1647]) ).
fof(c_0_2762,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_1648]) ).
fof(c_0_2763,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_1649]) ).
fof(c_0_2764,plain,
! [X5,X6,X7] :
( ~ class_Ring__and__Field_Oring__1(X7)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(X6,X5,tc_nat),X7) = c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(X6,X7),c_Nat_Osemiring__1__class_Oof__nat(X5,X7),X7)
| ~ c_lessequals(X5,X6,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1650]) ).
fof(c_0_2765,plain,
! [X23,X24,X25] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X25,X24,tc_nat),X23,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X25,X23,tc_nat),X24,tc_nat),
inference(variable_rename,[status(thm)],[c_0_1651]) ).
fof(c_0_2766,plain,
! [X6,X7,X8] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),c_HOL_Oplus__class_Oplus(X8,X6,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),
inference(variable_rename,[status(thm)],[c_0_1652]) ).
fof(c_0_2767,plain,
! [X6,X7,X8] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X7,X8,tc_nat),c_HOL_Oplus__class_Oplus(X6,X8,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),
inference(variable_rename,[status(thm)],[c_0_1653]) ).
fof(c_0_2768,plain,
! [X23,X24,X25] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X25,X24,tc_nat),X23,tc_nat) = c_HOL_Ominus__class_Ominus(X25,c_HOL_Oplus__class_Oplus(X24,X23,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1654]) ).
fof(c_0_2769,plain,
! [X6,X7,X8] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),X8,tc_nat) = c_HOL_Otimes__class_Otimes(X7,c_HOL_Otimes__class_Otimes(X6,X8,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1655]) ).
fof(c_0_2770,plain,
! [X6,X7,X8] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),X8,tc_nat) = c_HOL_Oplus__class_Oplus(X7,c_HOL_Oplus__class_Oplus(X6,X8,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1656]) ).
fof(c_0_2771,plain,
! [X16,X17,X18] : c_HOL_Oplus__class_Oplus(X18,c_HOL_Oplus__class_Oplus(X17,X16,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X17,c_HOL_Oplus__class_Oplus(X18,X16,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1657]) ).
fof(c_0_2772,plain,
! [X8,X9,X10] :
( X9 = X8
| ~ c_lessequals(c_Finite__Set_Ocard(X8,X10),c_Finite__Set_Ocard(X9,X10),tc_nat)
| ~ c_lessequals(X9,X8,tc_fun(X10,tc_bool))
| ~ c_Finite__Set_Ofinite(X8,X10) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1658])])]) ).
fof(c_0_2773,plain,
! [X11,X12,X13,X14] :
( c_in(X12,X13,X14)
| X12 = X11
| ~ c_in(X12,c_Set_Oinsert(X11,X13,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_1659]) ).
fof(c_0_2774,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_1660]) ).
fof(c_0_2775,plain,
! [X27,X28,X29] :
( hBOOL(hAPP(X29,X28))
| hBOOL(hAPP(X29,c_Suc(c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X29,X27))))
| ~ hBOOL(hAPP(X29,X27))
| ~ c_lessequals(X28,X27,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1661]) ).
fof(c_0_2776,plain,
! [X3,X4] :
( 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(X4,X3,tc_nat),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1662]) ).
fof(c_0_2777,plain,
! [X3,X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X4,X3,tc_nat),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1663])])]) ).
fof(c_0_2778,plain,
! [X8,X9,X10] : c_Lattices_Olower__semilattice__class_Oinf(X9,c_Lattices_Olower__semilattice__class_Oinf(X9,X8,tc_fun(X10,tc_bool)),tc_fun(X10,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X9,X8,tc_fun(X10,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1664]) ).
fof(c_0_2779,plain,
! [X8,X9,X10] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X9,X8,tc_fun(X10,tc_bool)),X8,tc_fun(X10,tc_bool)) = c_HOL_Ominus__class_Ominus(X9,X8,tc_fun(X10,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1665]) ).
fof(c_0_2780,plain,
! [X11,X12,X13,X14] :
( c_lessequals(X13,c_Set_Oinsert(X11,X12,X14),tc_fun(X14,tc_bool))
| ~ c_lessequals(X13,X12,tc_fun(X14,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1666]) ).
fof(c_0_2781,plain,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1667]) ).
fof(c_0_2782,plain,
! [X16,X17,X18] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X18,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X16,X17,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X16,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X17,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1668]) ).
fof(c_0_2783,plain,
! [X16,X17,X18] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X18,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X16,tc_nat)
| 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_1669]) ).
fof(c_0_2784,plain,
! [X25,X26,X27,X28] :
( c_HOL_Oplus__class_Oplus(X26,X27,tc_nat) != c_HOL_Oplus__class_Oplus(X28,X25,tc_nat)
| ~ c_HOL_Oord__class_Oless(X28,X27,tc_nat)
| c_HOL_Oord__class_Oless(X26,X25,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1670]) ).
fof(c_0_2785,plain,
! [X6,X7,X8] :
( c_lessequals(X7,X6,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X7,X8,tc_nat),X6,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1671])])]) ).
fof(c_0_2786,plain,
! [X6,X7,X8] :
( c_lessequals(X8,X6,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X7,X8,tc_nat),X6,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1672]) ).
fof(c_0_2787,plain,
! [X6,X7] :
( c_Ring__and__Field_Odvd__class_Odvd(X7,X6,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X7,c_HOL_Oplus__class_Oplus(X6,X7,tc_nat),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1673]) ).
fof(c_0_2788,plain,
! [X23,X24,X25] :
( c_HOL_Oord__class_Oless(X25,X23,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X25,X24,tc_nat),X23,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1674]) ).
fof(c_0_2789,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Oidom(X13)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X13),X12,X13),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X13),X11,X13),X13) ),
inference(variable_rename,[status(thm)],[c_0_1675]) ).
fof(c_0_2790,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Oidom(X13)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X12,c_HOL_Ozero__class_Ozero(X13),X13),c_HOL_Otimes__class_Otimes(X11,c_HOL_Ozero__class_Ozero(X13),X13),X13) ),
inference(variable_rename,[status(thm)],[c_0_1676]) ).
fof(c_0_2791,plain,
! [X8,X9,X10] :
( c_Finite__Set_Ofinite(X9,X10)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X9,X8,tc_fun(X10,tc_bool)),X10)
| ~ c_Finite__Set_Ofinite(X8,X10) ),
inference(variable_rename,[status(thm)],[c_0_1677]) ).
fof(c_0_2792,plain,
! [X21,X22,X23] : c_Fun_Oinj__on(X21,c_Orderings_Obot__class_Obot(tc_fun(X23,tc_bool)),X23,X22),
inference(variable_rename,[status(thm)],[c_0_1678]) ).
fof(c_0_2793,plain,
! [X27,X28] :
( ~ hBOOL(hAPP(X28,X27))
| hBOOL(hAPP(X28,c_Divides_Odiv__class_Omod(X27,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
inference(variable_rename,[status(thm)],[c_0_1679]) ).
fof(c_0_2794,plain,
! [X10,X11,X12] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X12)
| c_HOL_Oplus__class_Oplus(X11,X10,X12) != c_HOL_Ozero__class_Ozero(X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X10,X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X11,X12)
| X11 = c_HOL_Ozero__class_Ozero(X12) ),
inference(variable_rename,[status(thm)],[c_0_1680]) ).
fof(c_0_2795,plain,
! [X10,X11,X12] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X12)
| c_HOL_Oplus__class_Oplus(X11,X10,X12) != c_HOL_Ozero__class_Ozero(X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X10,X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X11,X12)
| X10 = c_HOL_Ozero__class_Ozero(X12) ),
inference(variable_rename,[status(thm)],[c_0_1681]) ).
fof(c_0_2796,plain,
! [X43,X44,X45,X46] :
( ~ class_HOL_Oord(X45)
| c_HOL_Oord__class_Oless(X44,X43,tc_fun(X46,X45))
| c_lessequals(X43,X44,tc_fun(X46,X45))
| ~ c_lessequals(X44,X43,tc_fun(X46,X45)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1682])])]) ).
fof(c_0_2797,plain,
! [X3,X4] :
( c_Divides_Odiv__class_Omod(X4,X3,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),X3,tc_nat)
| ~ c_lessequals(X3,X4,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1683]) ).
fof(c_0_2798,plain,
! [X5] : ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1684]) ).
fof(c_0_2799,plain,
! [X10,X11,X12,X13] :
( hBOOL(hAPP(c_Set_Oinsert(X10,X12,X13),X11))
| ~ hBOOL(hAPP(X12,X11)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1685])])]) ).
fof(c_0_2800,plain,
! [X27,X28,X29] :
( hBOOL(hAPP(X29,X28))
| ~ hBOOL(hAPP(X29,c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X29,X27)))
| ~ hBOOL(hAPP(X29,X27))
| ~ c_lessequals(X28,X27,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1686]) ).
fof(c_0_2801,plain,
! [X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5),tc_nat)
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5) ),
inference(variable_rename,[status(thm)],[c_0_1687]) ).
fof(c_0_2802,plain,
! [X5] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X5)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X5),c_HOL_Ozero__class_Ozero(X5),X5)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X5),c_HOL_Ozero__class_Ozero(X5),X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X5),c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1688]) ).
fof(c_0_2803,plain,
! [X47,X48,X49] :
( ~ class_Orderings_Olinorder(X49)
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X47,X49),c_Finite__Set_Olinorder__class_OMin(X48,X49),X49)
| ~ c_Finite__Set_Ofinite(X47,X49)
| X48 = c_Orderings_Obot__class_Obot(tc_fun(X49,tc_bool))
| ~ c_lessequals(X48,X47,tc_fun(X49,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1689]) ).
fof(c_0_2804,plain,
! [X47,X48,X49] :
( ~ class_Orderings_Olinorder(X49)
| c_lessequals(c_Finite__Set_Olinorder__class_OMax(X48,X49),c_Finite__Set_Olinorder__class_OMax(X47,X49),X49)
| ~ c_Finite__Set_Ofinite(X47,X49)
| X48 = c_Orderings_Obot__class_Obot(tc_fun(X49,tc_bool))
| ~ c_lessequals(X48,X47,tc_fun(X49,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1690]) ).
fof(c_0_2805,plain,
! [X10,X11,X12,X13] :
( c_Set_Oinsert(X10,X12,X13) != c_Set_Oinsert(X10,X11,X13)
| c_in(X10,X11,X13)
| c_in(X10,X12,X13)
| X12 = X11 ),
inference(variable_rename,[status(thm)],[c_0_1691]) ).
fof(c_0_2806,plain,
! [X3,X4] :
( c_Divides_Odiv__class_Omod(c_Suc(X4),X3,tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(X4,X3,tc_nat))
| c_Suc(c_Divides_Odiv__class_Omod(X4,X3,tc_nat)) = X3 ),
inference(variable_rename,[status(thm)],[c_0_1692]) ).
fof(c_0_2807,plain,
! [X16,X17,X18] :
( c_Ring__and__Field_Odvd__class_Odvd(X18,X16,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X16,tc_nat)
| 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_1693]) ).
fof(c_0_2808,plain,
! [X16,X17,X18] :
( c_Ring__and__Field_Odvd__class_Odvd(X18,X16,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X16,X17,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X16,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X17,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1694]) ).
fof(c_0_2809,plain,
! [X3,X4] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1695]) ).
fof(c_0_2810,plain,
! [X5,X6] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X6)
| c_lessequals(c_HOL_Oplus__class_Oplus(X5,X5,X6),c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1696]) ).
fof(c_0_2811,plain,
! [X5,X6] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X6)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_HOL_Oplus__class_Oplus(X5,X5,X6),X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_1697]) ).
fof(c_0_2812,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Oordered__idom(X6)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X5,X6),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_1698]) ).
fof(c_0_2813,plain,
! [X5,X6] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X6)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X5,X6),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_1699]) ).
fof(c_0_2814,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X5,X6),c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1700]) ).
fof(c_0_2815,plain,
! [X5,X6] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X6)
| c_lessequals(c_HOL_Ozero__class_Ozero(X6),c_HOL_Oplus__class_Oplus(X5,X5,X6),X6)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_1701]) ).
fof(c_0_2816,plain,
! [X10,X11] : c_HOL_Oord__class_Oless(X11,c_Suc(c_HOL_Oplus__class_Oplus(X11,X10,tc_nat)),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1702]) ).
fof(c_0_2817,plain,
! [X23,X24] : c_HOL_Oord__class_Oless(X24,c_Suc(c_HOL_Oplus__class_Oplus(X23,X24,tc_nat)),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1703]) ).
fof(c_0_2818,plain,
! [X23,X24] : c_HOL_Oord__class_Oless(X24,c_Suc(c_HOL_Oplus__class_Oplus(X24,X23,tc_nat)),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1704]) ).
fof(c_0_2819,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Oorder(X12)
| c_lessequals(X10,X11,X12)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeast(X11,X12),c_SetInterval_Oord__class_OatLeast(X10,X12),tc_fun(X12,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1705]) ).
fof(c_0_2820,plain,
! [X10,X11] : c_in(X10,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)),X11),X11),
inference(variable_rename,[status(thm)],[c_0_1706]) ).
fof(c_0_2821,plain,
! [X10,X11,X12,X13] :
( c_in(X10,X11,X13)
| ~ c_in(X10,X12,X13)
| ~ c_lessequals(X12,X11,tc_fun(X13,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1707]) ).
fof(c_0_2822,plain,
! [X12,X13,X14,X15] :
( c_in(X12,X13,X15)
| ~ c_in(X12,X14,X15)
| ~ c_lessequals(X14,X13,tc_fun(X15,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1708]) ).
fof(c_0_2823,plain,
! [X10,X11,X12,X13] :
( c_in(X10,X11,X13)
| ~ c_lessequals(X12,X11,tc_fun(X13,tc_bool))
| ~ c_in(X10,X12,X13) ),
inference(variable_rename,[status(thm)],[c_0_1709]) ).
fof(c_0_2824,plain,
! [X44,X45,X46,X47] :
( c_in(X44,X45,X47)
| ~ c_in(X44,X46,X47)
| ~ c_lessequals(X46,X45,tc_fun(X47,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1710]) ).
fof(c_0_2825,plain,
! [X12,X13,X14,X15] :
( c_in(X12,X13,X15)
| ~ c_in(X12,X14,X15)
| ~ c_HOL_Oord__class_Oless(X14,X13,tc_fun(X15,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1711]) ).
fof(c_0_2826,plain,
! [X3,X4] :
( c_Divides_Odiv__class_Omod(X4,X3,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),X3,tc_nat)
| c_HOL_Oord__class_Oless(X4,X3,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1712]) ).
fof(c_0_2827,plain,
! [X11,X12,X13] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X13)
| c_lessequals(c_HOL_Ominus__class_Ominus(X12,X11,X13),c_HOL_Ozero__class_Ozero(X13),X13)
| ~ c_lessequals(X12,X11,X13) ),
inference(variable_rename,[status(thm)],[c_0_1713]) ).
fof(c_0_2828,plain,
! [X43,X44,X45,X46] :
( ~ class_HOL_Oord(X45)
| ~ c_lessequals(X43,X44,tc_fun(X46,X45))
| ~ c_HOL_Oord__class_Oless(X44,X43,tc_fun(X46,X45)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1714])])]) ).
fof(c_0_2829,plain,
! [X11,X12,X13] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X13)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X12,X11,X13),c_HOL_Ozero__class_Ozero(X13),X13)
| ~ c_HOL_Oord__class_Oless(X12,X11,X13) ),
inference(variable_rename,[status(thm)],[c_0_1715]) ).
fof(c_0_2830,plain,
! [X8,X9] :
( c_Finite__Set_Ocard(X8,X9) != c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X9,tc_bool)),X9)
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X9,tc_bool)),X9)
| X8 = c_Orderings_Otop__class_Otop(tc_fun(X9,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1716]) ).
fof(c_0_2831,plain,
! [X23,X24] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X23,c_Suc(X24),tc_nat),X23,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X23,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1717])])]) ).
fof(c_0_2832,plain,
! [X6,X7,X8] :
( c_HOL_Otimes__class_Otimes(X8,X7,tc_nat) != c_HOL_Otimes__class_Otimes(X8,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat)
| X7 = X6 ),
inference(variable_rename,[status(thm)],[c_0_1718]) ).
fof(c_0_2833,plain,
! [X8,X9,X10] : c_Lattices_Olower__semilattice__class_Oinf(X9,c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X10,tc_bool)),tc_fun(X10,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1719]) ).
fof(c_0_2834,plain,
! [X3,X4] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1720]) ).
fof(c_0_2835,plain,
! [X11,X12,X13,X14] :
( ~ class_Lattices_Olower__semilattice(X14)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X13,X12,X14),X11,X14)
| ~ c_lessequals(X12,X11,X14) ),
inference(variable_rename,[status(thm)],[c_0_1721]) ).
fof(c_0_2836,plain,
! [X11,X12,X13,X14] :
( ~ class_Lattices_Olower__semilattice(X14)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X13,X12,X14),X11,X14)
| ~ c_lessequals(X13,X11,X14) ),
inference(variable_rename,[status(thm)],[c_0_1722]) ).
fof(c_0_2837,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_1723]) ).
fof(c_0_2838,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_1724]) ).
fof(c_0_2839,plain,
! [X11,X12,X13,X14] :
( ~ class_Lattices_Olower__semilattice(X14)
| c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X13,X12,X14),X11,X14)
| ~ c_HOL_Oord__class_Oless(X13,X11,X14) ),
inference(variable_rename,[status(thm)],[c_0_1725]) ).
fof(c_0_2840,plain,
! [X11,X12,X13,X14] :
( ~ class_Lattices_Olower__semilattice(X14)
| c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X13,X12,X14),X11,X14)
| ~ c_HOL_Oord__class_Oless(X12,X11,X14) ),
inference(variable_rename,[status(thm)],[c_0_1726]) ).
fof(c_0_2841,plain,
! [X2] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1727]) ).
fof(c_0_2842,plain,
! [X2] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X2,tc_nat),X2,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1728]) ).
fof(c_0_2843,plain,
! [X3,X4] :
( c_HOL_Ominus__class_Ominus(c_Suc(X4),X3,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(X4,X3,tc_nat))
| ~ c_lessequals(X3,X4,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1729]) ).
fof(c_0_2844,plain,
! [X8,X9,X10] :
( c_lessequals(c_Finite__Set_Ocard(X9,X10),c_Finite__Set_Ocard(X8,X10),tc_nat)
| ~ c_lessequals(X9,X8,tc_fun(X10,tc_bool))
| ~ c_Finite__Set_Ofinite(X8,X10) ),
inference(variable_rename,[status(thm)],[c_0_1730]) ).
fof(c_0_2845,plain,
! [X8,X9,X10] :
( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(X9,X10),c_Finite__Set_Ocard(X8,X10),tc_nat)
| ~ c_HOL_Oord__class_Oless(X9,X8,tc_fun(X10,tc_bool))
| ~ c_Finite__Set_Ofinite(X8,X10) ),
inference(variable_rename,[status(thm)],[c_0_1731]) ).
fof(c_0_2846,plain,
! [X3,X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1732]) ).
fof(c_0_2847,plain,
! [X3,X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1733])])]) ).
fof(c_0_2848,plain,
! [X11,X12,X13,X14] :
( c_in(X12,c_Set_Oinsert(X11,X13,X14),X14)
| ~ c_in(X12,X13,X14) ),
inference(variable_rename,[status(thm)],[c_0_1734]) ).
fof(c_0_2849,plain,
! [X11,X12,X13,X14] :
( c_in(X12,c_Set_Oinsert(X11,X13,X14),X14)
| ~ c_in(X12,X13,X14) ),
inference(variable_rename,[status(thm)],[c_0_1735]) ).
fof(c_0_2850,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X6)
| c_HOL_Oplus__class_Oplus(X5,X5,X6) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X6),c_HOL_Oone__class_Oone(X6),X6),X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_1736]) ).
fof(c_0_2851,plain,
! [X23,X24] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X23,X24,tc_nat),X24,tc_nat),
inference(variable_rename,[status(thm)],[c_0_1737]) ).
fof(c_0_2852,plain,
! [X23,X24] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X24,X23,tc_nat),X24,tc_nat),
inference(variable_rename,[status(thm)],[c_0_1738]) ).
fof(c_0_2853,plain,
! [X8,X9,X10] :
( X9 = X8
| ~ c_lessequals(X8,X9,tc_fun(X10,tc_bool))
| ~ c_lessequals(X9,X8,tc_fun(X10,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1739])])]) ).
fof(c_0_2854,plain,
! [X8,X9,X10] :
( X9 = X8
| ~ c_lessequals(X8,X9,tc_fun(X10,tc_bool))
| ~ c_lessequals(X9,X8,tc_fun(X10,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1740])])]) ).
fof(c_0_2855,plain,
! [X3,X4] :
( c_lessequals(c_Divides_Odiv__class_Omod(X4,X3,tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1741])])]) ).
fof(c_0_2856,plain,
! [X3,X4] :
( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X4,X3,tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1742])])]) ).
fof(c_0_2857,plain,
! [X10,X11,X12] :
( c_Finite__Set_Ocard(c_Set_Oinsert(X10,X11,X12),X12) = c_Finite__Set_Ocard(X11,X12)
| ~ c_in(X10,X11,X12)
| ~ c_Finite__Set_Ofinite(X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1743]) ).
fof(c_0_2858,plain,
! [X10,X11,X12] : hBOOL(hAPP(c_Set_Oinsert(X10,X11,X12),X10)),
inference(variable_rename,[status(thm)],[c_0_1744]) ).
fof(c_0_2859,plain,
! [X3,X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1745]) ).
fof(c_0_2860,plain,
! [X8,X9,X10] :
( c_Lattices_Olower__semilattice__class_Oinf(X9,X8,tc_fun(X10,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool))
| c_HOL_Ominus__class_Ominus(X9,X8,tc_fun(X10,tc_bool)) = X9 ),
inference(variable_rename,[status(thm)],[c_0_1746]) ).
fof(c_0_2861,plain,
! [X23,X24] :
( c_HOL_Ominus__class_Ominus(X23,c_HOL_Ominus__class_Ominus(X23,X24,tc_nat),tc_nat) = X24
| ~ c_lessequals(X24,X23,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1747]) ).
fof(c_0_2862,plain,
! [X3,X4] :
( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),X3,tc_nat) = X4
| ~ c_lessequals(X3,X4,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1748]) ).
fof(c_0_2863,plain,
! [X3,X4] :
( c_HOL_Oplus__class_Oplus(X3,c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),tc_nat) = X4
| ~ c_lessequals(X3,X4,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1749]) ).
fof(c_0_2864,plain,
! [X23,X24] :
( ~ c_lessequals(X24,X23,tc_nat)
| X23 = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X23,X24,tc_nat),X24,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1750]) ).
fof(c_0_2865,plain,
! [X27,X28,X29] :
( hBOOL(hAPP(X29,X28))
| c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X29,X27),X27,tc_nat)
| ~ hBOOL(hAPP(X29,X27))
| ~ c_lessequals(X28,X27,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1751]) ).
fof(c_0_2866,plain,
! [X43,X44,X45,X46,X47] :
( ~ class_HOL_Oord(X46)
| c_lessequals(hAPP(X45,X43),hAPP(X44,X43),X46)
| ~ c_lessequals(X45,X44,tc_fun(X47,X46)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1752])])]) ).
fof(c_0_2867,plain,
! [X22,X23,X24] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X24,X22,tc_nat),X23,tc_nat)
| ~ c_HOL_Oord__class_Oless(X24,X23,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1753]) ).
fof(c_0_2868,plain,
! [X16,X17,X18] :
( c_lessequals(X18,c_HOL_Oplus__class_Oplus(X17,X16,tc_nat),tc_nat)
| ~ c_lessequals(X18,X17,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1754]) ).
fof(c_0_2869,plain,
! [X16,X17,X18] :
( c_lessequals(X18,c_HOL_Oplus__class_Oplus(X17,X16,tc_nat),tc_nat)
| ~ c_lessequals(X18,X16,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1755]) ).
fof(c_0_2870,plain,
! [X23,X24,X25] :
( c_lessequals(X25,c_HOL_Oplus__class_Oplus(X24,X23,tc_nat),tc_nat)
| ~ c_lessequals(X25,X24,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1756]) ).
fof(c_0_2871,plain,
! [X23,X24,X25] :
( c_lessequals(X25,c_HOL_Oplus__class_Oplus(X23,X24,tc_nat),tc_nat)
| ~ c_lessequals(X25,X24,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1757]) ).
fof(c_0_2872,plain,
! [X6,X7] :
( c_Ring__and__Field_Odvd__class_Odvd(X7,c_HOL_Oplus__class_Oplus(X6,X7,tc_nat),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1758]) ).
fof(c_0_2873,plain,
! [X23,X24,X25] :
( c_HOL_Oord__class_Oless(X25,c_HOL_Oplus__class_Oplus(X23,X24,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X25,X24,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1759]) ).
fof(c_0_2874,plain,
! [X23,X24,X25] :
( c_HOL_Oord__class_Oless(X25,c_HOL_Oplus__class_Oplus(X24,X23,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X25,X24,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1760]) ).
fof(c_0_2875,plain,
! [X16,X17,X18] :
( c_HOL_Oord__class_Oless(X18,c_HOL_Oplus__class_Oplus(X17,X16,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X18,X16,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1761]) ).
fof(c_0_2876,plain,
! [X16,X17,X18] :
( c_HOL_Oord__class_Oless(X18,c_HOL_Oplus__class_Oplus(X17,X16,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X18,X17,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1762]) ).
fof(c_0_2877,plain,
! [X16,X17,X18,X19] :
( ~ class_Orderings_Oorder(X19)
| c_lessequals(X16,X18,X19)
| ~ c_lessequals(X16,X17,X19)
| ~ c_lessequals(X17,X18,X19) ),
inference(variable_rename,[status(thm)],[c_0_1763]) ).
fof(c_0_2878,plain,
! [X16,X17,X18,X19] :
( ~ class_Orderings_Opreorder(X19)
| c_lessequals(X18,X16,X19)
| ~ c_lessequals(X17,X16,X19)
| ~ c_lessequals(X18,X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_1764]) ).
fof(c_0_2879,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_1765]) ).
fof(c_0_2880,plain,
! [X16,X17,X18,X19] :
( ~ class_Orderings_Oorder(X19)
| c_HOL_Oord__class_Oless(X16,X18,X19)
| ~ c_lessequals(X16,X17,X19)
| ~ c_HOL_Oord__class_Oless(X17,X18,X19) ),
inference(variable_rename,[status(thm)],[c_0_1766]) ).
fof(c_0_2881,plain,
! [X16,X17,X18,X19] :
( ~ class_Orderings_Oorder(X19)
| c_HOL_Oord__class_Oless(X16,X18,X19)
| ~ c_HOL_Oord__class_Oless(X16,X17,X19)
| ~ c_lessequals(X17,X18,X19) ),
inference(variable_rename,[status(thm)],[c_0_1767]) ).
fof(c_0_2882,plain,
! [X16,X17,X18,X19] :
( ~ class_Orderings_Opreorder(X19)
| c_HOL_Oord__class_Oless(X18,X16,X19)
| ~ c_HOL_Oord__class_Oless(X17,X16,X19)
| ~ c_lessequals(X18,X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_1768]) ).
fof(c_0_2883,plain,
! [X16,X17,X18,X19] :
( ~ class_Orderings_Opreorder(X19)
| c_HOL_Oord__class_Oless(X18,X16,X19)
| ~ c_lessequals(X17,X16,X19)
| ~ c_HOL_Oord__class_Oless(X18,X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_1769]) ).
fof(c_0_2884,plain,
! [X16,X17,X18,X19] :
( ~ class_Orderings_Oorder(X19)
| c_HOL_Oord__class_Oless(X16,X18,X19)
| ~ c_HOL_Oord__class_Oless(X16,X17,X19)
| ~ c_HOL_Oord__class_Oless(X17,X18,X19) ),
inference(variable_rename,[status(thm)],[c_0_1770]) ).
fof(c_0_2885,plain,
! [X16,X17,X18,X19] :
( ~ class_Orderings_Opreorder(X19)
| c_HOL_Oord__class_Oless(X18,X16,X19)
| ~ c_HOL_Oord__class_Oless(X17,X16,X19)
| ~ c_HOL_Oord__class_Oless(X18,X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_1771]) ).
fof(c_0_2886,plain,
! [X3,X4] :
( c_Suc(c_Divides_Odiv__class_Omod(X4,X3,tc_nat)) != X3
| c_Divides_Odiv__class_Omod(c_Suc(X4),X3,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1772]) ).
fof(c_0_2887,plain,
! [X5,X6] :
( ~ class_Orderings_Olinorder(X6)
| c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X6),X6) = X5 ),
inference(variable_rename,[status(thm)],[c_0_1773]) ).
fof(c_0_2888,plain,
! [X5,X6] :
( ~ class_Orderings_Olinorder(X6)
| c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X6),X6) = X5 ),
inference(variable_rename,[status(thm)],[c_0_1774]) ).
fof(c_0_2889,plain,
! [X8,X9] :
( X8 = c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))
| ~ c_lessequals(X8,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),tc_fun(X9,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1775]) ).
fof(c_0_2890,plain,
! [X5,X6,X7] :
( ~ class_Ring__and__Field_Osemiring__1(X7)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X6,X5,tc_nat),X7) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(X6,X7),c_Nat_Osemiring__1__class_Oof__nat(X5,X7),X7) ),
inference(variable_rename,[status(thm)],[c_0_1776]) ).
fof(c_0_2891,plain,
! [X5,X6,X7] :
( ~ class_Ring__and__Field_Osemiring__1(X7)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X6,X5,tc_nat),X7) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(X6,X7),c_Nat_Osemiring__1__class_Oof__nat(X5,X7),X7) ),
inference(variable_rename,[status(thm)],[c_0_1777]) ).
fof(c_0_2892,plain,
! [X8,X9,X10] : c_lessequals(c_HOL_Ominus__class_Ominus(X9,X8,tc_fun(X10,tc_bool)),X9,tc_fun(X10,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1778]) ).
fof(c_0_2893,plain,
! [X8,X9,X10] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X9,X8,tc_fun(X10,tc_bool)),X9,tc_fun(X10,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1779]) ).
fof(c_0_2894,plain,
! [X8,X9,X10] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X9,X8,tc_fun(X10,tc_bool)),X8,tc_fun(X10,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1780]) ).
fof(c_0_2895,plain,
! [X10,X11,X12] :
( c_Finite__Set_Ocard(c_Set_Oinsert(X10,X11,X12),X12) = c_Suc(c_Finite__Set_Ocard(X11,X12))
| c_in(X10,X11,X12)
| ~ c_Finite__Set_Ofinite(X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1781]) ).
fof(c_0_2896,plain,
! [X5,X6,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X7)
| c_lessequals(X6,X5,tc_nat)
| ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X6,X7),c_Nat_Osemiring__1__class_Oof__nat(X5,X7),X7) ),
inference(variable_rename,[status(thm)],[c_0_1782]) ).
fof(c_0_2897,plain,
! [X5,X6,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X7)
| c_HOL_Oord__class_Oless(X6,X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X6,X7),c_Nat_Osemiring__1__class_Oof__nat(X5,X7),X7) ),
inference(variable_rename,[status(thm)],[c_0_1783]) ).
fof(c_0_2898,plain,
! [X23,X24,X25] :
( c_HOL_Oord__class_Oless(c_Suc(X25),X23,tc_nat)
| ~ c_HOL_Oord__class_Oless(X24,X23,tc_nat)
| ~ c_HOL_Oord__class_Oless(X25,X24,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1784]) ).
fof(c_0_2899,plain,
! [X6,X7] :
( c_lessequals(X7,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1785]) ).
fof(c_0_2900,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Oorder(X12)
| c_lessequals(c_SetInterval_Oord__class_OatLeast(X11,X12),c_SetInterval_Oord__class_OatLeast(X10,X12),tc_fun(X12,tc_bool))
| ~ c_lessequals(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1786]) ).
fof(c_0_2901,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Olower__semilattice(X12)
| c_Lattices_Olower__semilattice__class_Oinf(X11,c_Lattices_Olower__semilattice__class_Oinf(X11,X10,X12),X12) = c_Lattices_Olower__semilattice__class_Oinf(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1787]) ).
fof(c_0_2902,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Olattice(X12)
| c_Lattices_Olower__semilattice__class_Oinf(X11,c_Lattices_Olower__semilattice__class_Oinf(X11,X10,X12),X12) = c_Lattices_Olower__semilattice__class_Oinf(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1788]) ).
fof(c_0_2903,plain,
! [X11,X12,X13] :
( ~ class_Divides_Osemiring__div(X13)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X11,X12,X13),X11,X13) = c_Divides_Odiv__class_Omod(X12,X11,X13) ),
inference(variable_rename,[status(thm)],[c_0_1789]) ).
fof(c_0_2904,plain,
! [X11,X12,X13] :
( ~ class_Divides_Osemiring__div(X13)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X12,X11,X13),X11,X13) = c_Divides_Odiv__class_Omod(X12,X11,X13) ),
inference(variable_rename,[status(thm)],[c_0_1790]) ).
fof(c_0_2905,plain,
! [X10,X11,X12] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X12)
| c_HOL_Otimes__class_Otimes(X11,c_HOL_Otimes__class_Otimes(X11,X10,X12),X12) = c_HOL_Otimes__class_Otimes(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1791]) ).
fof(c_0_2906,plain,
! [X11,X12,X13] :
( ~ class_Divides_Osemiring__div(X13)
| c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X12,X11,X13),X11,X13) = c_Divides_Odiv__class_Omod(X12,X11,X13) ),
inference(variable_rename,[status(thm)],[c_0_1792]) ).
fof(c_0_2907,plain,
! [X35,X36,X37] :
( c_in(X36,X35,X37)
| c_Finite__Set_Ocard(c_Set_Oinsert(X36,X35,X37),X37) = c_Suc(c_Finite__Set_Ocard(X35,X37))
| c_Finite__Set_Ocard(X35,X37) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1793]) ).
fof(c_0_2908,plain,
! [X3] :
( c_Suc(c_HOL_Ominus__class_Ominus(X3,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X3
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1794]) ).
fof(c_0_2909,plain,
! [X3,X4] : c_HOL_Ominus__class_Ominus(X4,c_Suc(X3),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,tc_nat),
inference(variable_rename,[status(thm)],[c_0_1795]) ).
fof(c_0_2910,plain,
! [X23,X24,X25] :
( c_lessequals(X25,X23,tc_nat)
| ~ c_lessequals(X24,X23,tc_nat)
| ~ c_lessequals(X25,X24,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1796]) ).
fof(c_0_2911,plain,
! [X16,X17,X18] :
( c_Ring__and__Field_Odvd__class_Odvd(X18,X16,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X16,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X17,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1797]) ).
fof(c_0_2912,plain,
! [X10,X11,X12] : c_Set_Oinsert(X10,c_Set_Oinsert(X10,X11,X12),X12) = c_Set_Oinsert(X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_1798]) ).
fof(c_0_2913,plain,
! [X3,X4] : c_HOL_Otimes__class_Otimes(c_Suc(X4),X3,tc_nat) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X4,X3,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1799]) ).
fof(c_0_2914,plain,
! [X3,X4] : c_HOL_Otimes__class_Otimes(X4,c_Suc(X3),tc_nat) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X4,X3,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1800]) ).
fof(c_0_2915,plain,
! [X27,X28,X29] :
( ~ hBOOL(hAPP(X28,X27))
| ~ c_in(X27,c_Orderings_Obot__class_Obot(tc_fun(X29,tc_bool)),X29) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1801])])]) ).
fof(c_0_2916,plain,
! [X43,X44,X45,X46] :
( ~ class_HOL_Oord(X45)
| c_lessequals(X44,X43,tc_fun(X46,X45))
| ~ c_HOL_Oord__class_Oless(X44,X43,tc_fun(X46,X45)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1802])])]) ).
fof(c_0_2917,plain,
! [X26,X27,X28] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X28)
| c_lessequals(X27,c_Inductive_Ocomplete__lattice__class_Ogfp(X26,X28),X28)
| ~ c_lessequals(X27,hAPP(X26,X27),X28) ),
inference(variable_rename,[status(thm)],[c_0_1803]) ).
fof(c_0_2918,plain,
! [X8,X9,X10] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X9,X8,tc_fun(X10,tc_bool)),X10)
| ~ c_Finite__Set_Ofinite(X9,X10)
| ~ c_Finite__Set_Ofinite(X8,X10) ),
inference(variable_rename,[status(thm)],[c_0_1804]) ).
fof(c_0_2919,plain,
! [X3,X4] :
( c_HOL_Oplus__class_Oplus(X3,c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),tc_nat) = X4
| c_HOL_Oord__class_Oless(X4,X3,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1805]) ).
fof(c_0_2920,plain,
! [X10,X11] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)),X10)),
inference(variable_rename,[status(thm)],[c_0_1806]) ).
fof(c_0_2921,plain,
! [X8,X9,X10] :
( c_Finite__Set_Ofinite(X9,X10)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X8,X9,X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_1807]) ).
fof(c_0_2922,plain,
! [X3] :
( X3 = c_Suc(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1808]) ).
fof(c_0_2923,plain,
! [X3] :
( c_Suc(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X3
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1809]) ).
fof(c_0_2924,plain,
! [X8,X9] : ~ c_HOL_Oord__class_Oless(X8,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),tc_fun(X9,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1810]) ).
fof(c_0_2925,plain,
! [X49,X50,X51] :
( hBOOL(hAPP(X51,X50))
| c_lessequals(X49,c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1(X51,X49),tc_nat)
| ~ c_lessequals(c_Suc(X49),X50,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1811]) ).
fof(c_0_2926,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Opreorder(X12)
| c_HOL_Oord__class_Oless(X11,X10,X12)
| c_lessequals(X10,X11,X12)
| ~ c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1812]) ).
fof(c_0_2927,plain,
! [X8,X9,X10] :
( c_HOL_Oord__class_Oless(X9,X8,tc_fun(X10,tc_bool))
| X9 = X8
| ~ c_lessequals(X9,X8,tc_fun(X10,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1813]) ).
fof(c_0_2928,plain,
! [X8,X9,X10] :
( X9 = X8
| c_HOL_Oord__class_Oless(X9,X8,tc_fun(X10,tc_bool))
| ~ c_lessequals(X9,X8,tc_fun(X10,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1814])])]) ).
fof(c_0_2929,plain,
! [X8,X9,X10] :
( c_Lattices_Olower__semilattice__class_Oinf(X9,X8,tc_fun(X10,tc_bool)) = X8
| ~ c_lessequals(X8,X9,tc_fun(X10,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1815]) ).
fof(c_0_2930,plain,
! [X8,X9,X10] :
( c_Lattices_Olower__semilattice__class_Oinf(X9,X8,tc_fun(X10,tc_bool)) = X9
| ~ c_lessequals(X9,X8,tc_fun(X10,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1816]) ).
fof(c_0_2931,plain,
! [X51,X52,X53,X54] :
( hBOOL(hAPP(X52,X51))
| ~ hBOOL(hAPP(X53,X51))
| ~ c_lessequals(X53,X52,tc_fun(X54,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1817])])]) ).
fof(c_0_2932,plain,
! [X51,X52,X53,X54] :
( hBOOL(hAPP(X52,X51))
| ~ c_lessequals(X53,X52,tc_fun(X54,tc_bool))
| ~ hBOOL(hAPP(X53,X51)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1818])])]) ).
fof(c_0_2933,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_1819]) ).
fof(c_0_2934,plain,
! [X8,X9,X10] :
( c_lessequals(X9,X8,tc_fun(X10,tc_bool))
| ~ c_HOL_Oord__class_Oless(X9,X8,tc_fun(X10,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1820]) ).
fof(c_0_2935,plain,
! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X5),c_HOL_Oone__class_Oone(X5),X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1821]) ).
fof(c_0_2936,plain,
! [X27,X28,X29] :
( hBOOL(hAPP(X28,X27))
| ~ c_in(X27,c_Orderings_Obot__class_Obot(tc_fun(X29,tc_bool)),X29) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1822])])]) ).
fof(c_0_2937,plain,
! [X5,X6,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X7)
| c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X6,X7),c_Nat_Osemiring__1__class_Oof__nat(X5,X7),X7)
| ~ c_lessequals(X6,X5,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1823]) ).
fof(c_0_2938,plain,
! [X5,X6,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X7)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X6,X7),c_Nat_Osemiring__1__class_Oof__nat(X5,X7),X7)
| ~ c_HOL_Oord__class_Oless(X6,X5,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1824]) ).
fof(c_0_2939,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| c_lessequals(X10,c_Finite__Set_Olinorder__class_OMax(X11,X12),X12)
| ~ c_in(X10,X11,X12)
| ~ c_Finite__Set_Ofinite(X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1825]) ).
fof(c_0_2940,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X11,X12),X10,X12)
| ~ c_in(X10,X11,X12)
| ~ c_Finite__Set_Ofinite(X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1826]) ).
fof(c_0_2941,plain,
! [X27,X28,X29] :
( hBOOL(hAPP(hAPP(X29,X27),X28))
| c_HOL_Oord__class_Oless(X27,X28,tc_nat)
| X28 = X27
| c_HOL_Oord__class_Oless(X28,X27,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1827])])]) ).
fof(c_0_2942,plain,
! [X41,X42,X43] :
( c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X42,X41,tc_fun(X43,tc_bool)),X43)
| ~ c_Finite__Set_Ofinite(X42,X43) ),
inference(variable_rename,[status(thm)],[c_0_1828]) ).
fof(c_0_2943,plain,
! [X41,X42,X43] :
( c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X42,X41,tc_fun(X43,tc_bool)),X43)
| ~ c_Finite__Set_Ofinite(X41,X43) ),
inference(variable_rename,[status(thm)],[c_0_1829]) ).
fof(c_0_2944,plain,
! [X8,X9,X10] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X9,X8,tc_fun(X10,tc_bool)),X10)
| ~ c_Finite__Set_Ofinite(X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_1830]) ).
fof(c_0_2945,plain,
! [X23,X24,X25] :
( ~ class_HOL_Oord(X25)
| c_lessequals(X23,X24,X25)
| ~ c_in(X24,c_SetInterval_Oord__class_OatLeast(X23,X25),X25) ),
inference(variable_rename,[status(thm)],[c_0_1831]) ).
fof(c_0_2946,plain,
! [X6,X7,X8] :
( c_HOL_Otimes__class_Otimes(c_Suc(X8),X7,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X8),X6,tc_nat)
| X7 = X6 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1832])])]) ).
fof(c_0_2947,plain,
! [X16,X17,X18,X19] :
( ~ class_Ring__and__Field_Oidom(X19)
| ~ class_Int_Onumber__ring(X19)
| c_HOL_Oplus__class_Oplus(X18,X17,X19) != c_HOL_Oplus__class_Oplus(X18,X16,X19)
| X17 = X16 ),
inference(variable_rename,[status(thm)],[c_0_1833]) ).
fof(c_0_2948,plain,
! [X7,X8,X9] : c_lessequals(X8,c_Set_Oinsert(X7,X8,X9),tc_fun(X9,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1834]) ).
fof(c_0_2949,plain,
! [X35,X36,X37] :
( c_Set_Oinsert(X36,X35,X37) != c_Orderings_Obot__class_Obot(tc_fun(X37,tc_bool))
| c_in(X36,X35,X37) ),
inference(variable_rename,[status(thm)],[c_0_1835]) ).
fof(c_0_2950,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_1836]) ).
fof(c_0_2951,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Oorder(X12)
| X11 = X10
| ~ c_lessequals(X10,X11,X12)
| ~ c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1837]) ).
fof(c_0_2952,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Oorder(X12)
| X11 = X10
| ~ c_lessequals(X10,X11,X12)
| ~ c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1838]) ).
fof(c_0_2953,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Oorder(X12)
| X11 = X10
| ~ c_lessequals(X11,X10,X12)
| ~ c_lessequals(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1839]) ).
fof(c_0_2954,plain,
! [X5] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1840]) ).
fof(c_0_2955,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Oordered__semidom(X6)
| c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X5,c_HOL_Oone__class_Oone(X6),X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1841]) ).
fof(c_0_2956,plain,
! [X40,X41,X42,X43] :
( ~ class_OrderedGroup_Oab__group__add(X43)
| c_HOL_Ominus__class_Ominus(X42,X42,X43) != c_HOL_Ominus__class_Ominus(X41,X40,X43)
| X41 = X40 ),
inference(variable_rename,[status(thm)],[c_0_1842]) ).
fof(c_0_2957,plain,
! [X35,X36,X37,X38] :
( ~ class_OrderedGroup_Oab__group__add(X38)
| c_HOL_Ominus__class_Ominus(X36,X35,X38) != c_HOL_Ominus__class_Ominus(X37,X37,X38)
| X36 = X35 ),
inference(variable_rename,[status(thm)],[c_0_1843]) ).
fof(c_0_2958,plain,
! [X12,X13,X14,X15] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X15)
| c_HOL_Oplus__class_Oplus(X13,X14,X15) != c_HOL_Oplus__class_Oplus(X12,X14,X15)
| X13 = X12 ),
inference(variable_rename,[status(thm)],[c_0_1844]) ).
fof(c_0_2959,plain,
! [X12,X13,X14,X15] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X15)
| c_HOL_Oplus__class_Oplus(X14,X13,X15) != c_HOL_Oplus__class_Oplus(X14,X12,X15)
| X13 = X12 ),
inference(variable_rename,[status(thm)],[c_0_1845]) ).
fof(c_0_2960,plain,
! [X12,X13,X14,X15] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X15)
| c_HOL_Oplus__class_Oplus(X14,X13,X15) != c_HOL_Oplus__class_Oplus(X14,X12,X15)
| X13 = X12 ),
inference(variable_rename,[status(thm)],[c_0_1846]) ).
fof(c_0_2961,plain,
! [X11,X12,X13] :
( ~ class_Orderings_Opreorder(X13)
| ~ c_HOL_Oord__class_Oless(X11,X12,X13)
| ~ c_HOL_Oord__class_Oless(X12,X11,X13) ),
inference(variable_rename,[status(thm)],[c_0_1847]) ).
fof(c_0_2962,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Opreorder(X12)
| ~ c_HOL_Oord__class_Oless(X10,X11,X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1848]) ).
fof(c_0_2963,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12)
| ~ c_HOL_Oord__class_Oless(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1849]) ).
fof(c_0_2964,plain,
! [X11,X12,X13] :
( ~ class_Orderings_Oorder(X13)
| ~ c_HOL_Oord__class_Oless(X12,X11,X13)
| ~ c_HOL_Oord__class_Oless(X11,X12,X13) ),
inference(variable_rename,[status(thm)],[c_0_1850]) ).
fof(c_0_2965,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Opreorder(X12)
| ~ c_lessequals(X10,X11,X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1851]) ).
fof(c_0_2966,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| ~ c_lessequals(X11,X10,X12)
| ~ c_HOL_Oord__class_Oless(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1852]) ).
fof(c_0_2967,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12)
| ~ c_lessequals(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1853]) ).
fof(c_0_2968,plain,
! [X10,X11] :
( ~ class_Orderings_Olinorder(X11)
| ~ c_lessequals(X10,X10,X11)
| ~ c_HOL_Oord__class_Oless(X10,X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_1854]) ).
fof(c_0_2969,plain,
! [X3,X4] :
( X3 = X4
| ~ c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat)
| ~ c_lessequals(X4,X3,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1855]) ).
fof(c_0_2970,plain,
! [X3,X4] :
( ~ c_lessequals(X4,X3,tc_nat)
| ~ c_lessequals(c_Suc(X3),X4,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1856]) ).
fof(c_0_2971,plain,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1857]) ).
fof(c_0_2972,plain,
! [X3,X4] :
( c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X4,X3,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X4 = X3 ),
inference(variable_rename,[status(thm)],[c_0_1858]) ).
fof(c_0_2973,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X6)
| c_lessequals(c_HOL_Ozero__class_Ozero(X6),c_HOL_Otimes__class_Otimes(X5,X5,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1859]) ).
fof(c_0_2974,plain,
! [X23,X24,X25] :
( ~ class_HOL_Oord(X25)
| c_in(X24,c_SetInterval_Oord__class_OatLeast(X23,X25),X25)
| ~ c_lessequals(X23,X24,X25) ),
inference(variable_rename,[status(thm)],[c_0_1860]) ).
fof(c_0_2975,plain,
! [X11,X12,X13] :
( ~ class_Divides_Osemiring__div(X13)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X11,X12,X13),X11,X13) = c_HOL_Ozero__class_Ozero(X13) ),
inference(variable_rename,[status(thm)],[c_0_1861]) ).
fof(c_0_2976,plain,
! [X11,X12,X13] :
( ~ class_Divides_Osemiring__div(X13)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X12,X11,X13),X11,X13) = c_HOL_Ozero__class_Ozero(X13) ),
inference(variable_rename,[status(thm)],[c_0_1862]) ).
fof(c_0_2977,plain,
! [X6,X7,X8] :
( c_HOL_Otimes__class_Otimes(X7,X8,tc_nat) != c_HOL_Otimes__class_Otimes(X6,X8,tc_nat)
| X8 = c_HOL_Ozero__class_Ozero(tc_nat)
| X7 = X6 ),
inference(variable_rename,[status(thm)],[c_0_1863]) ).
fof(c_0_2978,plain,
! [X6,X7,X8] :
( c_HOL_Otimes__class_Otimes(X8,X7,tc_nat) != c_HOL_Otimes__class_Otimes(X8,X6,tc_nat)
| X8 = c_HOL_Ozero__class_Ozero(tc_nat)
| X7 = X6 ),
inference(variable_rename,[status(thm)],[c_0_1864]) ).
fof(c_0_2979,plain,
! [X6,X7,X8] :
( c_HOL_Otimes__class_Otimes(X8,X7,tc_nat) != c_HOL_Otimes__class_Otimes(X8,X6,tc_nat)
| X7 = X6
| X8 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1865]) ).
fof(c_0_2980,plain,
! [X3,X4] :
( X4 = X3
| ~ c_lessequals(X3,X4,tc_nat)
| ~ c_lessequals(X4,X3,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1866]) ).
fof(c_0_2981,plain,
! [X11,X12] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X12,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X12,X11,tc_nat)
| X12 = X11 ),
inference(variable_rename,[status(thm)],[c_0_1867]) ).
fof(c_0_2982,plain,
! [X11,X12] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X12,tc_nat)
| X12 = X11
| ~ c_Ring__and__Field_Odvd__class_Odvd(X12,X11,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1868]) ).
fof(c_0_2983,plain,
! [X10,X11] :
( X11 = X10
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X10,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X11,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1869]) ).
fof(c_0_2984,plain,
! [X3,X4] :
( X4 = X3
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1870]) ).
fof(c_0_2985,plain,
! [X10,X11] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X11,tc_nat)
| X11 = X10
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X10,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1871]) ).
fof(c_0_2986,plain,
! [X10,X11] :
( X11 = X10
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X11,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X10,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1872]) ).
fof(c_0_2987,plain,
! [X10,X11] :
( X11 = X10
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X11,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X10,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1873]) ).
fof(c_0_2988,plain,
! [X11,X12,X13] :
( ~ class_OrderedGroup_Ogroup__add(X13)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X12,X11,X13),X11,X13) = X12 ),
inference(variable_rename,[status(thm)],[c_0_1874]) ).
fof(c_0_2989,plain,
! [X11,X12,X13] :
( ~ class_OrderedGroup_Ogroup__add(X13)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X12,X11,X13),X11,X13) = X12 ),
inference(variable_rename,[status(thm)],[c_0_1875]) ).
fof(c_0_2990,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Olattice(X12)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X11,X10,X12),X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1876]) ).
fof(c_0_2991,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Olattice(X12)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X11,X10,X12),X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1877]) ).
fof(c_0_2992,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Olower__semilattice(X12)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X11,X10,X12),X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1878]) ).
fof(c_0_2993,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Olower__semilattice(X12)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X11,X10,X12),X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1879]) ).
fof(c_0_2994,plain,
! [X6,X7,X8] :
( c_HOL_Oplus__class_Oplus(X8,X7,tc_nat) != c_HOL_Oplus__class_Oplus(X8,X6,tc_nat)
| X7 = X6 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1880])])]) ).
fof(c_0_2995,plain,
! [X6,X7,X8] :
( c_HOL_Oplus__class_Oplus(X7,X8,tc_nat) != c_HOL_Oplus__class_Oplus(X6,X8,tc_nat)
| X7 = X6 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1881])])]) ).
fof(c_0_2996,plain,
! [X16,X17,X18] :
( c_HOL_Oplus__class_Oplus(X18,X17,tc_nat) != c_HOL_Oplus__class_Oplus(X18,X16,tc_nat)
| X17 = X16 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1882])])]) ).
fof(c_0_2997,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Odvd(X13)
| c_Ring__and__Field_Odvd__class_Odvd(X12,c_HOL_Otimes__class_Otimes(X12,X11,X13),X13) ),
inference(variable_rename,[status(thm)],[c_0_1883]) ).
fof(c_0_2998,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X13)
| c_Ring__and__Field_Odvd__class_Odvd(X12,c_HOL_Otimes__class_Otimes(X12,X11,X13),X13) ),
inference(variable_rename,[status(thm)],[c_0_1884]) ).
fof(c_0_2999,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X13)
| c_Ring__and__Field_Odvd__class_Odvd(X12,c_HOL_Otimes__class_Otimes(X11,X12,X13),X13) ),
inference(variable_rename,[status(thm)],[c_0_1885]) ).
fof(c_0_3000,plain,
! [X5,X6] : ~ c_in(X5,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X6),
inference(variable_rename,[status(thm)],[c_0_1886]) ).
fof(c_0_3001,plain,
! [X12,X13] : ~ c_in(X12,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X13),
inference(variable_rename,[status(thm)],[c_0_1887]) ).
fof(c_0_3002,plain,
! [X10,X11] : ~ c_in(X10,c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)),X11),
inference(variable_rename,[status(thm)],[c_0_1888]) ).
fof(c_0_3003,plain,
! [X3,X4] : c_HOL_Oplus__class_Oplus(X4,c_Suc(X3),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat)),
inference(variable_rename,[status(thm)],[c_0_1889]) ).
fof(c_0_3004,plain,
! [X3,X4] : c_HOL_Oplus__class_Oplus(c_Suc(X4),X3,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat)),
inference(variable_rename,[status(thm)],[c_0_1890]) ).
fof(c_0_3005,plain,
! [X27,X28,X29] :
( hBOOL(hAPP(X29,X27))
| hBOOL(hAPP(X29,X28))
| ~ c_lessequals(c_Suc(X28),c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1(X29),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1891]) ).
fof(c_0_3006,plain,
! [X3,X4] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),c_Suc(X4),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1892]) ).
fof(c_0_3007,plain,
! [X10,X11,X12] : c_in(X10,c_Set_Oinsert(X10,X11,X12),X12),
inference(variable_rename,[status(thm)],[c_0_1893]) ).
fof(c_0_3008,plain,
! [X7,X8,X9] : c_in(X7,c_Set_Oinsert(X7,X8,X9),X9),
inference(variable_rename,[status(thm)],[c_0_1894]) ).
fof(c_0_3009,plain,
! [X10,X11,X12] : c_in(X10,c_Set_Oinsert(X10,X11,X12),X12),
inference(variable_rename,[status(thm)],[c_0_1895]) ).
fof(c_0_3010,plain,
! [X8,X9,X10] :
( c_Finite__Set_Ofinite(X9,X10)
| ~ c_Finite__Set_Ofinite(X8,X10)
| ~ c_lessequals(X9,X8,tc_fun(X10,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1896]) ).
fof(c_0_3011,plain,
! [X8,X9,X10] :
( c_Finite__Set_Ofinite(X9,X10)
| ~ c_lessequals(X9,X8,tc_fun(X10,tc_bool))
| ~ c_Finite__Set_Ofinite(X8,X10) ),
inference(variable_rename,[status(thm)],[c_0_1897]) ).
fof(c_0_3012,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_1898]) ).
fof(c_0_3013,plain,
! [X3,X4] : c_HOL_Ominus__class_Ominus(X3,c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_1899]) ).
fof(c_0_3014,plain,
! [X3,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X3,tc_nat) = X4,
inference(variable_rename,[status(thm)],[c_0_1900]) ).
fof(c_0_3015,plain,
! [X3,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),X3,tc_nat) = X4,
inference(variable_rename,[status(thm)],[c_0_1901]) ).
fof(c_0_3016,plain,
! [X3,X4] : c_lessequals(c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),X4,tc_nat),
inference(variable_rename,[status(thm)],[c_0_1902]) ).
fof(c_0_3017,plain,
! [X2] : c_lessequals(X2,c_HOL_Otimes__class_Otimes(X2,X2,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1903]) ).
fof(c_0_3018,plain,
! [X3,X4] : c_lessequals(c_Divides_Odiv__class_Omod(X4,X3,tc_nat),X4,tc_nat),
inference(variable_rename,[status(thm)],[c_0_1904]) ).
fof(c_0_3019,plain,
! [X3,X4] : c_lessequals(X3,c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1905]) ).
fof(c_0_3020,plain,
! [X3,X4] : c_lessequals(X3,c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1906]) ).
fof(c_0_3021,plain,
! [X10,X11] : c_lessequals(X11,c_HOL_Oplus__class_Oplus(X11,X10,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1907]) ).
fof(c_0_3022,plain,
! [X3,X4] :
( c_lessequals(X3,X4,tc_nat)
| ~ c_lessequals(c_Suc(X3),c_Suc(X4),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1908]) ).
fof(c_0_3023,plain,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X4),c_Suc(X3),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1909]) ).
fof(c_0_3024,plain,
! [X8,X9] : c_HOL_Ominus__class_Ominus(X8,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_bool)),tc_fun(X9,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1910]) ).
fof(c_0_3025,plain,
! [X8,X9] : c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),X8,tc_fun(X9,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1911]) ).
fof(c_0_3026,plain,
! [X8,X9] : c_Lattices_Olower__semilattice__class_Oinf(X8,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),tc_fun(X9,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1912]) ).
fof(c_0_3027,plain,
! [X7,X8] : c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)),X7,tc_fun(X8,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1913]) ).
fof(c_0_3028,plain,
! [X8,X9,X10] : c_Lattices_Olower__semilattice__class_Oinf(X9,X8,tc_fun(X10,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X8,X9,tc_fun(X10,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1914]) ).
fof(c_0_3029,plain,
! [X11,X12,X13] :
( ~ class_Divides_Osemiring__div(X13)
| c_Divides_Odiv__class_Omod(X11,X12,X13) != c_HOL_Ozero__class_Ozero(X13)
| c_Ring__and__Field_Odvd__class_Odvd(X12,X11,X13) ),
inference(variable_rename,[status(thm)],[c_0_1915]) ).
fof(c_0_3030,plain,
! [X3,X4] :
( X4 = c_Suc(X3)
| c_lessequals(X4,X3,tc_nat)
| ~ c_lessequals(X4,c_Suc(X3),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1916]) ).
fof(c_0_3031,plain,
! [X11,X12,X13] :
( ~ class_Divides_Osemiring__div(X13)
| c_Divides_Odiv__class_Omod(X11,X12,X13) = c_HOL_Ozero__class_Ozero(X13)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X12,X11,X13) ),
inference(variable_rename,[status(thm)],[c_0_1917]) ).
fof(c_0_3032,plain,
! [X8,X9,X10] :
( c_Finite__Set_Ocard(X9,X10) != c_Suc(X8)
| c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(X9,X8,X10),X10) = X8 ),
inference(variable_rename,[status(thm)],[c_0_1918]) ).
fof(c_0_3033,plain,
! [X8,X9,X10] :
( c_Finite__Set_Ocard(X9,X10) != c_Suc(X8)
| c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(X9,X8,X10),X10) = X8 ),
inference(variable_rename,[status(thm)],[c_0_1919]) ).
fof(c_0_3034,plain,
! [X11,X12,X13] :
( ~ class_Orderings_Oorder(X13)
| c_HOL_Oord__class_Oless(X11,X12,X13)
| X12 = X11
| ~ c_lessequals(X11,X12,X13) ),
inference(variable_rename,[status(thm)],[c_0_1920]) ).
fof(c_0_3035,plain,
! [X11,X12,X13] :
( ~ class_Orderings_Oorder(X13)
| c_HOL_Oord__class_Oless(X11,X12,X13)
| ~ c_lessequals(X11,X12,X13)
| X12 = X11 ),
inference(variable_rename,[status(thm)],[c_0_1921]) ).
fof(c_0_3036,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Oorder(X12)
| X11 = X10
| c_HOL_Oord__class_Oless(X11,X10,X12)
| ~ c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1922]) ).
fof(c_0_3037,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Oorder(X12)
| c_HOL_Oord__class_Oless(X11,X10,X12)
| X11 = X10
| ~ c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1923]) ).
fof(c_0_3038,plain,
! [X11,X12,X13] :
( ~ class_Orderings_Oorder(X13)
| c_HOL_Oord__class_Oless(X12,X11,X13)
| X12 = X11
| ~ c_lessequals(X12,X11,X13) ),
inference(variable_rename,[status(thm)],[c_0_1924]) ).
fof(c_0_3039,plain,
! [X11,X12,X13] :
( ~ class_Orderings_Oorder(X13)
| c_HOL_Oord__class_Oless(X12,X11,X13)
| ~ c_lessequals(X12,X11,X13)
| X12 = X11 ),
inference(variable_rename,[status(thm)],[c_0_1925]) ).
fof(c_0_3040,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| X11 = X10
| ~ c_lessequals(X11,X10,X12)
| c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1926]) ).
fof(c_0_3041,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| X11 = X10
| c_HOL_Oord__class_Oless(X11,X10,X12)
| ~ c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1927]) ).
fof(c_0_3042,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Olower__semilattice(X12)
| c_Lattices_Olower__semilattice__class_Oinf(X11,X10,X12) != X11
| c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1928]) ).
fof(c_0_3043,plain,
! [X3,X4] :
( c_lessequals(c_Suc(X3),c_Suc(X4),tc_nat)
| ~ c_lessequals(X3,X4,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1929]) ).
fof(c_0_3044,plain,
! [X3,X4] :
( c_HOL_Oord__class_Oless(c_Suc(X4),c_Suc(X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1930]) ).
fof(c_0_3045,plain,
! [X10,X11] :
( c_HOL_Oord__class_Oless(c_Suc(X10),c_Suc(X11),tc_nat)
| ~ c_HOL_Oord__class_Oless(X10,X11,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1931]) ).
fof(c_0_3046,plain,
! [X3,X4] :
( X4 = X3
| c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1932]) ).
fof(c_0_3047,plain,
! [X3,X4] :
( X4 = X3
| ~ c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat)
| c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1933]) ).
fof(c_0_3048,plain,
! [X3,X4] :
( X3 = X4
| ~ c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat)
| c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1934]) ).
fof(c_0_3049,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Olower__semilattice(X12)
| c_Lattices_Olower__semilattice__class_Oinf(X11,X10,X12) = X10
| ~ c_lessequals(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1935]) ).
fof(c_0_3050,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Olower__semilattice(X12)
| c_Lattices_Olower__semilattice__class_Oinf(X11,X10,X12) = X11
| ~ c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1936]) ).
fof(c_0_3051,plain,
! [X3,X4] :
( c_HOL_Oord__class_Oless(c_Suc(X4),X3,tc_nat)
| c_Suc(X4) = X3
| ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1937]) ).
fof(c_0_3052,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Oorder(X12)
| c_lessequals(X11,X10,X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1938]) ).
fof(c_0_3053,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Opreorder(X12)
| c_lessequals(X11,X10,X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1939]) ).
fof(c_0_3054,plain,
! [X3,X4] :
( c_lessequals(X4,X3,tc_nat)
| ~ c_lessequals(c_Suc(X4),X3,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1940]) ).
fof(c_0_3055,plain,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_lessequals(c_Suc(X3),X4,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1941]) ).
fof(c_0_3056,plain,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_lessequals(c_Suc(X4),X3,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1942]) ).
fof(c_0_3057,plain,
! [X3,X4] :
( c_lessequals(X4,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1943]) ).
fof(c_0_3058,plain,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X4),X3,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1944]) ).
fof(c_0_3059,plain,
! [X8,X9,X10] :
( c_Finite__Set_Ofinite(c_Set_Oinsert(X8,X9,X10),X10)
| ~ c_Finite__Set_Ofinite(X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_1945]) ).
fof(c_0_3060,plain,
! [X8,X9] :
( c_Finite__Set_Ofinite(X8,X9)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(X8,X9),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1946]) ).
fof(c_0_3061,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Oordered__semidom(X6)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X5,X6),c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1947]) ).
fof(c_0_3062,plain,
! [X3,X4] :
( c_lessequals(X4,c_Suc(X3),tc_nat)
| ~ c_lessequals(X4,X3,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1948]) ).
fof(c_0_3063,plain,
! [X3,X4] :
( c_lessequals(c_Suc(X3),X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1949]) ).
fof(c_0_3064,plain,
! [X3,X4] :
( c_lessequals(c_Suc(X4),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1950]) ).
fof(c_0_3065,plain,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat)
| ~ c_lessequals(X4,X3,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1951]) ).
fof(c_0_3066,plain,
! [X10] :
( ~ c_lessequals(X10,X10,tc_nat)
| c_HOL_Oord__class_Oless(X10,c_Suc(X10),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1952]) ).
fof(c_0_3067,plain,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1953]) ).
fof(c_0_3068,plain,
! [X8,X9,X10] :
( c_Set_Oinsert(X8,X9,X10) = X9
| ~ c_in(X8,X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_1954]) ).
fof(c_0_3069,plain,
! [X3,X4] :
( c_HOL_Ominus__class_Ominus(X4,X3,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_lessequals(X4,X3,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1955]) ).
fof(c_0_3070,plain,
! [X3,X4] :
( c_HOL_Ominus__class_Ominus(X4,X3,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(X4,X3,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1956]) ).
fof(c_0_3071,plain,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| X4 = X3
| ~ c_lessequals(X4,X3,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1957]) ).
fof(c_0_3072,plain,
! [X3,X4] :
( X4 = X3
| c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_lessequals(X4,X3,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1958]) ).
fof(c_0_3073,plain,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| X4 = X3
| ~ c_lessequals(X4,X3,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1959]) ).
fof(c_0_3074,plain,
! [X8,X9] :
( ~ class_Orderings_Olinorder(X9)
| c_in(c_Finite__Set_Olinorder__class_OMax(X8,X9),X8,X9)
| X8 = c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))
| ~ c_Finite__Set_Ofinite(X8,X9) ),
inference(variable_rename,[status(thm)],[c_0_1960]) ).
fof(c_0_3075,plain,
! [X8,X9] :
( ~ class_Orderings_Olinorder(X9)
| c_in(c_Finite__Set_Olinorder__class_OMin(X8,X9),X8,X9)
| X8 = c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))
| ~ c_Finite__Set_Ofinite(X8,X9) ),
inference(variable_rename,[status(thm)],[c_0_1961]) ).
fof(c_0_3076,plain,
! [X3,X4] :
( c_Divides_Odiv__class_Omod(X4,X3,tc_nat) = X4
| ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1962]) ).
fof(c_0_3077,plain,
! [X10,X11] :
( c_lessequals(X11,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(X11,X10,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1963]) ).
fof(c_0_3078,plain,
! [X3,X4] :
( c_lessequals(X4,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1964]) ).
fof(c_0_3079,plain,
! [X10,X11] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X11,tc_bool)),X10)),
inference(variable_rename,[status(thm)],[c_0_1965]) ).
fof(c_0_3080,plain,
! [X8,X9] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(X8,X9),tc_nat)
| ~ c_Finite__Set_Ofinite(X8,X9)
| X8 = c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1966]) ).
fof(c_0_3081,plain,
! [X8,X9] : c_Lattices_Olower__semilattice__class_Oinf(X8,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_bool)),tc_fun(X9,tc_bool)) = X8,
inference(variable_rename,[status(thm)],[c_0_1967]) ).
fof(c_0_3082,plain,
! [X7,X8] : c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X8,tc_bool)),X7,tc_fun(X8,tc_bool)) = X7,
inference(variable_rename,[status(thm)],[c_0_1968]) ).
fof(c_0_3083,plain,
! [X8,X9] : c_HOL_Ominus__class_Ominus(X8,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),tc_fun(X9,tc_bool)) = X8,
inference(variable_rename,[status(thm)],[c_0_1969]) ).
fof(c_0_3084,plain,
! [X8,X9] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),X8,tc_fun(X9,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1970]) ).
fof(c_0_3085,plain,
! [X8,X9] : c_lessequals(X8,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_bool)),tc_fun(X9,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1971]) ).
fof(c_0_3086,plain,
! [X8,X9,X10] : c_Set_Oinsert(X8,X9,X10) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1972]) ).
fof(c_0_3087,plain,
! [X8,X9,X10] : c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)) != c_Set_Oinsert(X8,X9,X10),
inference(variable_rename,[status(thm)],[c_0_1973]) ).
fof(c_0_3088,plain,
! [X10,X11] : ~ c_HOL_Oord__class_Oless(X10,X10,tc_fun(X11,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1974]) ).
fof(c_0_3089,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| X11 = X10
| c_HOL_Oord__class_Oless(X11,X10,X12)
| c_HOL_Oord__class_Oless(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1975]) ).
fof(c_0_3090,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| c_HOL_Oord__class_Oless(X10,X11,X12)
| X11 = X10
| c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1976]) ).
fof(c_0_3091,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| c_HOL_Oord__class_Oless(X10,X11,X12)
| c_HOL_Oord__class_Oless(X11,X10,X12)
| X11 = X10 ),
inference(variable_rename,[status(thm)],[c_0_1977]) ).
fof(c_0_3092,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| X11 = X10
| c_HOL_Oord__class_Oless(X10,X11,X12)
| c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1978]) ).
fof(c_0_3093,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__idom(X12)
| c_HOL_Oord__class_Oless(X10,X11,X12)
| c_HOL_Oord__class_Oless(X11,X10,X12)
| X11 = X10 ),
inference(variable_rename,[status(thm)],[c_0_1979]) ).
fof(c_0_3094,plain,
! [X3,X4] : c_HOL_Ominus__class_Ominus(c_Suc(X4),c_Suc(X3),tc_nat) = c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),
inference(variable_rename,[status(thm)],[c_0_1980]) ).
fof(c_0_3095,plain,
! [X3,X4] : c_HOL_Oplus__class_Oplus(c_Suc(X4),X3,tc_nat) = c_HOL_Oplus__class_Oplus(X4,c_Suc(X3),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1981]) ).
fof(c_0_3096,plain,
! [X8,X9] :
( c_Finite__Set_Ocard(X8,X9) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(X8,c_HOL_Ozero__class_Ozero(tc_nat),X9) = c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1982]) ).
fof(c_0_3097,plain,
! [X8,X9] :
( c_Finite__Set_Ocard(X8,X9) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(X8,c_HOL_Ozero__class_Ozero(tc_nat),X9) = c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1983]) ).
fof(c_0_3098,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| c_lessequals(X10,X11,X12)
| c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1984]) ).
fof(c_0_3099,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| c_HOL_Oord__class_Oless(X10,X11,X12)
| c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1985]) ).
fof(c_0_3100,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| c_lessequals(X10,X11,X12)
| c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1986]) ).
fof(c_0_3101,plain,
! [X10,X11] :
( ~ class_Orderings_Olinorder(X11)
| c_HOL_Oord__class_Oless(X10,X10,X11)
| c_lessequals(X10,X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_1987]) ).
fof(c_0_3102,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| c_HOL_Oord__class_Oless(X11,X10,X12)
| c_lessequals(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1988]) ).
fof(c_0_3103,plain,
! [X48,X49,X50] :
( hBOOL(hAPP(X49,X48))
| ~ c_in(X48,X49,X50) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1989])])]) ).
fof(c_0_3104,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Olattice(X12)
| c_Lattices_Olower__semilattice__class_Oinf(X11,X10,X12) = c_Lattices_Olower__semilattice__class_Oinf(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1990]) ).
fof(c_0_3105,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Olower__semilattice(X12)
| c_Lattices_Olower__semilattice__class_Oinf(X11,X10,X12) = c_Lattices_Olower__semilattice__class_Oinf(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1991]) ).
fof(c_0_3106,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X12)
| c_HOL_Oplus__class_Oplus(X11,X10,X12) = c_HOL_Oplus__class_Oplus(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1992]) ).
fof(c_0_3107,plain,
! [X11,X12,X13] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X13)
| c_HOL_Oplus__class_Oplus(X12,X11,X13) = c_HOL_Oplus__class_Oplus(X11,X12,X13) ),
inference(variable_rename,[status(thm)],[c_0_1993]) ).
fof(c_0_3108,plain,
! [X12,X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X14)
| c_HOL_Oplus__class_Oplus(X13,X12,X14) = c_HOL_Oplus__class_Oplus(X12,X13,X14) ),
inference(variable_rename,[status(thm)],[c_0_1994]) ).
fof(c_0_3109,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X13)
| c_HOL_Otimes__class_Otimes(X12,X11,X13) = c_HOL_Otimes__class_Otimes(X11,X12,X13) ),
inference(variable_rename,[status(thm)],[c_0_1995]) ).
fof(c_0_3110,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X12)
| c_HOL_Otimes__class_Otimes(X11,X10,X12) = c_HOL_Otimes__class_Otimes(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1996]) ).
fof(c_0_3111,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Osemiring__1(X6)
| c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X5),X6) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X6),c_Nat_Osemiring__1__class_Oof__nat(X5,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1997]) ).
fof(c_0_3112,plain,
! [X3,X4] :
( c_lessequals(c_Suc(X3),X4,tc_nat)
| c_lessequals(X4,X3,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1998]) ).
fof(c_0_3113,plain,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat)
| c_HOL_Oord__class_Oless(X4,X3,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1999]) ).
fof(c_0_3114,plain,
! [X10] :
( c_HOL_Oord__class_Oless(X10,X10,tc_nat)
| c_HOL_Oord__class_Oless(X10,c_Suc(X10),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2000]) ).
fof(c_0_3115,plain,
! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X5),c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_2001]) ).
fof(c_0_3116,plain,
! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_2002]) ).
fof(c_0_3117,plain,
! [X3,X4] : c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_2003]) ).
fof(c_0_3118,plain,
! [X3,X4] : c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat),
inference(variable_rename,[status(thm)],[c_0_2004]) ).
fof(c_0_3119,plain,
! [X3,X4] :
( c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X3 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(variable_rename,[status(thm)],[c_0_2005]) ).
fof(c_0_3120,plain,
! [X3,X4] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X4,X3,tc_nat)
| X3 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(variable_rename,[status(thm)],[c_0_2006]) ).
fof(c_0_3121,plain,
! [X2] :
( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2007]) ).
fof(c_0_3122,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X13)
| c_HOL_Otimes__class_Otimes(X12,X11,X13) != c_HOL_Ozero__class_Ozero(X13)
| X12 = c_HOL_Ozero__class_Ozero(X13)
| X11 = c_HOL_Ozero__class_Ozero(X13) ),
inference(variable_rename,[status(thm)],[c_0_2008]) ).
fof(c_0_3123,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X13)
| c_HOL_Otimes__class_Otimes(X12,X11,X13) != c_HOL_Ozero__class_Ozero(X13)
| X11 = c_HOL_Ozero__class_Ozero(X13)
| X12 = c_HOL_Ozero__class_Ozero(X13) ),
inference(variable_rename,[status(thm)],[c_0_2009]) ).
fof(c_0_3124,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X13)
| c_HOL_Otimes__class_Otimes(X12,X11,X13) != c_HOL_Ozero__class_Ozero(X13)
| X11 = c_HOL_Ozero__class_Ozero(X13)
| X12 = c_HOL_Ozero__class_Ozero(X13) ),
inference(variable_rename,[status(thm)],[c_0_2010]) ).
fof(c_0_3125,plain,
! [X10,X11] :
( c_HOL_Oord__class_Oless(X10,X11,tc_nat)
| c_HOL_Oord__class_Oless(X11,X10,tc_nat)
| X11 = X10 ),
inference(variable_rename,[status(thm)],[c_0_2011]) ).
fof(c_0_3126,plain,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| X4 = X3 ),
inference(variable_rename,[status(thm)],[c_0_2012]) ).
fof(c_0_3127,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oidom(X12)
| ~ class_Int_Onumber__ring(X12)
| c_HOL_Ominus__class_Ominus(X11,X10,X12) != c_HOL_Ozero__class_Ozero(X12)
| X11 = X10 ),
inference(variable_rename,[status(thm)],[c_0_2013]) ).
fof(c_0_3128,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X6)
| X5 = c_HOL_Ozero__class_Ozero(X6)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_2014]) ).
fof(c_0_3129,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oidom(X12)
| ~ class_Int_Onumber__ring(X12)
| X10 != c_HOL_Oplus__class_Oplus(X10,X11,X12)
| X11 = c_HOL_Ozero__class_Ozero(X12) ),
inference(variable_rename,[status(thm)],[c_0_2015]) ).
fof(c_0_3130,plain,
! [X3,X4] :
( c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X4 = c_HOL_Ozero__class_Ozero(tc_nat)
| X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(variable_rename,[status(thm)],[c_0_2016]) ).
fof(c_0_3131,plain,
! [X3,X4] :
( c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X3 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X3 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_2017])])]) ).
fof(c_0_3132,plain,
! [X3,X4] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X4,X3,tc_nat)
| X4 = c_HOL_Ozero__class_Ozero(tc_nat)
| X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(variable_rename,[status(thm)],[c_0_2018]) ).
fof(c_0_3133,plain,
! [X3,X4] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X4,X3,tc_nat)
| X3 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X3 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_2019])])]) ).
fof(c_0_3134,plain,
! [X3] :
( X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2020]) ).
fof(c_0_3135,plain,
! [X3,X4] :
( c_lessequals(X3,X4,tc_nat)
| c_lessequals(X4,X3,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2021]) ).
fof(c_0_3136,plain,
! [X10,X11] : c_in(X10,c_Orderings_Otop__class_Otop(tc_fun(X11,tc_bool)),X11),
inference(variable_rename,[status(thm)],[c_0_2022]) ).
fof(c_0_3137,plain,
! [X3,X4] : c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) = c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),
inference(variable_rename,[status(thm)],[c_0_2023]) ).
fof(c_0_3138,plain,
! [X3,X4] : c_HOL_Otimes__class_Otimes(X4,X3,tc_nat) = c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),
inference(variable_rename,[status(thm)],[c_0_2024]) ).
fof(c_0_3139,plain,
! [X49,X50] :
( X50 = c_Suc(c_ATP__Linkup_Osko__Nat__XSuc__le__D__1__1(X50))
| ~ c_lessequals(c_Suc(X49),X50,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2025]) ).
fof(c_0_3140,plain,
! [X8,X9,X10] :
( ~ class_Lattices_Obounded__lattice(X10)
| c_Lattices_Olower__semilattice__class_Oinf(X9,X8,X10) != c_Orderings_Otop__class_Otop(X10)
| X9 = c_Orderings_Otop__class_Otop(X10) ),
inference(variable_rename,[status(thm)],[c_0_2026]) ).
fof(c_0_3141,plain,
! [X8,X9,X10] :
( ~ class_Lattices_Obounded__lattice(X10)
| c_Lattices_Olower__semilattice__class_Oinf(X9,X8,X10) != c_Orderings_Otop__class_Otop(X10)
| X8 = c_Orderings_Otop__class_Otop(X10) ),
inference(variable_rename,[status(thm)],[c_0_2027]) ).
fof(c_0_3142,plain,
! [X5,X6] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X6)
| c_HOL_Oplus__class_Oplus(X5,X5,X6) != c_HOL_Ozero__class_Ozero(X6)
| X5 = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_2028]) ).
fof(c_0_3143,plain,
! [X8,X9] : c_HOL_Ominus__class_Ominus(X8,X8,tc_fun(X9,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_2029]) ).
fof(c_0_3144,plain,
! [X3,X4] :
( c_HOL_Otimes__class_Otimes(X4,X3,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X3 = 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_2030])])]) ).
fof(c_0_3145,plain,
! [X3,X4] :
( c_HOL_Otimes__class_Otimes(X4,X3,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(variable_rename,[status(thm)],[c_0_2031]) ).
fof(c_0_3146,plain,
! [X48,X49,X50] :
( c_in(X48,X49,X50)
| ~ hBOOL(hAPP(X49,X48)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_2032])])]) ).
fof(c_0_3147,plain,
! [X3,X4] :
( c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X4 = c_HOL_Ozero__class_Ozero(tc_nat)
| X3 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2033]) ).
fof(c_0_3148,plain,
! [X3,X4] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X4,X3,tc_nat)
| X4 = c_HOL_Ozero__class_Ozero(tc_nat)
| X3 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2034]) ).
fof(c_0_3149,plain,
! [X11,X12,X13] :
( ~ class_OrderedGroup_Oab__group__add(X13)
| c_HOL_Ominus__class_Ominus(X12,X11,X13) != c_HOL_Ozero__class_Ozero(X13)
| X12 = X11 ),
inference(variable_rename,[status(thm)],[c_0_2035]) ).
fof(c_0_3150,plain,
! [X11,X12,X13] :
( ~ class_OrderedGroup_Ogroup__add(X13)
| c_HOL_Ominus__class_Ominus(X12,X11,X13) != c_HOL_Ozero__class_Ozero(X13)
| X12 = X11 ),
inference(variable_rename,[status(thm)],[c_0_2036]) ).
fof(c_0_3151,plain,
! [X27,X28] :
( hBOOL(hAPP(X28,X27))
| ~ hBOOL(hAPP(X28,c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1(X28))) ),
inference(variable_rename,[status(thm)],[c_0_2037]) ).
fof(c_0_3152,plain,
! [X3,X4] :
( c_HOL_Otimes__class_Otimes(X4,X3,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2038]) ).
fof(c_0_3153,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Oordered__semidom(X6)
| c_lessequals(c_HOL_Ozero__class_Ozero(X6),c_Nat_Osemiring__1__class_Oof__nat(X5,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_2039]) ).
fof(c_0_3154,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Oordered__semidom(X6)
| c_lessequals(c_HOL_Ozero__class_Ozero(X6),c_Nat_Osemiring__1__class_Oof__nat(X5,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_2040]) ).
fof(c_0_3155,plain,
! [X3] : ~ c_lessequals(c_Suc(X3),X3,tc_nat),
inference(variable_rename,[status(thm)],[c_0_2041]) ).
fof(c_0_3156,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_2042 ).
fof(c_0_3157,plain,
! [X10,X11] :
( ~ class_Orderings_Opreorder(X11)
| ~ c_HOL_Oord__class_Oless(X10,X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_2043]) ).
fof(c_0_3158,plain,
! [X10,X11] :
( ~ class_Orderings_Olinorder(X11)
| ~ c_HOL_Oord__class_Oless(X10,X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_2044]) ).
fof(c_0_3159,plain,
! [X10,X11] :
( ~ class_Orderings_Oorder(X11)
| ~ c_HOL_Oord__class_Oless(X10,X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_2045]) ).
fof(c_0_3160,plain,
! [X3,X4] :
( X4 != c_HOL_Otimes__class_Otimes(X4,X3,tc_nat)
| X4 = c_HOL_Ozero__class_Ozero(tc_nat)
| X3 = c_HOL_Oone__class_Oone(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2046]) ).
fof(c_0_3161,plain,
! [X3] :
( X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2047]) ).
fof(c_0_3162,plain,
! [X2] :
( X2 = c_HOL_Oone__class_Oone(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2048]) ).
fof(c_0_3163,plain,
! [X3,X4] :
( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X4,X3,tc_nat)
| X3 = c_HOL_Oone__class_Oone(tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_2049])])]) ).
fof(c_0_3164,plain,
! [X3,X4] :
( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X4,X3,tc_nat)
| X4 = c_HOL_Oone__class_Oone(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2050]) ).
fof(c_0_3165,plain,
! [X3,X4] :
( c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X3 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_2051])])]) ).
fof(c_0_3166,plain,
! [X3,X4] :
( c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2052]) ).
fof(c_0_3167,plain,
! [X3,X4] :
( c_HOL_Otimes__class_Otimes(X4,X3,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
| X4 = c_HOL_Oone__class_Oone(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2053]) ).
fof(c_0_3168,plain,
! [X3,X4] :
( c_HOL_Otimes__class_Otimes(X4,X3,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
| X3 = c_HOL_Oone__class_Oone(tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_2054])])]) ).
fof(c_0_3169,plain,
! [X10,X11] :
( X10 != c_HOL_Oplus__class_Oplus(X10,X11,tc_nat)
| X11 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2055]) ).
fof(c_0_3170,plain,
! [X3,X4] :
( c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) != X4
| X3 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_2056])])]) ).
fof(c_0_3171,plain,
! [X3] : ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_2057]) ).
fof(c_0_3172,plain,
! [X2] : ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_2058]) ).
fof(c_0_3173,plain,
! [X55,X56,X57] :
( X56 = X55
| ~ c_fequal(X56,X55,X57) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_2059])])]) ).
fof(c_0_3174,plain,
! [X5] : c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_2060]) ).
fof(c_0_3175,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_2061 ).
fof(c_0_3176,plain,
! [X3] : ~ c_HOL_Oord__class_Oless(X3,X3,tc_nat),
inference(variable_rename,[status(thm)],[c_0_2062]) ).
fof(c_0_3177,plain,
! [X10] : ~ c_HOL_Oord__class_Oless(X10,X10,tc_nat),
inference(variable_rename,[status(thm)],[c_0_2063]) ).
fof(c_0_3178,plain,
! [X8,X9] : c_Lattices_Olower__semilattice__class_Oinf(X8,X8,tc_fun(X9,tc_bool)) = X8,
inference(variable_rename,[status(thm)],[c_0_2064]) ).
fof(c_0_3179,plain,
! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X5),c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_2065]) ).
fof(c_0_3180,plain,
! [X10,X11] : c_lessequals(X10,X10,tc_fun(X11,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_2066]) ).
fof(c_0_3181,plain,
! [X8,X9] : c_lessequals(X8,X8,tc_fun(X9,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_2067]) ).
fof(c_0_3182,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_2068 ).
fof(c_0_3183,plain,
! [X8,X9] :
( c_Finite__Set_Ocard(X8,X9) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_Finite__Set_Ofinite(X8,X9)
| X8 = c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_2069]) ).
fof(c_0_3184,plain,
! [X10,X11] :
( ~ class_Ring__and__Field_Oidom(X11)
| ~ class_Int_Onumber__ring(X11)
| X10 = c_HOL_Oplus__class_Oplus(X10,c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_2070]) ).
fof(c_0_3185,axiom,
c_HOL_Oplus__class_Oplus(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_2071 ).
fof(c_0_3186,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_2072 ).
fof(c_0_3187,axiom,
c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_2073 ).
fof(c_0_3188,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
c_0_2074 ).
fof(c_0_3189,plain,
! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),c_HOL_Oone__class_Oone(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_2075]) ).
fof(c_0_3190,plain,
! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_lessequals(c_HOL_Ozero__class_Ozero(X5),c_HOL_Oone__class_Oone(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_2076]) ).
fof(c_0_3191,plain,
! [X5] :
( ~ class_Finite__Set_Ofinite_Ofinite(X5)
| c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5) ),
inference(variable_rename,[status(thm)],[c_0_2077]) ).
fof(c_0_3192,plain,
! [X10,X11] :
( ~ class_Ring__and__Field_Oidom(X11)
| ~ class_Int_Onumber__ring(X11)
| c_HOL_Ominus__class_Ominus(X10,X10,X11) = c_HOL_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[c_0_2078]) ).
fof(c_0_3193,plain,
! [X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| c_Divides_Odiv__class_Omod(X5,c_HOL_Oone__class_Oone(X6),X6) = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_2079]) ).
fof(c_0_3194,plain,
! [X10,X11] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X11)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X11),X10,X11) = c_HOL_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[c_0_2080]) ).
fof(c_0_3195,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Omult__zero(X6)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X6),X5,X6) = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_2081]) ).
fof(c_0_3196,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Omult__zero(X6)
| c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X6),X6) = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_2082]) ).
fof(c_0_3197,plain,
! [X11,X12] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X12)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X12),X11,X12) = c_HOL_Ozero__class_Ozero(X12) ),
inference(variable_rename,[status(thm)],[c_0_2083]) ).
fof(c_0_3198,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X6)
| c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X6),X6) = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_2084]) ).
fof(c_0_3199,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X6)
| c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X6),X6) = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_2085]) ).
fof(c_0_3200,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X6)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X6),X5,X6) = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_2086]) ).
fof(c_0_3201,plain,
! [X10,X11] :
( ~ class_Lattices_Obounded__lattice(X11)
| c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X11),X10,X11) = c_Orderings_Obot__class_Obot(X11) ),
inference(variable_rename,[status(thm)],[c_0_2087]) ).
fof(c_0_3202,plain,
! [X10,X11] :
( ~ class_Lattices_Obounded__lattice(X11)
| c_Lattices_Olower__semilattice__class_Oinf(X10,c_Orderings_Obot__class_Obot(X11),X11) = c_Orderings_Obot__class_Obot(X11) ),
inference(variable_rename,[status(thm)],[c_0_2088]) ).
fof(c_0_3203,plain,
! [X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X6),X5,X6) = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_2089]) ).
fof(c_0_3204,plain,
! [X5,X6] :
( ~ class_OrderedGroup_Ogroup__add(X6)
| c_HOL_Ominus__class_Ominus(X5,c_HOL_Ozero__class_Ozero(X6),X6) = X5 ),
inference(variable_rename,[status(thm)],[c_0_2090]) ).
fof(c_0_3205,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X6)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X6),X5,X6) = X5 ),
inference(variable_rename,[status(thm)],[c_0_2091]) ).
fof(c_0_3206,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X6)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X6),X6) = X5 ),
inference(variable_rename,[status(thm)],[c_0_2092]) ).
fof(c_0_3207,plain,
! [X5,X6] :
( ~ class_OrderedGroup_Omonoid__add(X6)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X6),X6) = X5 ),
inference(variable_rename,[status(thm)],[c_0_2093]) ).
fof(c_0_3208,plain,
! [X5,X6] :
( ~ class_OrderedGroup_Omonoid__add(X6)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X6),X5,X6) = X5 ),
inference(variable_rename,[status(thm)],[c_0_2094]) ).
fof(c_0_3209,plain,
! [X5,X6] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X6)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X6),X6) = X5 ),
inference(variable_rename,[status(thm)],[c_0_2095]) ).
fof(c_0_3210,plain,
! [X5,X6] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X6)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X6),X5,X6) = X5 ),
inference(variable_rename,[status(thm)],[c_0_2096]) ).
fof(c_0_3211,plain,
! [X10,X11] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X11)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X11),X10,X11) = X10 ),
inference(variable_rename,[status(thm)],[c_0_2097]) ).
fof(c_0_3212,plain,
! [X10,X11] :
( ~ class_Lattices_Obounded__lattice(X11)
| c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(X11),X10,X11) = X10 ),
inference(variable_rename,[status(thm)],[c_0_2098]) ).
fof(c_0_3213,plain,
! [X10,X11] :
( ~ class_Lattices_Obounded__lattice(X11)
| c_Lattices_Olower__semilattice__class_Oinf(X10,c_Orderings_Otop__class_Otop(X11),X11) = X10 ),
inference(variable_rename,[status(thm)],[c_0_2099]) ).
fof(c_0_3214,plain,
! [X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| c_Divides_Odiv__class_Omod(X5,c_HOL_Ozero__class_Ozero(X6),X6) = X5 ),
inference(variable_rename,[status(thm)],[c_0_2100]) ).
fof(c_0_3215,plain,
! [X10,X11] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X11)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X11),X10,X11) = X10 ),
inference(variable_rename,[status(thm)],[c_0_2101]) ).
fof(c_0_3216,plain,
! [X5,X6] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X6)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X6),X5,X6) = X5 ),
inference(variable_rename,[status(thm)],[c_0_2102]) ).
fof(c_0_3217,plain,
! [X5,X6] :
( ~ class_OrderedGroup_Omonoid__mult(X6)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X6),X5,X6) = X5 ),
inference(variable_rename,[status(thm)],[c_0_2103]) ).
fof(c_0_3218,plain,
! [X5,X6] :
( ~ class_OrderedGroup_Omonoid__mult(X6)
| c_HOL_Otimes__class_Otimes(X5,c_HOL_Oone__class_Oone(X6),X6) = X5 ),
inference(variable_rename,[status(thm)],[c_0_2104]) ).
fof(c_0_3219,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X6)
| c_HOL_Otimes__class_Otimes(X5,c_HOL_Oone__class_Oone(X6),X6) = X5 ),
inference(variable_rename,[status(thm)],[c_0_2105]) ).
fof(c_0_3220,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X6)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X6),X5,X6) = X5 ),
inference(variable_rename,[status(thm)],[c_0_2106]) ).
fof(c_0_3221,plain,
! [X5] : c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_2107]) ).
fof(c_0_3222,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_2108 ).
fof(c_0_3223,plain,
! [X10,X11] :
( ~ class_Orderings_Obot(X11)
| c_lessequals(c_Orderings_Obot__class_Obot(X11),X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_2109]) ).
fof(c_0_3224,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X6)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X6),X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_2110]) ).
fof(c_0_3225,plain,
! [X10,X11] :
( ~ class_Orderings_Otop(X11)
| c_lessequals(X10,c_Orderings_Otop__class_Otop(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_2111]) ).
fof(c_0_3226,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X6)
| c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_2112]) ).
fof(c_0_3227,plain,
! [X2] : c_Divides_Odiv__class_Omod(X2,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_2113]) ).
fof(c_0_3228,plain,
! [X5] : c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),
inference(variable_rename,[status(thm)],[c_0_2114]) ).
fof(c_0_3229,plain,
! [X10,X11] :
( ~ class_OrderedGroup_Oab__group__add(X11)
| c_HOL_Ominus__class_Ominus(X10,X10,X11) = c_HOL_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[c_0_2115]) ).
fof(c_0_3230,plain,
! [X10,X11] :
( ~ class_OrderedGroup_Ogroup__add(X11)
| c_HOL_Ominus__class_Ominus(X10,X10,X11) = c_HOL_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[c_0_2116]) ).
fof(c_0_3231,plain,
! [X5,X6] :
( ~ class_OrderedGroup_Ogroup__add(X6)
| c_HOL_Ominus__class_Ominus(X5,X5,X6) = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_2117]) ).
fof(c_0_3232,plain,
! [X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| c_Divides_Odiv__class_Omod(X5,X5,X6) = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_2118]) ).
fof(c_0_3233,plain,
! [X3] : c_lessequals(c_Suc(X3),c_Suc(X3),tc_nat),
inference(variable_rename,[status(thm)],[c_0_2119]) ).
fof(c_0_3234,plain,
! [X6] : c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X6,tc_nat),
inference(variable_rename,[status(thm)],[c_0_2120]) ).
fof(c_0_3235,plain,
! [X3] : c_HOL_Ominus__class_Ominus(c_Suc(X3),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X3,
inference(variable_rename,[status(thm)],[c_0_2121]) ).
fof(c_0_3236,plain,
! [X10,X11] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X11)
| c_HOL_Otimes__class_Otimes(X10,X10,X11) = X10 ),
inference(variable_rename,[status(thm)],[c_0_2122]) ).
fof(c_0_3237,plain,
! [X10,X11] :
( ~ class_Lattices_Olower__semilattice(X11)
| c_Lattices_Olower__semilattice__class_Oinf(X10,X10,X11) = X10 ),
inference(variable_rename,[status(thm)],[c_0_2123]) ).
fof(c_0_3238,plain,
! [X10] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X10),tc_nat),
inference(variable_rename,[status(thm)],[c_0_2124]) ).
fof(c_0_3239,plain,
! [X3] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X3),tc_nat),
inference(variable_rename,[status(thm)],[c_0_2125]) ).
fof(c_0_3240,plain,
! [X10,X11] :
( ~ class_Orderings_Oorder(X11)
| c_lessequals(X10,X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_2126]) ).
fof(c_0_3241,plain,
! [X10,X11] :
( ~ class_Orderings_Opreorder(X11)
| c_lessequals(X10,X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_2127]) ).
fof(c_0_3242,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X6)
| c_Ring__and__Field_Odvd__class_Odvd(X5,X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_2128]) ).
fof(c_0_3243,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_2129 ).
fof(c_0_3244,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_2130 ).
fof(c_0_3245,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_2131 ).
fof(c_0_3246,plain,
! [X3] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| X3 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2132]) ).
fof(c_0_3247,plain,
! [X3] : c_Suc(X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X3,tc_nat),
inference(variable_rename,[status(thm)],[c_0_2133]) ).
fof(c_0_3248,plain,
! [X3] : c_Suc(X3) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_2134]) ).
fof(c_0_3249,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_2135 ).
fof(c_0_3250,plain,
! [X3] : c_HOL_Oord__class_Oless(X3,c_Suc(X3),tc_nat),
inference(variable_rename,[status(thm)],[c_0_2136]) ).
fof(c_0_3251,plain,
! [X10] : c_HOL_Oord__class_Oless(X10,c_Suc(X10),tc_nat),
inference(variable_rename,[status(thm)],[c_0_2137]) ).
fof(c_0_3252,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_2138 ).
fof(c_0_3253,plain,
! [X3] : c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_2139]) ).
fof(c_0_3254,plain,
! [X2] : c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_2140]) ).
fof(c_0_3255,plain,
! [X3] : c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_2141]) ).
fof(c_0_3256,plain,
! [X2] : c_HOL_Ominus__class_Ominus(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X2,
inference(variable_rename,[status(thm)],[c_0_2142]) ).
fof(c_0_3257,plain,
! [X2] : c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X2,
inference(variable_rename,[status(thm)],[c_0_2143]) ).
fof(c_0_3258,plain,
! [X3] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) = X3,
inference(variable_rename,[status(thm)],[c_0_2144]) ).
fof(c_0_3259,plain,
! [X10] : X10 = c_HOL_Oplus__class_Oplus(X10,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_2145]) ).
fof(c_0_3260,plain,
! [X3] : c_HOL_Otimes__class_Otimes(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X3,
inference(variable_rename,[status(thm)],[c_0_2146]) ).
fof(c_0_3261,plain,
! [X3] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X3,tc_nat) = X3,
inference(variable_rename,[status(thm)],[c_0_2147]) ).
fof(c_0_3262,plain,
! [X3] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat),
inference(variable_rename,[status(thm)],[c_0_2148]) ).
fof(c_0_3263,plain,
! [X2] : c_HOL_Ominus__class_Ominus(X2,X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_2149]) ).
fof(c_0_3264,plain,
! [X10,X11] : c_fequal(X10,X10,X11),
inference(variable_rename,[status(thm)],[c_0_2150]) ).
fof(c_0_3265,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| c_SetInterval_Oord__class_OatLeast(X11,X12) != c_SetInterval_Oord__class_OatLeast(X10,X12)
| X11 = X10 ),
inference(variable_rename,[status(thm)],[c_0_2151]) ).
fof(c_0_3266,plain,
! [X5,X6,X7] :
( ~ class_Nat_Osemiring__char__0(X7)
| c_Nat_Osemiring__1__class_Oof__nat(X6,X7) != c_Nat_Osemiring__1__class_Oof__nat(X5,X7)
| X6 = X5 ),
inference(variable_rename,[status(thm)],[c_0_2152]) ).
fof(c_0_3267,plain,
! [X3] : c_lessequals(X3,X3,tc_nat),
inference(variable_rename,[status(thm)],[c_0_2153]) ).
fof(c_0_3268,plain,
! [X10] : c_lessequals(X10,X10,tc_nat),
inference(variable_rename,[status(thm)],[c_0_2154]) ).
fof(c_0_3269,plain,
! [X10] : c_Ring__and__Field_Odvd__class_Odvd(X10,X10,tc_nat),
inference(variable_rename,[status(thm)],[c_0_2155]) ).
fof(c_0_3270,plain,
! [X54,X55] :
( class_Finite__Set_Ofinite_Ofinite(tc_fun(X54,X55))
| ~ class_Finite__Set_Ofinite_Ofinite(X55)
| ~ class_Finite__Set_Ofinite_Ofinite(X54) ),
inference(variable_rename,[status(thm)],[c_0_2156]) ).
fof(c_0_3271,plain,
! [X54,X55] :
( class_HOL_Oord(tc_fun(X54,X55))
| ~ class_HOL_Oord(X55) ),
inference(variable_rename,[status(thm)],[c_0_2157]) ).
fof(c_0_3272,plain,
! [X54,X55] :
( class_Orderings_Obot(tc_fun(X54,X55))
| ~ class_Orderings_Obot(X55) ),
inference(variable_rename,[status(thm)],[c_0_2158]) ).
fof(c_0_3273,plain,
! [X54,X55] :
( class_Orderings_Otop(tc_fun(X54,X55))
| ~ class_Orderings_Otop(X55) ),
inference(variable_rename,[status(thm)],[c_0_2159]) ).
fof(c_0_3274,plain,
! [X54,X55] :
( class_Orderings_Oorder(tc_fun(X54,X55))
| ~ class_Orderings_Oorder(X55) ),
inference(variable_rename,[status(thm)],[c_0_2160]) ).
fof(c_0_3275,plain,
! [X54,X55] :
( class_Lattices_Olattice(tc_fun(X54,X55))
| ~ class_Lattices_Olattice(X55) ),
inference(variable_rename,[status(thm)],[c_0_2161]) ).
fof(c_0_3276,plain,
! [X54,X55] :
( class_Orderings_Opreorder(tc_fun(X54,X55))
| ~ class_Orderings_Opreorder(X55) ),
inference(variable_rename,[status(thm)],[c_0_2162]) ).
fof(c_0_3277,plain,
! [X54,X55] :
( class_Lattices_Obounded__lattice(tc_fun(X54,X55))
| ~ class_Lattices_Obounded__lattice(X55) ),
inference(variable_rename,[status(thm)],[c_0_2163]) ).
fof(c_0_3278,plain,
! [X54,X55] :
( class_Lattices_Olower__semilattice(tc_fun(X54,X55))
| ~ class_Lattices_Olattice(X55) ),
inference(variable_rename,[status(thm)],[c_0_2164]) ).
fof(c_0_3279,plain,
! [X54,X55] :
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X54,X55))
| ~ class_Complete__Lattice_Ocomplete__lattice(X55) ),
inference(variable_rename,[status(thm)],[c_0_2165]) ).
fof(c_0_3280,plain,
! [X8,X9] :
( c_Finite__Set_Ocard(X8,X9) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Finite__Set_Ofinite(X8,X9) ),
inference(variable_rename,[status(thm)],[c_0_2166]) ).
fof(c_0_3281,plain,
! [X5] :
( ~ class_Ring__and__Field_Osemiring__1(X5)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_2167]) ).
fof(c_0_3282,plain,
! [X5] :
( ~ class_Ring__and__Field_Osemiring__1(X5)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X5) = c_HOL_Oone__class_Oone(X5) ),
inference(variable_rename,[status(thm)],[c_0_2168]) ).
fof(c_0_3283,plain,
! [X8,X9] :
( ~ class_Finite__Set_Ofinite_Ofinite(X9)
| c_Finite__Set_Ofinite(X8,X9) ),
inference(variable_rename,[status(thm)],[c_0_2169]) ).
fof(c_0_3284,plain,
! [X5] :
( ~ class_Ring__and__Field_Ozero__neq__one(X5)
| c_HOL_Oone__class_Oone(X5) != c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_2170]) ).
fof(c_0_3285,plain,
! [X5] :
( ~ class_Ring__and__Field_Ozero__neq__one(X5)
| c_HOL_Ozero__class_Ozero(X5) != c_HOL_Oone__class_Oone(X5) ),
inference(variable_rename,[status(thm)],[c_0_2171]) ).
fof(c_0_3286,plain,
! [X10,X11] :
( c_Suc(X11) != c_Suc(X10)
| X11 = X10 ),
inference(variable_rename,[status(thm)],[c_0_2172]) ).
fof(c_0_3287,plain,
! [X52,X53] :
( c_Suc(X53) != c_Suc(X52)
| X53 = X52 ),
inference(variable_rename,[status(thm)],[c_0_2173]) ).
fof(c_0_3288,plain,
! [X42] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X42),
inference(variable_rename,[status(thm)],[c_0_2174]) ).
fof(c_0_3289,plain,
! [X2] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X2),
inference(variable_rename,[status(thm)],[c_0_2175]) ).
fof(c_0_3290,plain,
! [X42] : c_Suc(X42) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_2176]) ).
fof(c_0_3291,plain,
! [X2] : c_Suc(X2) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_2177]) ).
fof(c_0_3292,axiom,
c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_2178 ).
fof(c_0_3293,plain,
! [X3] : c_Suc(X3) != X3,
inference(variable_rename,[status(thm)],[c_0_2179]) ).
fof(c_0_3294,plain,
! [X3] : X3 != c_Suc(X3),
inference(variable_rename,[status(thm)],[c_0_2180]) ).
fof(c_0_3295,axiom,
class_HOL_Oord(tc_bool),
c_0_2181 ).
fof(c_0_3296,axiom,
class_Orderings_Obot(tc_bool),
c_0_2182 ).
fof(c_0_3297,axiom,
class_Orderings_Otop(tc_bool),
c_0_2183 ).
fof(c_0_3298,axiom,
class_Orderings_Oorder(tc_bool),
c_0_2184 ).
fof(c_0_3299,axiom,
class_Lattices_Olattice(tc_bool),
c_0_2185 ).
fof(c_0_3300,axiom,
class_Orderings_Opreorder(tc_bool),
c_0_2186 ).
fof(c_0_3301,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
c_0_2187 ).
fof(c_0_3302,axiom,
class_Lattices_Obounded__lattice(tc_bool),
c_0_2188 ).
fof(c_0_3303,axiom,
class_Lattices_Olower__semilattice(tc_bool),
c_0_2189 ).
fof(c_0_3304,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
c_0_2190 ).
fof(c_0_3305,axiom,
class_HOL_Oord(tc_nat),
c_0_2191 ).
fof(c_0_3306,axiom,
class_Orderings_Obot(tc_nat),
c_0_2192 ).
fof(c_0_3307,axiom,
class_Orderings_Oorder(tc_nat),
c_0_2193 ).
fof(c_0_3308,axiom,
class_Lattices_Olattice(tc_nat),
c_0_2194 ).
fof(c_0_3309,axiom,
class_Orderings_Olinorder(tc_nat),
c_0_2195 ).
fof(c_0_3310,axiom,
class_Orderings_Opreorder(tc_nat),
c_0_2196 ).
fof(c_0_3311,axiom,
class_Ring__and__Field_Odvd(tc_nat),
c_0_2197 ).
fof(c_0_3312,axiom,
class_Nat_Osemiring__char__0(tc_nat),
c_0_2198 ).
fof(c_0_3313,axiom,
class_Divides_Osemiring__div(tc_nat),
c_0_2199 ).
fof(c_0_3314,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
c_0_2200 ).
fof(c_0_3315,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
c_0_2201 ).
fof(c_0_3316,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
c_0_2202 ).
fof(c_0_3317,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
c_0_2203 ).
fof(c_0_3318,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
c_0_2204 ).
fof(c_0_3319,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
c_0_2205 ).
fof(c_0_3320,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
c_0_2206 ).
fof(c_0_3321,axiom,
class_Lattices_Olower__semilattice(tc_nat),
c_0_2207 ).
fof(c_0_3322,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
c_0_2208 ).
fof(c_0_3323,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
c_0_2209 ).
fof(c_0_3324,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
c_0_2210 ).
fof(c_0_3325,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
c_0_2211 ).
fof(c_0_3326,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
c_0_2212 ).
fof(c_0_3327,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
c_0_2213 ).
fof(c_0_3328,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
c_0_2214 ).
fof(c_0_3329,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
c_0_2215 ).
fof(c_0_3330,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
c_0_2216 ).
fof(c_0_3331,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
c_0_2217 ).
fof(c_0_3332,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
c_0_2218 ).
fof(c_0_3333,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
c_0_2219 ).
fof(c_0_3334,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
c_0_2220 ).
fof(c_0_3335,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
c_0_2221 ).
fof(c_0_3336,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
c_0_2222 ).
fof(c_0_3337,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
c_0_2223 ).
fof(c_0_3338,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
c_0_2224 ).
fof(c_0_3339,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
c_0_2225 ).
fof(c_0_3340,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
c_0_2226 ).
fof(c_0_3341,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
c_0_2227 ).
cnf(c_0_3342,plain,
( c_lessequals(c_Set_Oimage(X1,X2,X4,X5),X3,tc_fun(X5,tc_bool))
| ~ c_in(hAPP(X1,c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1(X2,X3,X1,X4,X5)),X3,X5) ),
inference(split_conjunct,[status(thm)],[c_0_2228]) ).
cnf(c_0_3343,plain,
( c_lessequals(c_Set_Oimage(X1,X2,X4,X5),X3,tc_fun(X5,tc_bool))
| ~ c_in(hAPP(X1,c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1(X2,X3,X1,X4,X5)),X3,X5) ),
inference(split_conjunct,[status(thm)],[c_0_2229]) ).
cnf(c_0_3344,plain,
( c_Set_Oimage(X1,X2,X3,X4) = c_Set_Oimage(X5,X2,X3,X4)
| hAPP(X1,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X2,X1,X5,X3,X4)) != hAPP(X5,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X2,X1,X5,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2230]) ).
cnf(c_0_3345,plain,
( X1 = X2
| c_Fun_Ofun__upd(c_Fun_Ofun__upd(X3,X1,X4,X5,X6),X2,X7,X5,X6) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X3,X2,X7,X5,X6),X1,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_2231]) ).
cnf(c_0_3346,plain,
c_Fun_Ofun__upd(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X2,X6,X4,X5) = c_Fun_Ofun__upd(X1,X2,X6,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_2232]) ).
cnf(c_0_3347,plain,
( c_Set_Oimage(c_Fun_Ofun__upd(X4,X1,X5,X3,X6),X2,X3,X6) = c_Set_Oinsert(X5,c_Set_Oimage(X4,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3,X6),X6)
| ~ c_in(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2233]) ).
cnf(c_0_3348,plain,
( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2),c_Finite__Set_Ocard(X1,X2),tc_nat)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_in(X3,X1,X2)
| ~ c_in(X4,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2234]) ).
cnf(c_0_3349,plain,
( c_in(X5,c_Set_Oimage(X1,X2,X3,X4),X4)
| c_Fun_Oinj__on(c_Fun_Ofun__upd(X1,X6,X5,X3,X4),X2,X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2235]) ).
cnf(c_0_3350,plain,
( X1 = c_Set_Oimage(X3,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X4,X1,X3,X5,X2),X5,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X1,c_Set_Oimage(X3,X4,X5,X2),tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2236]) ).
cnf(c_0_3351,plain,
( X1 = c_Set_Oimage(X2,c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(X3,X1,X2,X4,X5),X4,X5)
| ~ c_lessequals(X1,c_Set_Oimage(X2,X3,X4,X5),tc_fun(X5,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2237]) ).
cnf(c_0_3352,plain,
( c_lessequals(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X4,X1,X3,X5,X2),X4,tc_fun(X5,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X1,c_Set_Oimage(X3,X4,X5,X2),tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2238]) ).
cnf(c_0_3353,plain,
( c_lessequals(c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(X3,X1,X2,X4,X5),X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Set_Oimage(X2,X3,X4,X5),tc_fun(X5,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2239]) ).
cnf(c_0_3354,plain,
( c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X4,X1,X3,X5,X2),X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X1,c_Set_Oimage(X3,X4,X5,X2),tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2240]) ).
cnf(c_0_3355,plain,
( c_in(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(X3,X2,X1,X4,X5),X3,X4)
| ~ c_in(X1,c_Set_Oimage(X2,X3,X4,X5),X5) ),
inference(split_conjunct,[status(thm)],[c_0_2241]) ).
cnf(c_0_3356,plain,
( c_in(c_ATP__Linkup_Osko__Set__XimageE__1__1(X3,X1,X2,X4,X5),X3,X4)
| ~ c_in(X1,c_Set_Oimage(X2,X3,X4,X5),X5) ),
inference(split_conjunct,[status(thm)],[c_0_2242]) ).
cnf(c_0_3357,plain,
( X1 = X6
| ~ c_in(X1,c_Set_Oimage(X2,X3,X4,X5),X5)
| ~ c_in(X6,c_Set_Oimage(X2,X3,X4,X5),X5)
| hAPP(c_Hilbert__Choice_Oinv__into(X3,X2,X4,X5),X1) != hAPP(c_Hilbert__Choice_Oinv__into(X3,X2,X4,X5),X6) ),
inference(split_conjunct,[status(thm)],[c_0_2243]) ).
cnf(c_0_3358,plain,
( X1 = hAPP(X2,c_ATP__Linkup_Osko__Set__XimageE__1__1(X3,X1,X2,X4,X5))
| ~ c_in(X1,c_Set_Oimage(X2,X3,X4,X5),X5) ),
inference(split_conjunct,[status(thm)],[c_0_2244]) ).
cnf(c_0_3359,plain,
( X1 = hAPP(X2,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(X3,X2,X1,X4,X5))
| ~ c_in(X1,c_Set_Oimage(X2,X3,X4,X5),X5) ),
inference(split_conjunct,[status(thm)],[c_0_2245]) ).
cnf(c_0_3360,plain,
( ~ c_Fun_Oinj__on(X1,c_Set_Oinsert(X2,X3,X4),X4,X5)
| ~ c_in(hAPP(X1,X2),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4,X5),X5) ),
inference(split_conjunct,[status(thm)],[c_0_2246]) ).
cnf(c_0_3361,plain,
( c_in(c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1(X1,X2,X3,X4,X5),X1,X4)
| c_lessequals(c_Set_Oimage(X3,X1,X4,X5),X2,tc_fun(X5,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2247]) ).
cnf(c_0_3362,plain,
( c_in(c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1(X1,X2,X3,X4,X5),X1,X4)
| c_lessequals(c_Set_Oimage(X3,X1,X4,X5),X2,tc_fun(X5,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2248]) ).
cnf(c_0_3363,plain,
c_lessequals(c_Set_Oimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4,X5),c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,X2,X4,X5),c_Set_Oimage(X1,X3,X4,X5),tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_2249]) ).
cnf(c_0_3364,plain,
c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool)),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X3,tc_bool)),X3,X4),tc_fun(X4,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_2250]) ).
cnf(c_0_3365,plain,
( c_in(X1,X2,X3)
| c_Set_Oimage(c_Fun_Ofun__upd(X4,X1,X5,X3,X6),X2,X3,X6) = c_Set_Oimage(X4,X2,X3,X6) ),
inference(split_conjunct,[status(thm)],[c_0_2251]) ).
cnf(c_0_3366,plain,
( c_in(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X1,X2,X3,X4,X5),X1,X4)
| c_Set_Oimage(X2,X1,X4,X5) = c_Set_Oimage(X3,X1,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_2252]) ).
cnf(c_0_3367,plain,
( c_in(hAPP(X4,X1),c_Inductive_Ocomplete__lattice__class_Ogfp(X6,tc_fun(X5,tc_bool)),X5)
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(c_Set_Oimage(X4,X2,X3,X5),hAPP(X6,c_Set_Oimage(X4,X2,X3,X5)),tc_fun(X5,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2253]) ).
cnf(c_0_3368,plain,
( c_Finite__Set_Ocard(X2,X3) = c_Finite__Set_Ocard(X5,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| ~ c_Fun_Oinj__on(X6,X5,X4,X3)
| ~ c_lessequals(c_Set_Oimage(X6,X5,X4,X3),X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2254]) ).
cnf(c_0_3369,plain,
( c_in(hAPP(X1,X5),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3,X4),X4)
| c_Fun_Oinj__on(X1,c_Set_Oinsert(X5,X2,X3),X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2255]) ).
cnf(c_0_3370,plain,
( hBOOL(hAPP(X1,X2))
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X2,tc_nat),X3,tc_nat)))
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2256]) ).
cnf(c_0_3371,plain,
( X1 = X2
| hAPP(c_Fun_Ofun__upd(X3,X2,X4,X5,X6),X1) = hAPP(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_2257]) ).
cnf(c_0_3372,plain,
( X1 = X2
| hAPP(c_Fun_Ofun__upd(X3,X2,X4,X5,X6),X1) = hAPP(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_2258]) ).
cnf(c_0_3373,plain,
hAPP(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X2) = X3,
inference(split_conjunct,[status(thm)],[c_0_2259]) ).
cnf(c_0_3374,plain,
hAPP(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X2) = X3,
inference(split_conjunct,[status(thm)],[c_0_2260]) ).
cnf(c_0_3375,plain,
( c_lessequals(X4,X5,tc_fun(X2,tc_bool))
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| ~ c_lessequals(c_Set_Oimage(X1,X4,X2,X3),c_Set_Oimage(X1,X5,X2,X3),tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2261]) ).
cnf(c_0_3376,plain,
( c_Set_Oimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X3,tc_bool)),X3,X4) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,X5,X3,X4),c_Set_Oimage(X1,X6,X3,X4),tc_fun(X4,tc_bool))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X6,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2262]) ).
cnf(c_0_3377,plain,
( c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X3,tc_bool)),X3,X4) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X1,X5,X3,X4),c_Set_Oimage(X1,X6,X3,X4),tc_fun(X4,tc_bool))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X6,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2263]) ).
cnf(c_0_3378,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2264]) ).
cnf(c_0_3379,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X5,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X3,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X4,tc_nat),X5,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2265]) ).
cnf(c_0_3380,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X5,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X4,tc_nat),X5,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2266]) ).
cnf(c_0_3381,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2267]) ).
cnf(c_0_3382,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4),X4)
| ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4),X4)
| ~ class_Ring__and__Field_Opordered__ring(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2268]) ).
cnf(c_0_3383,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3),X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3),X6,X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2269]) ).
cnf(c_0_3384,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3),X6,X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2270]) ).
cnf(c_0_3385,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4),X4)
| ~ class_Ring__and__Field_Opordered__ring(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2271]) ).
cnf(c_0_3386,plain,
( c_lessequals(c_Set_Ovimage(X1,X4,X2,X3),X5,tc_fun(X2,tc_bool))
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| ~ c_lessequals(X4,c_Set_Oimage(X1,X5,X2,X3),tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2272]) ).
cnf(c_0_3387,plain,
( c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X2,tc_bool)),X2,X3) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X1,X4,X2,X3),c_Set_Oimage(X1,X5,X2,X3),tc_fun(X3,tc_bool))
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2273]) ).
cnf(c_0_3388,plain,
( c_Set_Oimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X2,tc_bool)),X2,X3) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,X4,X2,X3),c_Set_Oimage(X1,X5,X2,X3),tc_fun(X3,tc_bool))
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2274]) ).
cnf(c_0_3389,plain,
( c_in(hAPP(c_Hilbert__Choice_Oinv__into(X3,X2,X4,X5),X1),X3,X4)
| ~ c_in(X1,c_Set_Oimage(X2,X3,X4,X5),X5) ),
inference(split_conjunct,[status(thm)],[c_0_2275]) ).
cnf(c_0_3390,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2276]) ).
cnf(c_0_3391,plain,
( c_lessequals(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X5,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2277]) ).
cnf(c_0_3392,plain,
( c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X5,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2278]) ).
cnf(c_0_3393,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2279]) ).
cnf(c_0_3394,plain,
( hAPP(X1,X2) = X3
| c_Fun_Ofun__upd(X1,X2,X3,X4,X5) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_2280]) ).
cnf(c_0_3395,plain,
( c_lessequals(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X1,X3),X2,X3),X6,X3),X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2281]) ).
cnf(c_0_3396,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X6,X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2282]) ).
cnf(c_0_3397,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2283]) ).
cnf(c_0_3398,plain,
( c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X1,X3),X2,X3),X6,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2284]) ).
cnf(c_0_3399,plain,
( hAPP(X2,hAPP(c_Hilbert__Choice_Oinv__into(X3,X2,X4,X5),X1)) = X1
| ~ c_in(X1,c_Set_Oimage(X2,X3,X4,X5),X5) ),
inference(split_conjunct,[status(thm)],[c_0_2285]) ).
cnf(c_0_3400,plain,
( c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1,X2,X3),c_Set_Oimage(X1,X4,X2,X3),X3,X2) = X4
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2286]) ).
cnf(c_0_3401,plain,
( c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1,X2,X3),c_Set_Oimage(X1,X4,X2,X3),X3,X2) = X4
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2287]) ).
cnf(c_0_3402,plain,
( c_Set_Oimage(c_Hilbert__Choice_Oinv__into(X2,X1,X3,X4),c_Set_Oimage(X1,X5,X3,X4),X4,X3) = X5
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2288]) ).
cnf(c_0_3403,plain,
( hBOOL(hAPP(X2,hAPP(X1,X5)))
| ~ hBOOL(hAPP(c_Set_Ovimage(X1,X2,X3,X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_2289]) ).
cnf(c_0_3404,plain,
( c_lessequals(c_Set_Oimage(X1,X4,X2,X3),c_Set_Oimage(X1,X5,X2,X3),tc_fun(X3,tc_bool))
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| ~ c_lessequals(X4,X5,tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2290]) ).
cnf(c_0_3405,plain,
( c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X3,X2,X4,X5),X1,X5,X4)
| ~ c_lessequals(X1,c_Set_Oimage(X2,X3,X4,X5),tc_fun(X5,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2291]) ).
cnf(c_0_3406,plain,
( c_Set_Oimage(X3,X1,X2,X2) = X1
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(c_Set_Oimage(X3,X1,X2,X2),X1,tc_fun(X2,tc_bool))
| ~ c_Fun_Oinj__on(X3,X1,X2,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2292]) ).
cnf(c_0_3407,plain,
c_lessequals(c_Set_Oimage(X1,c_Set_Ovimage(X1,X2,X3,X4),X3,X4),X2,tc_fun(X4,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_2293]) ).
cnf(c_0_3408,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2294]) ).
cnf(c_0_3409,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X5,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2295]) ).
cnf(c_0_3410,plain,
( hAPP(X2,X1) = X3
| ~ c_in(X1,c_Set_Ovimage(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X5,X4),X5) ),
inference(split_conjunct,[status(thm)],[c_0_2296]) ).
cnf(c_0_3411,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X6,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X5,X2,X3),X3),X6,X3),X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2297]) ).
cnf(c_0_3412,plain,
c_Set_Ovimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X5,X4) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Ovimage(X1,X2,X5,X4),c_Set_Ovimage(X1,X3,X5,X4),tc_fun(X5,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_2298]) ).
cnf(c_0_3413,plain,
c_Set_Ovimage(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X5,X4) = c_HOL_Ominus__class_Ominus(c_Set_Ovimage(X1,X2,X5,X4),c_Set_Ovimage(X1,X3,X5,X4),tc_fun(X5,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_2299]) ).
cnf(c_0_3414,plain,
( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2300]) ).
cnf(c_0_3415,plain,
( c_in(X4,X5,X2)
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| ~ c_in(hAPP(X1,X4),c_Set_Oimage(X1,X5,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_2301]) ).
cnf(c_0_3416,plain,
( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2302]) ).
cnf(c_0_3417,plain,
( c_lessequals(c_Finite__Set_Ocard(X2,X3),c_Finite__Set_Ocard(X5,X4),tc_nat)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| ~ c_Finite__Set_Ofinite(X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2303]) ).
cnf(c_0_3418,plain,
c_Set_Oimage(X1,c_Set_Ovimage(X1,X2,X3,X4),X3,X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),tc_fun(X4,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_2304]) ).
cnf(c_0_3419,plain,
( c_in(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2305]) ).
cnf(c_0_3420,plain,
( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2),c_Finite__Set_Ocard(X1,X2),tc_nat)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_in(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2306]) ).
cnf(c_0_3421,plain,
( c_in(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_in(X1,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2307]) ).
cnf(c_0_3422,plain,
( c_lessequals(X1,c_Set_Oinsert(X2,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2308]) ).
cnf(c_0_3423,plain,
( c_Finite__Set_Ocard(c_Set_Oinsert(X3,X1,X2),X2) = c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2))
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2309]) ).
cnf(c_0_3424,plain,
( c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2)) = c_Finite__Set_Ocard(X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_in(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2310]) ).
cnf(c_0_3425,plain,
( c_lessequals(X1,c_Set_Oinsert(X2,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| ~ c_in(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2311]) ).
cnf(c_0_3426,plain,
( c_lessequals(X1,c_Set_Oinsert(X2,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| ~ c_in(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2312]) ).
cnf(c_0_3427,plain,
( c_lessequals(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2),c_Finite__Set_Ocard(X1,X2),tc_nat)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2313]) ).
cnf(c_0_3428,plain,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5)
| c_Set_Oimage(X3,X1,X4,X5) != c_Set_Oimage(X3,X2,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_2314]) ).
cnf(c_0_3429,plain,
c_Fun_Ofun__upd(X1,X2,hAPP(X1,X2),X3,X4) = X1,
inference(split_conjunct,[status(thm)],[c_0_2315]) ).
cnf(c_0_3430,plain,
c_Fun_Ofun__upd(X1,X2,hAPP(X1,X2),X3,X4) = X1,
inference(split_conjunct,[status(thm)],[c_0_2316]) ).
cnf(c_0_3431,plain,
c_Fun_Ofun__upd(X1,X2,hAPP(X1,X2),X3,X4) = X1,
inference(split_conjunct,[status(thm)],[c_0_2317]) ).
cnf(c_0_3432,plain,
( c_Set_Ovimage(X1,c_Set_Oimage(X1,X4,X2,X3),X2,X3) = X4
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2318]) ).
cnf(c_0_3433,plain,
( c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(X1,X2,X3,X4),X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2319]) ).
cnf(c_0_3434,plain,
( c_lessequals(c_Set_Oimage(X4,X1,X3,X5),c_Set_Oimage(X4,X2,X3,X5),tc_fun(X5,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2320]) ).
cnf(c_0_3435,plain,
( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2321]) ).
cnf(c_0_3436,plain,
( c_lessequals(c_Set_Ovimage(X4,X1,X5,X3),c_Set_Ovimage(X4,X2,X5,X3),tc_fun(X5,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2322]) ).
cnf(c_0_3437,plain,
( c_Fun_Oinj__on(X3,X1,X2,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X1,c_Set_Oimage(X3,X1,X2,X2),tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2323]) ).
cnf(c_0_3438,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X6,X2,X3),X3),X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2324]) ).
cnf(c_0_3439,plain,
( hBOOL(hAPP(c_Set_Ovimage(X2,X1,X4,X5),X3))
| ~ hBOOL(hAPP(X1,hAPP(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2325]) ).
cnf(c_0_3440,plain,
( c_in(hAPP(X1,X4),c_Set_Oimage(X1,X5,X2,X3),X3)
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| ~ c_in(X4,X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2326]) ).
cnf(c_0_3441,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,tc_nat),X2,tc_nat),X3,tc_nat),tc_nat)
| ~ c_lessequals(X4,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2327]) ).
cnf(c_0_3442,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),X2,tc_nat),X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),X4,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2328]) ).
cnf(c_0_3443,plain,
( c_lessequals(c_Finite__Set_Ocard(c_Set_Oimage(X3,X1,X2,X4),X4),c_Finite__Set_Ocard(X1,X2),tc_nat)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2329]) ).
cnf(c_0_3444,plain,
( hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,X1,X3),hAPP(X2,X4)) = X4
| ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2330]) ).
cnf(c_0_3445,plain,
( hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1,X2,X3),hAPP(X1,X4)) = X4
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2331]) ).
cnf(c_0_3446,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(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),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2332]) ).
cnf(c_0_3447,plain,
( c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_Finite__Set_Ofinite(X2,X3)
| c_Finite__Set_Ocard(c_Set_Oimage(X1,X2,X3,X4),X4) != c_Finite__Set_Ocard(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2333]) ).
cnf(c_0_3448,plain,
( c_in(X2,X3,X4)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| ~ c_in(X2,X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2334]) ).
cnf(c_0_3449,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X1,X3),X2,X3),X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,X3),X5,X3)
| ~ class_Ring__and__Field_Oring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2335]) ).
cnf(c_0_3450,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X3)
| ~ class_Ring__and__Field_Oring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2336]) ).
cnf(c_0_3451,plain,
c_in(X1,c_Set_Ovimage(X2,c_Set_Oinsert(hAPP(X2,X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X4,X3),X4),
inference(split_conjunct,[status(thm)],[c_0_2337]) ).
cnf(c_0_3452,plain,
( c_in(hAPP(X1,X6),X5,X4)
| ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| ~ c_in(X6,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2338]) ).
cnf(c_0_3453,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),X3,tc_nat))) ),
inference(split_conjunct,[status(thm)],[c_0_2339]) ).
cnf(c_0_3454,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),X3,tc_nat))) ),
inference(split_conjunct,[status(thm)],[c_0_2340]) ).
cnf(c_0_3455,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(X4,X1,tc_nat),tc_nat),X2,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_2341]) ).
cnf(c_0_3456,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| ~ c_in(X2,X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2342]) ).
cnf(c_0_3457,plain,
( hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),hAPP(X2,X5)) = X5
| ~ c_Fun_Oinj__on(X2,X1,X3,X4)
| ~ c_in(X5,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2343]) ).
cnf(c_0_3458,plain,
( hAPP(c_Hilbert__Choice_Oinv__into(X2,X1,X3,X4),hAPP(X1,X5)) = X5
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_in(X5,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2344]) ).
cnf(c_0_3459,plain,
( c_Finite__Set_Ofinite(c_Set_Ovimage(X3,X1,X4,X2),X4)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Fun_Oinj__on(X3,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2345]) ).
cnf(c_0_3460,plain,
( X3 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2346]) ).
cnf(c_0_3461,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2347]) ).
cnf(c_0_3462,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2348]) ).
cnf(c_0_3463,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),X4,tc_nat) = X5
| ~ c_lessequals(X2,X1,tc_nat)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2349]) ).
cnf(c_0_3464,plain,
( X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),X4,tc_nat),X5,tc_nat)
| ~ c_lessequals(X3,X2,tc_nat)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X1,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X5,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2350]) ).
cnf(c_0_3465,plain,
( c_in(hAPP(X2,X1),X3,X5)
| ~ c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4) ),
inference(split_conjunct,[status(thm)],[c_0_2351]) ).
cnf(c_0_3466,plain,
( c_in(hAPP(X2,X1),X3,X5)
| ~ c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4) ),
inference(split_conjunct,[status(thm)],[c_0_2352]) ).
cnf(c_0_3467,plain,
( c_Finite__Set_Ofinite(X3,X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,c_Set_Oimage(X4,X1,X2,X5),tc_fun(X5,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2353]) ).
cnf(c_0_3468,plain,
( c_Finite__Set_Ocard(c_Set_Oimage(X3,X1,X2,X4),X4) = c_Finite__Set_Ocard(X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Fun_Oinj__on(X3,X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2354]) ).
cnf(c_0_3469,plain,
( c_in(X3,X4,X2)
| c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,X4,X2),tc_fun(X2,tc_bool)),X2) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X2,tc_bool)),X2),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_in(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2355]) ).
cnf(c_0_3470,plain,
c_Set_Oimage(X1,c_Set_Oinsert(X2,X3,X4),X4,X5) = c_Set_Oinsert(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5),
inference(split_conjunct,[status(thm)],[c_0_2356]) ).
cnf(c_0_3471,plain,
( c_Finite__Set_Ocard(c_Set_Oimage(X1,X2,X3,X4),X4) = c_Finite__Set_Ocard(X2,X3)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2357]) ).
cnf(c_0_3472,plain,
( c_Set_Oinsert(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5) = c_Set_Oimage(X4,X2,X3,X5)
| ~ c_in(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2358]) ).
cnf(c_0_3473,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3) = X6
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3)
| ~ class_Ring__and__Field_Oring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2359]) ).
cnf(c_0_3474,plain,
( X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4)
| ~ class_Ring__and__Field_Oring(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2360]) ).
cnf(c_0_3475,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,X3),X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3),X5,X3)
| ~ class_Ring__and__Field_Osemiring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2361]) ).
cnf(c_0_3476,plain,
( X1 = X2
| X3 = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(split_conjunct,[status(thm)],[c_0_2362]) ).
cnf(c_0_3477,plain,
( X1 = X2
| X3 = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(split_conjunct,[status(thm)],[c_0_2363]) ).
cnf(c_0_3478,plain,
( c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(X1,X3),c_Finite__Set_Ocard(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3),tc_nat)
| ~ c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_2364]) ).
cnf(c_0_3479,plain,
( X1 = X2
| X1 = X3
| c_Set_Oinsert(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
inference(split_conjunct,[status(thm)],[c_0_2365]) ).
cnf(c_0_3480,plain,
( X1 = X2
| X3 = X2
| c_Set_Oinsert(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_2366]) ).
cnf(c_0_3481,plain,
( X1 = X2
| X3 = X2
| c_Set_Oinsert(X3,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_2367]) ).
cnf(c_0_3482,plain,
( X1 = X2
| X1 = X3
| c_Set_Oinsert(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
inference(split_conjunct,[status(thm)],[c_0_2368]) ).
cnf(c_0_3483,plain,
c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_2369]) ).
cnf(c_0_3484,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat),X4,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2370]) ).
cnf(c_0_3485,plain,
( X1 = X2
| X3 = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2371]) ).
cnf(c_0_3486,plain,
( X1 = X2
| X3 = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2372]) ).
cnf(c_0_3487,plain,
( c_Fun_Oinj__on(X1,X3,X4,X5)
| ~ c_Fun_Oinj__on(X1,c_Set_Oinsert(X2,X3,X4),X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_2373]) ).
cnf(c_0_3488,plain,
( c_Fun_Oinj__on(X1,c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X3,tc_bool)),X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2374]) ).
cnf(c_0_3489,plain,
( c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(X1,X2),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_in(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2375]) ).
cnf(c_0_3490,plain,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool)),X4)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)),X4) ),
inference(split_conjunct,[status(thm)],[c_0_2376]) ).
cnf(c_0_3491,plain,
( c_Fun_Oinj__on(X1,X5,X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2377]) ).
cnf(c_0_3492,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X1,X4,X3),c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3)
| ~ class_Divides_Oring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2378]) ).
cnf(c_0_3493,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_2379]) ).
cnf(c_0_3494,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(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_2380]) ).
cnf(c_0_3495,plain,
c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat)),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X3),X2,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2381]) ).
cnf(c_0_3496,plain,
( c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = X2
| ~ c_in(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2382]) ).
cnf(c_0_3497,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(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),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2383]) ).
cnf(c_0_3498,plain,
c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = c_Set_Oinsert(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_2384]) ).
cnf(c_0_3499,plain,
( c_in(X3,X1,X2)
| c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2) = c_Finite__Set_Ocard(X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2385]) ).
cnf(c_0_3500,plain,
c_in(hAPP(X1,X2),c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X4),
inference(split_conjunct,[status(thm)],[c_0_2386]) ).
cnf(c_0_3501,plain,
( c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5)
| ~ c_in(hAPP(X1,X2),X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2387]) ).
cnf(c_0_3502,plain,
( c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5)
| ~ c_in(hAPP(X1,X2),X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2388]) ).
cnf(c_0_3503,plain,
( c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5)
| ~ c_in(hAPP(X1,X2),X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2389]) ).
cnf(c_0_3504,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(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_Oring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2390]) ).
cnf(c_0_3505,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_2391]) ).
cnf(c_0_3506,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(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_2392]) ).
cnf(c_0_3507,plain,
( c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5)
| ~ c_in(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2393]) ).
cnf(c_0_3508,plain,
( c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5)
| ~ c_in(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2394]) ).
cnf(c_0_3509,plain,
( c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5)
| ~ c_in(X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2395]) ).
cnf(c_0_3510,plain,
( c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5)
| ~ c_in(X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2396]) ).
cnf(c_0_3511,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_2397]) ).
cnf(c_0_3512,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_2398]) ).
cnf(c_0_3513,plain,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_2399]) ).
cnf(c_0_3514,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2400]) ).
cnf(c_0_3515,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2401]) ).
cnf(c_0_3516,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2402]) ).
cnf(c_0_3517,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2403]) ).
cnf(c_0_3518,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2404]) ).
cnf(c_0_3519,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2405]) ).
cnf(c_0_3520,plain,
( c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2406]) ).
cnf(c_0_3521,plain,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2407]) ).
cnf(c_0_3522,plain,
( c_lessequals(hAPP(X1,X3),hAPP(X1,X4),X2)
| ~ c_lessequals(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1(X1,X2)),hAPP(X1,c_Suc(c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1(X1,X2))),X2)
| ~ c_lessequals(X3,X4,tc_nat)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2408]) ).
cnf(c_0_3523,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X5,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2409]) ).
cnf(c_0_3524,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2410]) ).
cnf(c_0_3525,plain,
c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool)),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_2411]) ).
cnf(c_0_3526,plain,
c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_2412]) ).
cnf(c_0_3527,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_2413]) ).
cnf(c_0_3528,plain,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X4,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_2414]) ).
cnf(c_0_3529,plain,
( X1 = X4
| ~ c_in(X1,X2,X3)
| ~ c_in(X4,X2,X3)
| ~ c_Fun_Oinj__on(X5,X2,X3,X6)
| hAPP(X5,X1) != hAPP(X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2415]) ).
cnf(c_0_3530,plain,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| ~ c_in(X1,X4,X5)
| ~ c_in(X2,X4,X5)
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2416]) ).
cnf(c_0_3531,plain,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| ~ c_in(X1,X4,X5)
| ~ c_in(X2,X4,X5)
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2417]) ).
cnf(c_0_3532,plain,
( X5 = X6
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_in(X5,X2,X3)
| ~ c_in(X6,X2,X3)
| hAPP(X1,X5) != hAPP(X1,X6) ),
inference(split_conjunct,[status(thm)],[c_0_2418]) ).
cnf(c_0_3533,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X2),c_HOL_Otimes__class_Otimes(X1,X1,X2),X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2419]) ).
cnf(c_0_3534,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2420]) ).
cnf(c_0_3535,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2421]) ).
cnf(c_0_3536,plain,
( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(X3,X2,tc_nat)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X2,X5,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2422]) ).
cnf(c_0_3537,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X1 = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| ~ c_lessequals(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2423]) ).
cnf(c_0_3538,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_2424]) ).
cnf(c_0_3539,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_2425]) ).
cnf(c_0_3540,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2426]) ).
cnf(c_0_3541,plain,
( c_lessequals(X2,X4,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2427]) ).
cnf(c_0_3542,plain,
( c_lessequals(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(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_2428]) ).
cnf(c_0_3543,plain,
( c_lessequals(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(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_2429]) ).
cnf(c_0_3544,plain,
( 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)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__semiring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2430]) ).
cnf(c_0_3545,plain,
( 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)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semiring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2431]) ).
cnf(c_0_3546,plain,
( 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)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2432]) ).
cnf(c_0_3547,plain,
( 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)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2433]) ).
cnf(c_0_3548,plain,
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2434]) ).
cnf(c_0_3549,plain,
( hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2435]) ).
cnf(c_0_3550,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_2436]) ).
cnf(c_0_3551,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_2437]) ).
cnf(c_0_3552,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_2438]) ).
cnf(c_0_3553,plain,
( c_lessequals(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_lessequals(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_2439]) ).
cnf(c_0_3554,plain,
( c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(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_2440]) ).
cnf(c_0_3555,plain,
( c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(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(split_conjunct,[status(thm)],[c_0_2441]) ).
cnf(c_0_3556,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_2442]) ).
cnf(c_0_3557,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_2443]) ).
cnf(c_0_3558,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2444]) ).
cnf(c_0_3559,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2445]) ).
cnf(c_0_3560,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_2446]) ).
cnf(c_0_3561,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_2447]) ).
cnf(c_0_3562,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_2448]) ).
cnf(c_0_3563,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_2449]) ).
cnf(c_0_3564,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X2,X3,X4),X4),X3,X4) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4)
| ~ class_Divides_Osemiring__div(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2450]) ).
cnf(c_0_3565,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X2,X3),X4,X3),X2,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2451]) ).
cnf(c_0_3566,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3)
| ~ class_Divides_Oring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2452]) ).
cnf(c_0_3567,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3),X4,X3)
| ~ class_Divides_Oring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2453]) ).
cnf(c_0_3568,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_2454]) ).
cnf(c_0_3569,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2455]) ).
cnf(c_0_3570,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_2456]) ).
cnf(c_0_3571,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_2457]) ).
cnf(c_0_3572,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_2458]) ).
cnf(c_0_3573,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2459]) ).
cnf(c_0_3574,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2460]) ).
cnf(c_0_3575,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_2461]) ).
cnf(c_0_3576,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_2462]) ).
cnf(c_0_3577,plain,
c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),
inference(split_conjunct,[status(thm)],[c_0_2463]) ).
cnf(c_0_3578,plain,
( c_Finite__Set_Ofinite(c_Set_Oimage(X3,X1,X2,X4),X4)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2464]) ).
cnf(c_0_3579,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = X4
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) != c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2465]) ).
cnf(c_0_3580,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2466]) ).
cnf(c_0_3581,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2467]) ).
cnf(c_0_3582,plain,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5)
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2468]) ).
cnf(c_0_3583,plain,
( c_HOL_Ominus__class_Ominus(X3,c_Suc(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_Suc(X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2469]) ).
cnf(c_0_3584,plain,
( c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X2),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2470]) ).
cnf(c_0_3585,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2471]) ).
cnf(c_0_3586,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2472]) ).
cnf(c_0_3587,plain,
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X5,X4),X4)
| ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| ~ c_lessequals(X3,X5,X4)
| ~ class_OrderedGroup_Opordered__ab__group__add(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2473]) ).
cnf(c_0_3588,plain,
( c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(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_2474]) ).
cnf(c_0_3589,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_2475]) ).
cnf(c_0_3590,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = X3
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2476]) ).
cnf(c_0_3591,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3),
inference(split_conjunct,[status(thm)],[c_0_2477]) ).
cnf(c_0_3592,plain,
( hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)))
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2478]) ).
cnf(c_0_3593,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_2479]) ).
cnf(c_0_3594,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_2480]) ).
cnf(c_0_3595,plain,
( c_lessequals(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2481]) ).
cnf(c_0_3596,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),X2,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2482]) ).
cnf(c_0_3597,plain,
( c_in(X4,X1,X3)
| c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2483]) ).
cnf(c_0_3598,plain,
( c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2484]) ).
cnf(c_0_3599,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2485]) ).
cnf(c_0_3600,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2486]) ).
cnf(c_0_3601,plain,
( c_lessequals(X2,X4,X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2487]) ).
cnf(c_0_3602,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2488]) ).
cnf(c_0_3603,plain,
( c_in(X2,X3,X4)
| c_in(X2,X1,X4)
| c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2489]) ).
cnf(c_0_3604,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2490]) ).
cnf(c_0_3605,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2491]) ).
cnf(c_0_3606,plain,
( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X1
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2492]) ).
cnf(c_0_3607,plain,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2493]) ).
cnf(c_0_3608,plain,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2494]) ).
cnf(c_0_3609,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_lessequals(X3,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2495]) ).
cnf(c_0_3610,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
| ~ c_lessequals(X3,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2496]) ).
cnf(c_0_3611,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_2497]) ).
cnf(c_0_3612,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_2498]) ).
cnf(c_0_3613,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_2499]) ).
cnf(c_0_3614,plain,
( c_Finite__Set_Ocard(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = c_Suc(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2))
| c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2500]) ).
cnf(c_0_3615,plain,
( c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2501]) ).
cnf(c_0_3616,plain,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2502]) ).
cnf(c_0_3617,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_2503]) ).
cnf(c_0_3618,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_2504]) ).
cnf(c_0_3619,plain,
c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_2505]) ).
cnf(c_0_3620,plain,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_2506]) ).
cnf(c_0_3621,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_2507]) ).
cnf(c_0_3622,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Set_Oimage(X4,X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2508]) ).
cnf(c_0_3623,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Set_Oimage(X3,X1,X2,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2509]) ).
cnf(c_0_3624,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Omult__mono1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2510]) ).
cnf(c_0_3625,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Omult__mono(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2511]) ).
cnf(c_0_3626,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Omult__mono(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2512]) ).
cnf(c_0_3627,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2513]) ).
cnf(c_0_3628,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2514]) ).
cnf(c_0_3629,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_2515]) ).
cnf(c_0_3630,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_2516]) ).
cnf(c_0_3631,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_2517]) ).
cnf(c_0_3632,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_2518]) ).
cnf(c_0_3633,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_2519]) ).
cnf(c_0_3634,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_2520]) ).
cnf(c_0_3635,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_2521]) ).
cnf(c_0_3636,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_2522]) ).
cnf(c_0_3637,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_2523]) ).
cnf(c_0_3638,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_2524]) ).
cnf(c_0_3639,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_2525]) ).
cnf(c_0_3640,plain,
( c_lessequals(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_lessequals(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2526]) ).
cnf(c_0_3641,plain,
( c_lessequals(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_lessequals(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2527]) ).
cnf(c_0_3642,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2528]) ).
cnf(c_0_3643,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2529]) ).
cnf(c_0_3644,plain,
( c_HOL_Oord__class_Oless(X1,X3,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| ~ c_in(X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2530]) ).
cnf(c_0_3645,plain,
( c_in(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_2531]) ).
cnf(c_0_3646,plain,
( c_lessequals(X3,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2532]) ).
cnf(c_0_3647,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2533]) ).
cnf(c_0_3648,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_2534]) ).
cnf(c_0_3649,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),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_2535]) ).
cnf(c_0_3650,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2536]) ).
cnf(c_0_3651,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2537]) ).
cnf(c_0_3652,plain,
( c_in(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X3,tc_bool)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_2538]) ).
cnf(c_0_3653,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2539]) ).
cnf(c_0_3654,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X2),c_HOL_Otimes__class_Otimes(X1,X1,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2540]) ).
cnf(c_0_3655,plain,
( c_lessequals(X1,X2,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2541]) ).
cnf(c_0_3656,plain,
( c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2542]) ).
cnf(c_0_3657,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2543]) ).
cnf(c_0_3658,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2544]) ).
cnf(c_0_3659,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2545]) ).
cnf(c_0_3660,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_2546]) ).
cnf(c_0_3661,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_2547]) ).
cnf(c_0_3662,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2548]) ).
cnf(c_0_3663,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4),X2,X4) = c_Divides_Odiv__class_Omod(X1,X2,X4)
| ~ class_Divides_Osemiring__div(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2549]) ).
cnf(c_0_3664,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4),X3,X4) = c_Divides_Odiv__class_Omod(X1,X3,X4)
| ~ class_Divides_Osemiring__div(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2550]) ).
cnf(c_0_3665,plain,
( c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_OrderedGroup_Olordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2551]) ).
cnf(c_0_3666,plain,
( c_HOL_Oplus__class_Oplus(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X2,X4),c_HOL_Oplus__class_Oplus(X1,X3,X4),X4)
| ~ class_OrderedGroup_Olordered__ab__group__add(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2552]) ).
cnf(c_0_3667,plain,
( c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_OrderedGroup_Olordered__ab__group__add__meet(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2553]) ).
cnf(c_0_3668,plain,
( c_HOL_Oplus__class_Oplus(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X2,X4),c_HOL_Oplus__class_Oplus(X1,X3,X4),X4)
| ~ class_OrderedGroup_Olordered__ab__group__add__meet(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2554]) ).
cnf(c_0_3669,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_2555]) ).
cnf(c_0_3670,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_2556]) ).
cnf(c_0_3671,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_2557]) ).
cnf(c_0_3672,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_2558]) ).
cnf(c_0_3673,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_2559]) ).
cnf(c_0_3674,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_2560]) ).
cnf(c_0_3675,plain,
( c_lessequals(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_lessequals(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2561]) ).
cnf(c_0_3676,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2562]) ).
cnf(c_0_3677,plain,
( hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2563]) ).
cnf(c_0_3678,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(X3,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2564]) ).
cnf(c_0_3679,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2565]) ).
cnf(c_0_3680,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X3,X4,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2566]) ).
cnf(c_0_3681,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X4,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X3,X4,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2567]) ).
cnf(c_0_3682,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X4,tc_nat),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_2568]) ).
cnf(c_0_3683,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_2569]) ).
cnf(c_0_3684,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_2570]) ).
cnf(c_0_3685,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_2571]) ).
cnf(c_0_3686,plain,
( c_in(X1,X2,X3)
| c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2572]) ).
cnf(c_0_3687,plain,
( c_in(X2,X1,X4)
| c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2573]) ).
cnf(c_0_3688,plain,
( X1 = X2
| ~ c_in(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_2574]) ).
cnf(c_0_3689,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(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_2575]) ).
cnf(c_0_3690,plain,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(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_2576]) ).
cnf(c_0_3691,plain,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(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_2577]) ).
cnf(c_0_3692,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(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_2578]) ).
cnf(c_0_3693,plain,
c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat),X2,tc_nat) = c_Divides_Odiv__class_Omod(X3,X2,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2579]) ).
cnf(c_0_3694,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_2580]) ).
cnf(c_0_3695,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_2581]) ).
cnf(c_0_3696,plain,
( c_in(X1,X2,X3)
| c_in(X1,X4,X3)
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2582]) ).
cnf(c_0_3697,plain,
( c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(X3,X2),c_Finite__Set_Ocard(X1,X2),tc_nat)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2583]) ).
cnf(c_0_3698,plain,
( X1 = X4
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2584]) ).
cnf(c_0_3699,plain,
( c_lessequals(c_Set_Oinsert(X4,X1,X3),c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2585]) ).
cnf(c_0_3700,plain,
( ~ c_in(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4)
| ~ c_in(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2586]) ).
cnf(c_0_3701,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat) = X1
| ~ c_lessequals(X2,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2587]) ).
cnf(c_0_3702,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat)
| ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2588]) ).
cnf(c_0_3703,plain,
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2589]) ).
cnf(c_0_3704,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2590]) ).
cnf(c_0_3705,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2591]) ).
cnf(c_0_3706,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_2592]) ).
cnf(c_0_3707,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_2593]) ).
cnf(c_0_3708,plain,
( c_HOL_Oplus__class_Oplus(X1,X2,X3) = X4
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X5,X2,X3),X3) != c_HOL_Oplus__class_Oplus(X5,X4,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2594]) ).
cnf(c_0_3709,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),X1,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2595]) ).
cnf(c_0_3710,plain,
( c_HOL_Oplus__class_Oplus(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),X1,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2596]) ).
cnf(c_0_3711,plain,
( c_HOL_Ominus__class_Ominus(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),X2,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2597]) ).
cnf(c_0_3712,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),X1,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2598]) ).
cnf(c_0_3713,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),X1,tc_nat) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2599]) ).
cnf(c_0_3714,plain,
( c_lessequals(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool))
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2600]) ).
cnf(c_0_3715,plain,
( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2601]) ).
cnf(c_0_3716,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2602]) ).
cnf(c_0_3717,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2603]) ).
cnf(c_0_3718,plain,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2604]) ).
cnf(c_0_3719,plain,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2605]) ).
cnf(c_0_3720,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2606]) ).
cnf(c_0_3721,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2607]) ).
cnf(c_0_3722,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2608]) ).
cnf(c_0_3723,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2609]) ).
cnf(c_0_3724,plain,
( c_HOL_Oord__class_Oless(X3,X1,tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(X3,X2),c_Finite__Set_Ocard(X1,X2),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2610]) ).
cnf(c_0_3725,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_2611]) ).
cnf(c_0_3726,plain,
( c_in(X1,X2,X4)
| ~ c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4) ),
inference(split_conjunct,[status(thm)],[c_0_2612]) ).
cnf(c_0_3727,plain,
( c_in(X1,X3,X4)
| ~ c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4) ),
inference(split_conjunct,[status(thm)],[c_0_2613]) ).
cnf(c_0_3728,plain,
( c_in(X1,X2,X4)
| ~ c_in(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4) ),
inference(split_conjunct,[status(thm)],[c_0_2614]) ).
cnf(c_0_3729,plain,
( c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,X3)
| ~ c_in(X1,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2615]) ).
cnf(c_0_3730,plain,
( c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,X3)
| ~ c_in(X1,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2616]) ).
cnf(c_0_3731,plain,
( c_in(X1,c_Inductive_Ocomplete__lattice__class_Ogfp(X4,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X2,hAPP(X4,X2),tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2617]) ).
cnf(c_0_3732,plain,
( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2618]) ).
cnf(c_0_3733,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_2619]) ).
cnf(c_0_3734,plain,
( c_lessequals(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_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2620]) ).
cnf(c_0_3735,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_2621]) ).
cnf(c_0_3736,plain,
( c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2622]) ).
cnf(c_0_3737,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2623]) ).
cnf(c_0_3738,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2624]) ).
cnf(c_0_3739,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2625]) ).
cnf(c_0_3740,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2626]) ).
cnf(c_0_3741,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2627]) ).
cnf(c_0_3742,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2628]) ).
cnf(c_0_3743,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2629]) ).
cnf(c_0_3744,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_2630]) ).
cnf(c_0_3745,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_2631]) ).
cnf(c_0_3746,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_2632]) ).
cnf(c_0_3747,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_2633]) ).
cnf(c_0_3748,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(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_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2634]) ).
cnf(c_0_3749,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2635]) ).
cnf(c_0_3750,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2636]) ).
cnf(c_0_3751,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_2637]) ).
cnf(c_0_3752,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_2638]) ).
cnf(c_0_3753,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2639]) ).
cnf(c_0_3754,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2640]) ).
cnf(c_0_3755,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2641]) ).
cnf(c_0_3756,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2642]) ).
cnf(c_0_3757,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2643]) ).
cnf(c_0_3758,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2644]) ).
cnf(c_0_3759,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2645]) ).
cnf(c_0_3760,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2646]) ).
cnf(c_0_3761,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2647]) ).
cnf(c_0_3762,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(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(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2648]) ).
cnf(c_0_3763,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2649]) ).
cnf(c_0_3764,plain,
c_lessequals(X1,c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X1,X1,tc_nat),tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2650]) ).
cnf(c_0_3765,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),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2651]) ).
cnf(c_0_3766,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_2652]) ).
cnf(c_0_3767,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_2653]) ).
cnf(c_0_3768,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),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_2654]) ).
cnf(c_0_3769,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2655]) ).
cnf(c_0_3770,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),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_2656]) ).
cnf(c_0_3771,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2657]) ).
cnf(c_0_3772,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2658]) ).
cnf(c_0_3773,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2659]) ).
cnf(c_0_3774,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2660]) ).
cnf(c_0_3775,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2661]) ).
cnf(c_0_3776,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_2662]) ).
cnf(c_0_3777,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_2663]) ).
cnf(c_0_3778,plain,
( c_in(X1,X2,X3)
| c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2664]) ).
cnf(c_0_3779,plain,
( c_in(X1,X2,X3)
| c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2665]) ).
cnf(c_0_3780,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_2666]) ).
cnf(c_0_3781,plain,
( c_lessequals(X3,c_HOL_Oplus__class_Oplus(X4,X2,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2667]) ).
cnf(c_0_3782,plain,
( c_lessequals(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2668]) ).
cnf(c_0_3783,plain,
( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2669]) ).
cnf(c_0_3784,plain,
( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2670]) ).
cnf(c_0_3785,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_2671]) ).
cnf(c_0_3786,plain,
( hBOOL(hAPP(X3,X2))
| ~ c_lessequals(c_Suc(X1),X2,tc_nat)
| ~ hBOOL(hAPP(X3,c_Suc(c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1(X3,X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_2672]) ).
cnf(c_0_3787,plain,
( hBOOL(hAPP(X1,c_Suc(c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1(X1))))
| hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2673]) ).
cnf(c_0_3788,plain,
( hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2674]) ).
cnf(c_0_3789,plain,
( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(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__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2675]) ).
cnf(c_0_3790,plain,
( c_in(X1,X4,X3)
| c_in(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2676]) ).
cnf(c_0_3791,plain,
( c_in(X1,X4,X3)
| c_in(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2677]) ).
cnf(c_0_3792,plain,
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X3,tc_bool))
| ~ c_in(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2678]) ).
cnf(c_0_3793,plain,
( c_in(X1,X4,X3)
| ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2679]) ).
cnf(c_0_3794,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2680]) ).
cnf(c_0_3795,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2681]) ).
cnf(c_0_3796,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2682]) ).
cnf(c_0_3797,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2683]) ).
cnf(c_0_3798,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2684]) ).
cnf(c_0_3799,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2685]) ).
cnf(c_0_3800,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2686]) ).
cnf(c_0_3801,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2687]) ).
cnf(c_0_3802,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2688]) ).
cnf(c_0_3803,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2689]) ).
cnf(c_0_3804,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_2690]) ).
cnf(c_0_3805,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X3),X3),X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2691]) ).
cnf(c_0_3806,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X2,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X3),X3),X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2692]) ).
cnf(c_0_3807,plain,
( c_lessequals(c_Finite__Set_Ocard(X1,X2),c_Finite__Set_Ocard(c_Set_Oinsert(X3,X1,X2),X2),tc_nat)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2693]) ).
cnf(c_0_3808,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(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_Ring__and__Field_Ocomm__ring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2694]) ).
cnf(c_0_3809,plain,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2695]) ).
cnf(c_0_3810,plain,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2696]) ).
cnf(c_0_3811,plain,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2697]) ).
cnf(c_0_3812,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(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_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2698]) ).
cnf(c_0_3813,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_2699]) ).
cnf(c_0_3814,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_2700]) ).
cnf(c_0_3815,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_2701]) ).
cnf(c_0_3816,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_2702]) ).
cnf(c_0_3817,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_2703]) ).
cnf(c_0_3818,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3)
| ~ c_in(X4,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2704]) ).
cnf(c_0_3819,plain,
( X1 = X2
| ~ c_lessequals(X3,X1,tc_nat)
| ~ c_lessequals(X3,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(X1,X3,tc_nat) != c_HOL_Ominus__class_Ominus(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2705]) ).
cnf(c_0_3820,plain,
( X1 = X2
| c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) != c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_2706]) ).
cnf(c_0_3821,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2707]) ).
cnf(c_0_3822,plain,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2708]) ).
cnf(c_0_3823,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_Oplus__class_Oplus(X2,X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2709]) ).
cnf(c_0_3824,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2710]) ).
cnf(c_0_3825,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2711]) ).
cnf(c_0_3826,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2712]) ).
cnf(c_0_3827,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X1),X2,tc_nat),c_Suc(X3),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2713]) ).
cnf(c_0_3828,plain,
( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_lessequals(c_Suc(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_2714]) ).
cnf(c_0_3829,plain,
( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
| ~ c_lessequals(c_Suc(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_2715]) ).
cnf(c_0_3830,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_2716]) ).
cnf(c_0_3831,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_2717]) ).
cnf(c_0_3832,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_2718]) ).
cnf(c_0_3833,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_2719]) ).
cnf(c_0_3834,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_2720]) ).
cnf(c_0_3835,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_2721]) ).
cnf(c_0_3836,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2722]) ).
cnf(c_0_3837,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2723]) ).
cnf(c_0_3838,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4),X4)
| ~ class_Lattices_Olattice(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2724]) ).
cnf(c_0_3839,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2725]) ).
cnf(c_0_3840,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2726]) ).
cnf(c_0_3841,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2727]) ).
cnf(c_0_3842,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2728]) ).
cnf(c_0_3843,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2729]) ).
cnf(c_0_3844,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_OrderedGroup_Oab__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2730]) ).
cnf(c_0_3845,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2731]) ).
cnf(c_0_3846,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2732]) ).
cnf(c_0_3847,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4)
| ~ class_OrderedGroup_Oab__group__add(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2733]) ).
cnf(c_0_3848,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2734]) ).
cnf(c_0_3849,plain,
( c_HOL_Oplus__class_Oplus(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) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2735]) ).
cnf(c_0_3850,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_2736]) ).
cnf(c_0_3851,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Set_Oimage(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X1),
inference(split_conjunct,[status(thm)],[c_0_2737]) ).
cnf(c_0_3852,plain,
c_Set_Oimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_2738]) ).
cnf(c_0_3853,plain,
c_Set_Ovimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_2739]) ).
cnf(c_0_3854,plain,
c_Set_Ovimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3,X2) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_2740]) ).
cnf(c_0_3855,plain,
( c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2741]) ).
cnf(c_0_3856,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2742]) ).
cnf(c_0_3857,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_2743]) ).
cnf(c_0_3858,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),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(split_conjunct,[status(thm)],[c_0_2744]) ).
cnf(c_0_3859,plain,
c_Set_Oinsert(X1,c_Set_Oinsert(X2,X3,X4),X4) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,X3,X4),X4),
inference(split_conjunct,[status(thm)],[c_0_2745]) ).
cnf(c_0_3860,plain,
( c_lessequals(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2746]) ).
cnf(c_0_3861,plain,
( c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2747]) ).
cnf(c_0_3862,plain,
( c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X2,X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2748]) ).
cnf(c_0_3863,plain,
( c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X2,X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2749]) ).
cnf(c_0_3864,plain,
( c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X5,X4,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2750]) ).
cnf(c_0_3865,plain,
( c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X5,X4,X3) != c_HOL_Ominus__class_Ominus(X2,X1,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2751]) ).
cnf(c_0_3866,plain,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2752]) ).
cnf(c_0_3867,plain,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2753]) ).
cnf(c_0_3868,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_lessequals(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_2754]) ).
cnf(c_0_3869,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2755]) ).
cnf(c_0_3870,plain,
( c_in(X1,X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2756]) ).
cnf(c_0_3871,plain,
( c_in(X1,X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2757]) ).
cnf(c_0_3872,plain,
( c_lessequals(X1,X3,X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2758]) ).
cnf(c_0_3873,plain,
( c_lessequals(X1,X2,X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2759]) ).
cnf(c_0_3874,plain,
( c_lessequals(X1,X3,X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2760]) ).
cnf(c_0_3875,plain,
( c_lessequals(X1,X2,X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2761]) ).
cnf(c_0_3876,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_2762]) ).
cnf(c_0_3877,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_2763]) ).
cnf(c_0_3878,plain,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3) = c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(X2,X3),c_Nat_Osemiring__1__class_Oof__nat(X1,X3),X3)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ class_Ring__and__Field_Oring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2764]) ).
cnf(c_0_3879,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2765]) ).
cnf(c_0_3880,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2766]) ).
cnf(c_0_3881,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2767]) ).
cnf(c_0_3882,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2768]) ).
cnf(c_0_3883,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_2769]) ).
cnf(c_0_3884,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2770]) ).
cnf(c_0_3885,plain,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2771]) ).
cnf(c_0_3886,plain,
( X3 = X1
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool))
| ~ c_lessequals(c_Finite__Set_Ocard(X1,X2),c_Finite__Set_Ocard(X3,X2),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2772]) ).
cnf(c_0_3887,plain,
( X1 = X2
| c_in(X1,X3,X4)
| ~ c_in(X1,c_Set_Oinsert(X2,X3,X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_2773]) ).
cnf(c_0_3888,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_2774]) ).
cnf(c_0_3889,plain,
( hBOOL(hAPP(X3,c_Suc(c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X3,X2))))
| hBOOL(hAPP(X3,X1))
| ~ c_lessequals(X1,X2,tc_nat)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2775]) ).
cnf(c_0_3890,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_2776]) ).
cnf(c_0_3891,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_2777]) ).
cnf(c_0_3892,plain,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_2778]) ).
cnf(c_0_3893,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_2779]) ).
cnf(c_0_3894,plain,
( c_lessequals(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2780]) ).
cnf(c_0_3895,plain,
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2781]) ).
cnf(c_0_3896,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_2782]) ).
cnf(c_0_3897,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_2783]) ).
cnf(c_0_3898,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X4,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2784]) ).
cnf(c_0_3899,plain,
( c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2785]) ).
cnf(c_0_3900,plain,
( c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2786]) ).
cnf(c_0_3901,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2787]) ).
cnf(c_0_3902,plain,
( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2788]) ).
cnf(c_0_3903,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_2789]) ).
cnf(c_0_3904,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_2790]) ).
cnf(c_0_3905,plain,
( c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2791]) ).
cnf(c_0_3906,plain,
c_Fun_Oinj__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3),
inference(split_conjunct,[status(thm)],[c_0_2792]) ).
cnf(c_0_3907,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_2793]) ).
cnf(c_0_3908,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| c_HOL_Oplus__class_Oplus(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2794]) ).
cnf(c_0_3909,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| c_HOL_Oplus__class_Oplus(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2795]) ).
cnf(c_0_3910,plain,
( c_lessequals(X2,X1,tc_fun(X3,X4))
| c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4))
| ~ c_lessequals(X1,X2,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2796]) ).
cnf(c_0_3911,plain,
( c_Divides_Odiv__class_Omod(X2,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X1,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2797]) ).
cnf(c_0_3912,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2798]) ).
cnf(c_0_3913,plain,
( hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2799]) ).
cnf(c_0_3914,plain,
( hBOOL(hAPP(X3,X1))
| ~ c_lessequals(X1,X2,tc_nat)
| ~ hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X3,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2800]) ).
cnf(c_0_3915,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1),tc_nat)
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_2801]) ).
cnf(c_0_3916,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2802]) ).
cnf(c_0_3917,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X2,X3),c_Finite__Set_Olinorder__class_OMin(X1,X3),X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2803]) ).
cnf(c_0_3918,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_lessequals(c_Finite__Set_Olinorder__class_OMax(X1,X3),c_Finite__Set_Olinorder__class_OMax(X2,X3),X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2804]) ).
cnf(c_0_3919,plain,
( X1 = X2
| c_in(X3,X1,X4)
| c_in(X3,X2,X4)
| c_Set_Oinsert(X3,X1,X4) != c_Set_Oinsert(X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2805]) ).
cnf(c_0_3920,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_2806]) ).
cnf(c_0_3921,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_2807]) ).
cnf(c_0_3922,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_2808]) ).
cnf(c_0_3923,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_2809]) ).
cnf(c_0_3924,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2810]) ).
cnf(c_0_3925,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),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_2811]) ).
cnf(c_0_3926,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),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_2812]) ).
cnf(c_0_3927,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),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_2813]) ).
cnf(c_0_3928,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_2814]) ).
cnf(c_0_3929,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2815]) ).
cnf(c_0_3930,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2816]) ).
cnf(c_0_3931,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2817]) ).
cnf(c_0_3932,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2818]) ).
cnf(c_0_3933,plain,
( c_lessequals(X3,X1,X2)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeast(X1,X2),c_SetInterval_Oord__class_OatLeast(X3,X2),tc_fun(X2,tc_bool))
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2819]) ).
cnf(c_0_3934,plain,
c_in(X1,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),
inference(split_conjunct,[status(thm)],[c_0_2820]) ).
cnf(c_0_3935,plain,
( c_in(X4,X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2821]) ).
cnf(c_0_3936,plain,
( c_in(X4,X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2822]) ).
cnf(c_0_3937,plain,
( c_in(X1,X4,X3)
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2823]) ).
cnf(c_0_3938,plain,
( c_in(X4,X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2824]) ).
cnf(c_0_3939,plain,
( c_in(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2825]) ).
cnf(c_0_3940,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2826]) ).
cnf(c_0_3941,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2827]) ).
cnf(c_0_3942,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4))
| ~ c_lessequals(X2,X1,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2828]) ).
cnf(c_0_3943,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2829]) ).
cnf(c_0_3944,plain,
( X1 = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2)
| c_Finite__Set_Ocard(X1,X2) != c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2830]) ).
cnf(c_0_3945,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Suc(X2),tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2831]) ).
cnf(c_0_3946,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_2832]) ).
cnf(c_0_3947,plain,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_2833]) ).
cnf(c_0_3948,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_2834]) ).
cnf(c_0_3949,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X1,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2835]) ).
cnf(c_0_3950,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2836]) ).
cnf(c_0_3951,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_2837]) ).
cnf(c_0_3952,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_2838]) ).
cnf(c_0_3953,plain,
( c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2839]) ).
cnf(c_0_3954,plain,
( c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X4,X1,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2840]) ).
cnf(c_0_3955,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_2841]) ).
cnf(c_0_3956,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_2842]) ).
cnf(c_0_3957,plain,
( c_HOL_Ominus__class_Ominus(c_Suc(X2),X1,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat))
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2843]) ).
cnf(c_0_3958,plain,
( c_lessequals(c_Finite__Set_Ocard(X3,X2),c_Finite__Set_Ocard(X1,X2),tc_nat)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2844]) ).
cnf(c_0_3959,plain,
( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(X3,X2),c_Finite__Set_Ocard(X1,X2),tc_nat)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,X1,tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2845]) ).
cnf(c_0_3960,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(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_2846]) ).
cnf(c_0_3961,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X2,X1,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_2847]) ).
cnf(c_0_3962,plain,
( c_in(X1,c_Set_Oinsert(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2848]) ).
cnf(c_0_3963,plain,
( c_in(X1,c_Set_Oinsert(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2849]) ).
cnf(c_0_3964,plain,
( c_HOL_Oplus__class_Oplus(X1,X1,X2) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X2),c_HOL_Oone__class_Oone(X2),X2),X1,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2850]) ).
cnf(c_0_3965,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2851]) ).
cnf(c_0_3966,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2852]) ).
cnf(c_0_3967,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2853]) ).
cnf(c_0_3968,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2854]) ).
cnf(c_0_3969,plain,
( c_lessequals(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_2855]) ).
cnf(c_0_3970,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_2856]) ).
cnf(c_0_3971,plain,
( c_Finite__Set_Ocard(c_Set_Oinsert(X3,X1,X2),X2) = c_Finite__Set_Ocard(X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_in(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2857]) ).
cnf(c_0_3972,plain,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
inference(split_conjunct,[status(thm)],[c_0_2858]) ).
cnf(c_0_3973,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2859]) ).
cnf(c_0_3974,plain,
( c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = X1
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2860]) ).
cnf(c_0_3975,plain,
( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = X1
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2861]) ).
cnf(c_0_3976,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X1,tc_nat) = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2862]) ).
cnf(c_0_3977,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2863]) ).
cnf(c_0_3978,plain,
( X1 = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat)
| ~ c_lessequals(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2864]) ).
cnf(c_0_3979,plain,
( c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X3,X2),X2,tc_nat)
| hBOOL(hAPP(X3,X1))
| ~ c_lessequals(X1,X2,tc_nat)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2865]) ).
cnf(c_0_3980,plain,
( c_lessequals(hAPP(X1,X5),hAPP(X2,X5),X4)
| ~ c_lessequals(X1,X2,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2866]) ).
cnf(c_0_3981,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2867]) ).
cnf(c_0_3982,plain,
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2868]) ).
cnf(c_0_3983,plain,
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2869]) ).
cnf(c_0_3984,plain,
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2870]) ).
cnf(c_0_3985,plain,
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2871]) ).
cnf(c_0_3986,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2872]) ).
cnf(c_0_3987,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2873]) ).
cnf(c_0_3988,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2874]) ).
cnf(c_0_3989,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2875]) ).
cnf(c_0_3990,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2876]) ).
cnf(c_0_3991,plain,
( c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2877]) ).
cnf(c_0_3992,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2878]) ).
cnf(c_0_3993,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_2879]) ).
cnf(c_0_3994,plain,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2880]) ).
cnf(c_0_3995,plain,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2881]) ).
cnf(c_0_3996,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2882]) ).
cnf(c_0_3997,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2883]) ).
cnf(c_0_3998,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_2884]) ).
cnf(c_0_3999,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_2885]) ).
cnf(c_0_4000,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_2886]) ).
cnf(c_0_4001,plain,
( c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2887]) ).
cnf(c_0_4002,plain,
( c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2888]) ).
cnf(c_0_4003,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2889]) ).
cnf(c_0_4004,plain,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3) = c_HOL_Oplus__class_Oplus(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_2890]) ).
cnf(c_0_4005,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_2891]) ).
cnf(c_0_4006,plain,
c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_2892]) ).
cnf(c_0_4007,plain,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_2893]) ).
cnf(c_0_4008,plain,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_2894]) ).
cnf(c_0_4009,plain,
( c_in(X3,X1,X2)
| c_Finite__Set_Ocard(c_Set_Oinsert(X3,X1,X2),X2) = c_Suc(c_Finite__Set_Ocard(X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2895]) ).
cnf(c_0_4010,plain,
( c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2896]) ).
cnf(c_0_4011,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_2897]) ).
cnf(c_0_4012,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_2898]) ).
cnf(c_0_4013,plain,
( c_lessequals(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2899]) ).
cnf(c_0_4014,plain,
( c_lessequals(c_SetInterval_Oord__class_OatLeast(X2,X3),c_SetInterval_Oord__class_OatLeast(X1,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2900]) ).
cnf(c_0_4015,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2901]) ).
cnf(c_0_4016,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3)
| ~ class_Lattices_Olattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2902]) ).
cnf(c_0_4017,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X1,X3) = c_Divides_Odiv__class_Omod(X2,X1,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2903]) ).
cnf(c_0_4018,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(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_2904]) ).
cnf(c_0_4019,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_2905]) ).
cnf(c_0_4020,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_2906]) ).
cnf(c_0_4021,plain,
( c_Finite__Set_Ocard(X1,X2) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Finite__Set_Ocard(c_Set_Oinsert(X3,X1,X2),X2) = c_Suc(c_Finite__Set_Ocard(X1,X2))
| c_in(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2907]) ).
cnf(c_0_4022,plain,
( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2908]) ).
cnf(c_0_4023,plain,
c_HOL_Ominus__class_Ominus(X1,c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2909]) ).
cnf(c_0_4024,plain,
( c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2910]) ).
cnf(c_0_4025,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_2911]) ).
cnf(c_0_4026,plain,
c_Set_Oinsert(X1,c_Set_Oinsert(X1,X2,X3),X3) = c_Set_Oinsert(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_2912]) ).
cnf(c_0_4027,plain,
c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2913]) ).
cnf(c_0_4028,plain,
c_HOL_Otimes__class_Otimes(X1,c_Suc(X2),tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2914]) ).
cnf(c_0_4029,plain,
( ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| ~ hBOOL(hAPP(X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2915]) ).
cnf(c_0_4030,plain,
( c_lessequals(X1,X2,tc_fun(X3,X4))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2916]) ).
cnf(c_0_4031,plain,
( c_lessequals(X1,c_Inductive_Ocomplete__lattice__class_Ogfp(X2,X3),X3)
| ~ c_lessequals(X1,hAPP(X2,X1),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2917]) ).
cnf(c_0_4032,plain,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2918]) ).
cnf(c_0_4033,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_2919]) ).
cnf(c_0_4034,plain,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
inference(split_conjunct,[status(thm)],[c_0_2920]) ).
cnf(c_0_4035,plain,
( c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_2921]) ).
cnf(c_0_4036,plain,
( X1 = c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2922]) ).
cnf(c_0_4037,plain,
( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2923]) ).
cnf(c_0_4038,plain,
~ c_HOL_Oord__class_Oless(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_2924]) ).
cnf(c_0_4039,plain,
( c_lessequals(X1,c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1(X3,X1),tc_nat)
| hBOOL(hAPP(X3,X2))
| ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2925]) ).
cnf(c_0_4040,plain,
( c_lessequals(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2926]) ).
cnf(c_0_4041,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2927]) ).
cnf(c_0_4042,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| X1 = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2928]) ).
cnf(c_0_4043,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)) = X1
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2929]) ).
cnf(c_0_4044,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = X1
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2930]) ).
cnf(c_0_4045,plain,
( hBOOL(hAPP(X2,X4))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2931]) ).
cnf(c_0_4046,plain,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2932]) ).
cnf(c_0_4047,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_2933]) ).
cnf(c_0_4048,plain,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2934]) ).
cnf(c_0_4049,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_HOL_Oone__class_Oone(X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2935]) ).
cnf(c_0_4050,plain,
( hBOOL(hAPP(X3,X1))
| ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2936]) ).
cnf(c_0_4051,plain,
( c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2937]) ).
cnf(c_0_4052,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_2938]) ).
cnf(c_0_4053,plain,
( c_lessequals(X3,c_Finite__Set_Olinorder__class_OMax(X1,X2),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_in(X3,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2939]) ).
cnf(c_0_4054,plain,
( c_lessequals(c_Finite__Set_Olinorder__class_OMin(X1,X2),X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_in(X3,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2940]) ).
cnf(c_0_4055,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_2941]) ).
cnf(c_0_4056,plain,
( c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2942]) ).
cnf(c_0_4057,plain,
( c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2943]) ).
cnf(c_0_4058,plain,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2944]) ).
cnf(c_0_4059,plain,
( c_lessequals(X2,X1,X3)
| ~ c_in(X1,c_SetInterval_Oord__class_OatLeast(X2,X3),X3)
| ~ class_HOL_Oord(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2945]) ).
cnf(c_0_4060,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_2946]) ).
cnf(c_0_4061,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| ~ class_Int_Onumber__ring(X4)
| ~ class_Ring__and__Field_Oidom(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2947]) ).
cnf(c_0_4062,plain,
c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_2948]) ).
cnf(c_0_4063,plain,
( c_in(X1,X2,X3)
| c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2949]) ).
cnf(c_0_4064,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_2950]) ).
cnf(c_0_4065,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2951]) ).
cnf(c_0_4066,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2952]) ).
cnf(c_0_4067,plain,
( X2 = X1
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2953]) ).
cnf(c_0_4068,plain,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_2954]) ).
cnf(c_0_4069,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X2),X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2955]) ).
cnf(c_0_4070,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
| ~ class_OrderedGroup_Oab__group__add(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2956]) ).
cnf(c_0_4071,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2957]) ).
cnf(c_0_4072,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X1,X3,X4) != c_HOL_Oplus__class_Oplus(X2,X3,X4)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2958]) ).
cnf(c_0_4073,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2959]) ).
cnf(c_0_4074,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2960]) ).
cnf(c_0_4075,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_2961]) ).
cnf(c_0_4076,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_2962]) ).
cnf(c_0_4077,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_2963]) ).
cnf(c_0_4078,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_2964]) ).
cnf(c_0_4079,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2965]) ).
cnf(c_0_4080,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2966]) ).
cnf(c_0_4081,plain,
( ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2967]) ).
cnf(c_0_4082,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ c_lessequals(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2968]) ).
cnf(c_0_4083,plain,
( X2 = X1
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2969]) ).
cnf(c_0_4084,plain,
( ~ c_lessequals(c_Suc(X1),X2,tc_nat)
| ~ c_lessequals(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2970]) ).
cnf(c_0_4085,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_2971]) ).
cnf(c_0_4086,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2972]) ).
cnf(c_0_4087,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2973]) ).
cnf(c_0_4088,plain,
( c_in(X2,c_SetInterval_Oord__class_OatLeast(X1,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_HOL_Oord(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2974]) ).
cnf(c_0_4089,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_2975]) ).
cnf(c_0_4090,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_2976]) ).
cnf(c_0_4091,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_2977]) ).
cnf(c_0_4092,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_2978]) ).
cnf(c_0_4093,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_2979]) ).
cnf(c_0_4094,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2980]) ).
cnf(c_0_4095,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_2981]) ).
cnf(c_0_4096,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_2982]) ).
cnf(c_0_4097,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_2983]) ).
cnf(c_0_4098,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_2984]) ).
cnf(c_0_4099,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_2985]) ).
cnf(c_0_4100,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_2986]) ).
cnf(c_0_4101,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_2987]) ).
cnf(c_0_4102,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X2,X3) = X1
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2988]) ).
cnf(c_0_4103,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X3),X2,X3) = X1
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2989]) ).
cnf(c_0_4104,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X1,X3)
| ~ class_Lattices_Olattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2990]) ).
cnf(c_0_4105,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X2,X3)
| ~ class_Lattices_Olattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2991]) ).
cnf(c_0_4106,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2992]) ).
cnf(c_0_4107,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X1,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2993]) ).
cnf(c_0_4108,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2994]) ).
cnf(c_0_4109,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X1,X3,tc_nat) != c_HOL_Oplus__class_Oplus(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2995]) ).
cnf(c_0_4110,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2996]) ).
cnf(c_0_4111,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_2997]) ).
cnf(c_0_4112,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_2998]) ).
cnf(c_0_4113,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_2999]) ).
cnf(c_0_4114,plain,
~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
inference(split_conjunct,[status(thm)],[c_0_3000]) ).
cnf(c_0_4115,plain,
~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
inference(split_conjunct,[status(thm)],[c_0_3001]) ).
cnf(c_0_4116,plain,
~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
inference(split_conjunct,[status(thm)],[c_0_3002]) ).
cnf(c_0_4117,plain,
c_HOL_Oplus__class_Oplus(X1,c_Suc(X2),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_3003]) ).
cnf(c_0_4118,plain,
c_HOL_Oplus__class_Oplus(c_Suc(X1),X2,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_3004]) ).
cnf(c_0_4119,plain,
( hBOOL(hAPP(X2,X1))
| hBOOL(hAPP(X2,X3))
| ~ c_lessequals(c_Suc(X1),c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1(X2),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3005]) ).
cnf(c_0_4120,plain,
c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_Suc(X1),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3006]) ).
cnf(c_0_4121,plain,
c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
inference(split_conjunct,[status(thm)],[c_0_3007]) ).
cnf(c_0_4122,plain,
c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
inference(split_conjunct,[status(thm)],[c_0_3008]) ).
cnf(c_0_4123,plain,
c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
inference(split_conjunct,[status(thm)],[c_0_3009]) ).
cnf(c_0_4124,plain,
( c_Finite__Set_Ofinite(X1,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3010]) ).
cnf(c_0_4125,plain,
( c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_3011]) ).
cnf(c_0_4126,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_3012]) ).
cnf(c_0_4127,plain,
c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3013]) ).
cnf(c_0_4128,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat) = X2,
inference(split_conjunct,[status(thm)],[c_0_3014]) ).
cnf(c_0_4129,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat) = X1,
inference(split_conjunct,[status(thm)],[c_0_3015]) ).
cnf(c_0_4130,plain,
c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X1,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3016]) ).
cnf(c_0_4131,plain,
c_lessequals(X1,c_HOL_Otimes__class_Otimes(X1,X1,tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3017]) ).
cnf(c_0_4132,plain,
c_lessequals(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X1,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3018]) ).
cnf(c_0_4133,plain,
c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3019]) ).
cnf(c_0_4134,plain,
c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3020]) ).
cnf(c_0_4135,plain,
c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3021]) ).
cnf(c_0_4136,plain,
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3022]) ).
cnf(c_0_4137,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_3023]) ).
cnf(c_0_4138,plain,
c_HOL_Ominus__class_Ominus(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_3024]) ).
cnf(c_0_4139,plain,
c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_3025]) ).
cnf(c_0_4140,plain,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_3026]) ).
cnf(c_0_4141,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_3027]) ).
cnf(c_0_4142,plain,
c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_3028]) ).
cnf(c_0_4143,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_3029]) ).
cnf(c_0_4144,plain,
( c_lessequals(X1,X2,tc_nat)
| X1 = c_Suc(X2)
| ~ c_lessequals(X1,c_Suc(X2),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3030]) ).
cnf(c_0_4145,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_3031]) ).
cnf(c_0_4146,plain,
( c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(X1,X2,X3),X3) = X2
| c_Finite__Set_Ocard(X1,X3) != c_Suc(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3032]) ).
cnf(c_0_4147,plain,
( c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(X1,X2,X3),X3) = X2
| c_Finite__Set_Ocard(X1,X3) != c_Suc(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3033]) ).
cnf(c_0_4148,plain,
( X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3034]) ).
cnf(c_0_4149,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3035]) ).
cnf(c_0_4150,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3036]) ).
cnf(c_0_4151,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3037]) ).
cnf(c_0_4152,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3038]) ).
cnf(c_0_4153,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3039]) ).
cnf(c_0_4154,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3040]) ).
cnf(c_0_4155,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3041]) ).
cnf(c_0_4156,plain,
( c_lessequals(X1,X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) != X1
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3042]) ).
cnf(c_0_4157,plain,
( c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3043]) ).
cnf(c_0_4158,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_3044]) ).
cnf(c_0_4159,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_3045]) ).
cnf(c_0_4160,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_3046]) ).
cnf(c_0_4161,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_3047]) ).
cnf(c_0_4162,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_3048]) ).
cnf(c_0_4163,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3) = X1
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3049]) ).
cnf(c_0_4164,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = X1
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3050]) ).
cnf(c_0_4165,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_3051]) ).
cnf(c_0_4166,plain,
( c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3052]) ).
cnf(c_0_4167,plain,
( c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3053]) ).
cnf(c_0_4168,plain,
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3054]) ).
cnf(c_0_4169,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3055]) ).
cnf(c_0_4170,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3056]) ).
cnf(c_0_4171,plain,
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3057]) ).
cnf(c_0_4172,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_3058]) ).
cnf(c_0_4173,plain,
( c_Finite__Set_Ofinite(c_Set_Oinsert(X3,X1,X2),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3059]) ).
cnf(c_0_4174,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(X1,X2),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3060]) ).
cnf(c_0_4175,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_3061]) ).
cnf(c_0_4176,plain,
( c_lessequals(X1,c_Suc(X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3062]) ).
cnf(c_0_4177,plain,
( c_lessequals(c_Suc(X1),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3063]) ).
cnf(c_0_4178,plain,
( c_lessequals(c_Suc(X1),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3064]) ).
cnf(c_0_4179,plain,
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3065]) ).
cnf(c_0_4180,plain,
( c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)
| ~ c_lessequals(X1,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3066]) ).
cnf(c_0_4181,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_3067]) ).
cnf(c_0_4182,plain,
( c_Set_Oinsert(X1,X2,X3) = X2
| ~ c_in(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3068]) ).
cnf(c_0_4183,plain,
( c_lessequals(X1,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3069]) ).
cnf(c_0_4184,plain,
( c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3070]) ).
cnf(c_0_4185,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3071]) ).
cnf(c_0_4186,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3072]) ).
cnf(c_0_4187,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3073]) ).
cnf(c_0_4188,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_in(c_Finite__Set_Olinorder__class_OMax(X1,X2),X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3074]) ).
cnf(c_0_4189,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_in(c_Finite__Set_Olinorder__class_OMin(X1,X2),X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3075]) ).
cnf(c_0_4190,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_3076]) ).
cnf(c_0_4191,plain,
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3077]) ).
cnf(c_0_4192,plain,
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3078]) ).
cnf(c_0_4193,plain,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
inference(split_conjunct,[status(thm)],[c_0_3079]) ).
cnf(c_0_4194,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(X1,X2),tc_nat)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3080]) ).
cnf(c_0_4195,plain,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
inference(split_conjunct,[status(thm)],[c_0_3081]) ).
cnf(c_0_4196,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = X2,
inference(split_conjunct,[status(thm)],[c_0_3082]) ).
cnf(c_0_4197,plain,
c_HOL_Ominus__class_Ominus(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
inference(split_conjunct,[status(thm)],[c_0_3083]) ).
cnf(c_0_4198,plain,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_3084]) ).
cnf(c_0_4199,plain,
c_lessequals(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_3085]) ).
cnf(c_0_4200,plain,
c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_3086]) ).
cnf(c_0_4201,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oinsert(X2,X3,X1),
inference(split_conjunct,[status(thm)],[c_0_3087]) ).
cnf(c_0_4202,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_fun(X2,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_3088]) ).
cnf(c_0_4203,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_3089]) ).
cnf(c_0_4204,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_3090]) ).
cnf(c_0_4205,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_3091]) ).
cnf(c_0_4206,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_3092]) ).
cnf(c_0_4207,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_3093]) ).
cnf(c_0_4208,plain,
c_HOL_Ominus__class_Ominus(c_Suc(X1),c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3094]) ).
cnf(c_0_4209,plain,
c_HOL_Oplus__class_Oplus(c_Suc(X1),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_Suc(X2),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3095]) ).
cnf(c_0_4210,plain,
( c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Finite__Set_Ocard(X1,X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_3096]) ).
cnf(c_0_4211,plain,
( c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Finite__Set_Ocard(X1,X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_3097]) ).
cnf(c_0_4212,plain,
( c_lessequals(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3098]) ).
cnf(c_0_4213,plain,
( c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3099]) ).
cnf(c_0_4214,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3100]) ).
cnf(c_0_4215,plain,
( c_lessequals(X1,X1,X2)
| c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3101]) ).
cnf(c_0_4216,plain,
( c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3102]) ).
cnf(c_0_4217,plain,
( hBOOL(hAPP(X2,X1))
| ~ c_in(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3103]) ).
cnf(c_0_4218,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3)
| ~ class_Lattices_Olattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3104]) ).
cnf(c_0_4219,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3105]) ).
cnf(c_0_4220,plain,
( c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3106]) ).
cnf(c_0_4221,plain,
( c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3107]) ).
cnf(c_0_4222,plain,
( c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3108]) ).
cnf(c_0_4223,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_3109]) ).
cnf(c_0_4224,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_3110]) ).
cnf(c_0_4225,plain,
( c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X1),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2)
| ~ class_Ring__and__Field_Osemiring__1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3111]) ).
cnf(c_0_4226,plain,
( c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_Suc(X2),X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3112]) ).
cnf(c_0_4227,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_3113]) ).
cnf(c_0_4228,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_3114]) ).
cnf(c_0_4229,plain,
( ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3115]) ).
cnf(c_0_4230,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_3116]) ).
cnf(c_0_4231,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_3117]) ).
cnf(c_0_4232,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_3118]) ).
cnf(c_0_4233,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_3119]) ).
cnf(c_0_4234,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)) != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3120]) ).
cnf(c_0_4235,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_3121]) ).
cnf(c_0_4236,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_3122]) ).
cnf(c_0_4237,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_3123]) ).
cnf(c_0_4238,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_3124]) ).
cnf(c_0_4239,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_3125]) ).
cnf(c_0_4240,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_3126]) ).
cnf(c_0_4241,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3127]) ).
cnf(c_0_4242,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_3128]) ).
cnf(c_0_4243,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 != c_HOL_Oplus__class_Oplus(X3,X1,X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3129]) ).
cnf(c_0_4244,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_3130]) ).
cnf(c_0_4245,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_3131]) ).
cnf(c_0_4246,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)) != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3132]) ).
cnf(c_0_4247,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)) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3133]) ).
cnf(c_0_4248,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_3134]) ).
cnf(c_0_4249,plain,
( c_lessequals(X1,X2,tc_nat)
| c_lessequals(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3135]) ).
cnf(c_0_4250,plain,
c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2),
inference(split_conjunct,[status(thm)],[c_0_3136]) ).
cnf(c_0_4251,plain,
c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3137]) ).
cnf(c_0_4252,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_3138]) ).
cnf(c_0_4253,plain,
( X2 = c_Suc(c_ATP__Linkup_Osko__Nat__XSuc__le__D__1__1(X2))
| ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3139]) ).
cnf(c_0_4254,plain,
( X1 = c_Orderings_Otop__class_Otop(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X2) != c_Orderings_Otop__class_Otop(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3140]) ).
cnf(c_0_4255,plain,
( X1 = c_Orderings_Otop__class_Otop(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X1,X2) != c_Orderings_Otop__class_Otop(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3141]) ).
cnf(c_0_4256,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(X1,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3142]) ).
cnf(c_0_4257,plain,
c_HOL_Ominus__class_Ominus(X1,X1,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_3143]) ).
cnf(c_0_4258,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_3144]) ).
cnf(c_0_4259,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_3145]) ).
cnf(c_0_4260,plain,
( c_in(X2,X1,X3)
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3146]) ).
cnf(c_0_4261,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_3147]) ).
cnf(c_0_4262,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)) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3148]) ).
cnf(c_0_4263,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3149]) ).
cnf(c_0_4264,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3150]) ).
cnf(c_0_4265,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_3151]) ).
cnf(c_0_4266,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_3152]) ).
cnf(c_0_4267,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3153]) ).
cnf(c_0_4268,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3154]) ).
cnf(c_0_4269,plain,
~ c_lessequals(c_Suc(X1),X1,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3155]) ).
cnf(c_0_4270,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_3156]) ).
cnf(c_0_4271,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3157]) ).
cnf(c_0_4272,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3158]) ).
cnf(c_0_4273,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3159]) ).
cnf(c_0_4274,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_3160]) ).
cnf(c_0_4275,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3161]) ).
cnf(c_0_4276,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_3162]) ).
cnf(c_0_4277,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_3163]) ).
cnf(c_0_4278,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_3164]) ).
cnf(c_0_4279,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3165]) ).
cnf(c_0_4280,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3166]) ).
cnf(c_0_4281,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_3167]) ).
cnf(c_0_4282,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_3168]) ).
cnf(c_0_4283,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3169]) ).
cnf(c_0_4284,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3170]) ).
cnf(c_0_4285,plain,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3171]) ).
cnf(c_0_4286,plain,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3172]) ).
cnf(c_0_4287,plain,
( X1 = X2
| ~ c_fequal(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3173]) ).
cnf(c_0_4288,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_3174]) ).
cnf(c_0_4289,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_3175]) ).
cnf(c_0_4290,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3176]) ).
cnf(c_0_4291,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3177]) ).
cnf(c_0_4292,plain,
c_Lattices_Olower__semilattice__class_Oinf(X1,X1,tc_fun(X2,tc_bool)) = X1,
inference(split_conjunct,[status(thm)],[c_0_3178]) ).
cnf(c_0_4293,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3179]) ).
cnf(c_0_4294,plain,
c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_3180]) ).
cnf(c_0_4295,plain,
c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_3181]) ).
cnf(c_0_4296,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_3182]) ).
cnf(c_0_4297,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ocard(X1,X2) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3183]) ).
cnf(c_0_4298,plain,
( X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3184]) ).
cnf(c_0_4299,plain,
c_HOL_Oplus__class_Oplus(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_3185]) ).
cnf(c_0_4300,plain,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3186]) ).
cnf(c_0_4301,plain,
c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),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_3187]) ).
cnf(c_0_4302,plain,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(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_3188]) ).
cnf(c_0_4303,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_3189]) ).
cnf(c_0_4304,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3190]) ).
cnf(c_0_4305,plain,
( c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1)
| ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3191]) ).
cnf(c_0_4306,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3192]) ).
cnf(c_0_4307,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_3193]) ).
cnf(c_0_4308,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_3194]) ).
cnf(c_0_4309,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_3195]) ).
cnf(c_0_4310,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_3196]) ).
cnf(c_0_4311,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_3197]) ).
cnf(c_0_4312,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_3198]) ).
cnf(c_0_4313,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_3199]) ).
cnf(c_0_4314,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_3200]) ).
cnf(c_0_4315,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X1),X2,X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3201]) ).
cnf(c_0_4316,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(X2),X2) = c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3202]) ).
cnf(c_0_4317,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_3203]) ).
cnf(c_0_4318,plain,
( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3204]) ).
cnf(c_0_4319,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3205]) ).
cnf(c_0_4320,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3206]) ).
cnf(c_0_4321,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Omonoid__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3207]) ).
cnf(c_0_4322,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3208]) ).
cnf(c_0_4323,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3209]) ).
cnf(c_0_4324,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3210]) ).
cnf(c_0_4325,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3211]) ).
cnf(c_0_4326,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(X1),X2,X1) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3212]) ).
cnf(c_0_4327,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Otop__class_Otop(X2),X2) = X1
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3213]) ).
cnf(c_0_4328,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_3214]) ).
cnf(c_0_4329,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_3215]) ).
cnf(c_0_4330,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_3216]) ).
cnf(c_0_4331,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_3217]) ).
cnf(c_0_4332,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_3218]) ).
cnf(c_0_4333,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_3219]) ).
cnf(c_0_4334,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_3220]) ).
cnf(c_0_4335,plain,
c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3221]) ).
cnf(c_0_4336,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_3222]) ).
cnf(c_0_4337,plain,
( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
| ~ class_Orderings_Obot(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3223]) ).
cnf(c_0_4338,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_3224]) ).
cnf(c_0_4339,plain,
( c_lessequals(X1,c_Orderings_Otop__class_Otop(X2),X2)
| ~ class_Orderings_Otop(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3225]) ).
cnf(c_0_4340,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_3226]) ).
cnf(c_0_4341,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_3227]) ).
cnf(c_0_4342,plain,
c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
inference(split_conjunct,[status(thm)],[c_0_3228]) ).
cnf(c_0_4343,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3229]) ).
cnf(c_0_4344,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3230]) ).
cnf(c_0_4345,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3231]) ).
cnf(c_0_4346,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_3232]) ).
cnf(c_0_4347,plain,
c_lessequals(c_Suc(X1),c_Suc(X1),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3233]) ).
cnf(c_0_4348,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_3234]) ).
cnf(c_0_4349,plain,
c_HOL_Ominus__class_Ominus(c_Suc(X1),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1,
inference(split_conjunct,[status(thm)],[c_0_3235]) ).
cnf(c_0_4350,plain,
( c_HOL_Otimes__class_Otimes(X1,X1,X2) = X1
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3236]) ).
cnf(c_0_4351,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X1,X2) = X1
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3237]) ).
cnf(c_0_4352,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_3238]) ).
cnf(c_0_4353,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_3239]) ).
cnf(c_0_4354,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3240]) ).
cnf(c_0_4355,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3241]) ).
cnf(c_0_4356,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_3242]) ).
cnf(c_0_4357,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_3243]) ).
cnf(c_0_4358,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_3244]) ).
cnf(c_0_4359,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3245]) ).
cnf(c_0_4360,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_3246]) ).
cnf(c_0_4361,plain,
c_Suc(X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3247]) ).
cnf(c_0_4362,plain,
c_Suc(X1) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3248]) ).
cnf(c_0_4363,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3249]) ).
cnf(c_0_4364,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3250]) ).
cnf(c_0_4365,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3251]) ).
cnf(c_0_4366,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_3252]) ).
cnf(c_0_4367,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3253]) ).
cnf(c_0_4368,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_3254]) ).
cnf(c_0_4369,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_3255]) ).
cnf(c_0_4370,plain,
c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
inference(split_conjunct,[status(thm)],[c_0_3256]) ).
cnf(c_0_4371,plain,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
inference(split_conjunct,[status(thm)],[c_0_3257]) ).
cnf(c_0_4372,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1,
inference(split_conjunct,[status(thm)],[c_0_3258]) ).
cnf(c_0_4373,plain,
X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3259]) ).
cnf(c_0_4374,plain,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1,
inference(split_conjunct,[status(thm)],[c_0_3260]) ).
cnf(c_0_4375,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) = X1,
inference(split_conjunct,[status(thm)],[c_0_3261]) ).
cnf(c_0_4376,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3262]) ).
cnf(c_0_4377,plain,
c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3263]) ).
cnf(c_0_4378,plain,
c_fequal(X1,X1,X2),
inference(split_conjunct,[status(thm)],[c_0_3264]) ).
cnf(c_0_4379,plain,
( X1 = X2
| c_SetInterval_Oord__class_OatLeast(X1,X3) != c_SetInterval_Oord__class_OatLeast(X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3265]) ).
cnf(c_0_4380,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_3266]) ).
cnf(c_0_4381,plain,
c_lessequals(X1,X1,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3267]) ).
cnf(c_0_4382,plain,
c_lessequals(X1,X1,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3268]) ).
cnf(c_0_4383,plain,
c_Ring__and__Field_Odvd__class_Odvd(X1,X1,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3269]) ).
cnf(c_0_4384,plain,
( class_Finite__Set_Ofinite_Ofinite(tc_fun(X1,X2))
| ~ class_Finite__Set_Ofinite_Ofinite(X1)
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3270]) ).
cnf(c_0_4385,plain,
( class_HOL_Oord(tc_fun(X2,X1))
| ~ class_HOL_Oord(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3271]) ).
cnf(c_0_4386,plain,
( class_Orderings_Obot(tc_fun(X2,X1))
| ~ class_Orderings_Obot(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3272]) ).
cnf(c_0_4387,plain,
( class_Orderings_Otop(tc_fun(X2,X1))
| ~ class_Orderings_Otop(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3273]) ).
cnf(c_0_4388,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3274]) ).
cnf(c_0_4389,plain,
( class_Lattices_Olattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3275]) ).
cnf(c_0_4390,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3276]) ).
cnf(c_0_4391,plain,
( class_Lattices_Obounded__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3277]) ).
cnf(c_0_4392,plain,
( class_Lattices_Olower__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3278]) ).
cnf(c_0_4393,plain,
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3279]) ).
cnf(c_0_4394,plain,
( c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ocard(X1,X2) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3280]) ).
cnf(c_0_4395,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_3281]) ).
cnf(c_0_4396,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_3282]) ).
cnf(c_0_4397,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3283]) ).
cnf(c_0_4398,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_3284]) ).
cnf(c_0_4399,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_3285]) ).
cnf(c_0_4400,plain,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3286]) ).
cnf(c_0_4401,plain,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3287]) ).
cnf(c_0_4402,plain,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
inference(split_conjunct,[status(thm)],[c_0_3288]) ).
cnf(c_0_4403,plain,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
inference(split_conjunct,[status(thm)],[c_0_3289]) ).
cnf(c_0_4404,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3290]) ).
cnf(c_0_4405,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3291]) ).
cnf(c_0_4406,plain,
c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_3292]) ).
cnf(c_0_4407,plain,
c_Suc(X1) != X1,
inference(split_conjunct,[status(thm)],[c_0_3293]) ).
cnf(c_0_4408,plain,
X1 != c_Suc(X1),
inference(split_conjunct,[status(thm)],[c_0_3294]) ).
cnf(c_0_4409,plain,
class_HOL_Oord(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_3295]) ).
cnf(c_0_4410,plain,
class_Orderings_Obot(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_3296]) ).
cnf(c_0_4411,plain,
class_Orderings_Otop(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_3297]) ).
cnf(c_0_4412,plain,
class_Orderings_Oorder(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_3298]) ).
cnf(c_0_4413,plain,
class_Lattices_Olattice(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_3299]) ).
cnf(c_0_4414,plain,
class_Orderings_Opreorder(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_3300]) ).
cnf(c_0_4415,plain,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_3301]) ).
cnf(c_0_4416,plain,
class_Lattices_Obounded__lattice(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_3302]) ).
cnf(c_0_4417,plain,
class_Lattices_Olower__semilattice(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_3303]) ).
cnf(c_0_4418,plain,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_3304]) ).
cnf(c_0_4419,plain,
class_HOL_Oord(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3305]) ).
cnf(c_0_4420,plain,
class_Orderings_Obot(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3306]) ).
cnf(c_0_4421,plain,
class_Orderings_Oorder(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3307]) ).
cnf(c_0_4422,plain,
class_Lattices_Olattice(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3308]) ).
cnf(c_0_4423,plain,
class_Orderings_Olinorder(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3309]) ).
cnf(c_0_4424,plain,
class_Orderings_Opreorder(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3310]) ).
cnf(c_0_4425,plain,
class_Ring__and__Field_Odvd(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3311]) ).
cnf(c_0_4426,plain,
class_Nat_Osemiring__char__0(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3312]) ).
cnf(c_0_4427,plain,
class_Divides_Osemiring__div(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3313]) ).
cnf(c_0_4428,plain,
class_OrderedGroup_Omonoid__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3314]) ).
cnf(c_0_4429,plain,
class_Ring__and__Field_Osemiring(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3315]) ).
cnf(c_0_4430,plain,
class_OrderedGroup_Omonoid__mult(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3316]) ).
cnf(c_0_4431,plain,
class_Ring__and__Field_Omult__mono(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3317]) ).
cnf(c_0_4432,plain,
class_Ring__and__Field_Omult__zero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3318]) ).
cnf(c_0_4433,plain,
class_Ring__and__Field_Omult__mono1(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3319]) ).
cnf(c_0_4434,plain,
class_Ring__and__Field_Osemiring__1(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3320]) ).
cnf(c_0_4435,plain,
class_Lattices_Olower__semilattice(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3321]) ).
cnf(c_0_4436,plain,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3322]) ).
cnf(c_0_4437,plain,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3323]) ).
cnf(c_0_4438,plain,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3324]) ).
cnf(c_0_4439,plain,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3325]) ).
cnf(c_0_4440,plain,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3326]) ).
cnf(c_0_4441,plain,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3327]) ).
cnf(c_0_4442,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3328]) ).
cnf(c_0_4443,plain,
class_Ring__and__Field_Oordered__semidom(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3329]) ).
cnf(c_0_4444,plain,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3330]) ).
cnf(c_0_4445,plain,
class_Ring__and__Field_Oordered__semiring(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3331]) ).
cnf(c_0_4446,plain,
class_Ring__and__Field_Opordered__semiring(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3332]) ).
cnf(c_0_4447,plain,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3333]) ).
cnf(c_0_4448,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3334]) ).
cnf(c_0_4449,plain,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3335]) ).
cnf(c_0_4450,plain,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3336]) ).
cnf(c_0_4451,plain,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3337]) ).
cnf(c_0_4452,plain,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3338]) ).
cnf(c_0_4453,plain,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3339]) ).
cnf(c_0_4454,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3340]) ).
cnf(c_0_4455,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3341]) ).
cnf(c_0_4456,plain,
( c_lessequals(c_Set_Oimage(X1,X2,X4,X5),X3,tc_fun(X5,tc_bool))
| ~ c_in(hAPP(X1,c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1(X2,X3,X1,X4,X5)),X3,X5) ),
c_0_3342,
[final] ).
cnf(c_0_4457,plain,
( c_lessequals(c_Set_Oimage(X1,X2,X4,X5),X3,tc_fun(X5,tc_bool))
| ~ c_in(hAPP(X1,c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1(X2,X3,X1,X4,X5)),X3,X5) ),
c_0_3343,
[final] ).
cnf(c_0_4458,plain,
( c_Set_Oimage(X1,X2,X3,X4) = c_Set_Oimage(X5,X2,X3,X4)
| hAPP(X1,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X2,X1,X5,X3,X4)) != hAPP(X5,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X2,X1,X5,X3,X4)) ),
c_0_3344,
[final] ).
cnf(c_0_4459,plain,
( X1 = X2
| c_Fun_Ofun__upd(c_Fun_Ofun__upd(X3,X1,X4,X5,X6),X2,X7,X5,X6) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X3,X2,X7,X5,X6),X1,X4,X5,X6) ),
c_0_3345,
[final] ).
cnf(c_0_4460,plain,
c_Fun_Ofun__upd(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X2,X6,X4,X5) = c_Fun_Ofun__upd(X1,X2,X6,X4,X5),
c_0_3346,
[final] ).
cnf(c_0_4461,plain,
( c_Set_Oinsert(X5,c_Set_Oimage(X4,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3,X6),X6) = c_Set_Oimage(c_Fun_Ofun__upd(X4,X1,X5,X3,X6),X2,X3,X6)
| ~ c_in(X1,X2,X3) ),
c_0_3347,
[final] ).
cnf(c_0_4462,plain,
( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2),c_Finite__Set_Ocard(X1,X2),tc_nat)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_in(X3,X1,X2)
| ~ c_in(X4,X1,X2) ),
c_0_3348,
[final] ).
cnf(c_0_4463,plain,
( c_in(X5,c_Set_Oimage(X1,X2,X3,X4),X4)
| c_Fun_Oinj__on(c_Fun_Ofun__upd(X1,X6,X5,X3,X4),X2,X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
c_0_3349,
[final] ).
cnf(c_0_4464,plain,
( c_Set_Oimage(X3,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X4,X1,X3,X5,X2),X5,X2) = X1
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X1,c_Set_Oimage(X3,X4,X5,X2),tc_fun(X2,tc_bool)) ),
c_0_3350,
[final] ).
cnf(c_0_4465,plain,
( c_Set_Oimage(X2,c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(X3,X1,X2,X4,X5),X4,X5) = X1
| ~ c_lessequals(X1,c_Set_Oimage(X2,X3,X4,X5),tc_fun(X5,tc_bool)) ),
c_0_3351,
[final] ).
cnf(c_0_4466,plain,
( c_lessequals(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X4,X1,X3,X5,X2),X4,tc_fun(X5,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X1,c_Set_Oimage(X3,X4,X5,X2),tc_fun(X2,tc_bool)) ),
c_0_3352,
[final] ).
cnf(c_0_4467,plain,
( c_lessequals(c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(X3,X1,X2,X4,X5),X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Set_Oimage(X2,X3,X4,X5),tc_fun(X5,tc_bool)) ),
c_0_3353,
[final] ).
cnf(c_0_4468,plain,
( c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X4,X1,X3,X5,X2),X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X1,c_Set_Oimage(X3,X4,X5,X2),tc_fun(X2,tc_bool)) ),
c_0_3354,
[final] ).
cnf(c_0_4469,plain,
( c_in(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(X3,X2,X1,X4,X5),X3,X4)
| ~ c_in(X1,c_Set_Oimage(X2,X3,X4,X5),X5) ),
c_0_3355,
[final] ).
cnf(c_0_4470,plain,
( c_in(c_ATP__Linkup_Osko__Set__XimageE__1__1(X3,X1,X2,X4,X5),X3,X4)
| ~ c_in(X1,c_Set_Oimage(X2,X3,X4,X5),X5) ),
c_0_3356,
[final] ).
cnf(c_0_4471,plain,
( X1 = X6
| ~ c_in(X1,c_Set_Oimage(X2,X3,X4,X5),X5)
| ~ c_in(X6,c_Set_Oimage(X2,X3,X4,X5),X5)
| hAPP(c_Hilbert__Choice_Oinv__into(X3,X2,X4,X5),X1) != hAPP(c_Hilbert__Choice_Oinv__into(X3,X2,X4,X5),X6) ),
c_0_3357,
[final] ).
cnf(c_0_4472,plain,
( hAPP(X2,c_ATP__Linkup_Osko__Set__XimageE__1__1(X3,X1,X2,X4,X5)) = X1
| ~ c_in(X1,c_Set_Oimage(X2,X3,X4,X5),X5) ),
c_0_3358,
[final] ).
cnf(c_0_4473,plain,
( hAPP(X2,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(X3,X2,X1,X4,X5)) = X1
| ~ c_in(X1,c_Set_Oimage(X2,X3,X4,X5),X5) ),
c_0_3359,
[final] ).
cnf(c_0_4474,plain,
( ~ c_Fun_Oinj__on(X1,c_Set_Oinsert(X2,X3,X4),X4,X5)
| ~ c_in(hAPP(X1,X2),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4,X5),X5) ),
c_0_3360,
[final] ).
cnf(c_0_4475,plain,
( c_in(c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1(X1,X2,X3,X4,X5),X1,X4)
| c_lessequals(c_Set_Oimage(X3,X1,X4,X5),X2,tc_fun(X5,tc_bool)) ),
c_0_3361,
[final] ).
cnf(c_0_4476,plain,
( c_in(c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1(X1,X2,X3,X4,X5),X1,X4)
| c_lessequals(c_Set_Oimage(X3,X1,X4,X5),X2,tc_fun(X5,tc_bool)) ),
c_0_3362,
[final] ).
cnf(c_0_4477,plain,
c_lessequals(c_Set_Oimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4,X5),c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,X2,X4,X5),c_Set_Oimage(X1,X3,X4,X5),tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
c_0_3363,
[final] ).
cnf(c_0_4478,plain,
c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool)),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X3,tc_bool)),X3,X4),tc_fun(X4,tc_bool)),
c_0_3364,
[final] ).
cnf(c_0_4479,plain,
( c_in(X1,X2,X3)
| c_Set_Oimage(c_Fun_Ofun__upd(X4,X1,X5,X3,X6),X2,X3,X6) = c_Set_Oimage(X4,X2,X3,X6) ),
c_0_3365,
[final] ).
cnf(c_0_4480,plain,
( c_in(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X1,X2,X3,X4,X5),X1,X4)
| c_Set_Oimage(X2,X1,X4,X5) = c_Set_Oimage(X3,X1,X4,X5) ),
c_0_3366,
[final] ).
cnf(c_0_4481,plain,
( c_in(hAPP(X4,X1),c_Inductive_Ocomplete__lattice__class_Ogfp(X6,tc_fun(X5,tc_bool)),X5)
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(c_Set_Oimage(X4,X2,X3,X5),hAPP(X6,c_Set_Oimage(X4,X2,X3,X5)),tc_fun(X5,tc_bool)) ),
c_0_3367,
[final] ).
cnf(c_0_4482,plain,
( c_Finite__Set_Ocard(X2,X3) = c_Finite__Set_Ocard(X5,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| ~ c_Fun_Oinj__on(X6,X5,X4,X3)
| ~ c_lessequals(c_Set_Oimage(X6,X5,X4,X3),X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(X5,X4) ),
c_0_3368,
[final] ).
cnf(c_0_4483,plain,
( c_in(hAPP(X1,X5),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3,X4),X4)
| c_Fun_Oinj__on(X1,c_Set_Oinsert(X5,X2,X3),X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
c_0_3369,
[final] ).
cnf(c_0_4484,plain,
( hBOOL(hAPP(X1,X2))
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X2,tc_nat),X3,tc_nat)))
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
c_0_3370,
[final] ).
cnf(c_0_4485,plain,
( X1 = X2
| hAPP(c_Fun_Ofun__upd(X3,X2,X4,X5,X6),X1) = hAPP(X3,X1) ),
c_0_3371,
[final] ).
cnf(c_0_4486,plain,
( X1 = X2
| hAPP(c_Fun_Ofun__upd(X3,X2,X4,X5,X6),X1) = hAPP(X3,X1) ),
c_0_3372,
[final] ).
cnf(c_0_4487,plain,
hAPP(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X2) = X3,
c_0_3373,
[final] ).
cnf(c_0_4488,plain,
hAPP(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X2) = X3,
c_0_3374,
[final] ).
cnf(c_0_4489,plain,
( c_lessequals(X4,X5,tc_fun(X2,tc_bool))
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| ~ c_lessequals(c_Set_Oimage(X1,X4,X2,X3),c_Set_Oimage(X1,X5,X2,X3),tc_fun(X3,tc_bool)) ),
c_0_3375,
[final] ).
cnf(c_0_4490,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,X5,X3,X4),c_Set_Oimage(X1,X6,X3,X4),tc_fun(X4,tc_bool)) = c_Set_Oimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X3,tc_bool)),X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X6,X2,tc_fun(X3,tc_bool)) ),
c_0_3376,
[final] ).
cnf(c_0_4491,plain,
( c_HOL_Ominus__class_Ominus(c_Set_Oimage(X1,X5,X3,X4),c_Set_Oimage(X1,X6,X3,X4),tc_fun(X4,tc_bool)) = c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X3,tc_bool)),X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X6,X2,tc_fun(X3,tc_bool)) ),
c_0_3377,
[final] ).
cnf(c_0_4492,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat) ),
c_0_3378,
[final] ).
cnf(c_0_4493,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X5,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X3,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X4,tc_nat),X5,tc_nat),tc_nat) ),
c_0_3379,
[final] ).
cnf(c_0_4494,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X5,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X4,tc_nat),X5,tc_nat),tc_nat) ),
c_0_3380,
[final] ).
cnf(c_0_4495,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat) ),
c_0_3381,
[final] ).
cnf(c_0_4496,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4),X4)
| ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4),X4)
| ~ class_Ring__and__Field_Opordered__ring(X4) ),
c_0_3382,
[final] ).
cnf(c_0_4497,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3),X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3),X6,X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
c_0_3383,
[final] ).
cnf(c_0_4498,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3),X6,X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
c_0_3384,
[final] ).
cnf(c_0_4499,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4),X4)
| ~ class_Ring__and__Field_Opordered__ring(X4) ),
c_0_3385,
[final] ).
cnf(c_0_4500,plain,
( c_lessequals(c_Set_Ovimage(X1,X4,X2,X3),X5,tc_fun(X2,tc_bool))
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| ~ c_lessequals(X4,c_Set_Oimage(X1,X5,X2,X3),tc_fun(X3,tc_bool)) ),
c_0_3386,
[final] ).
cnf(c_0_4501,plain,
( c_HOL_Ominus__class_Ominus(c_Set_Oimage(X1,X4,X2,X3),c_Set_Oimage(X1,X5,X2,X3),tc_fun(X3,tc_bool)) = c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X2,tc_bool)),X2,X3)
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3) ),
c_0_3387,
[final] ).
cnf(c_0_4502,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,X4,X2,X3),c_Set_Oimage(X1,X5,X2,X3),tc_fun(X3,tc_bool)) = c_Set_Oimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X2,tc_bool)),X2,X3)
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3) ),
c_0_3388,
[final] ).
cnf(c_0_4503,plain,
( c_in(hAPP(c_Hilbert__Choice_Oinv__into(X3,X2,X4,X5),X1),X3,X4)
| ~ c_in(X1,c_Set_Oimage(X2,X3,X4,X5),X5) ),
c_0_3389,
[final] ).
cnf(c_0_4504,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat) ),
c_0_3390,
[final] ).
cnf(c_0_4505,plain,
( c_lessequals(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X5,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat),tc_nat) ),
c_0_3391,
[final] ).
cnf(c_0_4506,plain,
( c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X5,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat),tc_nat) ),
c_0_3392,
[final] ).
cnf(c_0_4507,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat) ),
c_0_3393,
[final] ).
cnf(c_0_4508,plain,
( hAPP(X1,X2) = X3
| c_Fun_Ofun__upd(X1,X2,X3,X4,X5) != X1 ),
c_0_3394,
[final] ).
cnf(c_0_4509,plain,
( c_lessequals(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X1,X3),X2,X3),X6,X3),X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
c_0_3395,
[final] ).
cnf(c_0_4510,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X6,X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
c_0_3396,
[final] ).
cnf(c_0_4511,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
c_0_3397,
[final] ).
cnf(c_0_4512,plain,
( c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X1,X3),X2,X3),X6,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
c_0_3398,
[final] ).
cnf(c_0_4513,plain,
( hAPP(X2,hAPP(c_Hilbert__Choice_Oinv__into(X3,X2,X4,X5),X1)) = X1
| ~ c_in(X1,c_Set_Oimage(X2,X3,X4,X5),X5) ),
c_0_3399,
[final] ).
cnf(c_0_4514,plain,
( c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1,X2,X3),c_Set_Oimage(X1,X4,X2,X3),X3,X2) = X4
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3) ),
c_0_3400,
[final] ).
cnf(c_0_4515,plain,
( c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1,X2,X3),c_Set_Oimage(X1,X4,X2,X3),X3,X2) = X4
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3) ),
c_0_3401,
[final] ).
cnf(c_0_4516,plain,
( c_Set_Oimage(c_Hilbert__Choice_Oinv__into(X2,X1,X3,X4),c_Set_Oimage(X1,X5,X3,X4),X4,X3) = X5
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool)) ),
c_0_3402,
[final] ).
cnf(c_0_4517,plain,
( hBOOL(hAPP(X2,hAPP(X1,X5)))
| ~ hBOOL(hAPP(c_Set_Ovimage(X1,X2,X3,X4),X5)) ),
c_0_3403,
[final] ).
cnf(c_0_4518,plain,
( c_lessequals(c_Set_Oimage(X1,X4,X2,X3),c_Set_Oimage(X1,X5,X2,X3),tc_fun(X3,tc_bool))
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| ~ c_lessequals(X4,X5,tc_fun(X2,tc_bool)) ),
c_0_3404,
[final] ).
cnf(c_0_4519,plain,
( c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X3,X2,X4,X5),X1,X5,X4)
| ~ c_lessequals(X1,c_Set_Oimage(X2,X3,X4,X5),tc_fun(X5,tc_bool)) ),
c_0_3405,
[final] ).
cnf(c_0_4520,plain,
( c_Set_Oimage(X3,X1,X2,X2) = X1
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(c_Set_Oimage(X3,X1,X2,X2),X1,tc_fun(X2,tc_bool))
| ~ c_Fun_Oinj__on(X3,X1,X2,X2) ),
c_0_3406,
[final] ).
cnf(c_0_4521,plain,
c_lessequals(c_Set_Oimage(X1,c_Set_Ovimage(X1,X2,X3,X4),X3,X4),X2,tc_fun(X4,tc_bool)),
c_0_3407,
[final] ).
cnf(c_0_4522,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_3408,
[final] ).
cnf(c_0_4523,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X5,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_3409,
[final] ).
cnf(c_0_4524,plain,
( hAPP(X2,X1) = X3
| ~ c_in(X1,c_Set_Ovimage(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X5,X4),X5) ),
c_0_3410,
[final] ).
cnf(c_0_4525,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X6,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X5,X2,X3),X3),X6,X3),X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
c_0_3411,
[final] ).
cnf(c_0_4526,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Set_Ovimage(X1,X2,X5,X4),c_Set_Ovimage(X1,X3,X5,X4),tc_fun(X5,tc_bool)) = c_Set_Ovimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X5,X4),
c_0_3412,
[final] ).
cnf(c_0_4527,plain,
c_HOL_Ominus__class_Ominus(c_Set_Ovimage(X1,X2,X5,X4),c_Set_Ovimage(X1,X3,X5,X4),tc_fun(X5,tc_bool)) = c_Set_Ovimage(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X5,X4),
c_0_3413,
[final] ).
cnf(c_0_4528,plain,
( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_3414,
[final] ).
cnf(c_0_4529,plain,
( c_in(X4,X5,X2)
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| ~ c_in(hAPP(X1,X4),c_Set_Oimage(X1,X5,X2,X3),X3) ),
c_0_3415,
[final] ).
cnf(c_0_4530,plain,
( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
c_0_3416,
[final] ).
cnf(c_0_4531,plain,
( c_lessequals(c_Finite__Set_Ocard(X2,X3),c_Finite__Set_Ocard(X5,X4),tc_nat)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| ~ c_Finite__Set_Ofinite(X5,X4) ),
c_0_3417,
[final] ).
cnf(c_0_4532,plain,
c_Set_Oimage(X1,c_Set_Ovimage(X1,X2,X3,X4),X3,X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),tc_fun(X4,tc_bool)),
c_0_3418,
[final] ).
cnf(c_0_4533,plain,
( c_in(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
c_0_3419,
[final] ).
cnf(c_0_4534,plain,
( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2),c_Finite__Set_Ocard(X1,X2),tc_nat)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_in(X3,X1,X2) ),
c_0_3420,
[final] ).
cnf(c_0_4535,plain,
( c_in(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_in(X1,X4,X3) ),
c_0_3421,
[final] ).
cnf(c_0_4536,plain,
( c_lessequals(X1,c_Set_Oinsert(X2,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
c_0_3422,
[final] ).
cnf(c_0_4537,plain,
( c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2)) = c_Finite__Set_Ocard(c_Set_Oinsert(X3,X1,X2),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
c_0_3423,
[final] ).
cnf(c_0_4538,plain,
( c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2)) = c_Finite__Set_Ocard(X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_in(X3,X1,X2) ),
c_0_3424,
[final] ).
cnf(c_0_4539,plain,
( c_lessequals(X1,c_Set_Oinsert(X2,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| ~ c_in(X2,X1,X3) ),
c_0_3425,
[final] ).
cnf(c_0_4540,plain,
( c_lessequals(X1,c_Set_Oinsert(X2,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| ~ c_in(X2,X1,X3) ),
c_0_3426,
[final] ).
cnf(c_0_4541,plain,
( c_lessequals(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2),c_Finite__Set_Ocard(X1,X2),tc_nat)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
c_0_3427,
[final] ).
cnf(c_0_4542,plain,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5)
| c_Set_Oimage(X3,X1,X4,X5) != c_Set_Oimage(X3,X2,X4,X5) ),
c_0_3428,
[final] ).
cnf(c_0_4543,plain,
c_Fun_Ofun__upd(X1,X2,hAPP(X1,X2),X3,X4) = X1,
c_0_3429,
[final] ).
cnf(c_0_4544,plain,
c_Fun_Ofun__upd(X1,X2,hAPP(X1,X2),X3,X4) = X1,
c_0_3430,
[final] ).
cnf(c_0_4545,plain,
c_Fun_Ofun__upd(X1,X2,hAPP(X1,X2),X3,X4) = X1,
c_0_3431,
[final] ).
cnf(c_0_4546,plain,
( c_Set_Ovimage(X1,c_Set_Oimage(X1,X4,X2,X3),X2,X3) = X4
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3) ),
c_0_3432,
[final] ).
cnf(c_0_4547,plain,
( c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(X1,X2,X3,X4),X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
c_0_3433,
[final] ).
cnf(c_0_4548,plain,
( c_lessequals(c_Set_Oimage(X4,X1,X3,X5),c_Set_Oimage(X4,X2,X3,X5),tc_fun(X5,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_3434,
[final] ).
cnf(c_0_4549,plain,
( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool)) ),
c_0_3435,
[final] ).
cnf(c_0_4550,plain,
( c_lessequals(c_Set_Ovimage(X4,X1,X5,X3),c_Set_Ovimage(X4,X2,X5,X3),tc_fun(X5,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_3436,
[final] ).
cnf(c_0_4551,plain,
( c_Fun_Oinj__on(X3,X1,X2,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X1,c_Set_Oimage(X3,X1,X2,X2),tc_fun(X2,tc_bool)) ),
c_0_3437,
[final] ).
cnf(c_0_4552,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X6,X2,X3),X3),X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
c_0_3438,
[final] ).
cnf(c_0_4553,plain,
( hBOOL(hAPP(c_Set_Ovimage(X2,X1,X4,X5),X3))
| ~ hBOOL(hAPP(X1,hAPP(X2,X3))) ),
c_0_3439,
[final] ).
cnf(c_0_4554,plain,
( c_in(hAPP(X1,X4),c_Set_Oimage(X1,X5,X2,X3),X3)
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| ~ c_in(X4,X5,X2) ),
c_0_3440,
[final] ).
cnf(c_0_4555,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,tc_nat),X2,tc_nat),X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat)
| ~ c_lessequals(X4,X1,tc_nat) ),
c_0_3441,
[final] ).
cnf(c_0_4556,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),X2,tc_nat),X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),X4,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat) ),
c_0_3442,
[final] ).
cnf(c_0_4557,plain,
( c_lessequals(c_Finite__Set_Ocard(c_Set_Oimage(X3,X1,X2,X4),X4),c_Finite__Set_Ocard(X1,X2),tc_nat)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
c_0_3443,
[final] ).
cnf(c_0_4558,plain,
( hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,X1,X3),hAPP(X2,X4)) = X4
| ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X3) ),
c_0_3444,
[final] ).
cnf(c_0_4559,plain,
( hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1,X2,X3),hAPP(X1,X4)) = X4
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3) ),
c_0_3445,
[final] ).
cnf(c_0_4560,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(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),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_3446,
[final] ).
cnf(c_0_4561,plain,
( c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_Finite__Set_Ofinite(X2,X3)
| c_Finite__Set_Ocard(c_Set_Oimage(X1,X2,X3,X4),X4) != c_Finite__Set_Ocard(X2,X3) ),
c_0_3447,
[final] ).
cnf(c_0_4562,plain,
( c_in(X2,X3,X4)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| ~ c_in(X2,X1,X4) ),
c_0_3448,
[final] ).
cnf(c_0_4563,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X1,X3),X2,X3),X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,X3),X5,X3)
| ~ class_Ring__and__Field_Oring(X3) ),
c_0_3449,
[final] ).
cnf(c_0_4564,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Oring(X3) ),
c_0_3450,
[final] ).
cnf(c_0_4565,plain,
c_in(X1,c_Set_Ovimage(X2,c_Set_Oinsert(hAPP(X2,X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X4,X3),X4),
c_0_3451,
[final] ).
cnf(c_0_4566,plain,
( c_in(hAPP(X1,X6),X5,X4)
| ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| ~ c_in(X6,X2,X3) ),
c_0_3452,
[final] ).
cnf(c_0_4567,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),X3,tc_nat))) ),
c_0_3453,
[final] ).
cnf(c_0_4568,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),X3,tc_nat))) ),
c_0_3454,
[final] ).
cnf(c_0_4569,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(X4,X1,tc_nat),tc_nat),X2,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_3455,
[final] ).
cnf(c_0_4570,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| ~ c_in(X2,X1,X4) ),
c_0_3456,
[final] ).
cnf(c_0_4571,plain,
( hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),hAPP(X2,X5)) = X5
| ~ c_Fun_Oinj__on(X2,X1,X3,X4)
| ~ c_in(X5,X1,X3) ),
c_0_3457,
[final] ).
cnf(c_0_4572,plain,
( hAPP(c_Hilbert__Choice_Oinv__into(X2,X1,X3,X4),hAPP(X1,X5)) = X5
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_in(X5,X2,X3) ),
c_0_3458,
[final] ).
cnf(c_0_4573,plain,
( c_Finite__Set_Ofinite(c_Set_Ovimage(X3,X1,X4,X2),X4)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Fun_Oinj__on(X3,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X2) ),
c_0_3459,
[final] ).
cnf(c_0_4574,plain,
( X3 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_3460,
[final] ).
cnf(c_0_4575,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_3461,
[final] ).
cnf(c_0_4576,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_3462,
[final] ).
cnf(c_0_4577,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),X4,tc_nat) = X5
| ~ c_lessequals(X2,X1,tc_nat)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat) ),
c_0_3463,
[final] ).
cnf(c_0_4578,plain,
( X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),X4,tc_nat),X5,tc_nat)
| ~ c_lessequals(X3,X2,tc_nat)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X1,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X5,tc_nat) ),
c_0_3464,
[final] ).
cnf(c_0_4579,plain,
( c_in(hAPP(X2,X1),X3,X5)
| ~ c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4) ),
c_0_3465,
[final] ).
cnf(c_0_4580,plain,
( c_in(hAPP(X2,X1),X3,X5)
| ~ c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4) ),
c_0_3466,
[final] ).
cnf(c_0_4581,plain,
( c_Finite__Set_Ofinite(X3,X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,c_Set_Oimage(X4,X1,X2,X5),tc_fun(X5,tc_bool)) ),
c_0_3467,
[final] ).
cnf(c_0_4582,plain,
( c_Finite__Set_Ocard(c_Set_Oimage(X3,X1,X2,X4),X4) = c_Finite__Set_Ocard(X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Fun_Oinj__on(X3,X1,X2,X4) ),
c_0_3468,
[final] ).
cnf(c_0_4583,plain,
( c_in(X3,X4,X2)
| c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,X4,X2),tc_fun(X2,tc_bool)),X2) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X2,tc_bool)),X2),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_in(X3,X1,X2) ),
c_0_3469,
[final] ).
cnf(c_0_4584,plain,
c_Set_Oimage(X1,c_Set_Oinsert(X2,X3,X4),X4,X5) = c_Set_Oinsert(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5),
c_0_3470,
[final] ).
cnf(c_0_4585,plain,
( c_Finite__Set_Ocard(c_Set_Oimage(X1,X2,X3,X4),X4) = c_Finite__Set_Ocard(X2,X3)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
c_0_3471,
[final] ).
cnf(c_0_4586,plain,
( c_Set_Oinsert(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5) = c_Set_Oimage(X4,X2,X3,X5)
| ~ c_in(X1,X2,X3) ),
c_0_3472,
[final] ).
cnf(c_0_4587,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3) = X6
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3)
| ~ class_Ring__and__Field_Oring(X3) ),
c_0_3473,
[final] ).
cnf(c_0_4588,plain,
( X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4)
| ~ class_Ring__and__Field_Oring(X4) ),
c_0_3474,
[final] ).
cnf(c_0_4589,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,X3),X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3),X5,X3)
| ~ class_Ring__and__Field_Osemiring(X3) ),
c_0_3475,
[final] ).
cnf(c_0_4590,plain,
( X1 = X2
| X3 = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
c_0_3476,
[final] ).
cnf(c_0_4591,plain,
( X1 = X2
| X3 = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
c_0_3477,
[final] ).
cnf(c_0_4592,plain,
( c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(X1,X3),c_Finite__Set_Ocard(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3),tc_nat) = c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3) ),
c_0_3478,
[final] ).
cnf(c_0_4593,plain,
( X1 = X2
| X1 = X3
| c_Set_Oinsert(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
c_0_3479,
[final] ).
cnf(c_0_4594,plain,
( X1 = X2
| X3 = X2
| c_Set_Oinsert(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
c_0_3480,
[final] ).
cnf(c_0_4595,plain,
( X1 = X2
| X3 = X2
| c_Set_Oinsert(X3,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
c_0_3481,
[final] ).
cnf(c_0_4596,plain,
( X1 = X2
| X1 = X3
| c_Set_Oinsert(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
c_0_3482,
[final] ).
cnf(c_0_4597,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)),
c_0_3483,
[final] ).
cnf(c_0_4598,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat),X4,tc_nat),
c_0_3484,
[final] ).
cnf(c_0_4599,plain,
( X1 = X2
| X3 = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
c_0_3485,
[final] ).
cnf(c_0_4600,plain,
( X1 = X2
| X3 = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
c_0_3486,
[final] ).
cnf(c_0_4601,plain,
( c_Fun_Oinj__on(X1,X3,X4,X5)
| ~ c_Fun_Oinj__on(X1,c_Set_Oinsert(X2,X3,X4),X4,X5) ),
c_0_3487,
[final] ).
cnf(c_0_4602,plain,
( c_Fun_Oinj__on(X1,c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X3,tc_bool)),X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
c_0_3488,
[final] ).
cnf(c_0_4603,plain,
( c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(X1,X2),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_in(X3,X1,X2) ),
c_0_3489,
[final] ).
cnf(c_0_4604,plain,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool)),X4)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)),X4) ),
c_0_3490,
[final] ).
cnf(c_0_4605,plain,
( c_Fun_Oinj__on(X1,X5,X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool)) ),
c_0_3491,
[final] ).
cnf(c_0_4606,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(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_Ominus__class_Ominus(X1,X2,X3),X4,X3)
| ~ class_Divides_Oring__div(X3) ),
c_0_3492,
[final] ).
cnf(c_0_4607,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_3493,
[final] ).
cnf(c_0_4608,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(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_Oplus__class_Oplus(X1,X2,X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_3494,
[final] ).
cnf(c_0_4609,plain,
c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat)),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X3),X2,tc_nat),
c_0_3495,
[final] ).
cnf(c_0_4610,plain,
( c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = X2
| ~ c_in(X1,X2,X3) ),
c_0_3496,
[final] ).
cnf(c_0_4611,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(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),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_3497,
[final] ).
cnf(c_0_4612,plain,
c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = c_Set_Oinsert(X1,X2,X3),
c_0_3498,
[final] ).
cnf(c_0_4613,plain,
( c_in(X3,X1,X2)
| c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2) = c_Finite__Set_Ocard(X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
c_0_3499,
[final] ).
cnf(c_0_4614,plain,
c_in(hAPP(X1,X2),c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X4),
c_0_3500,
[final] ).
cnf(c_0_4615,plain,
( c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5)
| ~ c_in(hAPP(X1,X2),X3,X4) ),
c_0_3501,
[final] ).
cnf(c_0_4616,plain,
( c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5)
| ~ c_in(hAPP(X1,X2),X3,X4) ),
c_0_3502,
[final] ).
cnf(c_0_4617,plain,
( c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5)
| ~ c_in(hAPP(X1,X2),X3,X4) ),
c_0_3503,
[final] ).
cnf(c_0_4618,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(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_Oring__div(X3) ),
c_0_3504,
[final] ).
cnf(c_0_4619,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_3505,
[final] ).
cnf(c_0_4620,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(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_3506,
[final] ).
cnf(c_0_4621,plain,
( c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5)
| ~ c_in(X1,X2,X3) ),
c_0_3507,
[final] ).
cnf(c_0_4622,plain,
( c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5)
| ~ c_in(X1,X2,X3) ),
c_0_3508,
[final] ).
cnf(c_0_4623,plain,
( c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5)
| ~ c_in(X2,X3,X4) ),
c_0_3509,
[final] ).
cnf(c_0_4624,plain,
( c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5)
| ~ c_in(X2,X3,X4) ),
c_0_3510,
[final] ).
cnf(c_0_4625,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_3511,
[final] ).
cnf(c_0_4626,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_3512,
[final] ).
cnf(c_0_4627,plain,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3) ),
c_0_3513,
[final] ).
cnf(c_0_4628,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
c_0_3514,
[final] ).
cnf(c_0_4629,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
c_0_3515,
[final] ).
cnf(c_0_4630,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
c_0_3516,
[final] ).
cnf(c_0_4631,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
c_0_3517,
[final] ).
cnf(c_0_4632,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
c_0_3518,
[final] ).
cnf(c_0_4633,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
c_0_3519,
[final] ).
cnf(c_0_4634,plain,
( c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
c_0_3520,
[final] ).
cnf(c_0_4635,plain,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
c_0_3521,
[final] ).
cnf(c_0_4636,plain,
( c_lessequals(hAPP(X1,X3),hAPP(X1,X4),X2)
| ~ c_lessequals(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1(X1,X2)),hAPP(X1,c_Suc(c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1(X1,X2))),X2)
| ~ c_lessequals(X3,X4,tc_nat)
| ~ class_Orderings_Oorder(X2) ),
c_0_3522,
[final] ).
cnf(c_0_4637,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X5,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool)) ),
c_0_3523,
[final] ).
cnf(c_0_4638,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool)) ),
c_0_3524,
[final] ).
cnf(c_0_4639,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool)),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)),
c_0_3525,
[final] ).
cnf(c_0_4640,plain,
c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)),
c_0_3526,
[final] ).
cnf(c_0_4641,plain,
c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)),
c_0_3527,
[final] ).
cnf(c_0_4642,plain,
c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X4,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
c_0_3528,
[final] ).
cnf(c_0_4643,plain,
( X1 = X4
| ~ c_in(X1,X2,X3)
| ~ c_in(X4,X2,X3)
| ~ c_Fun_Oinj__on(X5,X2,X3,X6)
| hAPP(X5,X1) != hAPP(X5,X4) ),
c_0_3529,
[final] ).
cnf(c_0_4644,plain,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| ~ c_in(X1,X4,X5)
| ~ c_in(X2,X4,X5)
| hAPP(X3,X1) != hAPP(X3,X2) ),
c_0_3530,
[final] ).
cnf(c_0_4645,plain,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| ~ c_in(X1,X4,X5)
| ~ c_in(X2,X4,X5)
| hAPP(X3,X1) != hAPP(X3,X2) ),
c_0_3531,
[final] ).
cnf(c_0_4646,plain,
( X5 = X6
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_in(X5,X2,X3)
| ~ c_in(X6,X2,X3)
| hAPP(X1,X5) != hAPP(X1,X6) ),
c_0_3532,
[final] ).
cnf(c_0_4647,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X2),c_HOL_Otimes__class_Otimes(X1,X1,X2),X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_3533,
[final] ).
cnf(c_0_4648,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_3534,
[final] ).
cnf(c_0_4649,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_3535,
[final] ).
cnf(c_0_4650,plain,
( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(X3,X2,tc_nat)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X2,X5,tc_nat),tc_nat) ),
c_0_3536,
[final] ).
cnf(c_0_4651,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X1 = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| ~ c_lessequals(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) ),
c_0_3537,
[final] ).
cnf(c_0_4652,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_3538,
[final] ).
cnf(c_0_4653,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_3539,
[final] ).
cnf(c_0_4654,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
c_0_3540,
[final] ).
cnf(c_0_4655,plain,
( c_lessequals(X2,X4,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
c_0_3541,
[final] ).
cnf(c_0_4656,plain,
( c_lessequals(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(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_3542,
[final] ).
cnf(c_0_4657,plain,
( c_lessequals(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(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_3543,
[final] ).
cnf(c_0_4658,plain,
( 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)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__semiring(X3) ),
c_0_3544,
[final] ).
cnf(c_0_4659,plain,
( 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)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semiring(X3) ),
c_0_3545,
[final] ).
cnf(c_0_4660,plain,
( 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)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
c_0_3546,
[final] ).
cnf(c_0_4661,plain,
( 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)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
c_0_3547,
[final] ).
cnf(c_0_4662,plain,
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4)) ),
c_0_3548,
[final] ).
cnf(c_0_4663,plain,
( hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4)) ),
c_0_3549,
[final] ).
cnf(c_0_4664,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_3550,
[final] ).
cnf(c_0_4665,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_3551,
[final] ).
cnf(c_0_4666,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_3552,
[final] ).
cnf(c_0_4667,plain,
( c_lessequals(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
c_0_3553,
[final] ).
cnf(c_0_4668,plain,
( c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(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_3554,
[final] ).
cnf(c_0_4669,plain,
( c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(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) ),
c_0_3555,
[final] ).
cnf(c_0_4670,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_3556,
[final] ).
cnf(c_0_4671,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_3557,
[final] ).
cnf(c_0_4672,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
c_0_3558,
[final] ).
cnf(c_0_4673,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
c_0_3559,
[final] ).
cnf(c_0_4674,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_3560,
[final] ).
cnf(c_0_4675,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_3561,
[final] ).
cnf(c_0_4676,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_3562,
[final] ).
cnf(c_0_4677,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_3563,
[final] ).
cnf(c_0_4678,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X2,X3,X4),X4),X3,X4) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4)
| ~ class_Divides_Osemiring__div(X4) ),
c_0_3564,
[final] ).
cnf(c_0_4679,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X2,X3),X4,X3),X2,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_3565,
[final] ).
cnf(c_0_4680,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
| ~ class_Divides_Oring__div(X3) ),
c_0_3566,
[final] ).
cnf(c_0_4681,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
| ~ class_Divides_Oring__div(X3) ),
c_0_3567,
[final] ).
cnf(c_0_4682,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_3568,
[final] ).
cnf(c_0_4683,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_3569,
[final] ).
cnf(c_0_4684,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_3570,
[final] ).
cnf(c_0_4685,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_3571,
[final] ).
cnf(c_0_4686,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_3572,
[final] ).
cnf(c_0_4687,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_3573,
[final] ).
cnf(c_0_4688,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_3574,
[final] ).
cnf(c_0_4689,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_3575,
[final] ).
cnf(c_0_4690,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_3576,
[final] ).
cnf(c_0_4691,plain,
c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),
c_0_3577,
[final] ).
cnf(c_0_4692,plain,
( c_Finite__Set_Ofinite(c_Set_Oimage(X3,X1,X2,X4),X4)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
c_0_3578,
[final] ).
cnf(c_0_4693,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = X4
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) != c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_3579,
[final] ).
cnf(c_0_4694,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
c_0_3580,
[final] ).
cnf(c_0_4695,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
c_0_3581,
[final] ).
cnf(c_0_4696,plain,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5)
| hAPP(X3,X1) != hAPP(X3,X2) ),
c_0_3582,
[final] ).
cnf(c_0_4697,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(X3,c_Suc(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_3583,
[final] ).
cnf(c_0_4698,plain,
( c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X2),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_3584,
[final] ).
cnf(c_0_4699,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) ),
c_0_3585,
[final] ).
cnf(c_0_4700,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
c_0_3586,
[final] ).
cnf(c_0_4701,plain,
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X5,X4),X4)
| ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| ~ c_lessequals(X3,X5,X4)
| ~ class_OrderedGroup_Opordered__ab__group__add(X4) ),
c_0_3587,
[final] ).
cnf(c_0_4702,plain,
( c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(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_3588,
[final] ).
cnf(c_0_4703,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_3589,
[final] ).
cnf(c_0_4704,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = X3
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
c_0_3590,
[final] ).
cnf(c_0_4705,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3),
c_0_3591,
[final] ).
cnf(c_0_4706,plain,
( hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)))
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
c_0_3592,
[final] ).
cnf(c_0_4707,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_3593,
[final] ).
cnf(c_0_4708,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_3594,
[final] ).
cnf(c_0_4709,plain,
( c_lessequals(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),X2,tc_nat) ),
c_0_3595,
[final] ).
cnf(c_0_4710,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),X2,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ),
c_0_3596,
[final] ).
cnf(c_0_4711,plain,
( c_in(X4,X1,X3)
| c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_3597,
[final] ).
cnf(c_0_4712,plain,
( c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
c_0_3598,
[final] ).
cnf(c_0_4713,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
c_0_3599,
[final] ).
cnf(c_0_4714,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
c_0_3600,
[final] ).
cnf(c_0_4715,plain,
( c_lessequals(X2,X4,X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
c_0_3601,
[final] ).
cnf(c_0_4716,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat) ),
c_0_3602,
[final] ).
cnf(c_0_4717,plain,
( c_in(X2,X3,X4)
| c_in(X2,X1,X4)
| c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) ),
c_0_3603,
[final] ).
cnf(c_0_4718,plain,
( c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| ~ c_in(X1,X2,X3) ),
c_0_3604,
[final] ).
cnf(c_0_4719,plain,
( c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)),X3) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool))
| ~ c_in(X1,X2,X3) ),
c_0_3605,
[final] ).
cnf(c_0_4720,plain,
( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X1
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
c_0_3606,
[final] ).
cnf(c_0_4721,plain,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
c_0_3607,
[final] ).
cnf(c_0_4722,plain,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
c_0_3608,
[final] ).
cnf(c_0_4723,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_lessequals(X3,X2,tc_nat) ),
c_0_3609,
[final] ).
cnf(c_0_4724,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
| ~ c_lessequals(X3,X2,tc_nat) ),
c_0_3610,
[final] ).
cnf(c_0_4725,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_3611,
[final] ).
cnf(c_0_4726,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_3612,
[final] ).
cnf(c_0_4727,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_3613,
[final] ).
cnf(c_0_4728,plain,
( c_Finite__Set_Ocard(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = c_Suc(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2))
| c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
c_0_3614,
[final] ).
cnf(c_0_4729,plain,
( c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat) ),
c_0_3615,
[final] ).
cnf(c_0_4730,plain,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat) ),
c_0_3616,
[final] ).
cnf(c_0_4731,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_3617,
[final] ).
cnf(c_0_4732,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_3618,
[final] ).
cnf(c_0_4733,plain,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)),
c_0_3619,
[final] ).
cnf(c_0_4734,plain,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
c_0_3620,
[final] ).
cnf(c_0_4735,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
c_0_3621,
[final] ).
cnf(c_0_4736,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Set_Oimage(X4,X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
c_0_3622,
[final] ).
cnf(c_0_4737,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Set_Oimage(X3,X1,X2,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
c_0_3623,
[final] ).
cnf(c_0_4738,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Omult__mono1(X3) ),
c_0_3624,
[final] ).
cnf(c_0_4739,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Omult__mono(X3) ),
c_0_3625,
[final] ).
cnf(c_0_4740,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Omult__mono(X3) ),
c_0_3626,
[final] ).
cnf(c_0_4741,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
c_0_3627,
[final] ).
cnf(c_0_4742,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
c_0_3628,
[final] ).
cnf(c_0_4743,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_3629,
[final] ).
cnf(c_0_4744,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_3630,
[final] ).
cnf(c_0_4745,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_3631,
[final] ).
cnf(c_0_4746,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_3632,
[final] ).
cnf(c_0_4747,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_3633,
[final] ).
cnf(c_0_4748,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_3634,
[final] ).
cnf(c_0_4749,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_3635,
[final] ).
cnf(c_0_4750,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_3636,
[final] ).
cnf(c_0_4751,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_3637,
[final] ).
cnf(c_0_4752,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_3638,
[final] ).
cnf(c_0_4753,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_3639,
[final] ).
cnf(c_0_4754,plain,
( c_lessequals(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_lessequals(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_3640,
[final] ).
cnf(c_0_4755,plain,
( c_lessequals(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_lessequals(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_3641,
[final] ).
cnf(c_0_4756,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_3642,
[final] ).
cnf(c_0_4757,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_3643,
[final] ).
cnf(c_0_4758,plain,
( c_HOL_Oord__class_Oless(X1,X3,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| ~ c_in(X2,X3,X4) ),
c_0_3644,
[final] ).
cnf(c_0_4759,plain,
( c_in(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) = X2 ),
c_0_3645,
[final] ).
cnf(c_0_4760,plain,
( c_lessequals(X3,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_3646,
[final] ).
cnf(c_0_4761,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
c_0_3647,
[final] ).
cnf(c_0_4762,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_3648,
[final] ).
cnf(c_0_4763,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),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_3649,
[final] ).
cnf(c_0_4764,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
c_0_3650,
[final] ).
cnf(c_0_4765,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
c_0_3651,
[final] ).
cnf(c_0_4766,plain,
( c_in(X1,X2,X3)
| c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X3,tc_bool)),X3) = c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) ),
c_0_3652,
[final] ).
cnf(c_0_4767,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_3653,
[final] ).
cnf(c_0_4768,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X2),c_HOL_Otimes__class_Otimes(X1,X1,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_3654,
[final] ).
cnf(c_0_4769,plain,
( c_lessequals(X1,X2,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) ),
c_0_3655,
[final] ).
cnf(c_0_4770,plain,
( c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) ),
c_0_3656,
[final] ).
cnf(c_0_4771,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
c_0_3657,
[final] ).
cnf(c_0_4772,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring(X3) ),
c_0_3658,
[final] ).
cnf(c_0_4773,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_3659,
[final] ).
cnf(c_0_4774,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_3660,
[final] ).
cnf(c_0_4775,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_3661,
[final] ).
cnf(c_0_4776,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_3662,
[final] ).
cnf(c_0_4777,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4),X2,X4) = c_Divides_Odiv__class_Omod(X1,X2,X4)
| ~ class_Divides_Osemiring__div(X4) ),
c_0_3663,
[final] ).
cnf(c_0_4778,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4),X3,X4) = c_Divides_Odiv__class_Omod(X1,X3,X4)
| ~ class_Divides_Osemiring__div(X4) ),
c_0_3664,
[final] ).
cnf(c_0_4779,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3)
| ~ class_OrderedGroup_Olordered__ab__group__add(X3) ),
c_0_3665,
[final] ).
cnf(c_0_4780,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X2,X4),c_HOL_Oplus__class_Oplus(X1,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_OrderedGroup_Olordered__ab__group__add(X4) ),
c_0_3666,
[final] ).
cnf(c_0_4781,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3)
| ~ class_OrderedGroup_Olordered__ab__group__add__meet(X3) ),
c_0_3667,
[final] ).
cnf(c_0_4782,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X2,X4),c_HOL_Oplus__class_Oplus(X1,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_OrderedGroup_Olordered__ab__group__add__meet(X4) ),
c_0_3668,
[final] ).
cnf(c_0_4783,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_3669,
[final] ).
cnf(c_0_4784,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_3670,
[final] ).
cnf(c_0_4785,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_3671,
[final] ).
cnf(c_0_4786,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_3672,
[final] ).
cnf(c_0_4787,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_3673,
[final] ).
cnf(c_0_4788,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_3674,
[final] ).
cnf(c_0_4789,plain,
( c_lessequals(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_lessequals(X2,X3,tc_nat) ),
c_0_3675,
[final] ).
cnf(c_0_4790,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) ),
c_0_3676,
[final] ).
cnf(c_0_4791,plain,
( hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X3,X2)) ),
c_0_3677,
[final] ).
cnf(c_0_4792,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(X3,X1,tc_nat) ),
c_0_3678,
[final] ).
cnf(c_0_4793,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
c_0_3679,
[final] ).
cnf(c_0_4794,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X3,X4,tc_nat) ),
c_0_3680,
[final] ).
cnf(c_0_4795,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X4,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X3,X4,tc_nat) ),
c_0_3681,
[final] ).
cnf(c_0_4796,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
c_0_3682,
[final] ).
cnf(c_0_4797,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_3683,
[final] ).
cnf(c_0_4798,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_3684,
[final] ).
cnf(c_0_4799,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_3685,
[final] ).
cnf(c_0_4800,plain,
( c_in(X1,X2,X3)
| c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool)) ),
c_0_3686,
[final] ).
cnf(c_0_4801,plain,
( c_in(X2,X1,X4)
| c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) ),
c_0_3687,
[final] ).
cnf(c_0_4802,plain,
( X1 = X2
| ~ c_in(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
c_0_3688,
[final] ).
cnf(c_0_4803,plain,
c_HOL_Ominus__class_Ominus(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_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),
c_0_3689,
[final] ).
cnf(c_0_4804,plain,
c_HOL_Ominus__class_Ominus(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_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat),
c_0_3690,
[final] ).
cnf(c_0_4805,plain,
c_HOL_Oplus__class_Oplus(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_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),
c_0_3691,
[final] ).
cnf(c_0_4806,plain,
c_HOL_Oplus__class_Oplus(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_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat),
c_0_3692,
[final] ).
cnf(c_0_4807,plain,
c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat),X2,tc_nat) = c_Divides_Odiv__class_Omod(X3,X2,tc_nat),
c_0_3693,
[final] ).
cnf(c_0_4808,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_3694,
[final] ).
cnf(c_0_4809,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_3695,
[final] ).
cnf(c_0_4810,plain,
( c_in(X1,X2,X3)
| c_in(X1,X4,X3)
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
c_0_3696,
[final] ).
cnf(c_0_4811,plain,
( c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(X3,X2),c_Finite__Set_Ocard(X1,X2),tc_nat) = c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool)) ),
c_0_3697,
[final] ).
cnf(c_0_4812,plain,
( X1 = X4
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4)) ),
c_0_3698,
[final] ).
cnf(c_0_4813,plain,
( c_lessequals(c_Set_Oinsert(X4,X1,X3),c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_3699,
[final] ).
cnf(c_0_4814,plain,
( ~ c_in(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4)
| ~ c_in(X1,X3,X4) ),
c_0_3700,
[final] ).
cnf(c_0_4815,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat) = X1
| ~ c_lessequals(X2,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
c_0_3701,
[final] ).
cnf(c_0_4816,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat)
| ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) ),
c_0_3702,
[final] ).
cnf(c_0_4817,plain,
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) ),
c_0_3703,
[final] ).
cnf(c_0_4818,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ),
c_0_3704,
[final] ).
cnf(c_0_4819,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) ),
c_0_3705,
[final] ).
cnf(c_0_4820,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_3706,
[final] ).
cnf(c_0_4821,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_3707,
[final] ).
cnf(c_0_4822,plain,
( c_HOL_Oplus__class_Oplus(X1,X2,X3) = X4
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X5,X2,X3),X3) != c_HOL_Oplus__class_Oplus(X5,X4,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
c_0_3708,
[final] ).
cnf(c_0_4823,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),X1,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_3709,
[final] ).
cnf(c_0_4824,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),X1,tc_nat) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_3710,
[final] ).
cnf(c_0_4825,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),X2,tc_nat) = c_HOL_Ominus__class_Ominus(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_3711,
[final] ).
cnf(c_0_4826,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),X1,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_3712,
[final] ).
cnf(c_0_4827,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),X1,tc_nat) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_3713,
[final] ).
cnf(c_0_4828,plain,
( c_lessequals(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool))
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
c_0_3714,
[final] ).
cnf(c_0_4829,plain,
( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X2,X3) ),
c_0_3715,
[final] ).
cnf(c_0_4830,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
c_0_3716,
[final] ).
cnf(c_0_4831,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
c_0_3717,
[final] ).
cnf(c_0_4832,plain,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
c_0_3718,
[final] ).
cnf(c_0_4833,plain,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
c_0_3719,
[final] ).
cnf(c_0_4834,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_3720,
[final] ).
cnf(c_0_4835,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_3721,
[final] ).
cnf(c_0_4836,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_3722,
[final] ).
cnf(c_0_4837,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_3723,
[final] ).
cnf(c_0_4838,plain,
( c_HOL_Oord__class_Oless(X3,X1,tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(X3,X2),c_Finite__Set_Ocard(X1,X2),tc_nat) ),
c_0_3724,
[final] ).
cnf(c_0_4839,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat)) = c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
c_0_3725,
[final] ).
cnf(c_0_4840,plain,
( c_in(X1,X2,X4)
| ~ c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4) ),
c_0_3726,
[final] ).
cnf(c_0_4841,plain,
( c_in(X1,X3,X4)
| ~ c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4) ),
c_0_3727,
[final] ).
cnf(c_0_4842,plain,
( c_in(X1,X2,X4)
| ~ c_in(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4) ),
c_0_3728,
[final] ).
cnf(c_0_4843,plain,
( c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,X3)
| ~ c_in(X1,X4,X3) ),
c_0_3729,
[final] ).
cnf(c_0_4844,plain,
( c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,X3)
| ~ c_in(X1,X4,X3) ),
c_0_3730,
[final] ).
cnf(c_0_4845,plain,
( c_in(X1,c_Inductive_Ocomplete__lattice__class_Ogfp(X4,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X2,hAPP(X4,X2),tc_fun(X3,tc_bool)) ),
c_0_3731,
[final] ).
cnf(c_0_4846,plain,
( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
c_0_3732,
[final] ).
cnf(c_0_4847,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_3733,
[final] ).
cnf(c_0_4848,plain,
( c_lessequals(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_lessequals(X1,X2,tc_nat) ),
c_0_3734,
[final] ).
cnf(c_0_4849,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_3735,
[final] ).
cnf(c_0_4850,plain,
( c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) ),
c_0_3736,
[final] ).
cnf(c_0_4851,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
c_0_3737,
[final] ).
cnf(c_0_4852,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2) ),
c_0_3738,
[final] ).
cnf(c_0_4853,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2) ),
c_0_3739,
[final] ).
cnf(c_0_4854,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_3740,
[final] ).
cnf(c_0_4855,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_3741,
[final] ).
cnf(c_0_4856,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
c_0_3742,
[final] ).
cnf(c_0_4857,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
c_0_3743,
[final] ).
cnf(c_0_4858,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_3744,
[final] ).
cnf(c_0_4859,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_3745,
[final] ).
cnf(c_0_4860,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_3746,
[final] ).
cnf(c_0_4861,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_3747,
[final] ).
cnf(c_0_4862,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(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_OrderedGroup_Opordered__comm__monoid__add(X1) ),
c_0_3748,
[final] ).
cnf(c_0_4863,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
c_0_3749,
[final] ).
cnf(c_0_4864,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
c_0_3750,
[final] ).
cnf(c_0_4865,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_3751,
[final] ).
cnf(c_0_4866,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_3752,
[final] ).
cnf(c_0_4867,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
c_0_3753,
[final] ).
cnf(c_0_4868,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X2) ),
c_0_3754,
[final] ).
cnf(c_0_4869,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
c_0_3755,
[final] ).
cnf(c_0_4870,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X2) ),
c_0_3756,
[final] ).
cnf(c_0_4871,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
c_0_3757,
[final] ).
cnf(c_0_4872,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_3758,
[final] ).
cnf(c_0_4873,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_3759,
[final] ).
cnf(c_0_4874,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
c_0_3760,
[final] ).
cnf(c_0_4875,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
c_0_3761,
[final] ).
cnf(c_0_4876,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(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(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
c_0_3762,
[final] ).
cnf(c_0_4877,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
c_0_3763,
[final] ).
cnf(c_0_4878,plain,
c_lessequals(X1,c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X1,X1,tc_nat),tc_nat),tc_nat),
c_0_3764,
[final] ).
cnf(c_0_4879,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),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
c_0_3765,
[final] ).
cnf(c_0_4880,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_3766,
[final] ).
cnf(c_0_4881,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_3767,
[final] ).
cnf(c_0_4882,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
c_0_3768,
[final] ).
cnf(c_0_4883,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
c_0_3769,
[final] ).
cnf(c_0_4884,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
c_0_3770,
[final] ).
cnf(c_0_4885,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
c_0_3771,
[final] ).
cnf(c_0_4886,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
c_0_3772,
[final] ).
cnf(c_0_4887,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
c_0_3773,
[final] ).
cnf(c_0_4888,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
c_0_3774,
[final] ).
cnf(c_0_4889,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
c_0_3775,
[final] ).
cnf(c_0_4890,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_3776,
[final] ).
cnf(c_0_4891,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_3777,
[final] ).
cnf(c_0_4892,plain,
( c_in(X1,X2,X3)
| c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
c_0_3778,
[final] ).
cnf(c_0_4893,plain,
( c_in(X1,X2,X3)
| c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
c_0_3779,
[final] ).
cnf(c_0_4894,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_3780,
[final] ).
cnf(c_0_4895,plain,
( c_lessequals(X3,c_HOL_Oplus__class_Oplus(X4,X2,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
c_0_3781,
[final] ).
cnf(c_0_4896,plain,
( c_lessequals(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
c_0_3782,
[final] ).
cnf(c_0_4897,plain,
( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
c_0_3783,
[final] ).
cnf(c_0_4898,plain,
( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
c_0_3784,
[final] ).
cnf(c_0_4899,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_3785,
[final] ).
cnf(c_0_4900,plain,
( hBOOL(hAPP(X3,X2))
| ~ c_lessequals(c_Suc(X1),X2,tc_nat)
| ~ hBOOL(hAPP(X3,c_Suc(c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1(X3,X1)))) ),
c_0_3786,
[final] ).
cnf(c_0_4901,plain,
( hBOOL(hAPP(X1,c_Suc(c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1(X1))))
| hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)))
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_3787,
[final] ).
cnf(c_0_4902,plain,
( hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1(X1))) ),
c_0_3788,
[final] ).
cnf(c_0_4903,plain,
( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(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__semidom(X1) ),
c_0_3789,
[final] ).
cnf(c_0_4904,plain,
( c_in(X1,X4,X3)
| c_in(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,X3) ),
c_0_3790,
[final] ).
cnf(c_0_4905,plain,
( c_in(X1,X4,X3)
| c_in(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,X3) ),
c_0_3791,
[final] ).
cnf(c_0_4906,plain,
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X3,tc_bool))
| ~ c_in(X1,X2,X3) ),
c_0_3792,
[final] ).
cnf(c_0_4907,plain,
( c_in(X1,X4,X3)
| ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) ),
c_0_3793,
[final] ).
cnf(c_0_4908,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_3794,
[final] ).
cnf(c_0_4909,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_3795,
[final] ).
cnf(c_0_4910,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_3796,
[final] ).
cnf(c_0_4911,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_3797,
[final] ).
cnf(c_0_4912,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_3798,
[final] ).
cnf(c_0_4913,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_3799,
[final] ).
cnf(c_0_4914,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_3800,
[final] ).
cnf(c_0_4915,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_3801,
[final] ).
cnf(c_0_4916,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_3802,
[final] ).
cnf(c_0_4917,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_3803,
[final] ).
cnf(c_0_4918,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_3804,
[final] ).
cnf(c_0_4919,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X3),X3),X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_3805,
[final] ).
cnf(c_0_4920,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X2,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X3),X3),X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_3806,
[final] ).
cnf(c_0_4921,plain,
( c_lessequals(c_Finite__Set_Ocard(X1,X2),c_Finite__Set_Ocard(c_Set_Oinsert(X3,X1,X2),X2),tc_nat)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
c_0_3807,
[final] ).
cnf(c_0_4922,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(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_Ring__and__Field_Ocomm__ring__1(X3) ),
c_0_3808,
[final] ).
cnf(c_0_4923,plain,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_3809,
[final] ).
cnf(c_0_4924,plain,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_3810,
[final] ).
cnf(c_0_4925,plain,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_3811,
[final] ).
cnf(c_0_4926,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(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_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_3812,
[final] ).
cnf(c_0_4927,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_3813,
[final] ).
cnf(c_0_4928,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_3814,
[final] ).
cnf(c_0_4929,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_3815,
[final] ).
cnf(c_0_4930,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_3816,
[final] ).
cnf(c_0_4931,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_3817,
[final] ).
cnf(c_0_4932,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3)
| ~ c_in(X4,X2,X3) ),
c_0_3818,
[final] ).
cnf(c_0_4933,plain,
( X1 = X2
| ~ c_lessequals(X3,X1,tc_nat)
| ~ c_lessequals(X3,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(X1,X3,tc_nat) != c_HOL_Ominus__class_Ominus(X2,X3,tc_nat) ),
c_0_3819,
[final] ).
cnf(c_0_4934,plain,
( X1 = X2
| c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) != c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
c_0_3820,
[final] ).
cnf(c_0_4935,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
c_0_3821,
[final] ).
cnf(c_0_4936,plain,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
c_0_3822,
[final] ).
cnf(c_0_4937,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_Oplus__class_Oplus(X2,X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_3823,
[final] ).
cnf(c_0_4938,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
c_0_3824,
[final] ).
cnf(c_0_4939,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
c_0_3825,
[final] ).
cnf(c_0_4940,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_3826,
[final] ).
cnf(c_0_4941,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X1),X2,tc_nat),c_Suc(X3),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),
c_0_3827,
[final] ).
cnf(c_0_4942,plain,
( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
c_0_3828,
[final] ).
cnf(c_0_4943,plain,
( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
c_0_3829,
[final] ).
cnf(c_0_4944,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_3830,
[final] ).
cnf(c_0_4945,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_3831,
[final] ).
cnf(c_0_4946,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_3832,
[final] ).
cnf(c_0_4947,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_3833,
[final] ).
cnf(c_0_4948,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_3834,
[final] ).
cnf(c_0_4949,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_3835,
[final] ).
cnf(c_0_4950,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_3836,
[final] ).
cnf(c_0_4951,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
c_0_3837,
[final] ).
cnf(c_0_4952,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4),X4)
| ~ class_Lattices_Olattice(X4) ),
c_0_3838,
[final] ).
cnf(c_0_4953,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
c_0_3839,
[final] ).
cnf(c_0_4954,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_3840,
[final] ).
cnf(c_0_4955,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
c_0_3841,
[final] ).
cnf(c_0_4956,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_3842,
[final] ).
cnf(c_0_4957,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
c_0_3843,
[final] ).
cnf(c_0_4958,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_OrderedGroup_Oab__semigroup__add(X3) ),
c_0_3844,
[final] ).
cnf(c_0_4959,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
c_0_3845,
[final] ).
cnf(c_0_4960,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3) ),
c_0_3846,
[final] ).
cnf(c_0_4961,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4)
| ~ class_OrderedGroup_Oab__group__add(X4) ),
c_0_3847,
[final] ).
cnf(c_0_4962,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
c_0_3848,
[final] ).
cnf(c_0_4963,plain,
( c_HOL_Oplus__class_Oplus(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) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_3849,
[final] ).
cnf(c_0_4964,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_3850,
[final] ).
cnf(c_0_4965,plain,
c_Set_Oimage(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
c_0_3851,
[final] ).
cnf(c_0_4966,plain,
c_Set_Oimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
c_0_3852,
[final] ).
cnf(c_0_4967,plain,
c_Set_Ovimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
c_0_3853,
[final] ).
cnf(c_0_4968,plain,
c_Set_Ovimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3,X2) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),
c_0_3854,
[final] ).
cnf(c_0_4969,plain,
( c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_3855,
[final] ).
cnf(c_0_4970,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_3856,
[final] ).
cnf(c_0_4971,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_3857,
[final] ).
cnf(c_0_4972,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),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_0_3858,
[final] ).
cnf(c_0_4973,plain,
c_Set_Oinsert(X1,c_Set_Oinsert(X2,X3,X4),X4) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,X3,X4),X4),
c_0_3859,
[final] ).
cnf(c_0_4974,plain,
( c_lessequals(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
c_0_3860,
[final] ).
cnf(c_0_4975,plain,
( c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
c_0_3861,
[final] ).
cnf(c_0_4976,plain,
( c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X2,X4,tc_fun(X3,tc_bool)) ),
c_0_3862,
[final] ).
cnf(c_0_4977,plain,
( c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X2,X4,tc_fun(X3,tc_bool)) ),
c_0_3863,
[final] ).
cnf(c_0_4978,plain,
( c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X5,X4,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_3864,
[final] ).
cnf(c_0_4979,plain,
( c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X5,X4,X3) != c_HOL_Ominus__class_Ominus(X2,X1,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_3865,
[final] ).
cnf(c_0_4980,plain,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_3866,
[final] ).
cnf(c_0_4981,plain,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_3867,
[final] ).
cnf(c_0_4982,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
c_0_3868,
[final] ).
cnf(c_0_4983,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat) ),
c_0_3869,
[final] ).
cnf(c_0_4984,plain,
( c_in(X1,X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)) ),
c_0_3870,
[final] ).
cnf(c_0_4985,plain,
( c_in(X1,X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)) ),
c_0_3871,
[final] ).
cnf(c_0_4986,plain,
( c_lessequals(X1,X3,X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
c_0_3872,
[final] ).
cnf(c_0_4987,plain,
( c_lessequals(X1,X2,X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
c_0_3873,
[final] ).
cnf(c_0_4988,plain,
( c_lessequals(X1,X3,X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
c_0_3874,
[final] ).
cnf(c_0_4989,plain,
( c_lessequals(X1,X2,X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
c_0_3875,
[final] ).
cnf(c_0_4990,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_3876,
[final] ).
cnf(c_0_4991,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_3877,
[final] ).
cnf(c_0_4992,plain,
( c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(X2,X3),c_Nat_Osemiring__1__class_Oof__nat(X1,X3),X3) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ class_Ring__and__Field_Oring__1(X3) ),
c_0_3878,
[final] ).
cnf(c_0_4993,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat),
c_0_3879,
[final] ).
cnf(c_0_4994,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),
c_0_3880,
[final] ).
cnf(c_0_4995,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),
c_0_3881,
[final] ).
cnf(c_0_4996,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),
c_0_3882,
[final] ).
cnf(c_0_4997,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_3883,
[final] ).
cnf(c_0_4998,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),
c_0_3884,
[final] ).
cnf(c_0_4999,plain,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat),
c_0_3885,
[final] ).
cnf(c_0_5000,plain,
( X3 = X1
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool))
| ~ c_lessequals(c_Finite__Set_Ocard(X1,X2),c_Finite__Set_Ocard(X3,X2),tc_nat) ),
c_0_3886,
[final] ).
cnf(c_0_5001,plain,
( X1 = X2
| c_in(X1,X3,X4)
| ~ c_in(X1,c_Set_Oinsert(X2,X3,X4),X4) ),
c_0_3887,
[final] ).
cnf(c_0_5002,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_3888,
[final] ).
cnf(c_0_5003,plain,
( hBOOL(hAPP(X3,c_Suc(c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X3,X2))))
| hBOOL(hAPP(X3,X1))
| ~ c_lessequals(X1,X2,tc_nat)
| ~ hBOOL(hAPP(X3,X2)) ),
c_0_3889,
[final] ).
cnf(c_0_5004,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_3890,
[final] ).
cnf(c_0_5005,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_3891,
[final] ).
cnf(c_0_5006,plain,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),
c_0_3892,
[final] ).
cnf(c_0_5007,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),
c_0_3893,
[final] ).
cnf(c_0_5008,plain,
( c_lessequals(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_3894,
[final] ).
cnf(c_0_5009,plain,
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ),
c_0_3895,
[final] ).
cnf(c_0_5010,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_3896,
[final] ).
cnf(c_0_5011,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_3897,
[final] ).
cnf(c_0_5012,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X4,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
c_0_3898,
[final] ).
cnf(c_0_5013,plain,
( c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ),
c_0_3899,
[final] ).
cnf(c_0_5014,plain,
( c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ),
c_0_3900,
[final] ).
cnf(c_0_5015,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ),
c_0_3901,
[final] ).
cnf(c_0_5016,plain,
( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ),
c_0_3902,
[final] ).
cnf(c_0_5017,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_3903,
[final] ).
cnf(c_0_5018,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_3904,
[final] ).
cnf(c_0_5019,plain,
( c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2) ),
c_0_3905,
[final] ).
cnf(c_0_5020,plain,
c_Fun_Oinj__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3),
c_0_3906,
[final] ).
cnf(c_0_5021,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_3907,
[final] ).
cnf(c_0_5022,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| c_HOL_Oplus__class_Oplus(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
c_0_3908,
[final] ).
cnf(c_0_5023,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| c_HOL_Oplus__class_Oplus(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
c_0_3909,
[final] ).
cnf(c_0_5024,plain,
( c_lessequals(X2,X1,tc_fun(X3,X4))
| c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4))
| ~ c_lessequals(X1,X2,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
c_0_3910,
[final] ).
cnf(c_0_5025,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X1,tc_nat) = c_Divides_Odiv__class_Omod(X2,X1,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_3911,
[final] ).
cnf(c_0_5026,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_nat),
c_0_3912,
[final] ).
cnf(c_0_5027,plain,
( hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_3913,
[final] ).
cnf(c_0_5028,plain,
( hBOOL(hAPP(X3,X1))
| ~ c_lessequals(X1,X2,tc_nat)
| ~ hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X3,X2))) ),
c_0_3914,
[final] ).
cnf(c_0_5029,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1),tc_nat)
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1) ),
c_0_3915,
[final] ).
cnf(c_0_5030,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
c_0_3916,
[final] ).
cnf(c_0_5031,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X2,X3),c_Finite__Set_Olinorder__class_OMin(X1,X3),X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_3917,
[final] ).
cnf(c_0_5032,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_lessequals(c_Finite__Set_Olinorder__class_OMax(X1,X3),c_Finite__Set_Olinorder__class_OMax(X2,X3),X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_3918,
[final] ).
cnf(c_0_5033,plain,
( X1 = X2
| c_in(X3,X1,X4)
| c_in(X3,X2,X4)
| c_Set_Oinsert(X3,X1,X4) != c_Set_Oinsert(X3,X2,X4) ),
c_0_3919,
[final] ).
cnf(c_0_5034,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_3920,
[final] ).
cnf(c_0_5035,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_3921,
[final] ).
cnf(c_0_5036,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_3922,
[final] ).
cnf(c_0_5037,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_3923,
[final] ).
cnf(c_0_5038,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
c_0_3924,
[final] ).
cnf(c_0_5039,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_3925,
[final] ).
cnf(c_0_5040,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),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_3926,
[final] ).
cnf(c_0_5041,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),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_3927,
[final] ).
cnf(c_0_5042,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_3928,
[final] ).
cnf(c_0_5043,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_3929,
[final] ).
cnf(c_0_5044,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat),
c_0_3930,
[final] ).
cnf(c_0_5045,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)),tc_nat),
c_0_3931,
[final] ).
cnf(c_0_5046,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat),
c_0_3932,
[final] ).
cnf(c_0_5047,plain,
( c_lessequals(X3,X1,X2)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeast(X1,X2),c_SetInterval_Oord__class_OatLeast(X3,X2),tc_fun(X2,tc_bool))
| ~ class_Orderings_Oorder(X2) ),
c_0_3933,
[final] ).
cnf(c_0_5048,plain,
c_in(X1,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),
c_0_3934,
[final] ).
cnf(c_0_5049,plain,
( c_in(X4,X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
c_0_3935,
[final] ).
cnf(c_0_5050,plain,
( c_in(X4,X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
c_0_3936,
[final] ).
cnf(c_0_5051,plain,
( c_in(X1,X4,X3)
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
c_0_3937,
[final] ).
cnf(c_0_5052,plain,
( c_in(X4,X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
c_0_3938,
[final] ).
cnf(c_0_5053,plain,
( c_in(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
c_0_3939,
[final] ).
cnf(c_0_5054,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat) = c_Divides_Odiv__class_Omod(X1,X2,tc_nat) ),
c_0_3940,
[final] ).
cnf(c_0_5055,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_3941,
[final] ).
cnf(c_0_5056,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4))
| ~ c_lessequals(X2,X1,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
c_0_3942,
[final] ).
cnf(c_0_5057,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_3943,
[final] ).
cnf(c_0_5058,plain,
( X1 = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2)
| c_Finite__Set_Ocard(X1,X2) != c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2) ),
c_0_3944,
[final] ).
cnf(c_0_5059,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Suc(X2),tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
c_0_3945,
[final] ).
cnf(c_0_5060,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_3946,
[final] ).
cnf(c_0_5061,plain,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
c_0_3947,
[final] ).
cnf(c_0_5062,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_3948,
[final] ).
cnf(c_0_5063,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X1,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_3949,
[final] ).
cnf(c_0_5064,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_3950,
[final] ).
cnf(c_0_5065,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_3951,
[final] ).
cnf(c_0_5066,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_3952,
[final] ).
cnf(c_0_5067,plain,
( c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_3953,
[final] ).
cnf(c_0_5068,plain,
( c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X4,X1,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_3954,
[final] ).
cnf(c_0_5069,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_3955,
[final] ).
cnf(c_0_5070,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_3956,
[final] ).
cnf(c_0_5071,plain,
( c_Suc(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)) = c_HOL_Ominus__class_Ominus(c_Suc(X2),X1,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_3957,
[final] ).
cnf(c_0_5072,plain,
( c_lessequals(c_Finite__Set_Ocard(X3,X2),c_Finite__Set_Ocard(X1,X2),tc_nat)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool)) ),
c_0_3958,
[final] ).
cnf(c_0_5073,plain,
( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(X3,X2),c_Finite__Set_Ocard(X1,X2),tc_nat)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,X1,tc_fun(X2,tc_bool)) ),
c_0_3959,
[final] ).
cnf(c_0_5074,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
c_0_3960,
[final] ).
cnf(c_0_5075,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
c_0_3961,
[final] ).
cnf(c_0_5076,plain,
( c_in(X1,c_Set_Oinsert(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3) ),
c_0_3962,
[final] ).
cnf(c_0_5077,plain,
( c_in(X1,c_Set_Oinsert(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3) ),
c_0_3963,
[final] ).
cnf(c_0_5078,plain,
( c_HOL_Oplus__class_Oplus(X1,X1,X2) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X2),c_HOL_Oone__class_Oone(X2),X2),X1,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
c_0_3964,
[final] ).
cnf(c_0_5079,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat),
c_0_3965,
[final] ).
cnf(c_0_5080,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat),
c_0_3966,
[final] ).
cnf(c_0_5081,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
c_0_3967,
[final] ).
cnf(c_0_5082,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
c_0_3968,
[final] ).
cnf(c_0_5083,plain,
( c_lessequals(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_3969,
[final] ).
cnf(c_0_5084,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_3970,
[final] ).
cnf(c_0_5085,plain,
( c_Finite__Set_Ocard(c_Set_Oinsert(X3,X1,X2),X2) = c_Finite__Set_Ocard(X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_in(X3,X1,X2) ),
c_0_3971,
[final] ).
cnf(c_0_5086,plain,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
c_0_3972,
[final] ).
cnf(c_0_5087,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_3973,
[final] ).
cnf(c_0_5088,plain,
( c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = X1
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
c_0_3974,
[final] ).
cnf(c_0_5089,plain,
( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = X1
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_3975,
[final] ).
cnf(c_0_5090,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X1,tc_nat) = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_3976,
[final] ).
cnf(c_0_5091,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_3977,
[final] ).
cnf(c_0_5092,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat) = X1
| ~ c_lessequals(X2,X1,tc_nat) ),
c_0_3978,
[final] ).
cnf(c_0_5093,plain,
( c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X3,X2),X2,tc_nat)
| hBOOL(hAPP(X3,X1))
| ~ c_lessequals(X1,X2,tc_nat)
| ~ hBOOL(hAPP(X3,X2)) ),
c_0_3979,
[final] ).
cnf(c_0_5094,plain,
( c_lessequals(hAPP(X1,X5),hAPP(X2,X5),X4)
| ~ c_lessequals(X1,X2,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
c_0_3980,
[final] ).
cnf(c_0_5095,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_3981,
[final] ).
cnf(c_0_5096,plain,
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_3982,
[final] ).
cnf(c_0_5097,plain,
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_3983,
[final] ).
cnf(c_0_5098,plain,
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_3984,
[final] ).
cnf(c_0_5099,plain,
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_3985,
[final] ).
cnf(c_0_5100,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
c_0_3986,
[final] ).
cnf(c_0_5101,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_3987,
[final] ).
cnf(c_0_5102,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_3988,
[final] ).
cnf(c_0_5103,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_3989,
[final] ).
cnf(c_0_5104,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_3990,
[final] ).
cnf(c_0_5105,plain,
( c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_3991,
[final] ).
cnf(c_0_5106,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_3992,
[final] ).
cnf(c_0_5107,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_3993,
[final] ).
cnf(c_0_5108,plain,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_3994,
[final] ).
cnf(c_0_5109,plain,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_3995,
[final] ).
cnf(c_0_5110,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_3996,
[final] ).
cnf(c_0_5111,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_3997,
[final] ).
cnf(c_0_5112,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_3998,
[final] ).
cnf(c_0_5113,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_3999,
[final] ).
cnf(c_0_5114,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_4000,
[final] ).
cnf(c_0_5115,plain,
( c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1
| ~ class_Orderings_Olinorder(X2) ),
c_0_4001,
[final] ).
cnf(c_0_5116,plain,
( c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1
| ~ class_Orderings_Olinorder(X2) ),
c_0_4002,
[final] ).
cnf(c_0_5117,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
c_0_4003,
[final] ).
cnf(c_0_5118,plain,
( c_HOL_Oplus__class_Oplus(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_Oplus__class_Oplus(X1,X2,tc_nat),X3)
| ~ class_Ring__and__Field_Osemiring__1(X3) ),
c_0_4004,
[final] ).
cnf(c_0_5119,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_4005,
[final] ).
cnf(c_0_5120,plain,
c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
c_0_4006,
[final] ).
cnf(c_0_5121,plain,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
c_0_4007,
[final] ).
cnf(c_0_5122,plain,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)),
c_0_4008,
[final] ).
cnf(c_0_5123,plain,
( c_in(X3,X1,X2)
| c_Finite__Set_Ocard(c_Set_Oinsert(X3,X1,X2),X2) = c_Suc(c_Finite__Set_Ocard(X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2) ),
c_0_4009,
[final] ).
cnf(c_0_5124,plain,
( c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
c_0_4010,
[final] ).
cnf(c_0_5125,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_4011,
[final] ).
cnf(c_0_5126,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_4012,
[final] ).
cnf(c_0_5127,plain,
( c_lessequals(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
c_0_4013,
[final] ).
cnf(c_0_5128,plain,
( c_lessequals(c_SetInterval_Oord__class_OatLeast(X2,X3),c_SetInterval_Oord__class_OatLeast(X1,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_4014,
[final] ).
cnf(c_0_5129,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_4015,
[final] ).
cnf(c_0_5130,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3)
| ~ class_Lattices_Olattice(X3) ),
c_0_4016,
[final] ).
cnf(c_0_5131,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X1,X3) = c_Divides_Odiv__class_Omod(X2,X1,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_4017,
[final] ).
cnf(c_0_5132,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X2,X3) = c_Divides_Odiv__class_Omod(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_4018,
[final] ).
cnf(c_0_5133,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_4019,
[final] ).
cnf(c_0_5134,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_4020,
[final] ).
cnf(c_0_5135,plain,
( c_Finite__Set_Ocard(X1,X2) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Finite__Set_Ocard(c_Set_Oinsert(X3,X1,X2),X2) = c_Suc(c_Finite__Set_Ocard(X1,X2))
| c_in(X3,X1,X2) ),
c_0_4021,
[final] ).
cnf(c_0_5136,plain,
( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
c_0_4022,
[final] ).
cnf(c_0_5137,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) = c_HOL_Ominus__class_Ominus(X1,c_Suc(X2),tc_nat),
c_0_4023,
[final] ).
cnf(c_0_5138,plain,
( c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) ),
c_0_4024,
[final] ).
cnf(c_0_5139,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_4025,
[final] ).
cnf(c_0_5140,plain,
c_Set_Oinsert(X1,c_Set_Oinsert(X1,X2,X3),X3) = c_Set_Oinsert(X1,X2,X3),
c_0_4026,
[final] ).
cnf(c_0_5141,plain,
c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat),
c_0_4027,
[final] ).
cnf(c_0_5142,plain,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_Suc(X2),tc_nat),
c_0_4028,
[final] ).
cnf(c_0_5143,plain,
( ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| ~ hBOOL(hAPP(X3,X1)) ),
c_0_4029,
[final] ).
cnf(c_0_5144,plain,
( c_lessequals(X1,X2,tc_fun(X3,X4))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
c_0_4030,
[final] ).
cnf(c_0_5145,plain,
( c_lessequals(X1,c_Inductive_Ocomplete__lattice__class_Ogfp(X2,X3),X3)
| ~ c_lessequals(X1,hAPP(X2,X1),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
c_0_4031,
[final] ).
cnf(c_0_5146,plain,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
c_0_4032,
[final] ).
cnf(c_0_5147,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) = X1 ),
c_0_4033,
[final] ).
cnf(c_0_5148,plain,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
c_0_4034,
[final] ).
cnf(c_0_5149,plain,
( c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X1,X2,X3),X3) ),
c_0_4035,
[final] ).
cnf(c_0_5150,plain,
( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
c_0_4036,
[final] ).
cnf(c_0_5151,plain,
( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
c_0_4037,
[final] ).
cnf(c_0_5152,plain,
~ c_HOL_Oord__class_Oless(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
c_0_4038,
[final] ).
cnf(c_0_5153,plain,
( c_lessequals(X1,c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1(X3,X1),tc_nat)
| hBOOL(hAPP(X3,X2))
| ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
c_0_4039,
[final] ).
cnf(c_0_5154,plain,
( c_lessequals(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_4040,
[final] ).
cnf(c_0_5155,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_4041,
[final] ).
cnf(c_0_5156,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| X1 = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_4042,
[final] ).
cnf(c_0_5157,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)) = X1
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_4043,
[final] ).
cnf(c_0_5158,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = X1
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_4044,
[final] ).
cnf(c_0_5159,plain,
( hBOOL(hAPP(X2,X4))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(X1,X4)) ),
c_0_4045,
[final] ).
cnf(c_0_5160,plain,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
c_0_4046,
[final] ).
cnf(c_0_5161,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_4047,
[final] ).
cnf(c_0_5162,plain,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_4048,
[final] ).
cnf(c_0_5163,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_HOL_Oone__class_Oone(X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_4049,
[final] ).
cnf(c_0_5164,plain,
( hBOOL(hAPP(X3,X1))
| ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
c_0_4050,
[final] ).
cnf(c_0_5165,plain,
( c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
c_0_4051,
[final] ).
cnf(c_0_5166,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_4052,
[final] ).
cnf(c_0_5167,plain,
( c_lessequals(X3,c_Finite__Set_Olinorder__class_OMax(X1,X2),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_in(X3,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_4053,
[final] ).
cnf(c_0_5168,plain,
( c_lessequals(c_Finite__Set_Olinorder__class_OMin(X1,X2),X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_in(X3,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_4054,
[final] ).
cnf(c_0_5169,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_4055,
[final] ).
cnf(c_0_5170,plain,
( c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
c_0_4056,
[final] ).
cnf(c_0_5171,plain,
( c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
c_0_4057,
[final] ).
cnf(c_0_5172,plain,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
c_0_4058,
[final] ).
cnf(c_0_5173,plain,
( c_lessequals(X2,X1,X3)
| ~ c_in(X1,c_SetInterval_Oord__class_OatLeast(X2,X3),X3)
| ~ class_HOL_Oord(X3) ),
c_0_4059,
[final] ).
cnf(c_0_5174,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_4060,
[final] ).
cnf(c_0_5175,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| ~ class_Int_Onumber__ring(X4)
| ~ class_Ring__and__Field_Oidom(X4) ),
c_0_4061,
[final] ).
cnf(c_0_5176,plain,
c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
c_0_4062,
[final] ).
cnf(c_0_5177,plain,
( c_in(X1,X2,X3)
| c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
c_0_4063,
[final] ).
cnf(c_0_5178,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_4064,
[final] ).
cnf(c_0_5179,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_4065,
[final] ).
cnf(c_0_5180,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_4066,
[final] ).
cnf(c_0_5181,plain,
( X2 = X1
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_4067,
[final] ).
cnf(c_0_5182,plain,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
c_0_4068,
[final] ).
cnf(c_0_5183,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X2),X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
c_0_4069,
[final] ).
cnf(c_0_5184,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
| ~ class_OrderedGroup_Oab__group__add(X4) ),
c_0_4070,
[final] ).
cnf(c_0_5185,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
c_0_4071,
[final] ).
cnf(c_0_5186,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X1,X3,X4) != c_HOL_Oplus__class_Oplus(X2,X3,X4)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X4) ),
c_0_4072,
[final] ).
cnf(c_0_5187,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X4) ),
c_0_4073,
[final] ).
cnf(c_0_5188,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X4) ),
c_0_4074,
[final] ).
cnf(c_0_5189,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_4075,
[final] ).
cnf(c_0_5190,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_4076,
[final] ).
cnf(c_0_5191,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_4077,
[final] ).
cnf(c_0_5192,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_4078,
[final] ).
cnf(c_0_5193,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_4079,
[final] ).
cnf(c_0_5194,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_4080,
[final] ).
cnf(c_0_5195,plain,
( ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_4081,
[final] ).
cnf(c_0_5196,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ c_lessequals(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_4082,
[final] ).
cnf(c_0_5197,plain,
( X2 = X1
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
c_0_4083,
[final] ).
cnf(c_0_5198,plain,
( ~ c_lessequals(c_Suc(X1),X2,tc_nat)
| ~ c_lessequals(X2,X1,tc_nat) ),
c_0_4084,
[final] ).
cnf(c_0_5199,plain,
( ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
c_0_4085,
[final] ).
cnf(c_0_5200,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_4086,
[final] ).
cnf(c_0_5201,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_4087,
[final] ).
cnf(c_0_5202,plain,
( c_in(X2,c_SetInterval_Oord__class_OatLeast(X1,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_HOL_Oord(X3) ),
c_0_4088,
[final] ).
cnf(c_0_5203,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_4089,
[final] ).
cnf(c_0_5204,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_4090,
[final] ).
cnf(c_0_5205,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_4091,
[final] ).
cnf(c_0_5206,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_4092,
[final] ).
cnf(c_0_5207,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_4093,
[final] ).
cnf(c_0_5208,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X2,X1,tc_nat) ),
c_0_4094,
[final] ).
cnf(c_0_5209,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_4095,
[final] ).
cnf(c_0_5210,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_4096,
[final] ).
cnf(c_0_5211,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_4097,
[final] ).
cnf(c_0_5212,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_4098,
[final] ).
cnf(c_0_5213,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_4099,
[final] ).
cnf(c_0_5214,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_4100,
[final] ).
cnf(c_0_5215,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_4101,
[final] ).
cnf(c_0_5216,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X2,X3) = X1
| ~ class_OrderedGroup_Ogroup__add(X3) ),
c_0_4102,
[final] ).
cnf(c_0_5217,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X3),X2,X3) = X1
| ~ class_OrderedGroup_Ogroup__add(X3) ),
c_0_4103,
[final] ).
cnf(c_0_5218,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X1,X3)
| ~ class_Lattices_Olattice(X3) ),
c_0_4104,
[final] ).
cnf(c_0_5219,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X2,X3)
| ~ class_Lattices_Olattice(X3) ),
c_0_4105,
[final] ).
cnf(c_0_5220,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_4106,
[final] ).
cnf(c_0_5221,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X1,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_4107,
[final] ).
cnf(c_0_5222,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
c_0_4108,
[final] ).
cnf(c_0_5223,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X1,X3,tc_nat) != c_HOL_Oplus__class_Oplus(X2,X3,tc_nat) ),
c_0_4109,
[final] ).
cnf(c_0_5224,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
c_0_4110,
[final] ).
cnf(c_0_5225,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_4111,
[final] ).
cnf(c_0_5226,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_4112,
[final] ).
cnf(c_0_5227,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_4113,
[final] ).
cnf(c_0_5228,plain,
~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
c_0_4114,
[final] ).
cnf(c_0_5229,plain,
~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
c_0_4115,
[final] ).
cnf(c_0_5230,plain,
~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
c_0_4116,
[final] ).
cnf(c_0_5231,plain,
c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)) = c_HOL_Oplus__class_Oplus(X1,c_Suc(X2),tc_nat),
c_0_4117,
[final] ).
cnf(c_0_5232,plain,
c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(X1),X2,tc_nat),
c_0_4118,
[final] ).
cnf(c_0_5233,plain,
( hBOOL(hAPP(X2,X1))
| hBOOL(hAPP(X2,X3))
| ~ c_lessequals(c_Suc(X1),c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1(X2),tc_nat) ),
c_0_4119,
[final] ).
cnf(c_0_5234,plain,
c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_Suc(X1),tc_nat),
c_0_4120,
[final] ).
cnf(c_0_5235,plain,
c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
c_0_4121,
[final] ).
cnf(c_0_5236,plain,
c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
c_0_4122,
[final] ).
cnf(c_0_5237,plain,
c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
c_0_4123,
[final] ).
cnf(c_0_5238,plain,
( c_Finite__Set_Ofinite(X1,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3) ),
c_0_4124,
[final] ).
cnf(c_0_5239,plain,
( c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool)) ),
c_0_4125,
[final] ).
cnf(c_0_5240,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_4126,
[final] ).
cnf(c_0_5241,plain,
c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_4127,
[final] ).
cnf(c_0_5242,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat) = X2,
c_0_4128,
[final] ).
cnf(c_0_5243,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat) = X1,
c_0_4129,
[final] ).
cnf(c_0_5244,plain,
c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X1,tc_nat),
c_0_4130,
[final] ).
cnf(c_0_5245,plain,
c_lessequals(X1,c_HOL_Otimes__class_Otimes(X1,X1,tc_nat),tc_nat),
c_0_4131,
[final] ).
cnf(c_0_5246,plain,
c_lessequals(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X1,tc_nat),
c_0_4132,
[final] ).
cnf(c_0_5247,plain,
c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),
c_0_4133,
[final] ).
cnf(c_0_5248,plain,
c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat),
c_0_4134,
[final] ).
cnf(c_0_5249,plain,
c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),
c_0_4135,
[final] ).
cnf(c_0_5250,plain,
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat) ),
c_0_4136,
[final] ).
cnf(c_0_5251,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_4137,
[final] ).
cnf(c_0_5252,plain,
c_HOL_Ominus__class_Ominus(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
c_0_4138,
[final] ).
cnf(c_0_5253,plain,
c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
c_0_4139,
[final] ).
cnf(c_0_5254,plain,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
c_0_4140,
[final] ).
cnf(c_0_5255,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
c_0_4141,
[final] ).
cnf(c_0_5256,plain,
c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)),
c_0_4142,
[final] ).
cnf(c_0_5257,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_4143,
[final] ).
cnf(c_0_5258,plain,
( c_lessequals(X1,X2,tc_nat)
| X1 = c_Suc(X2)
| ~ c_lessequals(X1,c_Suc(X2),tc_nat) ),
c_0_4144,
[final] ).
cnf(c_0_5259,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_4145,
[final] ).
cnf(c_0_5260,plain,
( c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(X1,X2,X3),X3) = X2
| c_Finite__Set_Ocard(X1,X3) != c_Suc(X2) ),
c_0_4146,
[final] ).
cnf(c_0_5261,plain,
( c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(X1,X2,X3),X3) = X2
| c_Finite__Set_Ocard(X1,X3) != c_Suc(X2) ),
c_0_4147,
[final] ).
cnf(c_0_5262,plain,
( X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_4148,
[final] ).
cnf(c_0_5263,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_4149,
[final] ).
cnf(c_0_5264,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_4150,
[final] ).
cnf(c_0_5265,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_4151,
[final] ).
cnf(c_0_5266,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_4152,
[final] ).
cnf(c_0_5267,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_4153,
[final] ).
cnf(c_0_5268,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_4154,
[final] ).
cnf(c_0_5269,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_4155,
[final] ).
cnf(c_0_5270,plain,
( c_lessequals(X1,X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) != X1
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_4156,
[final] ).
cnf(c_0_5271,plain,
( c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_4157,
[final] ).
cnf(c_0_5272,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_4158,
[final] ).
cnf(c_0_5273,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_4159,
[final] ).
cnf(c_0_5274,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_4160,
[final] ).
cnf(c_0_5275,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_4161,
[final] ).
cnf(c_0_5276,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_4162,
[final] ).
cnf(c_0_5277,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3) = X1
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_4163,
[final] ).
cnf(c_0_5278,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = X1
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_4164,
[final] ).
cnf(c_0_5279,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_4165,
[final] ).
cnf(c_0_5280,plain,
( c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_4166,
[final] ).
cnf(c_0_5281,plain,
( c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_4167,
[final] ).
cnf(c_0_5282,plain,
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
c_0_4168,
[final] ).
cnf(c_0_5283,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
c_0_4169,
[final] ).
cnf(c_0_5284,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
c_0_4170,
[final] ).
cnf(c_0_5285,plain,
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
c_0_4171,
[final] ).
cnf(c_0_5286,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat) ),
c_0_4172,
[final] ).
cnf(c_0_5287,plain,
( c_Finite__Set_Ofinite(c_Set_Oinsert(X3,X1,X2),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
c_0_4173,
[final] ).
cnf(c_0_5288,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(X1,X2),tc_nat) ),
c_0_4174,
[final] ).
cnf(c_0_5289,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_4175,
[final] ).
cnf(c_0_5290,plain,
( c_lessequals(X1,c_Suc(X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_4176,
[final] ).
cnf(c_0_5291,plain,
( c_lessequals(c_Suc(X1),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_4177,
[final] ).
cnf(c_0_5292,plain,
( c_lessequals(c_Suc(X1),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_4178,
[final] ).
cnf(c_0_5293,plain,
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_4179,
[final] ).
cnf(c_0_5294,plain,
( c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)
| ~ c_lessequals(X1,X1,tc_nat) ),
c_0_4180,
[final] ).
cnf(c_0_5295,plain,
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_4181,
[final] ).
cnf(c_0_5296,plain,
( c_Set_Oinsert(X1,X2,X3) = X2
| ~ c_in(X1,X2,X3) ),
c_0_4182,
[final] ).
cnf(c_0_5297,plain,
( c_lessequals(X1,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_4183,
[final] ).
cnf(c_0_5298,plain,
( c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_4184,
[final] ).
cnf(c_0_5299,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_4185,
[final] ).
cnf(c_0_5300,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_4186,
[final] ).
cnf(c_0_5301,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_4187,
[final] ).
cnf(c_0_5302,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_in(c_Finite__Set_Olinorder__class_OMax(X1,X2),X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_4188,
[final] ).
cnf(c_0_5303,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_in(c_Finite__Set_Olinorder__class_OMin(X1,X2),X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_4189,
[final] ).
cnf(c_0_5304,plain,
( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = X1
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_4190,
[final] ).
cnf(c_0_5305,plain,
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_4191,
[final] ).
cnf(c_0_5306,plain,
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_4192,
[final] ).
cnf(c_0_5307,plain,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
c_0_4193,
[final] ).
cnf(c_0_5308,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(X1,X2),tc_nat)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
c_0_4194,
[final] ).
cnf(c_0_5309,plain,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
c_0_4195,
[final] ).
cnf(c_0_5310,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = X2,
c_0_4196,
[final] ).
cnf(c_0_5311,plain,
c_HOL_Ominus__class_Ominus(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
c_0_4197,
[final] ).
cnf(c_0_5312,plain,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
c_0_4198,
[final] ).
cnf(c_0_5313,plain,
c_lessequals(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
c_0_4199,
[final] ).
cnf(c_0_5314,plain,
c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
c_0_4200,
[final] ).
cnf(c_0_5315,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oinsert(X2,X3,X1),
c_0_4201,
[final] ).
cnf(c_0_5316,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_fun(X2,tc_bool)),
c_0_4202,
[final] ).
cnf(c_0_5317,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_4203,
[final] ).
cnf(c_0_5318,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_4204,
[final] ).
cnf(c_0_5319,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_4205,
[final] ).
cnf(c_0_5320,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_4206,
[final] ).
cnf(c_0_5321,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_4207,
[final] ).
cnf(c_0_5322,plain,
c_HOL_Ominus__class_Ominus(c_Suc(X1),c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),
c_0_4208,
[final] ).
cnf(c_0_5323,plain,
c_HOL_Oplus__class_Oplus(c_Suc(X1),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_Suc(X2),tc_nat),
c_0_4209,
[final] ).
cnf(c_0_5324,plain,
( c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Finite__Set_Ocard(X1,X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_4210,
[final] ).
cnf(c_0_5325,plain,
( c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Finite__Set_Ocard(X1,X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_4211,
[final] ).
cnf(c_0_5326,plain,
( c_lessequals(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_4212,
[final] ).
cnf(c_0_5327,plain,
( c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_4213,
[final] ).
cnf(c_0_5328,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_4214,
[final] ).
cnf(c_0_5329,plain,
( c_lessequals(X1,X1,X2)
| c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_4215,
[final] ).
cnf(c_0_5330,plain,
( c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_4216,
[final] ).
cnf(c_0_5331,plain,
( hBOOL(hAPP(X2,X1))
| ~ c_in(X1,X2,X3) ),
c_0_4217,
[final] ).
cnf(c_0_5332,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3)
| ~ class_Lattices_Olattice(X3) ),
c_0_4218,
[final] ).
cnf(c_0_5333,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_4219,
[final] ).
cnf(c_0_5334,plain,
( c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_4220,
[final] ).
cnf(c_0_5335,plain,
( c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3) ),
c_0_4221,
[final] ).
cnf(c_0_5336,plain,
( c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_4222,
[final] ).
cnf(c_0_5337,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_4223,
[final] ).
cnf(c_0_5338,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_4224,
[final] ).
cnf(c_0_5339,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2) = c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X1),X2)
| ~ class_Ring__and__Field_Osemiring__1(X2) ),
c_0_4225,
[final] ).
cnf(c_0_5340,plain,
( c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_Suc(X2),X1,tc_nat) ),
c_0_4226,
[final] ).
cnf(c_0_5341,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
c_0_4227,
[final] ).
cnf(c_0_5342,plain,
( c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
c_0_4228,
[final] ).
cnf(c_0_5343,plain,
( ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_4229,
[final] ).
cnf(c_0_5344,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_4230,
[final] ).
cnf(c_0_5345,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_4231,
[final] ).
cnf(c_0_5346,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_4232,
[final] ).
cnf(c_0_5347,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_4233,
[final] ).
cnf(c_0_5348,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_4234,
[final] ).
cnf(c_0_5349,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_4235,
[final] ).
cnf(c_0_5350,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_4236,
[final] ).
cnf(c_0_5351,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_4237,
[final] ).
cnf(c_0_5352,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_4238,
[final] ).
cnf(c_0_5353,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
c_0_4239,
[final] ).
cnf(c_0_5354,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
c_0_4240,
[final] ).
cnf(c_0_5355,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
c_0_4241,
[final] ).
cnf(c_0_5356,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_4242,
[final] ).
cnf(c_0_5357,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(X3,X1,X2) != X3
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_4243,
[final] ).
cnf(c_0_5358,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_4244,
[final] ).
cnf(c_0_5359,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_4245,
[final] ).
cnf(c_0_5360,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_4246,
[final] ).
cnf(c_0_5361,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_4247,
[final] ).
cnf(c_0_5362,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_4248,
[final] ).
cnf(c_0_5363,plain,
( c_lessequals(X1,X2,tc_nat)
| c_lessequals(X2,X1,tc_nat) ),
c_0_4249,
[final] ).
cnf(c_0_5364,plain,
c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2),
c_0_4250,
[final] ).
cnf(c_0_5365,plain,
c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),
c_0_4251,
[final] ).
cnf(c_0_5366,plain,
c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) = c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),
c_0_4252,
[final] ).
cnf(c_0_5367,plain,
( c_Suc(c_ATP__Linkup_Osko__Nat__XSuc__le__D__1__1(X2)) = X2
| ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
c_0_4253,
[final] ).
cnf(c_0_5368,plain,
( X1 = c_Orderings_Otop__class_Otop(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X2) != c_Orderings_Otop__class_Otop(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
c_0_4254,
[final] ).
cnf(c_0_5369,plain,
( X1 = c_Orderings_Otop__class_Otop(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X1,X2) != c_Orderings_Otop__class_Otop(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
c_0_4255,
[final] ).
cnf(c_0_5370,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(X1,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
c_0_4256,
[final] ).
cnf(c_0_5371,plain,
c_HOL_Ominus__class_Ominus(X1,X1,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
c_0_4257,
[final] ).
cnf(c_0_5372,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_4258,
[final] ).
cnf(c_0_5373,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_4259,
[final] ).
cnf(c_0_5374,plain,
( c_in(X2,X1,X3)
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_4260,
[final] ).
cnf(c_0_5375,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_4261,
[final] ).
cnf(c_0_5376,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_4262,
[final] ).
cnf(c_0_5377,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
c_0_4263,
[final] ).
cnf(c_0_5378,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
c_0_4264,
[final] ).
cnf(c_0_5379,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1(X1))) ),
c_0_4265,
[final] ).
cnf(c_0_5380,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_4266,
[final] ).
cnf(c_0_5381,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_4267,
[final] ).
cnf(c_0_5382,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_4268,
[final] ).
cnf(c_0_5383,plain,
~ c_lessequals(c_Suc(X1),X1,tc_nat),
c_0_4269,
[final] ).
cnf(c_0_5384,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_4270,
[final] ).
cnf(c_0_5385,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
c_0_4271,
[final] ).
cnf(c_0_5386,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_4272,
[final] ).
cnf(c_0_5387,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
c_0_4273,
[final] ).
cnf(c_0_5388,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_4274,
[final] ).
cnf(c_0_5389,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
c_0_4275,
[final] ).
cnf(c_0_5390,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_4276,
[final] ).
cnf(c_0_5391,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_4277,
[final] ).
cnf(c_0_5392,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_4278,
[final] ).
cnf(c_0_5393,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_4279,
[final] ).
cnf(c_0_5394,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_4280,
[final] ).
cnf(c_0_5395,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_4281,
[final] ).
cnf(c_0_5396,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_4282,
[final] ).
cnf(c_0_5397,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != X2 ),
c_0_4283,
[final] ).
cnf(c_0_5398,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != X2 ),
c_0_4284,
[final] ).
cnf(c_0_5399,plain,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_4285,
[final] ).
cnf(c_0_5400,plain,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_4286,
[final] ).
cnf(c_0_5401,plain,
( X1 = X2
| ~ c_fequal(X1,X2,X3) ),
c_0_4287,
[final] ).
cnf(c_0_5402,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
c_0_4288,
[final] ).
cnf(c_0_5403,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_4289,
[final] ).
cnf(c_0_5404,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
c_0_4290,
[final] ).
cnf(c_0_5405,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
c_0_4291,
[final] ).
cnf(c_0_5406,plain,
c_Lattices_Olower__semilattice__class_Oinf(X1,X1,tc_fun(X2,tc_bool)) = X1,
c_0_4292,
[final] ).
cnf(c_0_5407,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_4293,
[final] ).
cnf(c_0_5408,plain,
c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
c_0_4294,
[final] ).
cnf(c_0_5409,plain,
c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
c_0_4295,
[final] ).
cnf(c_0_5410,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_4296,
[final] ).
cnf(c_0_5411,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ocard(X1,X2) != c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_4297,
[final] ).
cnf(c_0_5412,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_4298,
[final] ).
cnf(c_0_5413,plain,
c_HOL_Oplus__class_Oplus(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_4299,
[final] ).
cnf(c_0_5414,plain,
c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_4300,
[final] ).
cnf(c_0_5415,plain,
c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_4301,
[final] ).
cnf(c_0_5416,plain,
c_HOL_Oplus__class_Oplus(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_4302,
[final] ).
cnf(c_0_5417,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_4303,
[final] ).
cnf(c_0_5418,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_4304,
[final] ).
cnf(c_0_5419,plain,
( c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1)
| ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
c_0_4305,
[final] ).
cnf(c_0_5420,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_4306,
[final] ).
cnf(c_0_5421,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_4307,
[final] ).
cnf(c_0_5422,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_4308,
[final] ).
cnf(c_0_5423,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_4309,
[final] ).
cnf(c_0_5424,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_4310,
[final] ).
cnf(c_0_5425,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_4311,
[final] ).
cnf(c_0_5426,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_4312,
[final] ).
cnf(c_0_5427,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_4313,
[final] ).
cnf(c_0_5428,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_4314,
[final] ).
cnf(c_0_5429,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X1),X2,X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
c_0_4315,
[final] ).
cnf(c_0_5430,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(X2),X2) = c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
c_0_4316,
[final] ).
cnf(c_0_5431,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_4317,
[final] ).
cnf(c_0_5432,plain,
( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_4318,
[final] ).
cnf(c_0_5433,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_4319,
[final] ).
cnf(c_0_5434,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
c_0_4320,
[final] ).
cnf(c_0_5435,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Omonoid__add(X2) ),
c_0_4321,
[final] ).
cnf(c_0_5436,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
c_0_4322,
[final] ).
cnf(c_0_5437,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
c_0_4323,
[final] ).
cnf(c_0_5438,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_4324,
[final] ).
cnf(c_0_5439,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_4325,
[final] ).
cnf(c_0_5440,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(X1),X2,X1) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
c_0_4326,
[final] ).
cnf(c_0_5441,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Otop__class_Otop(X2),X2) = X1
| ~ class_Lattices_Obounded__lattice(X2) ),
c_0_4327,
[final] ).
cnf(c_0_5442,plain,
( c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_Divides_Osemiring__div(X2) ),
c_0_4328,
[final] ).
cnf(c_0_5443,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_4329,
[final] ).
cnf(c_0_5444,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
c_0_4330,
[final] ).
cnf(c_0_5445,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
c_0_4331,
[final] ).
cnf(c_0_5446,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X2),X2) = X1
| ~ class_OrderedGroup_Omonoid__mult(X2) ),
c_0_4332,
[final] ).
cnf(c_0_5447,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_4333,
[final] ).
cnf(c_0_5448,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_4334,
[final] ).
cnf(c_0_5449,plain,
c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_4335,
[final] ).
cnf(c_0_5450,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_4336,
[final] ).
cnf(c_0_5451,plain,
( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
| ~ class_Orderings_Obot(X1) ),
c_0_4337,
[final] ).
cnf(c_0_5452,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_4338,
[final] ).
cnf(c_0_5453,plain,
( c_lessequals(X1,c_Orderings_Otop__class_Otop(X2),X2)
| ~ class_Orderings_Otop(X2) ),
c_0_4339,
[final] ).
cnf(c_0_5454,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_4340,
[final] ).
cnf(c_0_5455,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_4341,
[final] ).
cnf(c_0_5456,plain,
c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
c_0_4342,
[final] ).
cnf(c_0_5457,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
c_0_4343,
[final] ).
cnf(c_0_5458,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_4344,
[final] ).
cnf(c_0_5459,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_4345,
[final] ).
cnf(c_0_5460,plain,
( c_Divides_Odiv__class_Omod(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
c_0_4346,
[final] ).
cnf(c_0_5461,plain,
c_lessequals(c_Suc(X1),c_Suc(X1),tc_nat),
c_0_4347,
[final] ).
cnf(c_0_5462,plain,
c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat),
c_0_4348,
[final] ).
cnf(c_0_5463,plain,
c_HOL_Ominus__class_Ominus(c_Suc(X1),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1,
c_0_4349,
[final] ).
cnf(c_0_5464,plain,
( c_HOL_Otimes__class_Otimes(X1,X1,X2) = X1
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2) ),
c_0_4350,
[final] ).
cnf(c_0_5465,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X1,X2) = X1
| ~ class_Lattices_Olower__semilattice(X2) ),
c_0_4351,
[final] ).
cnf(c_0_5466,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
c_0_4352,
[final] ).
cnf(c_0_5467,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
c_0_4353,
[final] ).
cnf(c_0_5468,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
c_0_4354,
[final] ).
cnf(c_0_5469,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
c_0_4355,
[final] ).
cnf(c_0_5470,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X1,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
c_0_4356,
[final] ).
cnf(c_0_5471,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_4357,
[final] ).
cnf(c_0_5472,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_4358,
[final] ).
cnf(c_0_5473,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_4359,
[final] ).
cnf(c_0_5474,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_4360,
[final] ).
cnf(c_0_5475,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) = c_Suc(X1),
c_0_4361,
[final] ).
cnf(c_0_5476,plain,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_Suc(X1),
c_0_4362,
[final] ).
cnf(c_0_5477,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_4363,
[final] ).
cnf(c_0_5478,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
c_0_4364,
[final] ).
cnf(c_0_5479,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
c_0_4365,
[final] ).
cnf(c_0_5480,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_4366,
[final] ).
cnf(c_0_5481,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_4367,
[final] ).
cnf(c_0_5482,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_4368,
[final] ).
cnf(c_0_5483,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_4369,
[final] ).
cnf(c_0_5484,plain,
c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
c_0_4370,
[final] ).
cnf(c_0_5485,plain,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
c_0_4371,
[final] ).
cnf(c_0_5486,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1,
c_0_4372,
[final] ).
cnf(c_0_5487,plain,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
c_0_4373,
[final] ).
cnf(c_0_5488,plain,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1,
c_0_4374,
[final] ).
cnf(c_0_5489,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) = X1,
c_0_4375,
[final] ).
cnf(c_0_5490,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),
c_0_4376,
[final] ).
cnf(c_0_5491,plain,
c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_4377,
[final] ).
cnf(c_0_5492,plain,
c_fequal(X1,X1,X2),
c_0_4378,
[final] ).
cnf(c_0_5493,plain,
( X1 = X2
| c_SetInterval_Oord__class_OatLeast(X1,X3) != c_SetInterval_Oord__class_OatLeast(X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_4379,
[final] ).
cnf(c_0_5494,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_4380,
[final] ).
cnf(c_0_5495,plain,
c_lessequals(X1,X1,tc_nat),
c_0_4381,
[final] ).
cnf(c_0_5496,plain,
c_lessequals(X1,X1,tc_nat),
c_0_4382,
[final] ).
cnf(c_0_5497,plain,
c_Ring__and__Field_Odvd__class_Odvd(X1,X1,tc_nat),
c_0_4383,
[final] ).
cnf(c_0_5498,plain,
( class_Finite__Set_Ofinite_Ofinite(tc_fun(X1,X2))
| ~ class_Finite__Set_Ofinite_Ofinite(X1)
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
c_0_4384,
[final] ).
cnf(c_0_5499,plain,
( class_HOL_Oord(tc_fun(X2,X1))
| ~ class_HOL_Oord(X1) ),
c_0_4385,
[final] ).
cnf(c_0_5500,plain,
( class_Orderings_Obot(tc_fun(X2,X1))
| ~ class_Orderings_Obot(X1) ),
c_0_4386,
[final] ).
cnf(c_0_5501,plain,
( class_Orderings_Otop(tc_fun(X2,X1))
| ~ class_Orderings_Otop(X1) ),
c_0_4387,
[final] ).
cnf(c_0_5502,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
c_0_4388,
[final] ).
cnf(c_0_5503,plain,
( class_Lattices_Olattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
c_0_4389,
[final] ).
cnf(c_0_5504,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
c_0_4390,
[final] ).
cnf(c_0_5505,plain,
( class_Lattices_Obounded__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
c_0_4391,
[final] ).
cnf(c_0_5506,plain,
( class_Lattices_Olower__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
c_0_4392,
[final] ).
cnf(c_0_5507,plain,
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
c_0_4393,
[final] ).
cnf(c_0_5508,plain,
( c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ocard(X1,X2) = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_4394,
[final] ).
cnf(c_0_5509,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_4395,
[final] ).
cnf(c_0_5510,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_4396,
[final] ).
cnf(c_0_5511,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
c_0_4397,
[final] ).
cnf(c_0_5512,plain,
( c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
c_0_4398,
[final] ).
cnf(c_0_5513,plain,
( c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
c_0_4399,
[final] ).
cnf(c_0_5514,plain,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
c_0_4400,
[final] ).
cnf(c_0_5515,plain,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
c_0_4401,
[final] ).
cnf(c_0_5516,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_4402,
[final] ).
cnf(c_0_5517,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_4403,
[final] ).
cnf(c_0_5518,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_4404,
[final] ).
cnf(c_0_5519,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_4405,
[final] ).
cnf(c_0_5520,plain,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat),
c_0_4406,
[final] ).
cnf(c_0_5521,plain,
c_Suc(X1) != X1,
c_0_4407,
[final] ).
cnf(c_0_5522,plain,
c_Suc(X1) != X1,
c_0_4408,
[final] ).
cnf(c_0_5523,plain,
class_HOL_Oord(tc_bool),
c_0_4409,
[final] ).
cnf(c_0_5524,plain,
class_Orderings_Obot(tc_bool),
c_0_4410,
[final] ).
cnf(c_0_5525,plain,
class_Orderings_Otop(tc_bool),
c_0_4411,
[final] ).
cnf(c_0_5526,plain,
class_Orderings_Oorder(tc_bool),
c_0_4412,
[final] ).
cnf(c_0_5527,plain,
class_Lattices_Olattice(tc_bool),
c_0_4413,
[final] ).
cnf(c_0_5528,plain,
class_Orderings_Opreorder(tc_bool),
c_0_4414,
[final] ).
cnf(c_0_5529,plain,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
c_0_4415,
[final] ).
cnf(c_0_5530,plain,
class_Lattices_Obounded__lattice(tc_bool),
c_0_4416,
[final] ).
cnf(c_0_5531,plain,
class_Lattices_Olower__semilattice(tc_bool),
c_0_4417,
[final] ).
cnf(c_0_5532,plain,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
c_0_4418,
[final] ).
cnf(c_0_5533,plain,
class_HOL_Oord(tc_nat),
c_0_4419,
[final] ).
cnf(c_0_5534,plain,
class_Orderings_Obot(tc_nat),
c_0_4420,
[final] ).
cnf(c_0_5535,plain,
class_Orderings_Oorder(tc_nat),
c_0_4421,
[final] ).
cnf(c_0_5536,plain,
class_Lattices_Olattice(tc_nat),
c_0_4422,
[final] ).
cnf(c_0_5537,plain,
class_Orderings_Olinorder(tc_nat),
c_0_4423,
[final] ).
cnf(c_0_5538,plain,
class_Orderings_Opreorder(tc_nat),
c_0_4424,
[final] ).
cnf(c_0_5539,plain,
class_Ring__and__Field_Odvd(tc_nat),
c_0_4425,
[final] ).
cnf(c_0_5540,plain,
class_Nat_Osemiring__char__0(tc_nat),
c_0_4426,
[final] ).
cnf(c_0_5541,plain,
class_Divides_Osemiring__div(tc_nat),
c_0_4427,
[final] ).
cnf(c_0_5542,plain,
class_OrderedGroup_Omonoid__add(tc_nat),
c_0_4428,
[final] ).
cnf(c_0_5543,plain,
class_Ring__and__Field_Osemiring(tc_nat),
c_0_4429,
[final] ).
cnf(c_0_5544,plain,
class_OrderedGroup_Omonoid__mult(tc_nat),
c_0_4430,
[final] ).
cnf(c_0_5545,plain,
class_Ring__and__Field_Omult__mono(tc_nat),
c_0_4431,
[final] ).
cnf(c_0_5546,plain,
class_Ring__and__Field_Omult__zero(tc_nat),
c_0_4432,
[final] ).
cnf(c_0_5547,plain,
class_Ring__and__Field_Omult__mono1(tc_nat),
c_0_4433,
[final] ).
cnf(c_0_5548,plain,
class_Ring__and__Field_Osemiring__1(tc_nat),
c_0_4434,
[final] ).
cnf(c_0_5549,plain,
class_Lattices_Olower__semilattice(tc_nat),
c_0_4435,
[final] ).
cnf(c_0_5550,plain,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
c_0_4436,
[final] ).
cnf(c_0_5551,plain,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
c_0_4437,
[final] ).
cnf(c_0_5552,plain,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
c_0_4438,
[final] ).
cnf(c_0_5553,plain,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
c_0_4439,
[final] ).
cnf(c_0_5554,plain,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
c_0_4440,
[final] ).
cnf(c_0_5555,plain,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
c_0_4441,
[final] ).
cnf(c_0_5556,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
c_0_4442,
[final] ).
cnf(c_0_5557,plain,
class_Ring__and__Field_Oordered__semidom(tc_nat),
c_0_4443,
[final] ).
cnf(c_0_5558,plain,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
c_0_4444,
[final] ).
cnf(c_0_5559,plain,
class_Ring__and__Field_Oordered__semiring(tc_nat),
c_0_4445,
[final] ).
cnf(c_0_5560,plain,
class_Ring__and__Field_Opordered__semiring(tc_nat),
c_0_4446,
[final] ).
cnf(c_0_5561,plain,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
c_0_4447,
[final] ).
cnf(c_0_5562,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
c_0_4448,
[final] ).
cnf(c_0_5563,plain,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
c_0_4449,
[final] ).
cnf(c_0_5564,plain,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
c_0_4450,
[final] ).
cnf(c_0_5565,plain,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
c_0_4451,
[final] ).
cnf(c_0_5566,plain,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
c_0_4452,
[final] ).
cnf(c_0_5567,plain,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
c_0_4453,
[final] ).
cnf(c_0_5568,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
c_0_4454,
[final] ).
cnf(c_0_5569,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
c_0_4455,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_4456_0,axiom,
( c_lessequals(c_Set_Oimage(X1,X2,X4,X5),X3,tc_fun(X5,tc_bool))
| ~ c_in(hAPP(X1,c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1(X2,X3,X1,X4,X5)),X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_4456]) ).
cnf(c_0_4456_1,axiom,
( ~ c_in(hAPP(X1,c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1(X2,X3,X1,X4,X5)),X3,X5)
| c_lessequals(c_Set_Oimage(X1,X2,X4,X5),X3,tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4456]) ).
cnf(c_0_4457_0,axiom,
( c_lessequals(c_Set_Oimage(X1,X2,X4,X5),X3,tc_fun(X5,tc_bool))
| ~ c_in(hAPP(X1,c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1(X2,X3,X1,X4,X5)),X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_4457]) ).
cnf(c_0_4457_1,axiom,
( ~ c_in(hAPP(X1,c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1(X2,X3,X1,X4,X5)),X3,X5)
| c_lessequals(c_Set_Oimage(X1,X2,X4,X5),X3,tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4457]) ).
cnf(c_0_4458_0,axiom,
( c_Set_Oimage(X1,X2,X3,X4) = c_Set_Oimage(X5,X2,X3,X4)
| hAPP(X1,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X2,X1,X5,X3,X4)) != hAPP(X5,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X2,X1,X5,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4458]) ).
cnf(c_0_4458_1,axiom,
( hAPP(X1,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X2,X1,X5,X3,X4)) != hAPP(X5,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X2,X1,X5,X3,X4))
| c_Set_Oimage(X1,X2,X3,X4) = c_Set_Oimage(X5,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4458]) ).
cnf(c_0_4459_0,axiom,
( X1 = X2
| c_Fun_Ofun__upd(c_Fun_Ofun__upd(X3,X1,X4,X5,X6),X2,X7,X5,X6) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X3,X2,X7,X5,X6),X1,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_4459]) ).
cnf(c_0_4459_1,axiom,
( c_Fun_Ofun__upd(c_Fun_Ofun__upd(X3,X1,X4,X5,X6),X2,X7,X5,X6) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X3,X2,X7,X5,X6),X1,X4,X5,X6)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4459]) ).
cnf(c_0_4461_0,axiom,
( c_Set_Oinsert(X5,c_Set_Oimage(X4,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3,X6),X6) = c_Set_Oimage(c_Fun_Ofun__upd(X4,X1,X5,X3,X6),X2,X3,X6)
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4461]) ).
cnf(c_0_4461_1,axiom,
( ~ c_in(X1,X2,X3)
| c_Set_Oinsert(X5,c_Set_Oimage(X4,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3,X6),X6) = c_Set_Oimage(c_Fun_Ofun__upd(X4,X1,X5,X3,X6),X2,X3,X6) ),
inference(literals_permutation,[status(thm)],[c_0_4461]) ).
cnf(c_0_4462_0,axiom,
( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2),c_Finite__Set_Ocard(X1,X2),tc_nat)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_in(X3,X1,X2)
| ~ c_in(X4,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4462]) ).
cnf(c_0_4462_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2),c_Finite__Set_Ocard(X1,X2),tc_nat)
| ~ c_in(X3,X1,X2)
| ~ c_in(X4,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4462]) ).
cnf(c_0_4462_2,axiom,
( ~ c_in(X3,X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2),c_Finite__Set_Ocard(X1,X2),tc_nat)
| ~ c_in(X4,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4462]) ).
cnf(c_0_4462_3,axiom,
( ~ c_in(X4,X1,X2)
| ~ c_in(X3,X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2),c_Finite__Set_Ocard(X1,X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4462]) ).
cnf(c_0_4463_0,axiom,
( c_in(X5,c_Set_Oimage(X1,X2,X3,X4),X4)
| c_Fun_Oinj__on(c_Fun_Ofun__upd(X1,X6,X5,X3,X4),X2,X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4463]) ).
cnf(c_0_4463_1,axiom,
( c_Fun_Oinj__on(c_Fun_Ofun__upd(X1,X6,X5,X3,X4),X2,X3,X4)
| c_in(X5,c_Set_Oimage(X1,X2,X3,X4),X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4463]) ).
cnf(c_0_4463_2,axiom,
( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_Fun_Oinj__on(c_Fun_Ofun__upd(X1,X6,X5,X3,X4),X2,X3,X4)
| c_in(X5,c_Set_Oimage(X1,X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4463]) ).
cnf(c_0_4464_0,axiom,
( c_Set_Oimage(X3,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X4,X1,X3,X5,X2),X5,X2) = X1
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X1,c_Set_Oimage(X3,X4,X5,X2),tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4464]) ).
cnf(c_0_4464_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Set_Oimage(X3,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X4,X1,X3,X5,X2),X5,X2) = X1
| ~ c_lessequals(X1,c_Set_Oimage(X3,X4,X5,X2),tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4464]) ).
cnf(c_0_4464_2,axiom,
( ~ c_lessequals(X1,c_Set_Oimage(X3,X4,X5,X2),tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Set_Oimage(X3,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X4,X1,X3,X5,X2),X5,X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_4464]) ).
cnf(c_0_4465_0,axiom,
( c_Set_Oimage(X2,c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(X3,X1,X2,X4,X5),X4,X5) = X1
| ~ c_lessequals(X1,c_Set_Oimage(X2,X3,X4,X5),tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4465]) ).
cnf(c_0_4465_1,axiom,
( ~ c_lessequals(X1,c_Set_Oimage(X2,X3,X4,X5),tc_fun(X5,tc_bool))
| c_Set_Oimage(X2,c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(X3,X1,X2,X4,X5),X4,X5) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_4465]) ).
cnf(c_0_4466_0,axiom,
( c_lessequals(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X4,X1,X3,X5,X2),X4,tc_fun(X5,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X1,c_Set_Oimage(X3,X4,X5,X2),tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4466]) ).
cnf(c_0_4466_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_lessequals(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X4,X1,X3,X5,X2),X4,tc_fun(X5,tc_bool))
| ~ c_lessequals(X1,c_Set_Oimage(X3,X4,X5,X2),tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4466]) ).
cnf(c_0_4466_2,axiom,
( ~ c_lessequals(X1,c_Set_Oimage(X3,X4,X5,X2),tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_lessequals(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X4,X1,X3,X5,X2),X4,tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4466]) ).
cnf(c_0_4467_0,axiom,
( c_lessequals(c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(X3,X1,X2,X4,X5),X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Set_Oimage(X2,X3,X4,X5),tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4467]) ).
cnf(c_0_4467_1,axiom,
( ~ c_lessequals(X1,c_Set_Oimage(X2,X3,X4,X5),tc_fun(X5,tc_bool))
| c_lessequals(c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(X3,X1,X2,X4,X5),X3,tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4467]) ).
cnf(c_0_4468_0,axiom,
( c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X4,X1,X3,X5,X2),X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X1,c_Set_Oimage(X3,X4,X5,X2),tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4468]) ).
cnf(c_0_4468_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X4,X1,X3,X5,X2),X5)
| ~ c_lessequals(X1,c_Set_Oimage(X3,X4,X5,X2),tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4468]) ).
cnf(c_0_4468_2,axiom,
( ~ c_lessequals(X1,c_Set_Oimage(X3,X4,X5,X2),tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X4,X1,X3,X5,X2),X5) ),
inference(literals_permutation,[status(thm)],[c_0_4468]) ).
cnf(c_0_4469_0,axiom,
( c_in(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(X3,X2,X1,X4,X5),X3,X4)
| ~ c_in(X1,c_Set_Oimage(X2,X3,X4,X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_4469]) ).
cnf(c_0_4469_1,axiom,
( ~ c_in(X1,c_Set_Oimage(X2,X3,X4,X5),X5)
| c_in(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(X3,X2,X1,X4,X5),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4469]) ).
cnf(c_0_4470_0,axiom,
( c_in(c_ATP__Linkup_Osko__Set__XimageE__1__1(X3,X1,X2,X4,X5),X3,X4)
| ~ c_in(X1,c_Set_Oimage(X2,X3,X4,X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_4470]) ).
cnf(c_0_4470_1,axiom,
( ~ c_in(X1,c_Set_Oimage(X2,X3,X4,X5),X5)
| c_in(c_ATP__Linkup_Osko__Set__XimageE__1__1(X3,X1,X2,X4,X5),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4470]) ).
cnf(c_0_4471_0,axiom,
( X1 = X6
| ~ c_in(X1,c_Set_Oimage(X2,X3,X4,X5),X5)
| ~ c_in(X6,c_Set_Oimage(X2,X3,X4,X5),X5)
| hAPP(c_Hilbert__Choice_Oinv__into(X3,X2,X4,X5),X1) != hAPP(c_Hilbert__Choice_Oinv__into(X3,X2,X4,X5),X6) ),
inference(literals_permutation,[status(thm)],[c_0_4471]) ).
cnf(c_0_4471_1,axiom,
( ~ c_in(X1,c_Set_Oimage(X2,X3,X4,X5),X5)
| X1 = X6
| ~ c_in(X6,c_Set_Oimage(X2,X3,X4,X5),X5)
| hAPP(c_Hilbert__Choice_Oinv__into(X3,X2,X4,X5),X1) != hAPP(c_Hilbert__Choice_Oinv__into(X3,X2,X4,X5),X6) ),
inference(literals_permutation,[status(thm)],[c_0_4471]) ).
cnf(c_0_4471_2,axiom,
( ~ c_in(X6,c_Set_Oimage(X2,X3,X4,X5),X5)
| ~ c_in(X1,c_Set_Oimage(X2,X3,X4,X5),X5)
| X1 = X6
| hAPP(c_Hilbert__Choice_Oinv__into(X3,X2,X4,X5),X1) != hAPP(c_Hilbert__Choice_Oinv__into(X3,X2,X4,X5),X6) ),
inference(literals_permutation,[status(thm)],[c_0_4471]) ).
cnf(c_0_4471_3,axiom,
( hAPP(c_Hilbert__Choice_Oinv__into(X3,X2,X4,X5),X1) != hAPP(c_Hilbert__Choice_Oinv__into(X3,X2,X4,X5),X6)
| ~ c_in(X6,c_Set_Oimage(X2,X3,X4,X5),X5)
| ~ c_in(X1,c_Set_Oimage(X2,X3,X4,X5),X5)
| X1 = X6 ),
inference(literals_permutation,[status(thm)],[c_0_4471]) ).
cnf(c_0_4472_0,axiom,
( hAPP(X2,c_ATP__Linkup_Osko__Set__XimageE__1__1(X3,X1,X2,X4,X5)) = X1
| ~ c_in(X1,c_Set_Oimage(X2,X3,X4,X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_4472]) ).
cnf(c_0_4472_1,axiom,
( ~ c_in(X1,c_Set_Oimage(X2,X3,X4,X5),X5)
| hAPP(X2,c_ATP__Linkup_Osko__Set__XimageE__1__1(X3,X1,X2,X4,X5)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_4472]) ).
cnf(c_0_4473_0,axiom,
( hAPP(X2,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(X3,X2,X1,X4,X5)) = X1
| ~ c_in(X1,c_Set_Oimage(X2,X3,X4,X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_4473]) ).
cnf(c_0_4473_1,axiom,
( ~ c_in(X1,c_Set_Oimage(X2,X3,X4,X5),X5)
| hAPP(X2,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(X3,X2,X1,X4,X5)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_4473]) ).
cnf(c_0_4474_0,axiom,
( ~ c_Fun_Oinj__on(X1,c_Set_Oinsert(X2,X3,X4),X4,X5)
| ~ c_in(hAPP(X1,X2),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4,X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_4474]) ).
cnf(c_0_4474_1,axiom,
( ~ c_in(hAPP(X1,X2),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4,X5),X5)
| ~ c_Fun_Oinj__on(X1,c_Set_Oinsert(X2,X3,X4),X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_4474]) ).
cnf(c_0_4475_0,axiom,
( c_in(c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1(X1,X2,X3,X4,X5),X1,X4)
| c_lessequals(c_Set_Oimage(X3,X1,X4,X5),X2,tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4475]) ).
cnf(c_0_4475_1,axiom,
( c_lessequals(c_Set_Oimage(X3,X1,X4,X5),X2,tc_fun(X5,tc_bool))
| c_in(c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1(X1,X2,X3,X4,X5),X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4475]) ).
cnf(c_0_4476_0,axiom,
( c_in(c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1(X1,X2,X3,X4,X5),X1,X4)
| c_lessequals(c_Set_Oimage(X3,X1,X4,X5),X2,tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4476]) ).
cnf(c_0_4476_1,axiom,
( c_lessequals(c_Set_Oimage(X3,X1,X4,X5),X2,tc_fun(X5,tc_bool))
| c_in(c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1(X1,X2,X3,X4,X5),X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4476]) ).
cnf(c_0_4479_0,axiom,
( c_in(X1,X2,X3)
| c_Set_Oimage(c_Fun_Ofun__upd(X4,X1,X5,X3,X6),X2,X3,X6) = c_Set_Oimage(X4,X2,X3,X6) ),
inference(literals_permutation,[status(thm)],[c_0_4479]) ).
cnf(c_0_4479_1,axiom,
( c_Set_Oimage(c_Fun_Ofun__upd(X4,X1,X5,X3,X6),X2,X3,X6) = c_Set_Oimage(X4,X2,X3,X6)
| c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4479]) ).
cnf(c_0_4480_0,axiom,
( c_in(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X1,X2,X3,X4,X5),X1,X4)
| c_Set_Oimage(X2,X1,X4,X5) = c_Set_Oimage(X3,X1,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_4480]) ).
cnf(c_0_4480_1,axiom,
( c_Set_Oimage(X2,X1,X4,X5) = c_Set_Oimage(X3,X1,X4,X5)
| c_in(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X1,X2,X3,X4,X5),X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4480]) ).
cnf(c_0_4481_0,axiom,
( c_in(hAPP(X4,X1),c_Inductive_Ocomplete__lattice__class_Ogfp(X6,tc_fun(X5,tc_bool)),X5)
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(c_Set_Oimage(X4,X2,X3,X5),hAPP(X6,c_Set_Oimage(X4,X2,X3,X5)),tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4481]) ).
cnf(c_0_4481_1,axiom,
( ~ c_in(X1,X2,X3)
| c_in(hAPP(X4,X1),c_Inductive_Ocomplete__lattice__class_Ogfp(X6,tc_fun(X5,tc_bool)),X5)
| ~ c_lessequals(c_Set_Oimage(X4,X2,X3,X5),hAPP(X6,c_Set_Oimage(X4,X2,X3,X5)),tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4481]) ).
cnf(c_0_4481_2,axiom,
( ~ c_lessequals(c_Set_Oimage(X4,X2,X3,X5),hAPP(X6,c_Set_Oimage(X4,X2,X3,X5)),tc_fun(X5,tc_bool))
| ~ c_in(X1,X2,X3)
| c_in(hAPP(X4,X1),c_Inductive_Ocomplete__lattice__class_Ogfp(X6,tc_fun(X5,tc_bool)),X5) ),
inference(literals_permutation,[status(thm)],[c_0_4481]) ).
cnf(c_0_4482_0,axiom,
( c_Finite__Set_Ocard(X2,X3) = c_Finite__Set_Ocard(X5,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| ~ c_Fun_Oinj__on(X6,X5,X4,X3)
| ~ c_lessequals(c_Set_Oimage(X6,X5,X4,X3),X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4482]) ).
cnf(c_0_4482_1,axiom,
( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_Finite__Set_Ocard(X2,X3) = c_Finite__Set_Ocard(X5,X4)
| ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| ~ c_Fun_Oinj__on(X6,X5,X4,X3)
| ~ c_lessequals(c_Set_Oimage(X6,X5,X4,X3),X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4482]) ).
cnf(c_0_4482_2,axiom,
( ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_Finite__Set_Ocard(X2,X3) = c_Finite__Set_Ocard(X5,X4)
| ~ c_Fun_Oinj__on(X6,X5,X4,X3)
| ~ c_lessequals(c_Set_Oimage(X6,X5,X4,X3),X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4482]) ).
cnf(c_0_4482_3,axiom,
( ~ c_Fun_Oinj__on(X6,X5,X4,X3)
| ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_Finite__Set_Ocard(X2,X3) = c_Finite__Set_Ocard(X5,X4)
| ~ c_lessequals(c_Set_Oimage(X6,X5,X4,X3),X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4482]) ).
cnf(c_0_4482_4,axiom,
( ~ c_lessequals(c_Set_Oimage(X6,X5,X4,X3),X2,tc_fun(X3,tc_bool))
| ~ c_Fun_Oinj__on(X6,X5,X4,X3)
| ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_Finite__Set_Ocard(X2,X3) = c_Finite__Set_Ocard(X5,X4)
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4482]) ).
cnf(c_0_4482_5,axiom,
( ~ c_Finite__Set_Ofinite(X2,X3)
| ~ c_lessequals(c_Set_Oimage(X6,X5,X4,X3),X2,tc_fun(X3,tc_bool))
| ~ c_Fun_Oinj__on(X6,X5,X4,X3)
| ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_Finite__Set_Ocard(X2,X3) = c_Finite__Set_Ocard(X5,X4)
| ~ c_Finite__Set_Ofinite(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4482]) ).
cnf(c_0_4482_6,axiom,
( ~ c_Finite__Set_Ofinite(X5,X4)
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ c_lessequals(c_Set_Oimage(X6,X5,X4,X3),X2,tc_fun(X3,tc_bool))
| ~ c_Fun_Oinj__on(X6,X5,X4,X3)
| ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_Finite__Set_Ocard(X2,X3) = c_Finite__Set_Ocard(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4482]) ).
cnf(c_0_4483_0,axiom,
( c_in(hAPP(X1,X5),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3,X4),X4)
| c_Fun_Oinj__on(X1,c_Set_Oinsert(X5,X2,X3),X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4483]) ).
cnf(c_0_4483_1,axiom,
( c_Fun_Oinj__on(X1,c_Set_Oinsert(X5,X2,X3),X3,X4)
| c_in(hAPP(X1,X5),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3,X4),X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4483]) ).
cnf(c_0_4483_2,axiom,
( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_Fun_Oinj__on(X1,c_Set_Oinsert(X5,X2,X3),X3,X4)
| c_in(hAPP(X1,X5),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4483]) ).
cnf(c_0_4484_0,axiom,
( hBOOL(hAPP(X1,X2))
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X2,tc_nat),X3,tc_nat)))
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4484]) ).
cnf(c_0_4484_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X2,tc_nat),X3,tc_nat)))
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4484]) ).
cnf(c_0_4484_2,axiom,
( ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X2,tc_nat),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_4484]) ).
cnf(c_0_4484_3,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X2,tc_nat),X3,tc_nat)))
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4484]) ).
cnf(c_0_4485_0,axiom,
( X1 = X2
| hAPP(c_Fun_Ofun__upd(X3,X2,X4,X5,X6),X1) = hAPP(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_4485]) ).
cnf(c_0_4485_1,axiom,
( hAPP(c_Fun_Ofun__upd(X3,X2,X4,X5,X6),X1) = hAPP(X3,X1)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4485]) ).
cnf(c_0_4486_0,axiom,
( X1 = X2
| hAPP(c_Fun_Ofun__upd(X3,X2,X4,X5,X6),X1) = hAPP(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_4486]) ).
cnf(c_0_4486_1,axiom,
( hAPP(c_Fun_Ofun__upd(X3,X2,X4,X5,X6),X1) = hAPP(X3,X1)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4486]) ).
cnf(c_0_4489_0,axiom,
( c_lessequals(X4,X5,tc_fun(X2,tc_bool))
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| ~ c_lessequals(c_Set_Oimage(X1,X4,X2,X3),c_Set_Oimage(X1,X5,X2,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4489]) ).
cnf(c_0_4489_1,axiom,
( ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| c_lessequals(X4,X5,tc_fun(X2,tc_bool))
| ~ c_lessequals(c_Set_Oimage(X1,X4,X2,X3),c_Set_Oimage(X1,X5,X2,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4489]) ).
cnf(c_0_4489_2,axiom,
( ~ c_lessequals(c_Set_Oimage(X1,X4,X2,X3),c_Set_Oimage(X1,X5,X2,X3),tc_fun(X3,tc_bool))
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| c_lessequals(X4,X5,tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4489]) ).
cnf(c_0_4490_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,X5,X3,X4),c_Set_Oimage(X1,X6,X3,X4),tc_fun(X4,tc_bool)) = c_Set_Oimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X3,tc_bool)),X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X6,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4490]) ).
cnf(c_0_4490_1,axiom,
( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,X5,X3,X4),c_Set_Oimage(X1,X6,X3,X4),tc_fun(X4,tc_bool)) = c_Set_Oimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X3,tc_bool)),X3,X4)
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X6,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4490]) ).
cnf(c_0_4490_2,axiom,
( ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,X5,X3,X4),c_Set_Oimage(X1,X6,X3,X4),tc_fun(X4,tc_bool)) = c_Set_Oimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X3,tc_bool)),X3,X4)
| ~ c_lessequals(X6,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4490]) ).
cnf(c_0_4490_3,axiom,
( ~ c_lessequals(X6,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,X5,X3,X4),c_Set_Oimage(X1,X6,X3,X4),tc_fun(X4,tc_bool)) = c_Set_Oimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X3,tc_bool)),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4490]) ).
cnf(c_0_4491_0,axiom,
( c_HOL_Ominus__class_Ominus(c_Set_Oimage(X1,X5,X3,X4),c_Set_Oimage(X1,X6,X3,X4),tc_fun(X4,tc_bool)) = c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X3,tc_bool)),X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X6,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4491]) ).
cnf(c_0_4491_1,axiom,
( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_HOL_Ominus__class_Ominus(c_Set_Oimage(X1,X5,X3,X4),c_Set_Oimage(X1,X6,X3,X4),tc_fun(X4,tc_bool)) = c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X3,tc_bool)),X3,X4)
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X6,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4491]) ).
cnf(c_0_4491_2,axiom,
( ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_HOL_Ominus__class_Ominus(c_Set_Oimage(X1,X5,X3,X4),c_Set_Oimage(X1,X6,X3,X4),tc_fun(X4,tc_bool)) = c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X3,tc_bool)),X3,X4)
| ~ c_lessequals(X6,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4491]) ).
cnf(c_0_4491_3,axiom,
( ~ c_lessequals(X6,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_HOL_Ominus__class_Ominus(c_Set_Oimage(X1,X5,X3,X4),c_Set_Oimage(X1,X6,X3,X4),tc_fun(X4,tc_bool)) = c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X3,tc_bool)),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4491]) ).
cnf(c_0_4492_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4492]) ).
cnf(c_0_4492_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4492]) ).
cnf(c_0_4492_2,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4492]) ).
cnf(c_0_4493_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X5,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X3,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X4,tc_nat),X5,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4493]) ).
cnf(c_0_4493_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X5,tc_nat),tc_nat)
| ~ c_lessequals(X3,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X4,tc_nat),X5,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4493]) ).
cnf(c_0_4493_2,axiom,
( ~ c_lessequals(X3,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X4,tc_nat),X5,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X5,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4493]) ).
cnf(c_0_4494_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X5,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X4,tc_nat),X5,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4494]) ).
cnf(c_0_4494_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X5,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X4,tc_nat),X5,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4494]) ).
cnf(c_0_4494_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X4,tc_nat),X5,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X5,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4494]) ).
cnf(c_0_4495_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4495]) ).
cnf(c_0_4495_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4495]) ).
cnf(c_0_4495_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4495]) ).
cnf(c_0_4496_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4),X4)
| ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4),X4)
| ~ class_Ring__and__Field_Opordered__ring(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4496]) ).
cnf(c_0_4496_1,axiom,
( ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4),X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4),X4)
| ~ class_Ring__and__Field_Opordered__ring(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4496]) ).
cnf(c_0_4496_2,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X4)
| ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4),X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4496]) ).
cnf(c_0_4497_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3),X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3),X6,X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4497]) ).
cnf(c_0_4497_1,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3),X6,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4497]) ).
cnf(c_0_4497_2,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3),X6,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4497]) ).
cnf(c_0_4498_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3),X6,X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4498]) ).
cnf(c_0_4498_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3),X6,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4498]) ).
cnf(c_0_4498_2,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3),X6,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4498]) ).
cnf(c_0_4499_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4),X4)
| ~ class_Ring__and__Field_Opordered__ring(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4499]) ).
cnf(c_0_4499_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4),X4)
| ~ class_Ring__and__Field_Opordered__ring(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4499]) ).
cnf(c_0_4499_2,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4499]) ).
cnf(c_0_4500_0,axiom,
( c_lessequals(c_Set_Ovimage(X1,X4,X2,X3),X5,tc_fun(X2,tc_bool))
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| ~ c_lessequals(X4,c_Set_Oimage(X1,X5,X2,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4500]) ).
cnf(c_0_4500_1,axiom,
( ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| c_lessequals(c_Set_Ovimage(X1,X4,X2,X3),X5,tc_fun(X2,tc_bool))
| ~ c_lessequals(X4,c_Set_Oimage(X1,X5,X2,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4500]) ).
cnf(c_0_4500_2,axiom,
( ~ c_lessequals(X4,c_Set_Oimage(X1,X5,X2,X3),tc_fun(X3,tc_bool))
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| c_lessequals(c_Set_Ovimage(X1,X4,X2,X3),X5,tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4500]) ).
cnf(c_0_4501_0,axiom,
( c_HOL_Ominus__class_Ominus(c_Set_Oimage(X1,X4,X2,X3),c_Set_Oimage(X1,X5,X2,X3),tc_fun(X3,tc_bool)) = c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X2,tc_bool)),X2,X3)
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4501]) ).
cnf(c_0_4501_1,axiom,
( ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| c_HOL_Ominus__class_Ominus(c_Set_Oimage(X1,X4,X2,X3),c_Set_Oimage(X1,X5,X2,X3),tc_fun(X3,tc_bool)) = c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X2,tc_bool)),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4501]) ).
cnf(c_0_4502_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,X4,X2,X3),c_Set_Oimage(X1,X5,X2,X3),tc_fun(X3,tc_bool)) = c_Set_Oimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X2,tc_bool)),X2,X3)
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4502]) ).
cnf(c_0_4502_1,axiom,
( ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,X4,X2,X3),c_Set_Oimage(X1,X5,X2,X3),tc_fun(X3,tc_bool)) = c_Set_Oimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X2,tc_bool)),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4502]) ).
cnf(c_0_4503_0,axiom,
( c_in(hAPP(c_Hilbert__Choice_Oinv__into(X3,X2,X4,X5),X1),X3,X4)
| ~ c_in(X1,c_Set_Oimage(X2,X3,X4,X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_4503]) ).
cnf(c_0_4503_1,axiom,
( ~ c_in(X1,c_Set_Oimage(X2,X3,X4,X5),X5)
| c_in(hAPP(c_Hilbert__Choice_Oinv__into(X3,X2,X4,X5),X1),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4503]) ).
cnf(c_0_4504_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4504]) ).
cnf(c_0_4504_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4504]) ).
cnf(c_0_4504_2,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4504]) ).
cnf(c_0_4505_0,axiom,
( c_lessequals(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X5,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4505]) ).
cnf(c_0_4505_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X5,tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4505]) ).
cnf(c_0_4505_2,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X5,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4505]) ).
cnf(c_0_4506_0,axiom,
( c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X5,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4506]) ).
cnf(c_0_4506_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X5,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4506]) ).
cnf(c_0_4506_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X5,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4506]) ).
cnf(c_0_4507_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4507]) ).
cnf(c_0_4507_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4507]) ).
cnf(c_0_4507_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4507]) ).
cnf(c_0_4508_0,axiom,
( hAPP(X1,X2) = X3
| c_Fun_Ofun__upd(X1,X2,X3,X4,X5) != X1 ),
inference(literals_permutation,[status(thm)],[c_0_4508]) ).
cnf(c_0_4508_1,axiom,
( c_Fun_Ofun__upd(X1,X2,X3,X4,X5) != X1
| hAPP(X1,X2) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_4508]) ).
cnf(c_0_4509_0,axiom,
( c_lessequals(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X1,X3),X2,X3),X6,X3),X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4509]) ).
cnf(c_0_4509_1,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| c_lessequals(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X1,X3),X2,X3),X6,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4509]) ).
cnf(c_0_4509_2,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| c_lessequals(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X1,X3),X2,X3),X6,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4509]) ).
cnf(c_0_4510_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X6,X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4510]) ).
cnf(c_0_4510_1,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X6,X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4510]) ).
cnf(c_0_4510_2,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X6,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4510]) ).
cnf(c_0_4511_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4511]) ).
cnf(c_0_4511_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X6,X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4511]) ).
cnf(c_0_4511_2,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X6,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4511]) ).
cnf(c_0_4512_0,axiom,
( c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X1,X3),X2,X3),X6,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4512]) ).
cnf(c_0_4512_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X1,X3),X2,X3),X6,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4512]) ).
cnf(c_0_4512_2,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X1,X3),X2,X3),X6,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4512]) ).
cnf(c_0_4513_0,axiom,
( hAPP(X2,hAPP(c_Hilbert__Choice_Oinv__into(X3,X2,X4,X5),X1)) = X1
| ~ c_in(X1,c_Set_Oimage(X2,X3,X4,X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_4513]) ).
cnf(c_0_4513_1,axiom,
( ~ c_in(X1,c_Set_Oimage(X2,X3,X4,X5),X5)
| hAPP(X2,hAPP(c_Hilbert__Choice_Oinv__into(X3,X2,X4,X5),X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_4513]) ).
cnf(c_0_4514_0,axiom,
( c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1,X2,X3),c_Set_Oimage(X1,X4,X2,X3),X3,X2) = X4
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4514]) ).
cnf(c_0_4514_1,axiom,
( ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1,X2,X3),c_Set_Oimage(X1,X4,X2,X3),X3,X2) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_4514]) ).
cnf(c_0_4515_0,axiom,
( c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1,X2,X3),c_Set_Oimage(X1,X4,X2,X3),X3,X2) = X4
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4515]) ).
cnf(c_0_4515_1,axiom,
( ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1,X2,X3),c_Set_Oimage(X1,X4,X2,X3),X3,X2) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_4515]) ).
cnf(c_0_4516_0,axiom,
( c_Set_Oimage(c_Hilbert__Choice_Oinv__into(X2,X1,X3,X4),c_Set_Oimage(X1,X5,X3,X4),X4,X3) = X5
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4516]) ).
cnf(c_0_4516_1,axiom,
( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_Set_Oimage(c_Hilbert__Choice_Oinv__into(X2,X1,X3,X4),c_Set_Oimage(X1,X5,X3,X4),X4,X3) = X5
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4516]) ).
cnf(c_0_4516_2,axiom,
( ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_Set_Oimage(c_Hilbert__Choice_Oinv__into(X2,X1,X3,X4),c_Set_Oimage(X1,X5,X3,X4),X4,X3) = X5 ),
inference(literals_permutation,[status(thm)],[c_0_4516]) ).
cnf(c_0_4517_0,axiom,
( hBOOL(hAPP(X2,hAPP(X1,X5)))
| ~ hBOOL(hAPP(c_Set_Ovimage(X1,X2,X3,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_4517]) ).
cnf(c_0_4517_1,axiom,
( ~ hBOOL(hAPP(c_Set_Ovimage(X1,X2,X3,X4),X5))
| hBOOL(hAPP(X2,hAPP(X1,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_4517]) ).
cnf(c_0_4518_0,axiom,
( c_lessequals(c_Set_Oimage(X1,X4,X2,X3),c_Set_Oimage(X1,X5,X2,X3),tc_fun(X3,tc_bool))
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| ~ c_lessequals(X4,X5,tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4518]) ).
cnf(c_0_4518_1,axiom,
( ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| c_lessequals(c_Set_Oimage(X1,X4,X2,X3),c_Set_Oimage(X1,X5,X2,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4518]) ).
cnf(c_0_4518_2,axiom,
( ~ c_lessequals(X4,X5,tc_fun(X2,tc_bool))
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| c_lessequals(c_Set_Oimage(X1,X4,X2,X3),c_Set_Oimage(X1,X5,X2,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4518]) ).
cnf(c_0_4519_0,axiom,
( c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X3,X2,X4,X5),X1,X5,X4)
| ~ c_lessequals(X1,c_Set_Oimage(X2,X3,X4,X5),tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4519]) ).
cnf(c_0_4519_1,axiom,
( ~ c_lessequals(X1,c_Set_Oimage(X2,X3,X4,X5),tc_fun(X5,tc_bool))
| c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X3,X2,X4,X5),X1,X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4519]) ).
cnf(c_0_4520_0,axiom,
( c_Set_Oimage(X3,X1,X2,X2) = X1
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(c_Set_Oimage(X3,X1,X2,X2),X1,tc_fun(X2,tc_bool))
| ~ c_Fun_Oinj__on(X3,X1,X2,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4520]) ).
cnf(c_0_4520_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Set_Oimage(X3,X1,X2,X2) = X1
| ~ c_lessequals(c_Set_Oimage(X3,X1,X2,X2),X1,tc_fun(X2,tc_bool))
| ~ c_Fun_Oinj__on(X3,X1,X2,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4520]) ).
cnf(c_0_4520_2,axiom,
( ~ c_lessequals(c_Set_Oimage(X3,X1,X2,X2),X1,tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Set_Oimage(X3,X1,X2,X2) = X1
| ~ c_Fun_Oinj__on(X3,X1,X2,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4520]) ).
cnf(c_0_4520_3,axiom,
( ~ c_Fun_Oinj__on(X3,X1,X2,X2)
| ~ c_lessequals(c_Set_Oimage(X3,X1,X2,X2),X1,tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Set_Oimage(X3,X1,X2,X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_4520]) ).
cnf(c_0_4522_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4522]) ).
cnf(c_0_4522_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4522]) ).
cnf(c_0_4523_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X5,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4523]) ).
cnf(c_0_4523_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X5,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4523]) ).
cnf(c_0_4524_0,axiom,
( hAPP(X2,X1) = X3
| ~ c_in(X1,c_Set_Ovimage(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X5,X4),X5) ),
inference(literals_permutation,[status(thm)],[c_0_4524]) ).
cnf(c_0_4524_1,axiom,
( ~ c_in(X1,c_Set_Ovimage(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X5,X4),X5)
| hAPP(X2,X1) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_4524]) ).
cnf(c_0_4525_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X6,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X5,X2,X3),X3),X6,X3),X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4525]) ).
cnf(c_0_4525_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X6,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X5,X2,X3),X3),X6,X3),X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4525]) ).
cnf(c_0_4525_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X5,X2,X3),X3),X6,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X6,X3),X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4525]) ).
cnf(c_0_4525_3,axiom,
( ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X5,X2,X3),X3),X6,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X6,X3),X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4525]) ).
cnf(c_0_4525_4,axiom,
( ~ class_Ring__and__Field_Odvd(X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X5,X2,X3),X3),X6,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X6,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4525]) ).
cnf(c_0_4528_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4528]) ).
cnf(c_0_4528_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4528]) ).
cnf(c_0_4528_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4528]) ).
cnf(c_0_4528_3,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4528]) ).
cnf(c_0_4529_0,axiom,
( c_in(X4,X5,X2)
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| ~ c_in(hAPP(X1,X4),c_Set_Oimage(X1,X5,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4529]) ).
cnf(c_0_4529_1,axiom,
( ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| c_in(X4,X5,X2)
| ~ c_in(hAPP(X1,X4),c_Set_Oimage(X1,X5,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4529]) ).
cnf(c_0_4529_2,axiom,
( ~ c_in(hAPP(X1,X4),c_Set_Oimage(X1,X5,X2,X3),X3)
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| c_in(X4,X5,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4529]) ).
cnf(c_0_4530_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4530]) ).
cnf(c_0_4530_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4530]) ).
cnf(c_0_4530_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4530]) ).
cnf(c_0_4530_3,axiom,
( ~ c_in(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4530]) ).
cnf(c_0_4531_0,axiom,
( c_lessequals(c_Finite__Set_Ocard(X2,X3),c_Finite__Set_Ocard(X5,X4),tc_nat)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| ~ c_Finite__Set_Ofinite(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4531]) ).
cnf(c_0_4531_1,axiom,
( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_lessequals(c_Finite__Set_Ocard(X2,X3),c_Finite__Set_Ocard(X5,X4),tc_nat)
| ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| ~ c_Finite__Set_Ofinite(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4531]) ).
cnf(c_0_4531_2,axiom,
( ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_lessequals(c_Finite__Set_Ocard(X2,X3),c_Finite__Set_Ocard(X5,X4),tc_nat)
| ~ c_Finite__Set_Ofinite(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4531]) ).
cnf(c_0_4531_3,axiom,
( ~ c_Finite__Set_Ofinite(X5,X4)
| ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_lessequals(c_Finite__Set_Ocard(X2,X3),c_Finite__Set_Ocard(X5,X4),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4531]) ).
cnf(c_0_4533_0,axiom,
( c_in(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4533]) ).
cnf(c_0_4533_1,axiom,
( c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool))
| c_in(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4533]) ).
cnf(c_0_4533_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool))
| c_in(X1,X2,X3)
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4533]) ).
cnf(c_0_4533_3,axiom,
( ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool))
| c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4533]) ).
cnf(c_0_4534_0,axiom,
( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2),c_Finite__Set_Ocard(X1,X2),tc_nat)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_in(X3,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4534]) ).
cnf(c_0_4534_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2),c_Finite__Set_Ocard(X1,X2),tc_nat)
| ~ c_in(X3,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4534]) ).
cnf(c_0_4534_2,axiom,
( ~ c_in(X3,X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2),c_Finite__Set_Ocard(X1,X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4534]) ).
cnf(c_0_4535_0,axiom,
( c_in(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_in(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4535]) ).
cnf(c_0_4535_1,axiom,
( c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool))
| c_in(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_in(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4535]) ).
cnf(c_0_4535_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool))
| c_in(X1,X2,X3)
| ~ c_in(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4535]) ).
cnf(c_0_4535_3,axiom,
( ~ c_in(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool))
| c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4535]) ).
cnf(c_0_4536_0,axiom,
( c_lessequals(X1,c_Set_Oinsert(X2,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4536]) ).
cnf(c_0_4536_1,axiom,
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| c_lessequals(X1,c_Set_Oinsert(X2,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4536]) ).
cnf(c_0_4536_2,axiom,
( ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| c_lessequals(X1,c_Set_Oinsert(X2,X4,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4536]) ).
cnf(c_0_4537_0,axiom,
( c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2)) = c_Finite__Set_Ocard(c_Set_Oinsert(X3,X1,X2),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4537]) ).
cnf(c_0_4537_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2)) = c_Finite__Set_Ocard(c_Set_Oinsert(X3,X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4537]) ).
cnf(c_0_4538_0,axiom,
( c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2)) = c_Finite__Set_Ocard(X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_in(X3,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4538]) ).
cnf(c_0_4538_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2)) = c_Finite__Set_Ocard(X1,X2)
| ~ c_in(X3,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4538]) ).
cnf(c_0_4538_2,axiom,
( ~ c_in(X3,X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2)) = c_Finite__Set_Ocard(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4538]) ).
cnf(c_0_4539_0,axiom,
( c_lessequals(X1,c_Set_Oinsert(X2,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| ~ c_in(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4539]) ).
cnf(c_0_4539_1,axiom,
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| c_lessequals(X1,c_Set_Oinsert(X2,X4,X3),tc_fun(X3,tc_bool))
| ~ c_in(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4539]) ).
cnf(c_0_4539_2,axiom,
( ~ c_in(X2,X1,X3)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| c_lessequals(X1,c_Set_Oinsert(X2,X4,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4539]) ).
cnf(c_0_4540_0,axiom,
( c_lessequals(X1,c_Set_Oinsert(X2,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| ~ c_in(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4540]) ).
cnf(c_0_4540_1,axiom,
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| c_lessequals(X1,c_Set_Oinsert(X2,X4,X3),tc_fun(X3,tc_bool))
| ~ c_in(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4540]) ).
cnf(c_0_4540_2,axiom,
( ~ c_in(X2,X1,X3)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| c_lessequals(X1,c_Set_Oinsert(X2,X4,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4540]) ).
cnf(c_0_4541_0,axiom,
( c_lessequals(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2),c_Finite__Set_Ocard(X1,X2),tc_nat)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4541]) ).
cnf(c_0_4541_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_lessequals(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2),c_Finite__Set_Ocard(X1,X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4541]) ).
cnf(c_0_4542_0,axiom,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5)
| c_Set_Oimage(X3,X1,X4,X5) != c_Set_Oimage(X3,X2,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_4542]) ).
cnf(c_0_4542_1,axiom,
( ~ c_Fun_Oinj__on(X3,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5)
| X1 = X2
| c_Set_Oimage(X3,X1,X4,X5) != c_Set_Oimage(X3,X2,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_4542]) ).
cnf(c_0_4542_2,axiom,
( c_Set_Oimage(X3,X1,X4,X5) != c_Set_Oimage(X3,X2,X4,X5)
| ~ c_Fun_Oinj__on(X3,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4542]) ).
cnf(c_0_4546_0,axiom,
( c_Set_Ovimage(X1,c_Set_Oimage(X1,X4,X2,X3),X2,X3) = X4
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4546]) ).
cnf(c_0_4546_1,axiom,
( ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| c_Set_Ovimage(X1,c_Set_Oimage(X1,X4,X2,X3),X2,X3) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_4546]) ).
cnf(c_0_4547_0,axiom,
( c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(X1,X2,X3,X4),X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4547]) ).
cnf(c_0_4547_1,axiom,
( ~ c_Finite__Set_Ofinite(c_Set_Oimage(X1,X2,X3,X4),X4)
| c_Finite__Set_Ofinite(X2,X3)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4547]) ).
cnf(c_0_4547_2,axiom,
( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(X1,X2,X3,X4),X4)
| c_Finite__Set_Ofinite(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4547]) ).
cnf(c_0_4548_0,axiom,
( c_lessequals(c_Set_Oimage(X4,X1,X3,X5),c_Set_Oimage(X4,X2,X3,X5),tc_fun(X5,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4548]) ).
cnf(c_0_4548_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Set_Oimage(X4,X1,X3,X5),c_Set_Oimage(X4,X2,X3,X5),tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4548]) ).
cnf(c_0_4549_0,axiom,
( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4549]) ).
cnf(c_0_4549_1,axiom,
( ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool))
| c_lessequals(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4549]) ).
cnf(c_0_4550_0,axiom,
( c_lessequals(c_Set_Ovimage(X4,X1,X5,X3),c_Set_Ovimage(X4,X2,X5,X3),tc_fun(X5,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4550]) ).
cnf(c_0_4550_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Set_Ovimage(X4,X1,X5,X3),c_Set_Ovimage(X4,X2,X5,X3),tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4550]) ).
cnf(c_0_4551_0,axiom,
( c_Fun_Oinj__on(X3,X1,X2,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X1,c_Set_Oimage(X3,X1,X2,X2),tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4551]) ).
cnf(c_0_4551_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Fun_Oinj__on(X3,X1,X2,X2)
| ~ c_lessequals(X1,c_Set_Oimage(X3,X1,X2,X2),tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4551]) ).
cnf(c_0_4551_2,axiom,
( ~ c_lessequals(X1,c_Set_Oimage(X3,X1,X2,X2),tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Fun_Oinj__on(X3,X1,X2,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4551]) ).
cnf(c_0_4552_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X6,X2,X3),X3),X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4552]) ).
cnf(c_0_4552_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X6,X2,X3),X3),X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4552]) ).
cnf(c_0_4552_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X6,X2,X3),X3),X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4552]) ).
cnf(c_0_4552_3,axiom,
( ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X6,X2,X3),X3),X5,X3),X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4552]) ).
cnf(c_0_4552_4,axiom,
( ~ class_Ring__and__Field_Odvd(X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X6,X2,X3),X3),X5,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4552]) ).
cnf(c_0_4553_0,axiom,
( hBOOL(hAPP(c_Set_Ovimage(X2,X1,X4,X5),X3))
| ~ hBOOL(hAPP(X1,hAPP(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_4553]) ).
cnf(c_0_4553_1,axiom,
( ~ hBOOL(hAPP(X1,hAPP(X2,X3)))
| hBOOL(hAPP(c_Set_Ovimage(X2,X1,X4,X5),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4553]) ).
cnf(c_0_4554_0,axiom,
( c_in(hAPP(X1,X4),c_Set_Oimage(X1,X5,X2,X3),X3)
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| ~ c_in(X4,X5,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4554]) ).
cnf(c_0_4554_1,axiom,
( ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| c_in(hAPP(X1,X4),c_Set_Oimage(X1,X5,X2,X3),X3)
| ~ c_in(X4,X5,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4554]) ).
cnf(c_0_4554_2,axiom,
( ~ c_in(X4,X5,X2)
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| c_in(hAPP(X1,X4),c_Set_Oimage(X1,X5,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4554]) ).
cnf(c_0_4555_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,tc_nat),X2,tc_nat),X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat)
| ~ c_lessequals(X4,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4555]) ).
cnf(c_0_4555_1,axiom,
( ~ c_lessequals(X4,X1,tc_nat)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,tc_nat),X2,tc_nat),X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4555]) ).
cnf(c_0_4556_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),X2,tc_nat),X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),X4,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4556]) ).
cnf(c_0_4556_1,axiom,
( ~ c_lessequals(X1,X3,tc_nat)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),X2,tc_nat),X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),X4,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4556]) ).
cnf(c_0_4557_0,axiom,
( c_lessequals(c_Finite__Set_Ocard(c_Set_Oimage(X3,X1,X2,X4),X4),c_Finite__Set_Ocard(X1,X2),tc_nat)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4557]) ).
cnf(c_0_4557_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_lessequals(c_Finite__Set_Ocard(c_Set_Oimage(X3,X1,X2,X4),X4),c_Finite__Set_Ocard(X1,X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4557]) ).
cnf(c_0_4558_0,axiom,
( hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,X1,X3),hAPP(X2,X4)) = X4
| ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4558]) ).
cnf(c_0_4558_1,axiom,
( ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X3)
| hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,X1,X3),hAPP(X2,X4)) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_4558]) ).
cnf(c_0_4559_0,axiom,
( hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1,X2,X3),hAPP(X1,X4)) = X4
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4559]) ).
cnf(c_0_4559_1,axiom,
( ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1,X2,X3),hAPP(X1,X4)) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_4559]) ).
cnf(c_0_4560_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(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),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4560]) ).
cnf(c_0_4560_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(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),X1) ),
inference(literals_permutation,[status(thm)],[c_0_4560]) ).
cnf(c_0_4561_0,axiom,
( c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_Finite__Set_Ofinite(X2,X3)
| c_Finite__Set_Ocard(c_Set_Oimage(X1,X2,X3,X4),X4) != c_Finite__Set_Ocard(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4561]) ).
cnf(c_0_4561_1,axiom,
( ~ c_Finite__Set_Ofinite(X2,X3)
| c_Fun_Oinj__on(X1,X2,X3,X4)
| c_Finite__Set_Ocard(c_Set_Oimage(X1,X2,X3,X4),X4) != c_Finite__Set_Ocard(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4561]) ).
cnf(c_0_4561_2,axiom,
( c_Finite__Set_Ocard(c_Set_Oimage(X1,X2,X3,X4),X4) != c_Finite__Set_Ocard(X2,X3)
| ~ c_Finite__Set_Ofinite(X2,X3)
| c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4561]) ).
cnf(c_0_4562_0,axiom,
( c_in(X2,X3,X4)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| ~ c_in(X2,X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4562]) ).
cnf(c_0_4562_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool))
| c_in(X2,X3,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| ~ c_in(X2,X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4562]) ).
cnf(c_0_4562_2,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool))
| c_in(X2,X3,X4)
| ~ c_in(X2,X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4562]) ).
cnf(c_0_4562_3,axiom,
( ~ c_in(X2,X1,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool))
| c_in(X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4562]) ).
cnf(c_0_4563_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X1,X3),X2,X3),X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,X3),X5,X3)
| ~ class_Ring__and__Field_Oring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4563]) ).
cnf(c_0_4563_1,axiom,
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X1,X3),X2,X3),X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,X3),X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4563]) ).
cnf(c_0_4564_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Oring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4564]) ).
cnf(c_0_4564_1,axiom,
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4564]) ).
cnf(c_0_4566_0,axiom,
( c_in(hAPP(X1,X6),X5,X4)
| ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| ~ c_in(X6,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4566]) ).
cnf(c_0_4566_1,axiom,
( ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| c_in(hAPP(X1,X6),X5,X4)
| ~ c_in(X6,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4566]) ).
cnf(c_0_4566_2,axiom,
( ~ c_in(X6,X2,X3)
| ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| c_in(hAPP(X1,X6),X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4566]) ).
cnf(c_0_4567_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),X3,tc_nat))) ),
inference(literals_permutation,[status(thm)],[c_0_4567]) ).
cnf(c_0_4567_1,axiom,
( ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),X3,tc_nat)))
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4567]) ).
cnf(c_0_4568_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),X3,tc_nat))) ),
inference(literals_permutation,[status(thm)],[c_0_4568]) ).
cnf(c_0_4568_1,axiom,
( ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),X3,tc_nat)))
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4568]) ).
cnf(c_0_4569_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(X4,X1,tc_nat),tc_nat),X2,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_4569]) ).
cnf(c_0_4569_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(X4,X1,tc_nat),tc_nat),X2,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_4569]) ).
cnf(c_0_4569_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_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(X4,X1,tc_nat),tc_nat),X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4569]) ).
cnf(c_0_4570_0,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| ~ c_in(X2,X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4570]) ).
cnf(c_0_4570_1,axiom,
( ~ c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool))
| ~ c_in(X2,X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4570]) ).
cnf(c_0_4570_2,axiom,
( ~ c_in(X2,X1,X4)
| ~ c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4570]) ).
cnf(c_0_4571_0,axiom,
( hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),hAPP(X2,X5)) = X5
| ~ c_Fun_Oinj__on(X2,X1,X3,X4)
| ~ c_in(X5,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4571]) ).
cnf(c_0_4571_1,axiom,
( ~ c_Fun_Oinj__on(X2,X1,X3,X4)
| hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),hAPP(X2,X5)) = X5
| ~ c_in(X5,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4571]) ).
cnf(c_0_4571_2,axiom,
( ~ c_in(X5,X1,X3)
| ~ c_Fun_Oinj__on(X2,X1,X3,X4)
| hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),hAPP(X2,X5)) = X5 ),
inference(literals_permutation,[status(thm)],[c_0_4571]) ).
cnf(c_0_4572_0,axiom,
( hAPP(c_Hilbert__Choice_Oinv__into(X2,X1,X3,X4),hAPP(X1,X5)) = X5
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_in(X5,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4572]) ).
cnf(c_0_4572_1,axiom,
( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| hAPP(c_Hilbert__Choice_Oinv__into(X2,X1,X3,X4),hAPP(X1,X5)) = X5
| ~ c_in(X5,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4572]) ).
cnf(c_0_4572_2,axiom,
( ~ c_in(X5,X2,X3)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| hAPP(c_Hilbert__Choice_Oinv__into(X2,X1,X3,X4),hAPP(X1,X5)) = X5 ),
inference(literals_permutation,[status(thm)],[c_0_4572]) ).
cnf(c_0_4573_0,axiom,
( c_Finite__Set_Ofinite(c_Set_Ovimage(X3,X1,X4,X2),X4)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Fun_Oinj__on(X3,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4573]) ).
cnf(c_0_4573_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_Set_Ovimage(X3,X1,X4,X2),X4)
| ~ c_Fun_Oinj__on(X3,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4573]) ).
cnf(c_0_4573_2,axiom,
( ~ c_Fun_Oinj__on(X3,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_Set_Ovimage(X3,X1,X4,X2),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4573]) ).
cnf(c_0_4574_0,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4574]) ).
cnf(c_0_4574_1,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),c_HOL_Ozero__class_Ozero(X2),X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4574]) ).
cnf(c_0_4574_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),c_HOL_Ozero__class_Ozero(X2),X2)
| X3 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4574]) ).
cnf(c_0_4575_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4575]) ).
cnf(c_0_4575_1,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),c_HOL_Ozero__class_Ozero(X2),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4575]) ).
cnf(c_0_4575_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),c_HOL_Ozero__class_Ozero(X2),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4575]) ).
cnf(c_0_4576_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4576]) ).
cnf(c_0_4576_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4576]) ).
cnf(c_0_4577_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),X4,tc_nat) = X5
| ~ c_lessequals(X2,X1,tc_nat)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4577]) ).
cnf(c_0_4577_1,axiom,
( ~ c_lessequals(X2,X1,tc_nat)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),X4,tc_nat) = X5
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4577]) ).
cnf(c_0_4577_2,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat)
| ~ c_lessequals(X2,X1,tc_nat)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),X4,tc_nat) = X5 ),
inference(literals_permutation,[status(thm)],[c_0_4577]) ).
cnf(c_0_4578_0,axiom,
( X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),X4,tc_nat),X5,tc_nat)
| ~ c_lessequals(X3,X2,tc_nat)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X1,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X5,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4578]) ).
cnf(c_0_4578_1,axiom,
( ~ c_lessequals(X3,X2,tc_nat)
| X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),X4,tc_nat),X5,tc_nat)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X1,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X5,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4578]) ).
cnf(c_0_4578_2,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X1,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X5,tc_nat)
| ~ c_lessequals(X3,X2,tc_nat)
| X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),X4,tc_nat),X5,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4578]) ).
cnf(c_0_4579_0,axiom,
( c_in(hAPP(X2,X1),X3,X5)
| ~ c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4579]) ).
cnf(c_0_4579_1,axiom,
( ~ c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4)
| c_in(hAPP(X2,X1),X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_4579]) ).
cnf(c_0_4580_0,axiom,
( c_in(hAPP(X2,X1),X3,X5)
| ~ c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4580]) ).
cnf(c_0_4580_1,axiom,
( ~ c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4)
| c_in(hAPP(X2,X1),X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_4580]) ).
cnf(c_0_4581_0,axiom,
( c_Finite__Set_Ofinite(X3,X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,c_Set_Oimage(X4,X1,X2,X5),tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4581]) ).
cnf(c_0_4581_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(X3,X5)
| ~ c_lessequals(X3,c_Set_Oimage(X4,X1,X2,X5),tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4581]) ).
cnf(c_0_4581_2,axiom,
( ~ c_lessequals(X3,c_Set_Oimage(X4,X1,X2,X5),tc_fun(X5,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_4581]) ).
cnf(c_0_4582_0,axiom,
( c_Finite__Set_Ocard(c_Set_Oimage(X3,X1,X2,X4),X4) = c_Finite__Set_Ocard(X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Fun_Oinj__on(X3,X1,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4582]) ).
cnf(c_0_4582_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ocard(c_Set_Oimage(X3,X1,X2,X4),X4) = c_Finite__Set_Ocard(X1,X2)
| ~ c_Fun_Oinj__on(X3,X1,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4582]) ).
cnf(c_0_4582_2,axiom,
( ~ c_Fun_Oinj__on(X3,X1,X2,X4)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ocard(c_Set_Oimage(X3,X1,X2,X4),X4) = c_Finite__Set_Ocard(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4582]) ).
cnf(c_0_4583_0,axiom,
( c_in(X3,X4,X2)
| c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,X4,X2),tc_fun(X2,tc_bool)),X2) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X2,tc_bool)),X2),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_in(X3,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4583]) ).
cnf(c_0_4583_1,axiom,
( c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,X4,X2),tc_fun(X2,tc_bool)),X2) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X2,tc_bool)),X2),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_in(X3,X4,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_in(X3,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4583]) ).
cnf(c_0_4583_2,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,X4,X2),tc_fun(X2,tc_bool)),X2) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X2,tc_bool)),X2),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_in(X3,X4,X2)
| ~ c_in(X3,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4583]) ).
cnf(c_0_4583_3,axiom,
( ~ c_in(X3,X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,X4,X2),tc_fun(X2,tc_bool)),X2) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X2,tc_bool)),X2),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_in(X3,X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4583]) ).
cnf(c_0_4585_0,axiom,
( c_Finite__Set_Ocard(c_Set_Oimage(X1,X2,X3,X4),X4) = c_Finite__Set_Ocard(X2,X3)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4585]) ).
cnf(c_0_4585_1,axiom,
( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_Finite__Set_Ocard(c_Set_Oimage(X1,X2,X3,X4),X4) = c_Finite__Set_Ocard(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4585]) ).
cnf(c_0_4586_0,axiom,
( c_Set_Oinsert(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5) = c_Set_Oimage(X4,X2,X3,X5)
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4586]) ).
cnf(c_0_4586_1,axiom,
( ~ c_in(X1,X2,X3)
| c_Set_Oinsert(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5) = c_Set_Oimage(X4,X2,X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_4586]) ).
cnf(c_0_4587_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3) = X6
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3)
| ~ class_Ring__and__Field_Oring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4587]) ).
cnf(c_0_4587_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3) = X6
| ~ class_Ring__and__Field_Oring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4587]) ).
cnf(c_0_4587_2,axiom,
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3) = X6 ),
inference(literals_permutation,[status(thm)],[c_0_4587]) ).
cnf(c_0_4588_0,axiom,
( X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4)
| ~ class_Ring__and__Field_Oring(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4588]) ).
cnf(c_0_4588_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4)
| X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4)
| ~ class_Ring__and__Field_Oring(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4588]) ).
cnf(c_0_4588_2,axiom,
( ~ class_Ring__and__Field_Oring(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4)
| X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4588]) ).
cnf(c_0_4589_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,X3),X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3),X5,X3)
| ~ class_Ring__and__Field_Osemiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4589]) ).
cnf(c_0_4589_1,axiom,
( ~ class_Ring__and__Field_Osemiring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,X3),X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3),X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4589]) ).
cnf(c_0_4590_0,axiom,
( X1 = X2
| X3 = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_4590]) ).
cnf(c_0_4590_1,axiom,
( X3 = X4
| X1 = X2
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_4590]) ).
cnf(c_0_4590_2,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| X3 = X4
| X1 = X2
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_4590]) ).
cnf(c_0_4590_3,axiom,
( ~ class_Int_Onumber__ring(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| X3 = X4
| X1 = X2
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_4590]) ).
cnf(c_0_4590_4,axiom,
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| X3 = X4
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4590]) ).
cnf(c_0_4591_0,axiom,
( X1 = X2
| X3 = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_4591]) ).
cnf(c_0_4591_1,axiom,
( X3 = X4
| X1 = X2
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_4591]) ).
cnf(c_0_4591_2,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| X3 = X4
| X1 = X2
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_4591]) ).
cnf(c_0_4591_3,axiom,
( ~ class_Int_Onumber__ring(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| X3 = X4
| X1 = X2
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_4591]) ).
cnf(c_0_4591_4,axiom,
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
| X3 = X4
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4591]) ).
cnf(c_0_4592_0,axiom,
( c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(X1,X3),c_Finite__Set_Ocard(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3),tc_nat) = c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4592]) ).
cnf(c_0_4592_1,axiom,
( ~ c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3)
| c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(X1,X3),c_Finite__Set_Ocard(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3),tc_nat) = c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4592]) ).
cnf(c_0_4593_0,axiom,
( X1 = X2
| X1 = X3
| c_Set_Oinsert(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_4593]) ).
cnf(c_0_4593_1,axiom,
( X1 = X3
| X1 = X2
| c_Set_Oinsert(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_4593]) ).
cnf(c_0_4593_2,axiom,
( c_Set_Oinsert(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5)
| X1 = X3
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4593]) ).
cnf(c_0_4594_0,axiom,
( X1 = X2
| X3 = X2
| c_Set_Oinsert(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4594]) ).
cnf(c_0_4594_1,axiom,
( X3 = X2
| X1 = X2
| c_Set_Oinsert(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4594]) ).
cnf(c_0_4594_2,axiom,
( c_Set_Oinsert(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4)
| X3 = X2
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4594]) ).
cnf(c_0_4595_0,axiom,
( X1 = X2
| X3 = X2
| c_Set_Oinsert(X3,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4595]) ).
cnf(c_0_4595_1,axiom,
( X3 = X2
| X1 = X2
| c_Set_Oinsert(X3,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4595]) ).
cnf(c_0_4595_2,axiom,
( c_Set_Oinsert(X3,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4)
| X3 = X2
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4595]) ).
cnf(c_0_4596_0,axiom,
( X1 = X2
| X1 = X3
| c_Set_Oinsert(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_4596]) ).
cnf(c_0_4596_1,axiom,
( X1 = X3
| X1 = X2
| c_Set_Oinsert(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_4596]) ).
cnf(c_0_4596_2,axiom,
( c_Set_Oinsert(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5)
| X1 = X3
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4596]) ).
cnf(c_0_4599_0,axiom,
( X1 = X2
| X3 = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4599]) ).
cnf(c_0_4599_1,axiom,
( X3 = X4
| X1 = X2
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4599]) ).
cnf(c_0_4599_2,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
| X3 = X4
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4599]) ).
cnf(c_0_4600_0,axiom,
( X1 = X2
| X3 = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4600]) ).
cnf(c_0_4600_1,axiom,
( X3 = X4
| X1 = X2
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4600]) ).
cnf(c_0_4600_2,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
| X3 = X4
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4600]) ).
cnf(c_0_4601_0,axiom,
( c_Fun_Oinj__on(X1,X3,X4,X5)
| ~ c_Fun_Oinj__on(X1,c_Set_Oinsert(X2,X3,X4),X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_4601]) ).
cnf(c_0_4601_1,axiom,
( ~ c_Fun_Oinj__on(X1,c_Set_Oinsert(X2,X3,X4),X4,X5)
| c_Fun_Oinj__on(X1,X3,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_4601]) ).
cnf(c_0_4602_0,axiom,
( c_Fun_Oinj__on(X1,c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X3,tc_bool)),X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4602]) ).
cnf(c_0_4602_1,axiom,
( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_Fun_Oinj__on(X1,c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X3,tc_bool)),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4602]) ).
cnf(c_0_4603_0,axiom,
( c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(X1,X2),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_in(X3,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4603]) ).
cnf(c_0_4603_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(X1,X2),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ c_in(X3,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4603]) ).
cnf(c_0_4603_2,axiom,
( ~ c_in(X3,X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(X1,X2),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4603]) ).
cnf(c_0_4604_0,axiom,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool)),X4)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4604]) ).
cnf(c_0_4604_1,axiom,
( ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)),X4)
| c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4604]) ).
cnf(c_0_4605_0,axiom,
( c_Fun_Oinj__on(X1,X5,X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4605]) ).
cnf(c_0_4605_1,axiom,
( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_Fun_Oinj__on(X1,X5,X3,X4)
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4605]) ).
cnf(c_0_4605_2,axiom,
( ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_Fun_Oinj__on(X1,X5,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4605]) ).
cnf(c_0_4606_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(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_Ominus__class_Ominus(X1,X2,X3),X4,X3)
| ~ class_Divides_Oring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4606]) ).
cnf(c_0_4606_1,axiom,
( ~ class_Divides_Oring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(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_Ominus__class_Ominus(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4606]) ).
cnf(c_0_4607_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_4607]) ).
cnf(c_0_4607_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_4607]) ).
cnf(c_0_4608_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(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_Oplus__class_Oplus(X1,X2,X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4608]) ).
cnf(c_0_4608_1,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(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_Oplus__class_Oplus(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4608]) ).
cnf(c_0_4610_0,axiom,
( c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = X2
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4610]) ).
cnf(c_0_4610_1,axiom,
( ~ c_in(X1,X2,X3)
| c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4610]) ).
cnf(c_0_4611_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(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),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4611]) ).
cnf(c_0_4611_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_lessequals(c_HOL_Oplus__class_Oplus(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),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_4611]) ).
cnf(c_0_4613_0,axiom,
( c_in(X3,X1,X2)
| c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2) = c_Finite__Set_Ocard(X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4613]) ).
cnf(c_0_4613_1,axiom,
( c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2) = c_Finite__Set_Ocard(X1,X2)
| c_in(X3,X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4613]) ).
cnf(c_0_4613_2,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2) = c_Finite__Set_Ocard(X1,X2)
| c_in(X3,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4613]) ).
cnf(c_0_4615_0,axiom,
( c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5)
| ~ c_in(hAPP(X1,X2),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4615]) ).
cnf(c_0_4615_1,axiom,
( ~ c_in(hAPP(X1,X2),X3,X4)
| c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5) ),
inference(literals_permutation,[status(thm)],[c_0_4615]) ).
cnf(c_0_4616_0,axiom,
( c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5)
| ~ c_in(hAPP(X1,X2),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4616]) ).
cnf(c_0_4616_1,axiom,
( ~ c_in(hAPP(X1,X2),X3,X4)
| c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5) ),
inference(literals_permutation,[status(thm)],[c_0_4616]) ).
cnf(c_0_4617_0,axiom,
( c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5)
| ~ c_in(hAPP(X1,X2),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4617]) ).
cnf(c_0_4617_1,axiom,
( ~ c_in(hAPP(X1,X2),X3,X4)
| c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5) ),
inference(literals_permutation,[status(thm)],[c_0_4617]) ).
cnf(c_0_4618_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(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_Oring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4618]) ).
cnf(c_0_4618_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_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,X6,X3),X4,X3)
| c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X6,X4,X3)
| ~ class_Divides_Oring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4618]) ).
cnf(c_0_4618_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_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,X6,X3),X4,X3)
| ~ class_Divides_Oring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4618]) ).
cnf(c_0_4618_3,axiom,
( ~ class_Divides_Oring__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_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,X6,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4618]) ).
cnf(c_0_4619_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_4619]) ).
cnf(c_0_4619_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_4619]) ).
cnf(c_0_4619_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_4619]) ).
cnf(c_0_4619_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_4619]) ).
cnf(c_0_4620_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(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_4620]) ).
cnf(c_0_4620_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_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(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_4620]) ).
cnf(c_0_4620_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_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X5,X6,X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4620]) ).
cnf(c_0_4620_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_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X5,X6,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4620]) ).
cnf(c_0_4621_0,axiom,
( c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5)
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4621]) ).
cnf(c_0_4621_1,axiom,
( ~ c_in(X1,X2,X3)
| c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_4621]) ).
cnf(c_0_4622_0,axiom,
( c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5)
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4622]) ).
cnf(c_0_4622_1,axiom,
( ~ c_in(X1,X2,X3)
| c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_4622]) ).
cnf(c_0_4623_0,axiom,
( c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5)
| ~ c_in(X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4623]) ).
cnf(c_0_4623_1,axiom,
( ~ c_in(X2,X3,X4)
| c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_4623]) ).
cnf(c_0_4624_0,axiom,
( c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5)
| ~ c_in(X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4624]) ).
cnf(c_0_4624_1,axiom,
( ~ c_in(X2,X3,X4)
| c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_4624]) ).
cnf(c_0_4625_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_4625]) ).
cnf(c_0_4625_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_4625]) ).
cnf(c_0_4626_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_4626]) ).
cnf(c_0_4626_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_4626]) ).
cnf(c_0_4627_0,axiom,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4627]) ).
cnf(c_0_4627_1,axiom,
( ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3)
| c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4627]) ).
cnf(c_0_4628_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4628]) ).
cnf(c_0_4628_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,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4628]) ).
cnf(c_0_4628_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,X5,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,X5,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4628]) ).
cnf(c_0_4628_3,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4628]) ).
cnf(c_0_4628_4,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4628]) ).
cnf(c_0_4628_5,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4628]) ).
cnf(c_0_4629_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4629]) ).
cnf(c_0_4629_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4629]) ).
cnf(c_0_4629_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4629]) ).
cnf(c_0_4629_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4629]) ).
cnf(c_0_4629_4,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4629]) ).
cnf(c_0_4629_5,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4629]) ).
cnf(c_0_4630_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4630]) ).
cnf(c_0_4630_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,X5,X3),X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4630]) ).
cnf(c_0_4630_2,axiom,
( ~ c_lessequals(X4,X5,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,X5,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4630]) ).
cnf(c_0_4630_3,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,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_4630]) ).
cnf(c_0_4630_4,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4630]) ).
cnf(c_0_4630_5,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4630]) ).
cnf(c_0_4631_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4631]) ).
cnf(c_0_4631_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4631]) ).
cnf(c_0_4631_2,axiom,
( ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4631]) ).
cnf(c_0_4631_3,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4631]) ).
cnf(c_0_4631_4,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4631]) ).
cnf(c_0_4631_5,axiom,
( ~ class_Ring__and__Field_Opordered__semiring(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4631]) ).
cnf(c_0_4632_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4632]) ).
cnf(c_0_4632_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4632]) ).
cnf(c_0_4632_2,axiom,
( ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4632]) ).
cnf(c_0_4632_3,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4632]) ).
cnf(c_0_4632_4,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4632]) ).
cnf(c_0_4632_5,axiom,
( ~ class_Ring__and__Field_Opordered__semiring(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4632]) ).
cnf(c_0_4633_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4633]) ).
cnf(c_0_4633_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,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4633]) ).
cnf(c_0_4633_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,X5,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,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4633]) ).
cnf(c_0_4633_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4633]) ).
cnf(c_0_4633_4,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4633]) ).
cnf(c_0_4633_5,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4633]) ).
cnf(c_0_4634_0,axiom,
( c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4634]) ).
cnf(c_0_4634_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4634]) ).
cnf(c_0_4634_2,axiom,
( ~ c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4634]) ).
cnf(c_0_4634_3,axiom,
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4634]) ).
cnf(c_0_4635_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4635]) ).
cnf(c_0_4635_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4635]) ).
cnf(c_0_4635_2,axiom,
( ~ c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4635]) ).
cnf(c_0_4635_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4635]) ).
cnf(c_0_4636_0,axiom,
( c_lessequals(hAPP(X1,X3),hAPP(X1,X4),X2)
| ~ c_lessequals(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1(X1,X2)),hAPP(X1,c_Suc(c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1(X1,X2))),X2)
| ~ c_lessequals(X3,X4,tc_nat)
| ~ class_Orderings_Oorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4636]) ).
cnf(c_0_4636_1,axiom,
( ~ c_lessequals(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1(X1,X2)),hAPP(X1,c_Suc(c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1(X1,X2))),X2)
| c_lessequals(hAPP(X1,X3),hAPP(X1,X4),X2)
| ~ c_lessequals(X3,X4,tc_nat)
| ~ class_Orderings_Oorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4636]) ).
cnf(c_0_4636_2,axiom,
( ~ c_lessequals(X3,X4,tc_nat)
| ~ c_lessequals(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1(X1,X2)),hAPP(X1,c_Suc(c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1(X1,X2))),X2)
| c_lessequals(hAPP(X1,X3),hAPP(X1,X4),X2)
| ~ class_Orderings_Oorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4636]) ).
cnf(c_0_4636_3,axiom,
( ~ class_Orderings_Oorder(X2)
| ~ c_lessequals(X3,X4,tc_nat)
| ~ c_lessequals(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1(X1,X2)),hAPP(X1,c_Suc(c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1(X1,X2))),X2)
| c_lessequals(hAPP(X1,X3),hAPP(X1,X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4636]) ).
cnf(c_0_4637_0,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X5,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4637]) ).
cnf(c_0_4637_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X5,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4637]) ).
cnf(c_0_4637_2,axiom,
( ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X5,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4637]) ).
cnf(c_0_4638_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4638]) ).
cnf(c_0_4638_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4638]) ).
cnf(c_0_4638_2,axiom,
( ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4638]) ).
cnf(c_0_4643_0,axiom,
( X1 = X4
| ~ c_in(X1,X2,X3)
| ~ c_in(X4,X2,X3)
| ~ c_Fun_Oinj__on(X5,X2,X3,X6)
| hAPP(X5,X1) != hAPP(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4643]) ).
cnf(c_0_4643_1,axiom,
( ~ c_in(X1,X2,X3)
| X1 = X4
| ~ c_in(X4,X2,X3)
| ~ c_Fun_Oinj__on(X5,X2,X3,X6)
| hAPP(X5,X1) != hAPP(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4643]) ).
cnf(c_0_4643_2,axiom,
( ~ c_in(X4,X2,X3)
| ~ c_in(X1,X2,X3)
| X1 = X4
| ~ c_Fun_Oinj__on(X5,X2,X3,X6)
| hAPP(X5,X1) != hAPP(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4643]) ).
cnf(c_0_4643_3,axiom,
( ~ c_Fun_Oinj__on(X5,X2,X3,X6)
| ~ c_in(X4,X2,X3)
| ~ c_in(X1,X2,X3)
| X1 = X4
| hAPP(X5,X1) != hAPP(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4643]) ).
cnf(c_0_4643_4,axiom,
( hAPP(X5,X1) != hAPP(X5,X4)
| ~ c_Fun_Oinj__on(X5,X2,X3,X6)
| ~ c_in(X4,X2,X3)
| ~ c_in(X1,X2,X3)
| X1 = X4 ),
inference(literals_permutation,[status(thm)],[c_0_4643]) ).
cnf(c_0_4644_0,axiom,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| ~ c_in(X1,X4,X5)
| ~ c_in(X2,X4,X5)
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4644]) ).
cnf(c_0_4644_1,axiom,
( ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| X1 = X2
| ~ c_in(X1,X4,X5)
| ~ c_in(X2,X4,X5)
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4644]) ).
cnf(c_0_4644_2,axiom,
( ~ c_in(X1,X4,X5)
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| X1 = X2
| ~ c_in(X2,X4,X5)
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4644]) ).
cnf(c_0_4644_3,axiom,
( ~ c_in(X2,X4,X5)
| ~ c_in(X1,X4,X5)
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| X1 = X2
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4644]) ).
cnf(c_0_4644_4,axiom,
( hAPP(X3,X1) != hAPP(X3,X2)
| ~ c_in(X2,X4,X5)
| ~ c_in(X1,X4,X5)
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4644]) ).
cnf(c_0_4645_0,axiom,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| ~ c_in(X1,X4,X5)
| ~ c_in(X2,X4,X5)
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4645]) ).
cnf(c_0_4645_1,axiom,
( ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| X1 = X2
| ~ c_in(X1,X4,X5)
| ~ c_in(X2,X4,X5)
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4645]) ).
cnf(c_0_4645_2,axiom,
( ~ c_in(X1,X4,X5)
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| X1 = X2
| ~ c_in(X2,X4,X5)
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4645]) ).
cnf(c_0_4645_3,axiom,
( ~ c_in(X2,X4,X5)
| ~ c_in(X1,X4,X5)
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| X1 = X2
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4645]) ).
cnf(c_0_4645_4,axiom,
( hAPP(X3,X1) != hAPP(X3,X2)
| ~ c_in(X2,X4,X5)
| ~ c_in(X1,X4,X5)
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4645]) ).
cnf(c_0_4646_0,axiom,
( X5 = X6
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_in(X5,X2,X3)
| ~ c_in(X6,X2,X3)
| hAPP(X1,X5) != hAPP(X1,X6) ),
inference(literals_permutation,[status(thm)],[c_0_4646]) ).
cnf(c_0_4646_1,axiom,
( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| X5 = X6
| ~ c_in(X5,X2,X3)
| ~ c_in(X6,X2,X3)
| hAPP(X1,X5) != hAPP(X1,X6) ),
inference(literals_permutation,[status(thm)],[c_0_4646]) ).
cnf(c_0_4646_2,axiom,
( ~ c_in(X5,X2,X3)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| X5 = X6
| ~ c_in(X6,X2,X3)
| hAPP(X1,X5) != hAPP(X1,X6) ),
inference(literals_permutation,[status(thm)],[c_0_4646]) ).
cnf(c_0_4646_3,axiom,
( ~ c_in(X6,X2,X3)
| ~ c_in(X5,X2,X3)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| X5 = X6
| hAPP(X1,X5) != hAPP(X1,X6) ),
inference(literals_permutation,[status(thm)],[c_0_4646]) ).
cnf(c_0_4646_4,axiom,
( hAPP(X1,X5) != hAPP(X1,X6)
| ~ c_in(X6,X2,X3)
| ~ c_in(X5,X2,X3)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| X5 = X6 ),
inference(literals_permutation,[status(thm)],[c_0_4646]) ).
cnf(c_0_4647_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X2),c_HOL_Otimes__class_Otimes(X1,X1,X2),X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4647]) ).
cnf(c_0_4647_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X2),c_HOL_Otimes__class_Otimes(X1,X1,X2),X2),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4647]) ).
cnf(c_0_4647_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X2),c_HOL_Otimes__class_Otimes(X1,X1,X2),X2),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4647]) ).
cnf(c_0_4648_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4648]) ).
cnf(c_0_4648_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4648]) ).
cnf(c_0_4648_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4648]) ).
cnf(c_0_4649_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4649]) ).
cnf(c_0_4649_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_4649]) ).
cnf(c_0_4650_0,axiom,
( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(X3,X2,tc_nat)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X2,X5,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4650]) ).
cnf(c_0_4650_1,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X2,X5,tc_nat),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_4650]) ).
cnf(c_0_4651_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X1 = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| ~ c_lessequals(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4651]) ).
cnf(c_0_4651_1,axiom,
( X1 = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4651]) ).
cnf(c_0_4651_2,axiom,
( ~ c_lessequals(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool))
| X1 = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4651]) ).
cnf(c_0_4652_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_4652]) ).
cnf(c_0_4652_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_4652]) ).
cnf(c_0_4652_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_4652]) ).
cnf(c_0_4652_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_4652]) ).
cnf(c_0_4653_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_4653]) ).
cnf(c_0_4653_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_4653]) ).
cnf(c_0_4653_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_4653]) ).
cnf(c_0_4653_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_4653]) ).
cnf(c_0_4654_0,axiom,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4654]) ).
cnf(c_0_4654_1,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| c_lessequals(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4654]) ).
cnf(c_0_4654_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| c_lessequals(X1,X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4654]) ).
cnf(c_0_4654_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| c_lessequals(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4654]) ).
cnf(c_0_4655_0,axiom,
( c_lessequals(X2,X4,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4655]) ).
cnf(c_0_4655_1,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| c_lessequals(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4655]) ).
cnf(c_0_4655_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| c_lessequals(X2,X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4655]) ).
cnf(c_0_4655_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| c_lessequals(X2,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4655]) ).
cnf(c_0_4656_0,axiom,
( c_lessequals(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(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_4656]) ).
cnf(c_0_4656_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,X4,X1)
| ~ c_lessequals(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_4656]) ).
cnf(c_0_4656_2,axiom,
( ~ c_lessequals(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_lessequals(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4656]) ).
cnf(c_0_4656_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(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_lessequals(X3,X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_4656]) ).
cnf(c_0_4657_0,axiom,
( c_lessequals(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(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_4657]) ).
cnf(c_0_4657_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(X4,X3,X2)
| ~ c_lessequals(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_4657]) ).
cnf(c_0_4657_2,axiom,
( ~ c_lessequals(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_lessequals(X4,X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4657]) ).
cnf(c_0_4657_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_lessequals(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_lessequals(X4,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4657]) ).
cnf(c_0_4658_0,axiom,
( 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)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4658]) ).
cnf(c_0_4658_1,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(X2,X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4658]) ).
cnf(c_0_4658_2,axiom,
( ~ c_lessequals(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)
| c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4658]) ).
cnf(c_0_4658_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring(X3)
| ~ c_lessequals(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)
| c_HOL_Oord__class_Oless(X2,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4658]) ).
cnf(c_0_4659_0,axiom,
( 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)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4659]) ).
cnf(c_0_4659_1,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(X1,X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4659]) ).
cnf(c_0_4659_2,axiom,
( ~ c_lessequals(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)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4659]) ).
cnf(c_0_4659_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring(X3)
| ~ c_lessequals(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)
| c_HOL_Oord__class_Oless(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4659]) ).
cnf(c_0_4660_0,axiom,
( 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)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4660]) ).
cnf(c_0_4660_1,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(X2,X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4660]) ).
cnf(c_0_4660_2,axiom,
( ~ c_lessequals(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)
| c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4660]) ).
cnf(c_0_4660_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_lessequals(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)
| c_HOL_Oord__class_Oless(X2,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4660]) ).
cnf(c_0_4661_0,axiom,
( 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)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4661]) ).
cnf(c_0_4661_1,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(X1,X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4661]) ).
cnf(c_0_4661_2,axiom,
( ~ c_lessequals(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)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4661]) ).
cnf(c_0_4661_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_lessequals(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)
| c_HOL_Oord__class_Oless(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4661]) ).
cnf(c_0_4662_0,axiom,
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4662]) ).
cnf(c_0_4662_1,axiom,
( ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4))
| hBOOL(hAPP(X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4662]) ).
cnf(c_0_4663_0,axiom,
( hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4663]) ).
cnf(c_0_4663_1,axiom,
( ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4))
| hBOOL(hAPP(X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4663]) ).
cnf(c_0_4664_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_4664]) ).
cnf(c_0_4664_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_4664]) ).
cnf(c_0_4664_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_4664]) ).
cnf(c_0_4665_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_4665]) ).
cnf(c_0_4665_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_4665]) ).
cnf(c_0_4665_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_4665]) ).
cnf(c_0_4666_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_4666]) ).
cnf(c_0_4666_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_4666]) ).
cnf(c_0_4666_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_4666]) ).
cnf(c_0_4667_0,axiom,
( c_lessequals(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_lessequals(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_4667]) ).
cnf(c_0_4667_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(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_4667]) ).
cnf(c_0_4667_2,axiom,
( ~ c_lessequals(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_lessequals(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4667]) ).
cnf(c_0_4668_0,axiom,
( c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(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_4668]) ).
cnf(c_0_4668_1,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| c_lessequals(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_4668]) ).
cnf(c_0_4668_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| c_lessequals(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4668]) ).
cnf(c_0_4669_0,axiom,
( c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(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_4669]) ).
cnf(c_0_4669_1,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| c_lessequals(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4669]) ).
cnf(c_0_4669_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| c_lessequals(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4669]) ).
cnf(c_0_4670_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_4670]) ).
cnf(c_0_4670_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_4670]) ).
cnf(c_0_4670_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_4670]) ).
cnf(c_0_4670_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_4670]) ).
cnf(c_0_4671_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_4671]) ).
cnf(c_0_4671_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_4671]) ).
cnf(c_0_4671_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_4671]) ).
cnf(c_0_4671_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_4671]) ).
cnf(c_0_4672_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4672]) ).
cnf(c_0_4672_1,axiom,
( ~ class_Int_Onumber__ring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4672]) ).
cnf(c_0_4672_2,axiom,
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4672]) ).
cnf(c_0_4673_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4673]) ).
cnf(c_0_4673_1,axiom,
( ~ class_Int_Onumber__ring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4673]) ).
cnf(c_0_4673_2,axiom,
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4673]) ).
cnf(c_0_4674_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_4674]) ).
cnf(c_0_4674_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_4674]) ).
cnf(c_0_4674_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_4674]) ).
cnf(c_0_4674_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_4674]) ).
cnf(c_0_4675_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_4675]) ).
cnf(c_0_4675_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_4675]) ).
cnf(c_0_4675_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_4675]) ).
cnf(c_0_4675_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_4675]) ).
cnf(c_0_4676_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_4676]) ).
cnf(c_0_4676_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_4676]) ).
cnf(c_0_4676_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_4676]) ).
cnf(c_0_4676_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_4676]) ).
cnf(c_0_4677_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_4677]) ).
cnf(c_0_4677_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_4677]) ).
cnf(c_0_4677_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_4677]) ).
cnf(c_0_4677_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_4677]) ).
cnf(c_0_4678_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X2,X3,X4),X4),X3,X4) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4)
| ~ class_Divides_Osemiring__div(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4678]) ).
cnf(c_0_4678_1,axiom,
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X2,X3,X4),X4),X3,X4) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4678]) ).
cnf(c_0_4679_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X2,X3),X4,X3),X2,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4679]) ).
cnf(c_0_4679_1,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X2,X3),X4,X3),X2,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4679]) ).
cnf(c_0_4680_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
| ~ class_Divides_Oring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4680]) ).
cnf(c_0_4680_1,axiom,
( ~ class_Divides_Oring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4680]) ).
cnf(c_0_4681_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
| ~ class_Divides_Oring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4681]) ).
cnf(c_0_4681_1,axiom,
( ~ class_Divides_Oring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4681]) ).
cnf(c_0_4682_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_4682]) ).
cnf(c_0_4682_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_4682]) ).
cnf(c_0_4683_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4683]) ).
cnf(c_0_4683_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4683]) ).
cnf(c_0_4684_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_4684]) ).
cnf(c_0_4684_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_4684]) ).
cnf(c_0_4685_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_4685]) ).
cnf(c_0_4685_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_4685]) ).
cnf(c_0_4686_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_4686]) ).
cnf(c_0_4686_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_4686]) ).
cnf(c_0_4687_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4687]) ).
cnf(c_0_4687_1,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4687]) ).
cnf(c_0_4688_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4688]) ).
cnf(c_0_4688_1,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4688]) ).
cnf(c_0_4689_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_4689]) ).
cnf(c_0_4689_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_4689]) ).
cnf(c_0_4689_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_4689]) ).
cnf(c_0_4689_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_4689]) ).
cnf(c_0_4690_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_4690]) ).
cnf(c_0_4690_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_4690]) ).
cnf(c_0_4690_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_4690]) ).
cnf(c_0_4690_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_4690]) ).
cnf(c_0_4692_0,axiom,
( c_Finite__Set_Ofinite(c_Set_Oimage(X3,X1,X2,X4),X4)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4692]) ).
cnf(c_0_4692_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_Set_Oimage(X3,X1,X2,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4692]) ).
cnf(c_0_4693_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = X4
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) != c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4693]) ).
cnf(c_0_4693_1,axiom,
( X3 = X4
| X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) != c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4693]) ).
cnf(c_0_4693_2,axiom,
( c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) != c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X4,X2),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_4693]) ).
cnf(c_0_4693_3,axiom,
( ~ class_Int_Onumber__ring(X2)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) != c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| X3 = X4
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4693]) ).
cnf(c_0_4693_4,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) != c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| X3 = X4
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4693]) ).
cnf(c_0_4696_0,axiom,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5)
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4696]) ).
cnf(c_0_4696_1,axiom,
( ~ c_Fun_Oinj__on(X3,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5)
| X1 = X2
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4696]) ).
cnf(c_0_4696_2,axiom,
( hAPP(X3,X1) != hAPP(X3,X2)
| ~ c_Fun_Oinj__on(X3,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4696]) ).
cnf(c_0_4697_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(X3,c_Suc(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4697]) ).
cnf(c_0_4697_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(X3,c_Suc(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4697]) ).
cnf(c_0_4698_0,axiom,
( c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X2),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4698]) ).
cnf(c_0_4698_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X2),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4698]) ).
cnf(c_0_4699_0,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4699]) ).
cnf(c_0_4699_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4699]) ).
cnf(c_0_4699_2,axiom,
( ~ c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4699]) ).
cnf(c_0_4699_3,axiom,
( ~ c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4699]) ).
cnf(c_0_4700_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4700]) ).
cnf(c_0_4700_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4700]) ).
cnf(c_0_4700_2,axiom,
( ~ c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4700]) ).
cnf(c_0_4700_3,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4700]) ).
cnf(c_0_4701_0,axiom,
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X5,X4),X4)
| ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| ~ c_lessequals(X3,X5,X4)
| ~ class_OrderedGroup_Opordered__ab__group__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4701]) ).
cnf(c_0_4701_1,axiom,
( ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X5,X4),X4)
| ~ c_lessequals(X3,X5,X4)
| ~ class_OrderedGroup_Opordered__ab__group__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4701]) ).
cnf(c_0_4701_2,axiom,
( ~ c_lessequals(X3,X5,X4)
| ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X5,X4),X4)
| ~ class_OrderedGroup_Opordered__ab__group__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4701]) ).
cnf(c_0_4701_3,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| ~ c_lessequals(X3,X5,X4)
| ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X5,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4701]) ).
cnf(c_0_4702_0,axiom,
( c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(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_4702]) ).
cnf(c_0_4702_1,axiom,
( ~ c_lessequals(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_lessequals(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4702]) ).
cnf(c_0_4703_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_4703]) ).
cnf(c_0_4703_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_4703]) ).
cnf(c_0_4704_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = X3
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4704]) ).
cnf(c_0_4704_1,axiom,
( X2 = X3
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4704]) ).
cnf(c_0_4704_2,axiom,
( c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| X2 = X3
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4704]) ).
cnf(c_0_4706_0,axiom,
( hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)))
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4706]) ).
cnf(c_0_4706_1,axiom,
( ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)))
| hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4706]) ).
cnf(c_0_4706_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)))
| hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(literals_permutation,[status(thm)],[c_0_4706]) ).
cnf(c_0_4707_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_4707]) ).
cnf(c_0_4707_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_4707]) ).
cnf(c_0_4707_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_4707]) ).
cnf(c_0_4707_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_4707]) ).
cnf(c_0_4708_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_4708]) ).
cnf(c_0_4708_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_4708]) ).
cnf(c_0_4708_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_4708]) ).
cnf(c_0_4708_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_4708]) ).
cnf(c_0_4709_0,axiom,
( c_lessequals(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4709]) ).
cnf(c_0_4709_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4709]) ).
cnf(c_0_4709_2,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),X2,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4709]) ).
cnf(c_0_4710_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),X2,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4710]) ).
cnf(c_0_4710_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),X2,tc_nat)
| ~ c_lessequals(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4710]) ).
cnf(c_0_4710_2,axiom,
( ~ c_lessequals(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4710]) ).
cnf(c_0_4711_0,axiom,
( c_in(X4,X1,X3)
| c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4711]) ).
cnf(c_0_4711_1,axiom,
( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| c_in(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4711]) ).
cnf(c_0_4711_2,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| c_in(X4,X1,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4711]) ).
cnf(c_0_4711_3,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| c_in(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4711]) ).
cnf(c_0_4712_0,axiom,
( c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4712]) ).
cnf(c_0_4712_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
| c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4712]) ).
cnf(c_0_4712_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
| c_HOL_Oord__class_Oless(X2,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4712]) ).
cnf(c_0_4713_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4713]) ).
cnf(c_0_4713_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4713]) ).
cnf(c_0_4713_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4713]) ).
cnf(c_0_4714_0,axiom,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4714]) ).
cnf(c_0_4714_1,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| c_lessequals(X1,X4,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4714]) ).
cnf(c_0_4714_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| c_lessequals(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4714]) ).
cnf(c_0_4715_0,axiom,
( c_lessequals(X2,X4,X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4715]) ).
cnf(c_0_4715_1,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
| c_lessequals(X2,X4,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4715]) ).
cnf(c_0_4715_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
| c_lessequals(X2,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4715]) ).
cnf(c_0_4716_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4716]) ).
cnf(c_0_4716_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4716]) ).
cnf(c_0_4716_2,axiom,
( ~ c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4716]) ).
cnf(c_0_4717_0,axiom,
( c_in(X2,X3,X4)
| c_in(X2,X1,X4)
| c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4717]) ).
cnf(c_0_4717_1,axiom,
( c_in(X2,X1,X4)
| c_in(X2,X3,X4)
| c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4717]) ).
cnf(c_0_4717_2,axiom,
( c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| c_in(X2,X1,X4)
| c_in(X2,X3,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4717]) ).
cnf(c_0_4717_3,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| c_in(X2,X1,X4)
| c_in(X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4717]) ).
cnf(c_0_4718_0,axiom,
( c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4718]) ).
cnf(c_0_4718_1,axiom,
( ~ c_in(X1,X2,X3)
| c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4718]) ).
cnf(c_0_4719_0,axiom,
( c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)),X3) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool))
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4719]) ).
cnf(c_0_4719_1,axiom,
( ~ c_in(X1,X2,X3)
| c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)),X3) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4719]) ).
cnf(c_0_4720_0,axiom,
( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X1
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4720]) ).
cnf(c_0_4720_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X1
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4720]) ).
cnf(c_0_4720_2,axiom,
( ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_4720]) ).
cnf(c_0_4721_0,axiom,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4721]) ).
cnf(c_0_4721_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4721]) ).
cnf(c_0_4721_2,axiom,
( ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4721]) ).
cnf(c_0_4722_0,axiom,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4722]) ).
cnf(c_0_4722_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4722]) ).
cnf(c_0_4722_2,axiom,
( ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4722]) ).
cnf(c_0_4723_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_lessequals(X3,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4723]) ).
cnf(c_0_4723_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),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_lessequals(X3,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4723]) ).
cnf(c_0_4723_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
| ~ c_lessequals(X3,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4723]) ).
cnf(c_0_4723_3,axiom,
( ~ c_lessequals(X3,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4723]) ).
cnf(c_0_4724_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
| ~ c_lessequals(X3,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4724]) ).
cnf(c_0_4724_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),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_lessequals(X3,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4724]) ).
cnf(c_0_4724_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_lessequals(X3,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4724]) ).
cnf(c_0_4724_3,axiom,
( ~ c_lessequals(X3,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4724]) ).
cnf(c_0_4725_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_4725]) ).
cnf(c_0_4725_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_4725]) ).
cnf(c_0_4725_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_4725]) ).
cnf(c_0_4726_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_4726]) ).
cnf(c_0_4726_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_4726]) ).
cnf(c_0_4727_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_4727]) ).
cnf(c_0_4727_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_4727]) ).
cnf(c_0_4728_0,axiom,
( c_Finite__Set_Ocard(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = c_Suc(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2))
| c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4728]) ).
cnf(c_0_4728_1,axiom,
( c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| c_Finite__Set_Ocard(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = c_Suc(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4728]) ).
cnf(c_0_4729_0,axiom,
( c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4729]) ).
cnf(c_0_4729_1,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat)
| c_lessequals(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4729]) ).
cnf(c_0_4730_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4730]) ).
cnf(c_0_4730_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4730]) ).
cnf(c_0_4731_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_4731]) ).
cnf(c_0_4731_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_4731]) ).
cnf(c_0_4732_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_4732]) ).
cnf(c_0_4732_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_4732]) ).
cnf(c_0_4736_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Set_Oimage(X4,X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4736]) ).
cnf(c_0_4736_1,axiom,
( c_Set_Oimage(X4,X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4736]) ).
cnf(c_0_4737_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Set_Oimage(X3,X1,X2,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4737]) ).
cnf(c_0_4737_1,axiom,
( c_Set_Oimage(X3,X1,X2,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4737]) ).
cnf(c_0_4738_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Omult__mono1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4738]) ).
cnf(c_0_4738_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Omult__mono1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4738]) ).
cnf(c_0_4738_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Omult__mono1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4738]) ).
cnf(c_0_4738_3,axiom,
( ~ class_Ring__and__Field_Omult__mono1(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4738]) ).
cnf(c_0_4739_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Omult__mono(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4739]) ).
cnf(c_0_4739_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Omult__mono(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4739]) ).
cnf(c_0_4739_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Omult__mono(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4739]) ).
cnf(c_0_4739_3,axiom,
( ~ class_Ring__and__Field_Omult__mono(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4739]) ).
cnf(c_0_4740_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Omult__mono(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4740]) ).
cnf(c_0_4740_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Omult__mono(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4740]) ).
cnf(c_0_4740_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Omult__mono(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4740]) ).
cnf(c_0_4740_3,axiom,
( ~ class_Ring__and__Field_Omult__mono(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4740]) ).
cnf(c_0_4741_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4741]) ).
cnf(c_0_4741_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4741]) ).
cnf(c_0_4741_2,axiom,
( ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4741]) ).
cnf(c_0_4741_3,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4741]) ).
cnf(c_0_4742_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4742]) ).
cnf(c_0_4742_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4742]) ).
cnf(c_0_4742_2,axiom,
( ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4742]) ).
cnf(c_0_4742_3,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4742]) ).
cnf(c_0_4743_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_4743]) ).
cnf(c_0_4743_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_4743]) ).
cnf(c_0_4743_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_4743]) ).
cnf(c_0_4743_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_4743]) ).
cnf(c_0_4744_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_4744]) ).
cnf(c_0_4744_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_4744]) ).
cnf(c_0_4744_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_4744]) ).
cnf(c_0_4744_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_4744]) ).
cnf(c_0_4745_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_4745]) ).
cnf(c_0_4745_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_4745]) ).
cnf(c_0_4745_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_4745]) ).
cnf(c_0_4745_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_4745]) ).
cnf(c_0_4746_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_4746]) ).
cnf(c_0_4746_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_4746]) ).
cnf(c_0_4746_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_4746]) ).
cnf(c_0_4746_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_4746]) ).
cnf(c_0_4747_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_4747]) ).
cnf(c_0_4747_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_4747]) ).
cnf(c_0_4747_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_4747]) ).
cnf(c_0_4747_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_4747]) ).
cnf(c_0_4748_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_4748]) ).
cnf(c_0_4748_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_4748]) ).
cnf(c_0_4748_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_4748]) ).
cnf(c_0_4748_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_4748]) ).
cnf(c_0_4749_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_4749]) ).
cnf(c_0_4749_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_4749]) ).
cnf(c_0_4749_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_4749]) ).
cnf(c_0_4749_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_4749]) ).
cnf(c_0_4750_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_4750]) ).
cnf(c_0_4750_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_4750]) ).
cnf(c_0_4750_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_4750]) ).
cnf(c_0_4750_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_4750]) ).
cnf(c_0_4751_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_4751]) ).
cnf(c_0_4751_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_4751]) ).
cnf(c_0_4751_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_4751]) ).
cnf(c_0_4751_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_4751]) ).
cnf(c_0_4752_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_4752]) ).
cnf(c_0_4752_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_4752]) ).
cnf(c_0_4752_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_4752]) ).
cnf(c_0_4752_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_4752]) ).
cnf(c_0_4753_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_4753]) ).
cnf(c_0_4753_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_4753]) ).
cnf(c_0_4753_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_4753]) ).
cnf(c_0_4753_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_4753]) ).
cnf(c_0_4754_0,axiom,
( c_lessequals(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_lessequals(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4754]) ).
cnf(c_0_4754_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4754]) ).
cnf(c_0_4754_2,axiom,
( ~ c_lessequals(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(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_4754]) ).
cnf(c_0_4754_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_4754]) ).
cnf(c_0_4755_0,axiom,
( c_lessequals(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_lessequals(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4755]) ).
cnf(c_0_4755_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_lessequals(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4755]) ).
cnf(c_0_4755_2,axiom,
( ~ c_lessequals(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(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_4755]) ).
cnf(c_0_4755_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_lessequals(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4755]) ).
cnf(c_0_4756_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4756]) ).
cnf(c_0_4756_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4756]) ).
cnf(c_0_4756_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4756]) ).
cnf(c_0_4756_3,axiom,
( ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4756]) ).
cnf(c_0_4756_4,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_4756]) ).
cnf(c_0_4757_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4757]) ).
cnf(c_0_4757_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4757]) ).
cnf(c_0_4757_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4757]) ).
cnf(c_0_4757_3,axiom,
( ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4757]) ).
cnf(c_0_4757_4,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_4757]) ).
cnf(c_0_4758_0,axiom,
( c_HOL_Oord__class_Oless(X1,X3,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| ~ c_in(X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4758]) ).
cnf(c_0_4758_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| c_HOL_Oord__class_Oless(X1,X3,tc_fun(X4,tc_bool))
| ~ c_in(X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4758]) ).
cnf(c_0_4758_2,axiom,
( ~ c_in(X2,X3,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| c_HOL_Oord__class_Oless(X1,X3,tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4758]) ).
cnf(c_0_4759_0,axiom,
( c_in(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4759]) ).
cnf(c_0_4759_1,axiom,
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) = X2
| c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4759]) ).
cnf(c_0_4760_0,axiom,
( c_lessequals(X3,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4760]) ).
cnf(c_0_4760_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(X3,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4760]) ).
cnf(c_0_4761_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4761]) ).
cnf(c_0_4761_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ c_lessequals(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4761]) ).
cnf(c_0_4761_2,axiom,
( ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4761]) ).
cnf(c_0_4761_3,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4761]) ).
cnf(c_0_4762_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_4762]) ).
cnf(c_0_4762_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_4762]) ).
cnf(c_0_4762_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_4762]) ).
cnf(c_0_4762_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_4762]) ).
cnf(c_0_4763_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),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_4763]) ).
cnf(c_0_4763_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4763]) ).
cnf(c_0_4763_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4763]) ).
cnf(c_0_4763_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(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4763]) ).
cnf(c_0_4764_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4764]) ).
cnf(c_0_4764_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ c_lessequals(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4764]) ).
cnf(c_0_4764_2,axiom,
( ~ c_lessequals(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4764]) ).
cnf(c_0_4764_3,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4764]) ).
cnf(c_0_4765_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4765]) ).
cnf(c_0_4765_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4765]) ).
cnf(c_0_4765_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4765]) ).
cnf(c_0_4765_3,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4765]) ).
cnf(c_0_4766_0,axiom,
( c_in(X1,X2,X3)
| c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X3,tc_bool)),X3) = c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4766]) ).
cnf(c_0_4766_1,axiom,
( c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X3,tc_bool)),X3) = c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool))
| c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4766]) ).
cnf(c_0_4767_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4767]) ).
cnf(c_0_4767_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),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_4767]) ).
cnf(c_0_4767_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4767]) ).
cnf(c_0_4768_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X2),c_HOL_Otimes__class_Otimes(X1,X1,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4768]) ).
cnf(c_0_4768_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X2),c_HOL_Otimes__class_Otimes(X1,X1,X2),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_4768]) ).
cnf(c_0_4768_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X2),c_HOL_Otimes__class_Otimes(X1,X1,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4768]) ).
cnf(c_0_4769_0,axiom,
( c_lessequals(X1,X2,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4769]) ).
cnf(c_0_4769_1,axiom,
( ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
| c_lessequals(X1,X2,tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4769]) ).
cnf(c_0_4770_0,axiom,
( c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4770]) ).
cnf(c_0_4770_1,axiom,
( ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
| c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4770]) ).
cnf(c_0_4771_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4771]) ).
cnf(c_0_4771_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4771]) ).
cnf(c_0_4772_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4772]) ).
cnf(c_0_4772_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4772]) ).
cnf(c_0_4773_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4773]) ).
cnf(c_0_4773_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4773]) ).
cnf(c_0_4774_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_4774]) ).
cnf(c_0_4774_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_4774]) ).
cnf(c_0_4775_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_4775]) ).
cnf(c_0_4775_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_4775]) ).
cnf(c_0_4776_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4776]) ).
cnf(c_0_4776_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4776]) ).
cnf(c_0_4777_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4),X2,X4) = c_Divides_Odiv__class_Omod(X1,X2,X4)
| ~ class_Divides_Osemiring__div(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4777]) ).
cnf(c_0_4777_1,axiom,
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4),X2,X4) = c_Divides_Odiv__class_Omod(X1,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4777]) ).
cnf(c_0_4778_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4),X3,X4) = c_Divides_Odiv__class_Omod(X1,X3,X4)
| ~ class_Divides_Osemiring__div(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4778]) ).
cnf(c_0_4778_1,axiom,
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4),X3,X4) = c_Divides_Odiv__class_Omod(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4778]) ).
cnf(c_0_4779_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3)
| ~ class_OrderedGroup_Olordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4779]) ).
cnf(c_0_4779_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4779]) ).
cnf(c_0_4780_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X2,X4),c_HOL_Oplus__class_Oplus(X1,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_OrderedGroup_Olordered__ab__group__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4780]) ).
cnf(c_0_4780_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X2,X4),c_HOL_Oplus__class_Oplus(X1,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4780]) ).
cnf(c_0_4781_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3)
| ~ class_OrderedGroup_Olordered__ab__group__add__meet(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4781]) ).
cnf(c_0_4781_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(X3)
| c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4781]) ).
cnf(c_0_4782_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X2,X4),c_HOL_Oplus__class_Oplus(X1,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_OrderedGroup_Olordered__ab__group__add__meet(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4782]) ).
cnf(c_0_4782_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(X4)
| c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X2,X4),c_HOL_Oplus__class_Oplus(X1,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4782]) ).
cnf(c_0_4783_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_4783]) ).
cnf(c_0_4783_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_4783]) ).
cnf(c_0_4783_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_4783]) ).
cnf(c_0_4784_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_4784]) ).
cnf(c_0_4784_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_4784]) ).
cnf(c_0_4784_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_4784]) ).
cnf(c_0_4785_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_4785]) ).
cnf(c_0_4785_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_4785]) ).
cnf(c_0_4785_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_4785]) ).
cnf(c_0_4786_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_4786]) ).
cnf(c_0_4786_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_4786]) ).
cnf(c_0_4786_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_4786]) ).
cnf(c_0_4787_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_4787]) ).
cnf(c_0_4787_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_4787]) ).
cnf(c_0_4787_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_4787]) ).
cnf(c_0_4788_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_4788]) ).
cnf(c_0_4788_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_4788]) ).
cnf(c_0_4788_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_4788]) ).
cnf(c_0_4789_0,axiom,
( c_lessequals(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_lessequals(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4789]) ).
cnf(c_0_4789_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4789]) ).
cnf(c_0_4789_2,axiom,
( ~ c_lessequals(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_lessequals(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_4789]) ).
cnf(c_0_4790_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4790]) ).
cnf(c_0_4790_1,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4790]) ).
cnf(c_0_4791_0,axiom,
( hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4791]) ).
cnf(c_0_4791_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4791]) ).
cnf(c_0_4791_2,axiom,
( ~ hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4791]) ).
cnf(c_0_4792_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(X3,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4792]) ).
cnf(c_0_4792_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X3,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4792]) ).
cnf(c_0_4792_2,axiom,
( ~ c_lessequals(X3,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4792]) ).
cnf(c_0_4793_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4793]) ).
cnf(c_0_4793_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4793]) ).
cnf(c_0_4793_2,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4793]) ).
cnf(c_0_4794_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X3,X4,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4794]) ).
cnf(c_0_4794_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat)
| ~ c_lessequals(X3,X4,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4794]) ).
cnf(c_0_4794_2,axiom,
( ~ c_lessequals(X3,X4,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4794]) ).
cnf(c_0_4795_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X4,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X3,X4,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4795]) ).
cnf(c_0_4795_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X4,tc_nat),tc_nat)
| ~ c_lessequals(X3,X4,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4795]) ).
cnf(c_0_4795_2,axiom,
( ~ c_lessequals(X3,X4,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X4,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4795]) ).
cnf(c_0_4796_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X4,tc_nat),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_4796]) ).
cnf(c_0_4796_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4796]) ).
cnf(c_0_4796_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(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X4,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4796]) ).
cnf(c_0_4797_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_4797]) ).
cnf(c_0_4797_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_4797]) ).
cnf(c_0_4797_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_4797]) ).
cnf(c_0_4797_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_4797]) ).
cnf(c_0_4798_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_4798]) ).
cnf(c_0_4798_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_4798]) ).
cnf(c_0_4798_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_4798]) ).
cnf(c_0_4798_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_4798]) ).
cnf(c_0_4799_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_4799]) ).
cnf(c_0_4799_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_4799]) ).
cnf(c_0_4800_0,axiom,
( c_in(X1,X2,X3)
| c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4800]) ).
cnf(c_0_4800_1,axiom,
( c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| c_in(X1,X2,X3)
| ~ c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4800]) ).
cnf(c_0_4800_2,axiom,
( ~ c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4800]) ).
cnf(c_0_4801_0,axiom,
( c_in(X2,X1,X4)
| c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4801]) ).
cnf(c_0_4801_1,axiom,
( c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| c_in(X2,X1,X4)
| ~ c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4801]) ).
cnf(c_0_4801_2,axiom,
( ~ c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| c_in(X2,X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4801]) ).
cnf(c_0_4802_0,axiom,
( X1 = X2
| ~ c_in(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4802]) ).
cnf(c_0_4802_1,axiom,
( ~ c_in(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4802]) ).
cnf(c_0_4810_0,axiom,
( c_in(X1,X2,X3)
| c_in(X1,X4,X3)
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4810]) ).
cnf(c_0_4810_1,axiom,
( c_in(X1,X4,X3)
| c_in(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4810]) ).
cnf(c_0_4810_2,axiom,
( c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool))
| c_in(X1,X4,X3)
| c_in(X1,X2,X3)
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4810]) ).
cnf(c_0_4810_3,axiom,
( ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool))
| c_in(X1,X4,X3)
| c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4810]) ).
cnf(c_0_4811_0,axiom,
( c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(X3,X2),c_Finite__Set_Ocard(X1,X2),tc_nat) = c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4811]) ).
cnf(c_0_4811_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(X3,X2),c_Finite__Set_Ocard(X1,X2),tc_nat) = c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2)
| ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4811]) ).
cnf(c_0_4811_2,axiom,
( ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(X3,X2),c_Finite__Set_Ocard(X1,X2),tc_nat) = c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4811]) ).
cnf(c_0_4812_0,axiom,
( X1 = X4
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4812]) ).
cnf(c_0_4812_1,axiom,
( hBOOL(hAPP(X2,X4))
| X1 = X4
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4812]) ).
cnf(c_0_4812_2,axiom,
( ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4))
| hBOOL(hAPP(X2,X4))
| X1 = X4 ),
inference(literals_permutation,[status(thm)],[c_0_4812]) ).
cnf(c_0_4813_0,axiom,
( c_lessequals(c_Set_Oinsert(X4,X1,X3),c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4813]) ).
cnf(c_0_4813_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Set_Oinsert(X4,X1,X3),c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4813]) ).
cnf(c_0_4814_0,axiom,
( ~ c_in(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4)
| ~ c_in(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4814]) ).
cnf(c_0_4814_1,axiom,
( ~ c_in(X1,X3,X4)
| ~ c_in(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4814]) ).
cnf(c_0_4815_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat) = X1
| ~ c_lessequals(X2,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4815]) ).
cnf(c_0_4815_1,axiom,
( ~ c_lessequals(X2,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_4815]) ).
cnf(c_0_4816_0,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat)
| ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4816]) ).
cnf(c_0_4816_1,axiom,
( ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4816]) ).
cnf(c_0_4817_0,axiom,
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4817]) ).
cnf(c_0_4817_1,axiom,
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4817]) ).
cnf(c_0_4818_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4818]) ).
cnf(c_0_4818_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4818]) ).
cnf(c_0_4819_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4819]) ).
cnf(c_0_4819_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4819]) ).
cnf(c_0_4820_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_4820]) ).
cnf(c_0_4820_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_4820]) ).
cnf(c_0_4820_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_4820]) ).
cnf(c_0_4820_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_4820]) ).
cnf(c_0_4821_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_4821]) ).
cnf(c_0_4821_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_4821]) ).
cnf(c_0_4821_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_4821]) ).
cnf(c_0_4821_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_4821]) ).
cnf(c_0_4822_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,X2,X3) = X4
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X5,X2,X3),X3) != c_HOL_Oplus__class_Oplus(X5,X4,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4822]) ).
cnf(c_0_4822_1,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X5,X2,X3),X3) != c_HOL_Oplus__class_Oplus(X5,X4,X3)
| c_HOL_Oplus__class_Oplus(X1,X2,X3) = X4
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4822]) ).
cnf(c_0_4822_2,axiom,
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X5,X2,X3),X3) != c_HOL_Oplus__class_Oplus(X5,X4,X3)
| c_HOL_Oplus__class_Oplus(X1,X2,X3) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_4822]) ).
cnf(c_0_4823_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),X1,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4823]) ).
cnf(c_0_4823_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),X1,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4823]) ).
cnf(c_0_4824_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),X1,tc_nat) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4824]) ).
cnf(c_0_4824_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),X1,tc_nat) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4824]) ).
cnf(c_0_4825_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),X2,tc_nat) = c_HOL_Ominus__class_Ominus(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4825]) ).
cnf(c_0_4825_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),X2,tc_nat) = c_HOL_Ominus__class_Ominus(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4825]) ).
cnf(c_0_4826_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),X1,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4826]) ).
cnf(c_0_4826_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),X1,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4826]) ).
cnf(c_0_4827_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),X1,tc_nat) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4827]) ).
cnf(c_0_4827_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),X1,tc_nat) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4827]) ).
cnf(c_0_4828_0,axiom,
( c_lessequals(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool))
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4828]) ).
cnf(c_0_4828_1,axiom,
( ~ c_in(X1,X2,X3)
| c_lessequals(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4828]) ).
cnf(c_0_4828_2,axiom,
( ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool))
| ~ c_in(X1,X2,X3)
| c_lessequals(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4828]) ).
cnf(c_0_4829_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4829]) ).
cnf(c_0_4829_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_in(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4829]) ).
cnf(c_0_4829_2,axiom,
( ~ c_in(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4829]) ).
cnf(c_0_4830_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4830]) ).
cnf(c_0_4830_1,axiom,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4830]) ).
cnf(c_0_4830_2,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4830]) ).
cnf(c_0_4830_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4830]) ).
cnf(c_0_4831_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4831]) ).
cnf(c_0_4831_1,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4831]) ).
cnf(c_0_4831_2,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4831]) ).
cnf(c_0_4831_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4831]) ).
cnf(c_0_4832_0,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4832]) ).
cnf(c_0_4832_1,axiom,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4832]) ).
cnf(c_0_4832_2,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4832]) ).
cnf(c_0_4832_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4832]) ).
cnf(c_0_4833_0,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4833]) ).
cnf(c_0_4833_1,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4833]) ).
cnf(c_0_4833_2,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4833]) ).
cnf(c_0_4833_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4833]) ).
cnf(c_0_4834_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4834]) ).
cnf(c_0_4834_1,axiom,
( c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4834]) ).
cnf(c_0_4834_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4834]) ).
cnf(c_0_4834_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_4834]) ).
cnf(c_0_4835_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4835]) ).
cnf(c_0_4835_1,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4835]) ).
cnf(c_0_4835_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4835]) ).
cnf(c_0_4835_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_4835]) ).
cnf(c_0_4836_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4836]) ).
cnf(c_0_4836_1,axiom,
( c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4836]) ).
cnf(c_0_4836_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4836]) ).
cnf(c_0_4836_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_4836]) ).
cnf(c_0_4837_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4837]) ).
cnf(c_0_4837_1,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4837]) ).
cnf(c_0_4837_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4837]) ).
cnf(c_0_4837_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_4837]) ).
cnf(c_0_4838_0,axiom,
( c_HOL_Oord__class_Oless(X3,X1,tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(X3,X2),c_Finite__Set_Ocard(X1,X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4838]) ).
cnf(c_0_4838_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_HOL_Oord__class_Oless(X3,X1,tc_fun(X2,tc_bool))
| ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(X3,X2),c_Finite__Set_Ocard(X1,X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4838]) ).
cnf(c_0_4838_2,axiom,
( ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_HOL_Oord__class_Oless(X3,X1,tc_fun(X2,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(X3,X2),c_Finite__Set_Ocard(X1,X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4838]) ).
cnf(c_0_4838_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(X3,X2),c_Finite__Set_Ocard(X1,X2),tc_nat)
| ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_HOL_Oord__class_Oless(X3,X1,tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4838]) ).
cnf(c_0_4839_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat)) = c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4839]) ).
cnf(c_0_4839_1,axiom,
( c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat)) = c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4839]) ).
cnf(c_0_4840_0,axiom,
( c_in(X1,X2,X4)
| ~ c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4840]) ).
cnf(c_0_4840_1,axiom,
( ~ c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4)
| c_in(X1,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4840]) ).
cnf(c_0_4841_0,axiom,
( c_in(X1,X3,X4)
| ~ c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4841]) ).
cnf(c_0_4841_1,axiom,
( ~ c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4)
| c_in(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4841]) ).
cnf(c_0_4842_0,axiom,
( c_in(X1,X2,X4)
| ~ c_in(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4842]) ).
cnf(c_0_4842_1,axiom,
( ~ c_in(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4)
| c_in(X1,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4842]) ).
cnf(c_0_4843_0,axiom,
( c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,X3)
| ~ c_in(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4843]) ).
cnf(c_0_4843_1,axiom,
( ~ c_in(X1,X2,X3)
| c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4843]) ).
cnf(c_0_4843_2,axiom,
( ~ c_in(X1,X4,X3)
| ~ c_in(X1,X2,X3)
| c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4843]) ).
cnf(c_0_4844_0,axiom,
( c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,X3)
| ~ c_in(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4844]) ).
cnf(c_0_4844_1,axiom,
( ~ c_in(X1,X2,X3)
| c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4844]) ).
cnf(c_0_4844_2,axiom,
( ~ c_in(X1,X4,X3)
| ~ c_in(X1,X2,X3)
| c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4844]) ).
cnf(c_0_4845_0,axiom,
( c_in(X1,c_Inductive_Ocomplete__lattice__class_Ogfp(X4,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X2,hAPP(X4,X2),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4845]) ).
cnf(c_0_4845_1,axiom,
( ~ c_in(X1,X2,X3)
| c_in(X1,c_Inductive_Ocomplete__lattice__class_Ogfp(X4,tc_fun(X3,tc_bool)),X3)
| ~ c_lessequals(X2,hAPP(X4,X2),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4845]) ).
cnf(c_0_4845_2,axiom,
( ~ c_lessequals(X2,hAPP(X4,X2),tc_fun(X3,tc_bool))
| ~ c_in(X1,X2,X3)
| c_in(X1,c_Inductive_Ocomplete__lattice__class_Ogfp(X4,tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4845]) ).
cnf(c_0_4846_0,axiom,
( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4846]) ).
cnf(c_0_4846_1,axiom,
( ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4846]) ).
cnf(c_0_4846_2,axiom,
( ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| c_lessequals(c_Suc(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_4846]) ).
cnf(c_0_4847_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_4847]) ).
cnf(c_0_4847_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_4847]) ).
cnf(c_0_4847_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_4847]) ).
cnf(c_0_4848_0,axiom,
( c_lessequals(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_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4848]) ).
cnf(c_0_4848_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(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_4848]) ).
cnf(c_0_4849_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_4849]) ).
cnf(c_0_4849_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_4849]) ).
cnf(c_0_4850_0,axiom,
( c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4850]) ).
cnf(c_0_4850_1,axiom,
( ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool))
| c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4850]) ).
cnf(c_0_4851_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4851]) ).
cnf(c_0_4851_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4851]) ).
cnf(c_0_4851_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4851]) ).
cnf(c_0_4851_3,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_4851]) ).
cnf(c_0_4852_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4852]) ).
cnf(c_0_4852_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4852]) ).
cnf(c_0_4852_2,axiom,
( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4852]) ).
cnf(c_0_4852_3,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4852]) ).
cnf(c_0_4853_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4853]) ).
cnf(c_0_4853_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4853]) ).
cnf(c_0_4853_2,axiom,
( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4853]) ).
cnf(c_0_4853_3,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4853]) ).
cnf(c_0_4854_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4854]) ).
cnf(c_0_4854_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4854]) ).
cnf(c_0_4854_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4854]) ).
cnf(c_0_4854_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_4854]) ).
cnf(c_0_4855_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4855]) ).
cnf(c_0_4855_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4855]) ).
cnf(c_0_4855_2,axiom,
( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4855]) ).
cnf(c_0_4855_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4855]) ).
cnf(c_0_4856_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4856]) ).
cnf(c_0_4856_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4856]) ).
cnf(c_0_4856_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4856]) ).
cnf(c_0_4856_3,axiom,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_4856]) ).
cnf(c_0_4857_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4857]) ).
cnf(c_0_4857_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4857]) ).
cnf(c_0_4857_2,axiom,
( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4857]) ).
cnf(c_0_4857_3,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4857]) ).
cnf(c_0_4858_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_4858]) ).
cnf(c_0_4858_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_4858]) ).
cnf(c_0_4858_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_4858]) ).
cnf(c_0_4858_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_4858]) ).
cnf(c_0_4859_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_4859]) ).
cnf(c_0_4859_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_4859]) ).
cnf(c_0_4859_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_4859]) ).
cnf(c_0_4859_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_4859]) ).
cnf(c_0_4860_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_4860]) ).
cnf(c_0_4860_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_4860]) ).
cnf(c_0_4860_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_4860]) ).
cnf(c_0_4860_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_4860]) ).
cnf(c_0_4861_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_4861]) ).
cnf(c_0_4861_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_4861]) ).
cnf(c_0_4861_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_4861]) ).
cnf(c_0_4861_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_4861]) ).
cnf(c_0_4862_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(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_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4862]) ).
cnf(c_0_4862_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_Oplus__class_Oplus(X2,X3,X1),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_4862]) ).
cnf(c_0_4862_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_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4862]) ).
cnf(c_0_4862_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),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_4862]) ).
cnf(c_0_4863_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4863]) ).
cnf(c_0_4863_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4863]) ).
cnf(c_0_4863_2,axiom,
( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4863]) ).
cnf(c_0_4863_3,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4863]) ).
cnf(c_0_4864_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4864]) ).
cnf(c_0_4864_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),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_4864]) ).
cnf(c_0_4864_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4864]) ).
cnf(c_0_4864_3,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4864]) ).
cnf(c_0_4865_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_4865]) ).
cnf(c_0_4865_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_4865]) ).
cnf(c_0_4865_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_4865]) ).
cnf(c_0_4865_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_4865]) ).
cnf(c_0_4866_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_4866]) ).
cnf(c_0_4866_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_4866]) ).
cnf(c_0_4866_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_4866]) ).
cnf(c_0_4866_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_4866]) ).
cnf(c_0_4867_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4867]) ).
cnf(c_0_4867_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4867]) ).
cnf(c_0_4867_2,axiom,
( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4867]) ).
cnf(c_0_4867_3,axiom,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_4867]) ).
cnf(c_0_4868_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4868]) ).
cnf(c_0_4868_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4868]) ).
cnf(c_0_4868_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4868]) ).
cnf(c_0_4868_3,axiom,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4868]) ).
cnf(c_0_4869_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4869]) ).
cnf(c_0_4869_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4869]) ).
cnf(c_0_4869_2,axiom,
( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4869]) ).
cnf(c_0_4869_3,axiom,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_4869]) ).
cnf(c_0_4870_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4870]) ).
cnf(c_0_4870_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4870]) ).
cnf(c_0_4870_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4870]) ).
cnf(c_0_4870_3,axiom,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4870]) ).
cnf(c_0_4871_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4871]) ).
cnf(c_0_4871_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4871]) ).
cnf(c_0_4871_2,axiom,
( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4871]) ).
cnf(c_0_4871_3,axiom,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_4871]) ).
cnf(c_0_4872_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4872]) ).
cnf(c_0_4872_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4872]) ).
cnf(c_0_4872_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4872]) ).
cnf(c_0_4872_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4872]) ).
cnf(c_0_4873_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4873]) ).
cnf(c_0_4873_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4873]) ).
cnf(c_0_4873_2,axiom,
( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4873]) ).
cnf(c_0_4873_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_4873]) ).
cnf(c_0_4874_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4874]) ).
cnf(c_0_4874_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_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4874]) ).
cnf(c_0_4874_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4874]) ).
cnf(c_0_4874_3,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_4874]) ).
cnf(c_0_4875_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4875]) ).
cnf(c_0_4875_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),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_4875]) ).
cnf(c_0_4875_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4875]) ).
cnf(c_0_4875_3,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_4875]) ).
cnf(c_0_4876_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(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(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4876]) ).
cnf(c_0_4876_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),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_4876]) ).
cnf(c_0_4876_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_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4876]) ).
cnf(c_0_4876_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(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4876]) ).
cnf(c_0_4877_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4877]) ).
cnf(c_0_4877_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4877]) ).
cnf(c_0_4877_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4877]) ).
cnf(c_0_4877_3,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_4877]) ).
cnf(c_0_4879_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),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4879]) ).
cnf(c_0_4879_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),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4879]) ).
cnf(c_0_4879_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),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_4879]) ).
cnf(c_0_4880_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_4880]) ).
cnf(c_0_4880_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_4880]) ).
cnf(c_0_4880_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_4880]) ).
cnf(c_0_4881_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_4881]) ).
cnf(c_0_4881_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_4881]) ).
cnf(c_0_4881_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_4881]) ).
cnf(c_0_4882_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),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_4882]) ).
cnf(c_0_4882_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4882]) ).
cnf(c_0_4882_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4882]) ).
cnf(c_0_4883_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4883]) ).
cnf(c_0_4883_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4883]) ).
cnf(c_0_4883_2,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4883]) ).
cnf(c_0_4884_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),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_4884]) ).
cnf(c_0_4884_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4884]) ).
cnf(c_0_4884_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4884]) ).
cnf(c_0_4885_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4885]) ).
cnf(c_0_4885_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4885]) ).
cnf(c_0_4885_2,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4885]) ).
cnf(c_0_4886_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4886]) ).
cnf(c_0_4886_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4886]) ).
cnf(c_0_4886_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4886]) ).
cnf(c_0_4887_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4887]) ).
cnf(c_0_4887_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4887]) ).
cnf(c_0_4887_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4887]) ).
cnf(c_0_4888_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4888]) ).
cnf(c_0_4888_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4888]) ).
cnf(c_0_4888_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4888]) ).
cnf(c_0_4889_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4889]) ).
cnf(c_0_4889_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4889]) ).
cnf(c_0_4889_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4889]) ).
cnf(c_0_4890_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_4890]) ).
cnf(c_0_4890_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_4890]) ).
cnf(c_0_4890_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_4890]) ).
cnf(c_0_4891_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_4891]) ).
cnf(c_0_4891_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_4891]) ).
cnf(c_0_4891_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_4891]) ).
cnf(c_0_4892_0,axiom,
( c_in(X1,X2,X3)
| c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4892]) ).
cnf(c_0_4892_1,axiom,
( c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| c_in(X1,X2,X3)
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4892]) ).
cnf(c_0_4892_2,axiom,
( ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4892]) ).
cnf(c_0_4893_0,axiom,
( c_in(X1,X2,X3)
| c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4893]) ).
cnf(c_0_4893_1,axiom,
( c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| c_in(X1,X2,X3)
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4893]) ).
cnf(c_0_4893_2,axiom,
( ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4893]) ).
cnf(c_0_4894_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_4894]) ).
cnf(c_0_4894_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_4894]) ).
cnf(c_0_4894_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_4894]) ).
cnf(c_0_4894_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_4894]) ).
cnf(c_0_4894_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_4894]) ).
cnf(c_0_4895_0,axiom,
( c_lessequals(X3,c_HOL_Oplus__class_Oplus(X4,X2,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4895]) ).
cnf(c_0_4895_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,c_HOL_Oplus__class_Oplus(X4,X2,X1),X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4895]) ).
cnf(c_0_4895_2,axiom,
( ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,c_HOL_Oplus__class_Oplus(X4,X2,X1),X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4895]) ).
cnf(c_0_4895_3,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,c_HOL_Oplus__class_Oplus(X4,X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4895]) ).
cnf(c_0_4895_4,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,c_HOL_Oplus__class_Oplus(X4,X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_4895]) ).
cnf(c_0_4896_0,axiom,
( c_lessequals(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4896]) ).
cnf(c_0_4896_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4896]) ).
cnf(c_0_4896_2,axiom,
( ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4896]) ).
cnf(c_0_4896_3,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4896]) ).
cnf(c_0_4896_4,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_4896]) ).
cnf(c_0_4897_0,axiom,
( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4897]) ).
cnf(c_0_4897_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4897]) ).
cnf(c_0_4897_2,axiom,
( ~ c_lessequals(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4897]) ).
cnf(c_0_4897_3,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4897]) ).
cnf(c_0_4897_4,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_4897]) ).
cnf(c_0_4898_0,axiom,
( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4898]) ).
cnf(c_0_4898_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4898]) ).
cnf(c_0_4898_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4898]) ).
cnf(c_0_4898_3,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4898]) ).
cnf(c_0_4898_4,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_4898]) ).
cnf(c_0_4899_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_4899]) ).
cnf(c_0_4899_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_4899]) ).
cnf(c_0_4900_0,axiom,
( hBOOL(hAPP(X3,X2))
| ~ c_lessequals(c_Suc(X1),X2,tc_nat)
| ~ hBOOL(hAPP(X3,c_Suc(c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1(X3,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_4900]) ).
cnf(c_0_4900_1,axiom,
( ~ c_lessequals(c_Suc(X1),X2,tc_nat)
| hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(X3,c_Suc(c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1(X3,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_4900]) ).
cnf(c_0_4900_2,axiom,
( ~ hBOOL(hAPP(X3,c_Suc(c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1(X3,X1))))
| ~ c_lessequals(c_Suc(X1),X2,tc_nat)
| hBOOL(hAPP(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4900]) ).
cnf(c_0_4901_0,axiom,
( hBOOL(hAPP(X1,c_Suc(c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1(X1))))
| hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4901]) ).
cnf(c_0_4901_1,axiom,
( hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)))
| hBOOL(hAPP(X1,c_Suc(c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1(X1))))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4901]) ).
cnf(c_0_4901_2,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)))
| hBOOL(hAPP(X1,c_Suc(c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_4901]) ).
cnf(c_0_4902_0,axiom,
( hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_4902]) ).
cnf(c_0_4902_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_4902]) ).
cnf(c_0_4902_2,axiom,
( ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1(X1)))
| ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat))) ),
inference(literals_permutation,[status(thm)],[c_0_4902]) ).
cnf(c_0_4903_0,axiom,
( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(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__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4903]) ).
cnf(c_0_4903_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4903]) ).
cnf(c_0_4903_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,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4903]) ).
cnf(c_0_4903_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,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_4903]) ).
cnf(c_0_4904_0,axiom,
( c_in(X1,X4,X3)
| c_in(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4904]) ).
cnf(c_0_4904_1,axiom,
( c_in(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3)
| c_in(X1,X4,X3)
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4904]) ).
cnf(c_0_4904_2,axiom,
( ~ c_in(X1,X2,X3)
| c_in(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3)
| c_in(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4904]) ).
cnf(c_0_4905_0,axiom,
( c_in(X1,X4,X3)
| c_in(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4905]) ).
cnf(c_0_4905_1,axiom,
( c_in(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3)
| c_in(X1,X4,X3)
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4905]) ).
cnf(c_0_4905_2,axiom,
( ~ c_in(X1,X2,X3)
| c_in(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3)
| c_in(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4905]) ).
cnf(c_0_4906_0,axiom,
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X3,tc_bool))
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4906]) ).
cnf(c_0_4906_1,axiom,
( ~ c_in(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4906]) ).
cnf(c_0_4907_0,axiom,
( c_in(X1,X4,X3)
| ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4907]) ).
cnf(c_0_4907_1,axiom,
( ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool))
| c_in(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4907]) ).
cnf(c_0_4908_0,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4908]) ).
cnf(c_0_4908_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4908]) ).
cnf(c_0_4909_0,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4909]) ).
cnf(c_0_4909_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4909]) ).
cnf(c_0_4910_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4910]) ).
cnf(c_0_4910_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4910]) ).
cnf(c_0_4911_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4911]) ).
cnf(c_0_4911_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4911]) ).
cnf(c_0_4912_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4912]) ).
cnf(c_0_4912_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(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_4912]) ).
cnf(c_0_4913_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4913]) ).
cnf(c_0_4913_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(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_4913]) ).
cnf(c_0_4914_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4914]) ).
cnf(c_0_4914_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(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_4914]) ).
cnf(c_0_4915_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4915]) ).
cnf(c_0_4915_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(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_4915]) ).
cnf(c_0_4916_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4916]) ).
cnf(c_0_4916_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4916]) ).
cnf(c_0_4917_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4917]) ).
cnf(c_0_4917_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4917]) ).
cnf(c_0_4918_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_4918]) ).
cnf(c_0_4918_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_4918]) ).
cnf(c_0_4919_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X3),X3),X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4919]) ).
cnf(c_0_4919_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X3),X3),X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4919]) ).
cnf(c_0_4920_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X2,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X3),X3),X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4920]) ).
cnf(c_0_4920_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X2,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X3),X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4920]) ).
cnf(c_0_4921_0,axiom,
( c_lessequals(c_Finite__Set_Ocard(X1,X2),c_Finite__Set_Ocard(c_Set_Oinsert(X3,X1,X2),X2),tc_nat)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4921]) ).
cnf(c_0_4921_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_lessequals(c_Finite__Set_Ocard(X1,X2),c_Finite__Set_Ocard(c_Set_Oinsert(X3,X1,X2),X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4921]) ).
cnf(c_0_4922_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(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_Ring__and__Field_Ocomm__ring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4922]) ).
cnf(c_0_4922_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4922]) ).
cnf(c_0_4922_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_HOL_Ominus__class_Ominus(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4922]) ).
cnf(c_0_4922_3,axiom,
( ~ class_Ring__and__Field_Ocomm__ring__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,c_HOL_Ominus__class_Ominus(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4922]) ).
cnf(c_0_4923_0,axiom,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4923]) ).
cnf(c_0_4923_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4923]) ).
cnf(c_0_4923_2,axiom,
( ~ c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4923]) ).
cnf(c_0_4923_3,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| ~ c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4923]) ).
cnf(c_0_4924_0,axiom,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4924]) ).
cnf(c_0_4924_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4924]) ).
cnf(c_0_4924_2,axiom,
( ~ c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4924]) ).
cnf(c_0_4924_3,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| ~ c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4924]) ).
cnf(c_0_4925_0,axiom,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4925]) ).
cnf(c_0_4925_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4925]) ).
cnf(c_0_4925_2,axiom,
( ~ c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4925]) ).
cnf(c_0_4925_3,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| ~ c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4925]) ).
cnf(c_0_4926_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(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_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4926]) ).
cnf(c_0_4926_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),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_4926]) ).
cnf(c_0_4926_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_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4926]) ).
cnf(c_0_4926_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,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4926]) ).
cnf(c_0_4927_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_4927]) ).
cnf(c_0_4927_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_4927]) ).
cnf(c_0_4927_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_4927]) ).
cnf(c_0_4927_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_4927]) ).
cnf(c_0_4928_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_4928]) ).
cnf(c_0_4928_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_4928]) ).
cnf(c_0_4928_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_4928]) ).
cnf(c_0_4928_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_4928]) ).
cnf(c_0_4929_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_4929]) ).
cnf(c_0_4929_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_4929]) ).
cnf(c_0_4929_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_4929]) ).
cnf(c_0_4930_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_4930]) ).
cnf(c_0_4930_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_4930]) ).
cnf(c_0_4930_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_4930]) ).
cnf(c_0_4931_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_4931]) ).
cnf(c_0_4931_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_4931]) ).
cnf(c_0_4931_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_4931]) ).
cnf(c_0_4932_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3)
| ~ c_in(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4932]) ).
cnf(c_0_4932_1,axiom,
( ~ c_in(X4,X1,X3)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_in(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4932]) ).
cnf(c_0_4932_2,axiom,
( ~ c_in(X4,X2,X3)
| ~ c_in(X4,X1,X3)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4932]) ).
cnf(c_0_4933_0,axiom,
( X1 = X2
| ~ c_lessequals(X3,X1,tc_nat)
| ~ c_lessequals(X3,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(X1,X3,tc_nat) != c_HOL_Ominus__class_Ominus(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4933]) ).
cnf(c_0_4933_1,axiom,
( ~ c_lessequals(X3,X1,tc_nat)
| X1 = X2
| ~ c_lessequals(X3,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(X1,X3,tc_nat) != c_HOL_Ominus__class_Ominus(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4933]) ).
cnf(c_0_4933_2,axiom,
( ~ c_lessequals(X3,X2,tc_nat)
| ~ c_lessequals(X3,X1,tc_nat)
| X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X3,tc_nat) != c_HOL_Ominus__class_Ominus(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4933]) ).
cnf(c_0_4933_3,axiom,
( c_HOL_Ominus__class_Ominus(X1,X3,tc_nat) != c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)
| ~ c_lessequals(X3,X2,tc_nat)
| ~ c_lessequals(X3,X1,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4933]) ).
cnf(c_0_4934_0,axiom,
( X1 = X2
| c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) != c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4934]) ).
cnf(c_0_4934_1,axiom,
( c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) != c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4934]) ).
cnf(c_0_4935_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4935]) ).
cnf(c_0_4935_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4935]) ).
cnf(c_0_4935_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4935]) ).
cnf(c_0_4936_0,axiom,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4936]) ).
cnf(c_0_4936_1,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4936]) ).
cnf(c_0_4936_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4936]) ).
cnf(c_0_4937_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_Oplus__class_Oplus(X2,X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4937]) ).
cnf(c_0_4937_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),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_4937]) ).
cnf(c_0_4937_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_4937]) ).
cnf(c_0_4938_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4938]) ).
cnf(c_0_4938_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),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_4938]) ).
cnf(c_0_4938_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4938]) ).
cnf(c_0_4939_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4939]) ).
cnf(c_0_4939_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),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_4939]) ).
cnf(c_0_4939_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4939]) ).
cnf(c_0_4940_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4940]) ).
cnf(c_0_4940_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4940]) ).
cnf(c_0_4940_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_4940]) ).
cnf(c_0_4942_0,axiom,
( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_lessequals(c_Suc(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_4942]) ).
cnf(c_0_4942_1,axiom,
( ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4942]) ).
cnf(c_0_4943_0,axiom,
( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
| ~ c_lessequals(c_Suc(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_4943]) ).
cnf(c_0_4943_1,axiom,
( ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4943]) ).
cnf(c_0_4944_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_4944]) ).
cnf(c_0_4944_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_4944]) ).
cnf(c_0_4945_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_4945]) ).
cnf(c_0_4945_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_4945]) ).
cnf(c_0_4946_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_4946]) ).
cnf(c_0_4946_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_4946]) ).
cnf(c_0_4947_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_4947]) ).
cnf(c_0_4947_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_4947]) ).
cnf(c_0_4948_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_4948]) ).
cnf(c_0_4948_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_4948]) ).
cnf(c_0_4949_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_4949]) ).
cnf(c_0_4949_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_4949]) ).
cnf(c_0_4950_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4950]) ).
cnf(c_0_4950_1,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4950]) ).
cnf(c_0_4951_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4951]) ).
cnf(c_0_4951_1,axiom,
( ~ class_Lattices_Olower__semilattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4951]) ).
cnf(c_0_4952_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4),X4)
| ~ class_Lattices_Olattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4952]) ).
cnf(c_0_4952_1,axiom,
( ~ class_Lattices_Olattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4952]) ).
cnf(c_0_4953_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4953]) ).
cnf(c_0_4953_1,axiom,
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4953]) ).
cnf(c_0_4954_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4954]) ).
cnf(c_0_4954_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4954]) ).
cnf(c_0_4955_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4955]) ).
cnf(c_0_4955_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4955]) ).
cnf(c_0_4956_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4956]) ).
cnf(c_0_4956_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4956]) ).
cnf(c_0_4957_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4957]) ).
cnf(c_0_4957_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4957]) ).
cnf(c_0_4958_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_OrderedGroup_Oab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4958]) ).
cnf(c_0_4958_1,axiom,
( ~ class_OrderedGroup_Oab__semigroup__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4958]) ).
cnf(c_0_4959_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4959]) ).
cnf(c_0_4959_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4959]) ).
cnf(c_0_4960_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4960]) ).
cnf(c_0_4960_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4960]) ).
cnf(c_0_4961_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4)
| ~ class_OrderedGroup_Oab__group__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4961]) ).
cnf(c_0_4961_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4961]) ).
cnf(c_0_4962_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4962]) ).
cnf(c_0_4962_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4962]) ).
cnf(c_0_4963_0,axiom,
( c_HOL_Oplus__class_Oplus(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) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4963]) ).
cnf(c_0_4963_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Oplus__class_Oplus(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) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4963]) ).
cnf(c_0_4964_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_4964]) ).
cnf(c_0_4964_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_4964]) ).
cnf(c_0_4964_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_4964]) ).
cnf(c_0_4964_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_4964]) ).
cnf(c_0_4964_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_4964]) ).
cnf(c_0_4969_0,axiom,
( c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4969]) ).
cnf(c_0_4969_1,axiom,
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4969]) ).
cnf(c_0_4969_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4969]) ).
cnf(c_0_4970_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4970]) ).
cnf(c_0_4970_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4970]) ).
cnf(c_0_4970_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4970]) ).
cnf(c_0_4972_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),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_4972]) ).
cnf(c_0_4972_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4972]) ).
cnf(c_0_4972_2,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(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_4972]) ).
cnf(c_0_4974_0,axiom,
( c_lessequals(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4974]) ).
cnf(c_0_4974_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4974]) ).
cnf(c_0_4974_2,axiom,
( ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4974]) ).
cnf(c_0_4975_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4975]) ).
cnf(c_0_4975_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4975]) ).
cnf(c_0_4975_2,axiom,
( ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4975]) ).
cnf(c_0_4976_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4976]) ).
cnf(c_0_4976_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4976]) ).
cnf(c_0_4976_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4976]) ).
cnf(c_0_4977_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4977]) ).
cnf(c_0_4977_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4977]) ).
cnf(c_0_4977_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X4,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4977]) ).
cnf(c_0_4978_0,axiom,
( c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X5,X4,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4978]) ).
cnf(c_0_4978_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X5,X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X5,X4,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4978]) ).
cnf(c_0_4978_2,axiom,
( c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X5,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4978]) ).
cnf(c_0_4978_3,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X5,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4978]) ).
cnf(c_0_4979_0,axiom,
( c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X5,X4,X3) != c_HOL_Ominus__class_Ominus(X2,X1,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4979]) ).
cnf(c_0_4979_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X5,X3)
| c_HOL_Ominus__class_Ominus(X5,X4,X3) != c_HOL_Ominus__class_Ominus(X2,X1,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4979]) ).
cnf(c_0_4979_2,axiom,
( c_HOL_Ominus__class_Ominus(X5,X4,X3) != c_HOL_Ominus__class_Ominus(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4979]) ).
cnf(c_0_4979_3,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X5,X4,X3) != c_HOL_Ominus__class_Ominus(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4979]) ).
cnf(c_0_4980_0,axiom,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4980]) ).
cnf(c_0_4980_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4980]) ).
cnf(c_0_4980_2,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4980]) ).
cnf(c_0_4980_3,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4980]) ).
cnf(c_0_4981_0,axiom,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4981]) ).
cnf(c_0_4981_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3)
| c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4981]) ).
cnf(c_0_4981_2,axiom,
( c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4981]) ).
cnf(c_0_4981_3,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4981]) ).
cnf(c_0_4982_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_lessequals(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_4982]) ).
cnf(c_0_4982_1,axiom,
( c_lessequals(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_4982]) ).
cnf(c_0_4983_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_lessequals(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_4983]) ).
cnf(c_0_4983_1,axiom,
( c_lessequals(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) ),
inference(literals_permutation,[status(thm)],[c_0_4983]) ).
cnf(c_0_4984_0,axiom,
( c_in(X1,X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4984]) ).
cnf(c_0_4984_1,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool))
| c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4984]) ).
cnf(c_0_4985_0,axiom,
( c_in(X1,X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4985]) ).
cnf(c_0_4985_1,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool))
| c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4985]) ).
cnf(c_0_4986_0,axiom,
( c_lessequals(X1,X3,X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4986]) ).
cnf(c_0_4986_1,axiom,
( ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| c_lessequals(X1,X3,X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4986]) ).
cnf(c_0_4986_2,axiom,
( ~ class_Lattices_Olower__semilattice(X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| c_lessequals(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4986]) ).
cnf(c_0_4987_0,axiom,
( c_lessequals(X1,X2,X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4987]) ).
cnf(c_0_4987_1,axiom,
( ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| c_lessequals(X1,X2,X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4987]) ).
cnf(c_0_4987_2,axiom,
( ~ class_Lattices_Olower__semilattice(X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| c_lessequals(X1,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4987]) ).
cnf(c_0_4988_0,axiom,
( c_lessequals(X1,X3,X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4988]) ).
cnf(c_0_4988_1,axiom,
( ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| c_lessequals(X1,X3,X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4988]) ).
cnf(c_0_4988_2,axiom,
( ~ class_Lattices_Olower__semilattice(X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| c_lessequals(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4988]) ).
cnf(c_0_4989_0,axiom,
( c_lessequals(X1,X2,X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4989]) ).
cnf(c_0_4989_1,axiom,
( ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| c_lessequals(X1,X2,X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4989]) ).
cnf(c_0_4989_2,axiom,
( ~ class_Lattices_Olower__semilattice(X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| c_lessequals(X1,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4989]) ).
cnf(c_0_4990_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_4990]) ).
cnf(c_0_4990_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_4990]) ).
cnf(c_0_4990_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_4990]) ).
cnf(c_0_4991_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_4991]) ).
cnf(c_0_4991_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_4991]) ).
cnf(c_0_4991_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_4991]) ).
cnf(c_0_4992_0,axiom,
( c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(X2,X3),c_Nat_Osemiring__1__class_Oof__nat(X1,X3),X3) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ class_Ring__and__Field_Oring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4992]) ).
cnf(c_0_4992_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(X2,X3),c_Nat_Osemiring__1__class_Oof__nat(X1,X3),X3) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3)
| ~ class_Ring__and__Field_Oring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4992]) ).
cnf(c_0_4992_2,axiom,
( ~ class_Ring__and__Field_Oring__1(X3)
| ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(X2,X3),c_Nat_Osemiring__1__class_Oof__nat(X1,X3),X3) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4992]) ).
cnf(c_0_5000_0,axiom,
( X3 = X1
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool))
| ~ c_lessequals(c_Finite__Set_Ocard(X1,X2),c_Finite__Set_Ocard(X3,X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5000]) ).
cnf(c_0_5000_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| X3 = X1
| ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool))
| ~ c_lessequals(c_Finite__Set_Ocard(X1,X2),c_Finite__Set_Ocard(X3,X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5000]) ).
cnf(c_0_5000_2,axiom,
( ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| X3 = X1
| ~ c_lessequals(c_Finite__Set_Ocard(X1,X2),c_Finite__Set_Ocard(X3,X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5000]) ).
cnf(c_0_5000_3,axiom,
( ~ c_lessequals(c_Finite__Set_Ocard(X1,X2),c_Finite__Set_Ocard(X3,X2),tc_nat)
| ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| X3 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_5000]) ).
cnf(c_0_5001_0,axiom,
( X1 = X2
| c_in(X1,X3,X4)
| ~ c_in(X1,c_Set_Oinsert(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5001]) ).
cnf(c_0_5001_1,axiom,
( c_in(X1,X3,X4)
| X1 = X2
| ~ c_in(X1,c_Set_Oinsert(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5001]) ).
cnf(c_0_5001_2,axiom,
( ~ c_in(X1,c_Set_Oinsert(X2,X3,X4),X4)
| c_in(X1,X3,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5001]) ).
cnf(c_0_5002_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_5002]) ).
cnf(c_0_5002_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_5002]) ).
cnf(c_0_5002_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_5002]) ).
cnf(c_0_5003_0,axiom,
( hBOOL(hAPP(X3,c_Suc(c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X3,X2))))
| hBOOL(hAPP(X3,X1))
| ~ c_lessequals(X1,X2,tc_nat)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5003]) ).
cnf(c_0_5003_1,axiom,
( hBOOL(hAPP(X3,X1))
| hBOOL(hAPP(X3,c_Suc(c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X3,X2))))
| ~ c_lessequals(X1,X2,tc_nat)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5003]) ).
cnf(c_0_5003_2,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| hBOOL(hAPP(X3,X1))
| hBOOL(hAPP(X3,c_Suc(c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X3,X2))))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5003]) ).
cnf(c_0_5003_3,axiom,
( ~ hBOOL(hAPP(X3,X2))
| ~ c_lessequals(X1,X2,tc_nat)
| hBOOL(hAPP(X3,X1))
| hBOOL(hAPP(X3,c_Suc(c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X3,X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_5003]) ).
cnf(c_0_5004_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_5004]) ).
cnf(c_0_5004_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_5004]) ).
cnf(c_0_5005_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_5005]) ).
cnf(c_0_5005_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_5005]) ).
cnf(c_0_5008_0,axiom,
( c_lessequals(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_5008]) ).
cnf(c_0_5008_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_5008]) ).
cnf(c_0_5009_0,axiom,
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5009]) ).
cnf(c_0_5009_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5009]) ).
cnf(c_0_5010_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_5010]) ).
cnf(c_0_5010_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_5010]) ).
cnf(c_0_5010_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_5010]) ).
cnf(c_0_5010_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_5010]) ).
cnf(c_0_5011_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_5011]) ).
cnf(c_0_5011_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_5011]) ).
cnf(c_0_5011_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_5011]) ).
cnf(c_0_5011_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_5011]) ).
cnf(c_0_5012_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X4,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5012]) ).
cnf(c_0_5012_1,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X4,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5012]) ).
cnf(c_0_5012_2,axiom,
( c_HOL_Oplus__class_Oplus(X1,X4,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat)
| ~ 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_5012]) ).
cnf(c_0_5013_0,axiom,
( c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5013]) ).
cnf(c_0_5013_1,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat)
| c_lessequals(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5013]) ).
cnf(c_0_5014_0,axiom,
( c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5014]) ).
cnf(c_0_5014_1,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat)
| c_lessequals(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5014]) ).
cnf(c_0_5015_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5015]) ).
cnf(c_0_5015_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5015]) ).
cnf(c_0_5016_0,axiom,
( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5016]) ).
cnf(c_0_5016_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat)
| c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5016]) ).
cnf(c_0_5017_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_5017]) ).
cnf(c_0_5017_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_5017]) ).
cnf(c_0_5018_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_5018]) ).
cnf(c_0_5018_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_5018]) ).
cnf(c_0_5019_0,axiom,
( c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5019]) ).
cnf(c_0_5019_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5019]) ).
cnf(c_0_5019_2,axiom,
( ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5019]) ).
cnf(c_0_5021_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_5021]) ).
cnf(c_0_5021_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_5021]) ).
cnf(c_0_5022_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| c_HOL_Oplus__class_Oplus(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5022]) ).
cnf(c_0_5022_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| c_HOL_Oplus__class_Oplus(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5022]) ).
cnf(c_0_5022_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5022]) ).
cnf(c_0_5022_3,axiom,
( c_HOL_Oplus__class_Oplus(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5022]) ).
cnf(c_0_5022_4,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| c_HOL_Oplus__class_Oplus(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5022]) ).
cnf(c_0_5023_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| c_HOL_Oplus__class_Oplus(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5023]) ).
cnf(c_0_5023_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| c_HOL_Oplus__class_Oplus(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5023]) ).
cnf(c_0_5023_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5023]) ).
cnf(c_0_5023_3,axiom,
( c_HOL_Oplus__class_Oplus(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5023]) ).
cnf(c_0_5023_4,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| c_HOL_Oplus__class_Oplus(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5023]) ).
cnf(c_0_5024_0,axiom,
( c_lessequals(X2,X1,tc_fun(X3,X4))
| c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4))
| ~ c_lessequals(X1,X2,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5024]) ).
cnf(c_0_5024_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4))
| c_lessequals(X2,X1,tc_fun(X3,X4))
| ~ c_lessequals(X1,X2,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5024]) ).
cnf(c_0_5024_2,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,X4))
| c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4))
| c_lessequals(X2,X1,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5024]) ).
cnf(c_0_5024_3,axiom,
( ~ class_HOL_Oord(X4)
| ~ c_lessequals(X1,X2,tc_fun(X3,X4))
| c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4))
| c_lessequals(X2,X1,tc_fun(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5024]) ).
cnf(c_0_5025_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X1,tc_nat) = c_Divides_Odiv__class_Omod(X2,X1,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5025]) ).
cnf(c_0_5025_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X1,tc_nat) = c_Divides_Odiv__class_Omod(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5025]) ).
cnf(c_0_5027_0,axiom,
( hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5027]) ).
cnf(c_0_5027_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5027]) ).
cnf(c_0_5028_0,axiom,
( hBOOL(hAPP(X3,X1))
| ~ c_lessequals(X1,X2,tc_nat)
| ~ hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X3,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5028]) ).
cnf(c_0_5028_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| hBOOL(hAPP(X3,X1))
| ~ hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X3,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5028]) ).
cnf(c_0_5028_2,axiom,
( ~ hBOOL(hAPP(X3,X2))
| ~ c_lessequals(X1,X2,tc_nat)
| hBOOL(hAPP(X3,X1))
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X3,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5028]) ).
cnf(c_0_5028_3,axiom,
( ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X3,X2)))
| ~ hBOOL(hAPP(X3,X2))
| ~ c_lessequals(X1,X2,tc_nat)
| hBOOL(hAPP(X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5028]) ).
cnf(c_0_5029_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1),tc_nat)
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5029]) ).
cnf(c_0_5029_1,axiom,
( ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5029]) ).
cnf(c_0_5030_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5030]) ).
cnf(c_0_5030_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5030]) ).
cnf(c_0_5030_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5030]) ).
cnf(c_0_5030_3,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oplus__class_Oplus(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_5030]) ).
cnf(c_0_5031_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X2,X3),c_Finite__Set_Olinorder__class_OMin(X1,X3),X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5031]) ).
cnf(c_0_5031_1,axiom,
( c_lessequals(c_Finite__Set_Olinorder__class_OMin(X2,X3),c_Finite__Set_Olinorder__class_OMin(X1,X3),X3)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5031]) ).
cnf(c_0_5031_2,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X2,X3),c_Finite__Set_Olinorder__class_OMin(X1,X3),X3)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5031]) ).
cnf(c_0_5031_3,axiom,
( ~ c_Finite__Set_Ofinite(X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X2,X3),c_Finite__Set_Olinorder__class_OMin(X1,X3),X3)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5031]) ).
cnf(c_0_5031_4,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X2,X3),c_Finite__Set_Olinorder__class_OMin(X1,X3),X3)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_5031]) ).
cnf(c_0_5032_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_lessequals(c_Finite__Set_Olinorder__class_OMax(X1,X3),c_Finite__Set_Olinorder__class_OMax(X2,X3),X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5032]) ).
cnf(c_0_5032_1,axiom,
( c_lessequals(c_Finite__Set_Olinorder__class_OMax(X1,X3),c_Finite__Set_Olinorder__class_OMax(X2,X3),X3)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5032]) ).
cnf(c_0_5032_2,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Finite__Set_Olinorder__class_OMax(X1,X3),c_Finite__Set_Olinorder__class_OMax(X2,X3),X3)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5032]) ).
cnf(c_0_5032_3,axiom,
( ~ c_Finite__Set_Ofinite(X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Finite__Set_Olinorder__class_OMax(X1,X3),c_Finite__Set_Olinorder__class_OMax(X2,X3),X3)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5032]) ).
cnf(c_0_5032_4,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Finite__Set_Olinorder__class_OMax(X1,X3),c_Finite__Set_Olinorder__class_OMax(X2,X3),X3)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_5032]) ).
cnf(c_0_5033_0,axiom,
( X1 = X2
| c_in(X3,X1,X4)
| c_in(X3,X2,X4)
| c_Set_Oinsert(X3,X1,X4) != c_Set_Oinsert(X3,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5033]) ).
cnf(c_0_5033_1,axiom,
( c_in(X3,X1,X4)
| X1 = X2
| c_in(X3,X2,X4)
| c_Set_Oinsert(X3,X1,X4) != c_Set_Oinsert(X3,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5033]) ).
cnf(c_0_5033_2,axiom,
( c_in(X3,X2,X4)
| c_in(X3,X1,X4)
| X1 = X2
| c_Set_Oinsert(X3,X1,X4) != c_Set_Oinsert(X3,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5033]) ).
cnf(c_0_5033_3,axiom,
( c_Set_Oinsert(X3,X1,X4) != c_Set_Oinsert(X3,X2,X4)
| c_in(X3,X2,X4)
| c_in(X3,X1,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5033]) ).
cnf(c_0_5034_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_5034]) ).
cnf(c_0_5034_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_5034]) ).
cnf(c_0_5035_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_5035]) ).
cnf(c_0_5035_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_5035]) ).
cnf(c_0_5035_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_5035]) ).
cnf(c_0_5035_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_5035]) ).
cnf(c_0_5036_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_5036]) ).
cnf(c_0_5036_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_5036]) ).
cnf(c_0_5036_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_5036]) ).
cnf(c_0_5036_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_5036]) ).
cnf(c_0_5038_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5038]) ).
cnf(c_0_5038_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5038]) ).
cnf(c_0_5038_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5038]) ).
cnf(c_0_5039_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),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_5039]) ).
cnf(c_0_5039_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_Oplus__class_Oplus(X2,X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5039]) ).
cnf(c_0_5039_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),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5039]) ).
cnf(c_0_5040_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),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_5040]) ).
cnf(c_0_5040_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5040]) ).
cnf(c_0_5040_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(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5040]) ).
cnf(c_0_5041_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),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_5041]) ).
cnf(c_0_5041_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5041]) ).
cnf(c_0_5041_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(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5041]) ).
cnf(c_0_5042_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_5042]) ).
cnf(c_0_5042_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_5042]) ).
cnf(c_0_5043_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5043]) ).
cnf(c_0_5043_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5043]) ).
cnf(c_0_5043_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5043]) ).
cnf(c_0_5047_0,axiom,
( c_lessequals(X3,X1,X2)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeast(X1,X2),c_SetInterval_Oord__class_OatLeast(X3,X2),tc_fun(X2,tc_bool))
| ~ class_Orderings_Oorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5047]) ).
cnf(c_0_5047_1,axiom,
( ~ c_lessequals(c_SetInterval_Oord__class_OatLeast(X1,X2),c_SetInterval_Oord__class_OatLeast(X3,X2),tc_fun(X2,tc_bool))
| c_lessequals(X3,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5047]) ).
cnf(c_0_5047_2,axiom,
( ~ class_Orderings_Oorder(X2)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeast(X1,X2),c_SetInterval_Oord__class_OatLeast(X3,X2),tc_fun(X2,tc_bool))
| c_lessequals(X3,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5047]) ).
cnf(c_0_5049_0,axiom,
( c_in(X4,X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5049]) ).
cnf(c_0_5049_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_in(X4,X2,X3)
| ~ c_in(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5049]) ).
cnf(c_0_5049_2,axiom,
( ~ c_in(X4,X1,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_in(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5049]) ).
cnf(c_0_5050_0,axiom,
( c_in(X4,X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5050]) ).
cnf(c_0_5050_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_in(X4,X2,X3)
| ~ c_in(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5050]) ).
cnf(c_0_5050_2,axiom,
( ~ c_in(X4,X1,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_in(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5050]) ).
cnf(c_0_5051_0,axiom,
( c_in(X1,X4,X3)
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_5051]) ).
cnf(c_0_5051_1,axiom,
( ~ c_in(X1,X2,X3)
| c_in(X1,X4,X3)
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_5051]) ).
cnf(c_0_5051_2,axiom,
( ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_in(X1,X2,X3)
| c_in(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5051]) ).
cnf(c_0_5052_0,axiom,
( c_in(X4,X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5052]) ).
cnf(c_0_5052_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_in(X4,X2,X3)
| ~ c_in(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5052]) ).
cnf(c_0_5052_2,axiom,
( ~ c_in(X4,X1,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_in(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5052]) ).
cnf(c_0_5053_0,axiom,
( c_in(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5053]) ).
cnf(c_0_5053_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_in(X4,X2,X3)
| ~ c_in(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5053]) ).
cnf(c_0_5053_2,axiom,
( ~ c_in(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_in(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5053]) ).
cnf(c_0_5054_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat) = c_Divides_Odiv__class_Omod(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5054]) ).
cnf(c_0_5054_1,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat) = c_Divides_Odiv__class_Omod(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5054]) ).
cnf(c_0_5055_0,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5055]) ).
cnf(c_0_5055_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5055]) ).
cnf(c_0_5055_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5055]) ).
cnf(c_0_5056_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4))
| ~ c_lessequals(X2,X1,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5056]) ).
cnf(c_0_5056_1,axiom,
( ~ c_lessequals(X2,X1,tc_fun(X3,X4))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5056]) ).
cnf(c_0_5056_2,axiom,
( ~ class_HOL_Oord(X4)
| ~ c_lessequals(X2,X1,tc_fun(X3,X4))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5056]) ).
cnf(c_0_5057_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5057]) ).
cnf(c_0_5057_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5057]) ).
cnf(c_0_5057_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5057]) ).
cnf(c_0_5058_0,axiom,
( X1 = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2)
| c_Finite__Set_Ocard(X1,X2) != c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5058]) ).
cnf(c_0_5058_1,axiom,
( ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2)
| X1 = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))
| c_Finite__Set_Ocard(X1,X2) != c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5058]) ).
cnf(c_0_5058_2,axiom,
( c_Finite__Set_Ocard(X1,X2) != c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2)
| X1 = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_5058]) ).
cnf(c_0_5059_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Suc(X2),tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5059]) ).
cnf(c_0_5059_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Suc(X2),tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5059]) ).
cnf(c_0_5060_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_5060]) ).
cnf(c_0_5060_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_5060]) ).
cnf(c_0_5060_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_5060]) ).
cnf(c_0_5062_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_5062]) ).
cnf(c_0_5062_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_5062]) ).
cnf(c_0_5062_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_5062]) ).
cnf(c_0_5063_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X1,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5063]) ).
cnf(c_0_5063_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X1,X3),X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5063]) ).
cnf(c_0_5063_2,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X1,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5063]) ).
cnf(c_0_5064_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5064]) ).
cnf(c_0_5064_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,X3),X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5064]) ).
cnf(c_0_5064_2,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5064]) ).
cnf(c_0_5065_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_5065]) ).
cnf(c_0_5065_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_5065]) ).
cnf(c_0_5065_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_5065]) ).
cnf(c_0_5066_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_5066]) ).
cnf(c_0_5066_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_5066]) ).
cnf(c_0_5066_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_5066]) ).
cnf(c_0_5067_0,axiom,
( c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5067]) ).
cnf(c_0_5067_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,X3),X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5067]) ).
cnf(c_0_5067_2,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5067]) ).
cnf(c_0_5068_0,axiom,
( c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X4,X1,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5068]) ).
cnf(c_0_5068_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X4,X1,X3),X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5068]) ).
cnf(c_0_5068_2,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X4,X1,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5068]) ).
cnf(c_0_5069_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_5069]) ).
cnf(c_0_5069_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_5069]) ).
cnf(c_0_5070_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_5070]) ).
cnf(c_0_5070_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_5070]) ).
cnf(c_0_5071_0,axiom,
( c_Suc(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)) = c_HOL_Ominus__class_Ominus(c_Suc(X2),X1,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5071]) ).
cnf(c_0_5071_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_Suc(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)) = c_HOL_Ominus__class_Ominus(c_Suc(X2),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5071]) ).
cnf(c_0_5072_0,axiom,
( c_lessequals(c_Finite__Set_Ocard(X3,X2),c_Finite__Set_Ocard(X1,X2),tc_nat)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_5072]) ).
cnf(c_0_5072_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_lessequals(c_Finite__Set_Ocard(X3,X2),c_Finite__Set_Ocard(X1,X2),tc_nat)
| ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_5072]) ).
cnf(c_0_5072_2,axiom,
( ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_lessequals(c_Finite__Set_Ocard(X3,X2),c_Finite__Set_Ocard(X1,X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5072]) ).
cnf(c_0_5073_0,axiom,
( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(X3,X2),c_Finite__Set_Ocard(X1,X2),tc_nat)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,X1,tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_5073]) ).
cnf(c_0_5073_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(X3,X2),c_Finite__Set_Ocard(X1,X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X1,tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_5073]) ).
cnf(c_0_5073_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X1,tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(X3,X2),c_Finite__Set_Ocard(X1,X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5073]) ).
cnf(c_0_5074_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(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_5074]) ).
cnf(c_0_5074_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_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5074]) ).
cnf(c_0_5075_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X2,X1,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_5075]) ).
cnf(c_0_5075_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_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5075]) ).
cnf(c_0_5076_0,axiom,
( c_in(X1,c_Set_Oinsert(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5076]) ).
cnf(c_0_5076_1,axiom,
( ~ c_in(X1,X2,X3)
| c_in(X1,c_Set_Oinsert(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5076]) ).
cnf(c_0_5077_0,axiom,
( c_in(X1,c_Set_Oinsert(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5077]) ).
cnf(c_0_5077_1,axiom,
( ~ c_in(X1,X2,X3)
| c_in(X1,c_Set_Oinsert(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5077]) ).
cnf(c_0_5078_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,X1,X2) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X2),c_HOL_Oone__class_Oone(X2),X2),X1,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5078]) ).
cnf(c_0_5078_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Oplus__class_Oplus(X1,X1,X2) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X2),c_HOL_Oone__class_Oone(X2),X2),X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5078]) ).
cnf(c_0_5081_0,axiom,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_5081]) ).
cnf(c_0_5081_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| X1 = X2
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_5081]) ).
cnf(c_0_5081_2,axiom,
( ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5081]) ).
cnf(c_0_5082_0,axiom,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_5082]) ).
cnf(c_0_5082_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| X1 = X2
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_5082]) ).
cnf(c_0_5082_2,axiom,
( ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5082]) ).
cnf(c_0_5083_0,axiom,
( c_lessequals(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_5083]) ).
cnf(c_0_5083_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_lessequals(c_Divides_Odiv__class_Omod(X2,X1,tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5083]) ).
cnf(c_0_5084_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_5084]) ).
cnf(c_0_5084_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_5084]) ).
cnf(c_0_5085_0,axiom,
( c_Finite__Set_Ocard(c_Set_Oinsert(X3,X1,X2),X2) = c_Finite__Set_Ocard(X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_in(X3,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5085]) ).
cnf(c_0_5085_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ocard(c_Set_Oinsert(X3,X1,X2),X2) = c_Finite__Set_Ocard(X1,X2)
| ~ c_in(X3,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5085]) ).
cnf(c_0_5085_2,axiom,
( ~ c_in(X3,X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ocard(c_Set_Oinsert(X3,X1,X2),X2) = c_Finite__Set_Ocard(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5085]) ).
cnf(c_0_5087_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5087]) ).
cnf(c_0_5087_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5087]) ).
cnf(c_0_5088_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = X1
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_5088]) ).
cnf(c_0_5088_1,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_5088]) ).
cnf(c_0_5089_0,axiom,
( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = X1
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5089]) ).
cnf(c_0_5089_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_5089]) ).
cnf(c_0_5090_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X1,tc_nat) = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5090]) ).
cnf(c_0_5090_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X1,tc_nat) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5090]) ).
cnf(c_0_5091_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5091]) ).
cnf(c_0_5091_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5091]) ).
cnf(c_0_5092_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat) = X1
| ~ c_lessequals(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5092]) ).
cnf(c_0_5092_1,axiom,
( ~ c_lessequals(X2,X1,tc_nat)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_5092]) ).
cnf(c_0_5093_0,axiom,
( c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X3,X2),X2,tc_nat)
| hBOOL(hAPP(X3,X1))
| ~ c_lessequals(X1,X2,tc_nat)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5093]) ).
cnf(c_0_5093_1,axiom,
( hBOOL(hAPP(X3,X1))
| c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X3,X2),X2,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5093]) ).
cnf(c_0_5093_2,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| hBOOL(hAPP(X3,X1))
| c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X3,X2),X2,tc_nat)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5093]) ).
cnf(c_0_5093_3,axiom,
( ~ hBOOL(hAPP(X3,X2))
| ~ c_lessequals(X1,X2,tc_nat)
| hBOOL(hAPP(X3,X1))
| c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X3,X2),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5093]) ).
cnf(c_0_5094_0,axiom,
( c_lessequals(hAPP(X1,X5),hAPP(X2,X5),X4)
| ~ c_lessequals(X1,X2,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5094]) ).
cnf(c_0_5094_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,X4))
| c_lessequals(hAPP(X1,X5),hAPP(X2,X5),X4)
| ~ class_HOL_Oord(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5094]) ).
cnf(c_0_5094_2,axiom,
( ~ class_HOL_Oord(X4)
| ~ c_lessequals(X1,X2,tc_fun(X3,X4))
| c_lessequals(hAPP(X1,X5),hAPP(X2,X5),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5094]) ).
cnf(c_0_5095_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5095]) ).
cnf(c_0_5095_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5095]) ).
cnf(c_0_5096_0,axiom,
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5096]) ).
cnf(c_0_5096_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5096]) ).
cnf(c_0_5097_0,axiom,
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5097]) ).
cnf(c_0_5097_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5097]) ).
cnf(c_0_5098_0,axiom,
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5098]) ).
cnf(c_0_5098_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5098]) ).
cnf(c_0_5099_0,axiom,
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5099]) ).
cnf(c_0_5099_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5099]) ).
cnf(c_0_5100_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5100]) ).
cnf(c_0_5100_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5100]) ).
cnf(c_0_5101_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5101]) ).
cnf(c_0_5101_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5101]) ).
cnf(c_0_5102_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5102]) ).
cnf(c_0_5102_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5102]) ).
cnf(c_0_5103_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5103]) ).
cnf(c_0_5103_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5103]) ).
cnf(c_0_5104_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5104]) ).
cnf(c_0_5104_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5104]) ).
cnf(c_0_5105_0,axiom,
( c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5105]) ).
cnf(c_0_5105_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5105]) ).
cnf(c_0_5105_2,axiom,
( ~ c_lessequals(X4,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5105]) ).
cnf(c_0_5105_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X4,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5105]) ).
cnf(c_0_5106_0,axiom,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5106]) ).
cnf(c_0_5106_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,X4,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5106]) ).
cnf(c_0_5106_2,axiom,
( ~ c_lessequals(X2,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5106]) ).
cnf(c_0_5106_3,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X2,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5106]) ).
cnf(c_0_5107_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_5107]) ).
cnf(c_0_5107_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_5107]) ).
cnf(c_0_5107_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_5107]) ).
cnf(c_0_5107_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_5107]) ).
cnf(c_0_5108_0,axiom,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5108]) ).
cnf(c_0_5108_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5108]) ).
cnf(c_0_5108_2,axiom,
( ~ c_lessequals(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5108]) ).
cnf(c_0_5108_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5108]) ).
cnf(c_0_5109_0,axiom,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5109]) ).
cnf(c_0_5109_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5109]) ).
cnf(c_0_5109_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5109]) ).
cnf(c_0_5109_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5109]) ).
cnf(c_0_5110_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5110]) ).
cnf(c_0_5110_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5110]) ).
cnf(c_0_5110_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5110]) ).
cnf(c_0_5110_3,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5110]) ).
cnf(c_0_5111_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5111]) ).
cnf(c_0_5111_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5111]) ).
cnf(c_0_5111_2,axiom,
( ~ c_lessequals(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5111]) ).
cnf(c_0_5111_3,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5111]) ).
cnf(c_0_5112_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_5112]) ).
cnf(c_0_5112_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_5112]) ).
cnf(c_0_5112_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_5112]) ).
cnf(c_0_5112_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_5112]) ).
cnf(c_0_5113_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_5113]) ).
cnf(c_0_5113_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_5113]) ).
cnf(c_0_5113_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_5113]) ).
cnf(c_0_5113_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_5113]) ).
cnf(c_0_5114_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_5114]) ).
cnf(c_0_5114_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_5114]) ).
cnf(c_0_5115_0,axiom,
( c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5115]) ).
cnf(c_0_5115_1,axiom,
( ~ class_Orderings_Olinorder(X2)
| c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_5115]) ).
cnf(c_0_5116_0,axiom,
( c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5116]) ).
cnf(c_0_5116_1,axiom,
( ~ class_Orderings_Olinorder(X2)
| c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_5116]) ).
cnf(c_0_5117_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_5117]) ).
cnf(c_0_5117_1,axiom,
( ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_5117]) ).
cnf(c_0_5118_0,axiom,
( c_HOL_Oplus__class_Oplus(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_Oplus__class_Oplus(X1,X2,tc_nat),X3)
| ~ class_Ring__and__Field_Osemiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5118]) ).
cnf(c_0_5118_1,axiom,
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_HOL_Oplus__class_Oplus(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_Oplus__class_Oplus(X1,X2,tc_nat),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5118]) ).
cnf(c_0_5119_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_5119]) ).
cnf(c_0_5119_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_5119]) ).
cnf(c_0_5123_0,axiom,
( c_in(X3,X1,X2)
| c_Finite__Set_Ocard(c_Set_Oinsert(X3,X1,X2),X2) = c_Suc(c_Finite__Set_Ocard(X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5123]) ).
cnf(c_0_5123_1,axiom,
( c_Finite__Set_Ocard(c_Set_Oinsert(X3,X1,X2),X2) = c_Suc(c_Finite__Set_Ocard(X1,X2))
| c_in(X3,X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5123]) ).
cnf(c_0_5123_2,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ocard(c_Set_Oinsert(X3,X1,X2),X2) = c_Suc(c_Finite__Set_Ocard(X1,X2))
| c_in(X3,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5123]) ).
cnf(c_0_5124_0,axiom,
( c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5124]) ).
cnf(c_0_5124_1,axiom,
( ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
| c_lessequals(X1,X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5124]) ).
cnf(c_0_5124_2,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
| c_lessequals(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5124]) ).
cnf(c_0_5125_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_5125]) ).
cnf(c_0_5125_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_5125]) ).
cnf(c_0_5125_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_5125]) ).
cnf(c_0_5126_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_5126]) ).
cnf(c_0_5126_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_5126]) ).
cnf(c_0_5126_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_5126]) ).
cnf(c_0_5127_0,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,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_5127]) ).
cnf(c_0_5127_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| c_lessequals(X1,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_5127]) ).
cnf(c_0_5127_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5127]) ).
cnf(c_0_5128_0,axiom,
( c_lessequals(c_SetInterval_Oord__class_OatLeast(X2,X3),c_SetInterval_Oord__class_OatLeast(X1,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5128]) ).
cnf(c_0_5128_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_SetInterval_Oord__class_OatLeast(X2,X3),c_SetInterval_Oord__class_OatLeast(X1,X3),tc_fun(X3,tc_bool))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5128]) ).
cnf(c_0_5128_2,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_SetInterval_Oord__class_OatLeast(X2,X3),c_SetInterval_Oord__class_OatLeast(X1,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_5128]) ).
cnf(c_0_5129_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5129]) ).
cnf(c_0_5129_1,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5129]) ).
cnf(c_0_5130_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3)
| ~ class_Lattices_Olattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5130]) ).
cnf(c_0_5130_1,axiom,
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5130]) ).
cnf(c_0_5131_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X1,X3) = c_Divides_Odiv__class_Omod(X2,X1,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5131]) ).
cnf(c_0_5131_1,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X1,X3) = c_Divides_Odiv__class_Omod(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5131]) ).
cnf(c_0_5132_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(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_5132]) ).
cnf(c_0_5132_1,axiom,
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X2,X3) = c_Divides_Odiv__class_Omod(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5132]) ).
cnf(c_0_5133_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_5133]) ).
cnf(c_0_5133_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_5133]) ).
cnf(c_0_5134_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_5134]) ).
cnf(c_0_5134_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_5134]) ).
cnf(c_0_5135_0,axiom,
( c_Finite__Set_Ocard(X1,X2) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Finite__Set_Ocard(c_Set_Oinsert(X3,X1,X2),X2) = c_Suc(c_Finite__Set_Ocard(X1,X2))
| c_in(X3,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5135]) ).
cnf(c_0_5135_1,axiom,
( c_Finite__Set_Ocard(c_Set_Oinsert(X3,X1,X2),X2) = c_Suc(c_Finite__Set_Ocard(X1,X2))
| c_Finite__Set_Ocard(X1,X2) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_in(X3,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5135]) ).
cnf(c_0_5135_2,axiom,
( c_in(X3,X1,X2)
| c_Finite__Set_Ocard(c_Set_Oinsert(X3,X1,X2),X2) = c_Suc(c_Finite__Set_Ocard(X1,X2))
| c_Finite__Set_Ocard(X1,X2) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5135]) ).
cnf(c_0_5136_0,axiom,
( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5136]) ).
cnf(c_0_5136_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_Suc(c_HOL_Ominus__class_Ominus(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_5136]) ).
cnf(c_0_5138_0,axiom,
( c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5138]) ).
cnf(c_0_5138_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5138]) ).
cnf(c_0_5138_2,axiom,
( ~ c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5138]) ).
cnf(c_0_5139_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_5139]) ).
cnf(c_0_5139_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_5139]) ).
cnf(c_0_5139_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_5139]) ).
cnf(c_0_5143_0,axiom,
( ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| ~ hBOOL(hAPP(X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5143]) ).
cnf(c_0_5143_1,axiom,
( ~ hBOOL(hAPP(X3,X1))
| ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5143]) ).
cnf(c_0_5144_0,axiom,
( c_lessequals(X1,X2,tc_fun(X3,X4))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5144]) ).
cnf(c_0_5144_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4))
| c_lessequals(X1,X2,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5144]) ).
cnf(c_0_5144_2,axiom,
( ~ class_HOL_Oord(X4)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4))
| c_lessequals(X1,X2,tc_fun(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5144]) ).
cnf(c_0_5145_0,axiom,
( c_lessequals(X1,c_Inductive_Ocomplete__lattice__class_Ogfp(X2,X3),X3)
| ~ c_lessequals(X1,hAPP(X2,X1),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5145]) ).
cnf(c_0_5145_1,axiom,
( ~ c_lessequals(X1,hAPP(X2,X1),X3)
| c_lessequals(X1,c_Inductive_Ocomplete__lattice__class_Ogfp(X2,X3),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5145]) ).
cnf(c_0_5145_2,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ c_lessequals(X1,hAPP(X2,X1),X3)
| c_lessequals(X1,c_Inductive_Ocomplete__lattice__class_Ogfp(X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5145]) ).
cnf(c_0_5146_0,axiom,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5146]) ).
cnf(c_0_5146_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5146]) ).
cnf(c_0_5146_2,axiom,
( ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5146]) ).
cnf(c_0_5147_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_5147]) ).
cnf(c_0_5147_1,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) = X1
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5147]) ).
cnf(c_0_5149_0,axiom,
( c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5149]) ).
cnf(c_0_5149_1,axiom,
( ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X1,X2,X3),X3)
| c_Finite__Set_Ofinite(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5149]) ).
cnf(c_0_5150_0,axiom,
( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5150]) ).
cnf(c_0_5150_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_5150]) ).
cnf(c_0_5151_0,axiom,
( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5151]) ).
cnf(c_0_5151_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_5151]) ).
cnf(c_0_5153_0,axiom,
( c_lessequals(X1,c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1(X3,X1),tc_nat)
| hBOOL(hAPP(X3,X2))
| ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5153]) ).
cnf(c_0_5153_1,axiom,
( hBOOL(hAPP(X3,X2))
| c_lessequals(X1,c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1(X3,X1),tc_nat)
| ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5153]) ).
cnf(c_0_5153_2,axiom,
( ~ c_lessequals(c_Suc(X1),X2,tc_nat)
| hBOOL(hAPP(X3,X2))
| c_lessequals(X1,c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1(X3,X1),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5153]) ).
cnf(c_0_5154_0,axiom,
( c_lessequals(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5154]) ).
cnf(c_0_5154_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5154]) ).
cnf(c_0_5154_2,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5154]) ).
cnf(c_0_5154_3,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5154]) ).
cnf(c_0_5155_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_5155]) ).
cnf(c_0_5155_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| X1 = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_5155]) ).
cnf(c_0_5155_2,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5155]) ).
cnf(c_0_5156_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| X1 = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_5156]) ).
cnf(c_0_5156_1,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_5156]) ).
cnf(c_0_5156_2,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_5156]) ).
cnf(c_0_5157_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)) = X1
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_5157]) ).
cnf(c_0_5157_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_5157]) ).
cnf(c_0_5158_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = X1
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_5158]) ).
cnf(c_0_5158_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_5158]) ).
cnf(c_0_5159_0,axiom,
( hBOOL(hAPP(X2,X4))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5159]) ).
cnf(c_0_5159_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5159]) ).
cnf(c_0_5159_2,axiom,
( ~ hBOOL(hAPP(X1,X4))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hBOOL(hAPP(X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5159]) ).
cnf(c_0_5160_0,axiom,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_5160]) ).
cnf(c_0_5160_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X3,X2))
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_5160]) ).
cnf(c_0_5160_2,axiom,
( ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5160]) ).
cnf(c_0_5161_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_5161]) ).
cnf(c_0_5161_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_5161]) ).
cnf(c_0_5161_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_5161]) ).
cnf(c_0_5162_0,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_5162]) ).
cnf(c_0_5162_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_5162]) ).
cnf(c_0_5163_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_HOL_Oone__class_Oone(X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5163]) ).
cnf(c_0_5163_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_HOL_Oone__class_Oone(X1),X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5163]) ).
cnf(c_0_5164_0,axiom,
( hBOOL(hAPP(X3,X1))
| ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5164]) ).
cnf(c_0_5164_1,axiom,
( ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| hBOOL(hAPP(X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5164]) ).
cnf(c_0_5165_0,axiom,
( c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5165]) ).
cnf(c_0_5165_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5165]) ).
cnf(c_0_5165_2,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5165]) ).
cnf(c_0_5166_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_5166]) ).
cnf(c_0_5166_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_5166]) ).
cnf(c_0_5166_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_5166]) ).
cnf(c_0_5167_0,axiom,
( c_lessequals(X3,c_Finite__Set_Olinorder__class_OMax(X1,X2),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_in(X3,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5167]) ).
cnf(c_0_5167_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_lessequals(X3,c_Finite__Set_Olinorder__class_OMax(X1,X2),X2)
| ~ c_in(X3,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5167]) ).
cnf(c_0_5167_2,axiom,
( ~ c_in(X3,X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_lessequals(X3,c_Finite__Set_Olinorder__class_OMax(X1,X2),X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5167]) ).
cnf(c_0_5167_3,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ c_in(X3,X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_lessequals(X3,c_Finite__Set_Olinorder__class_OMax(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5167]) ).
cnf(c_0_5168_0,axiom,
( c_lessequals(c_Finite__Set_Olinorder__class_OMin(X1,X2),X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_in(X3,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5168]) ).
cnf(c_0_5168_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X1,X2),X3,X2)
| ~ c_in(X3,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5168]) ).
cnf(c_0_5168_2,axiom,
( ~ c_in(X3,X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X1,X2),X3,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5168]) ).
cnf(c_0_5168_3,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ c_in(X3,X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X1,X2),X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5168]) ).
cnf(c_0_5169_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_5169]) ).
cnf(c_0_5169_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_5169]) ).
cnf(c_0_5169_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_5169]) ).
cnf(c_0_5169_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_5169]) ).
cnf(c_0_5170_0,axiom,
( c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5170]) ).
cnf(c_0_5170_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5170]) ).
cnf(c_0_5171_0,axiom,
( c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5171]) ).
cnf(c_0_5171_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5171]) ).
cnf(c_0_5172_0,axiom,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5172]) ).
cnf(c_0_5172_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5172]) ).
cnf(c_0_5173_0,axiom,
( c_lessequals(X2,X1,X3)
| ~ c_in(X1,c_SetInterval_Oord__class_OatLeast(X2,X3),X3)
| ~ class_HOL_Oord(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5173]) ).
cnf(c_0_5173_1,axiom,
( ~ c_in(X1,c_SetInterval_Oord__class_OatLeast(X2,X3),X3)
| c_lessequals(X2,X1,X3)
| ~ class_HOL_Oord(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5173]) ).
cnf(c_0_5173_2,axiom,
( ~ class_HOL_Oord(X3)
| ~ c_in(X1,c_SetInterval_Oord__class_OatLeast(X2,X3),X3)
| c_lessequals(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5173]) ).
cnf(c_0_5174_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_5174]) ).
cnf(c_0_5174_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_5174]) ).
cnf(c_0_5175_0,axiom,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| ~ class_Int_Onumber__ring(X4)
| ~ class_Ring__and__Field_Oidom(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5175]) ).
cnf(c_0_5175_1,axiom,
( c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| X1 = X2
| ~ class_Int_Onumber__ring(X4)
| ~ class_Ring__and__Field_Oidom(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5175]) ).
cnf(c_0_5175_2,axiom,
( ~ class_Int_Onumber__ring(X4)
| c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| X1 = X2
| ~ class_Ring__and__Field_Oidom(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5175]) ).
cnf(c_0_5175_3,axiom,
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5175]) ).
cnf(c_0_5177_0,axiom,
( c_in(X1,X2,X3)
| c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_5177]) ).
cnf(c_0_5177_1,axiom,
( c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5177]) ).
cnf(c_0_5178_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_5178]) ).
cnf(c_0_5178_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_5178]) ).
cnf(c_0_5178_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_5178]) ).
cnf(c_0_5179_0,axiom,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5179]) ).
cnf(c_0_5179_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5179]) ).
cnf(c_0_5179_2,axiom,
( ~ c_lessequals(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| X1 = X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5179]) ).
cnf(c_0_5179_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5179]) ).
cnf(c_0_5180_0,axiom,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5180]) ).
cnf(c_0_5180_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5180]) ).
cnf(c_0_5180_2,axiom,
( ~ c_lessequals(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| X1 = X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5180]) ).
cnf(c_0_5180_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5180]) ).
cnf(c_0_5181_0,axiom,
( X2 = X1
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5181]) ).
cnf(c_0_5181_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| X2 = X1
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5181]) ).
cnf(c_0_5181_2,axiom,
( ~ c_lessequals(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| X2 = X1
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5181]) ).
cnf(c_0_5181_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_5181]) ).
cnf(c_0_5183_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X2),X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5183]) ).
cnf(c_0_5183_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X2),X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5183]) ).
cnf(c_0_5184_0,axiom,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
| ~ class_OrderedGroup_Oab__group__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5184]) ).
cnf(c_0_5184_1,axiom,
( c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
| X1 = X2
| ~ class_OrderedGroup_Oab__group__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5184]) ).
cnf(c_0_5184_2,axiom,
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5184]) ).
cnf(c_0_5185_0,axiom,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5185]) ).
cnf(c_0_5185_1,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
| X1 = X2
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5185]) ).
cnf(c_0_5185_2,axiom,
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5185]) ).
cnf(c_0_5186_0,axiom,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X1,X3,X4) != c_HOL_Oplus__class_Oplus(X2,X3,X4)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5186]) ).
cnf(c_0_5186_1,axiom,
( c_HOL_Oplus__class_Oplus(X1,X3,X4) != c_HOL_Oplus__class_Oplus(X2,X3,X4)
| X1 = X2
| ~ class_OrderedGroup_Ocancel__semigroup__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5186]) ).
cnf(c_0_5186_2,axiom,
( ~ class_OrderedGroup_Ocancel__semigroup__add(X4)
| c_HOL_Oplus__class_Oplus(X1,X3,X4) != c_HOL_Oplus__class_Oplus(X2,X3,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5186]) ).
cnf(c_0_5187_0,axiom,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5187]) ).
cnf(c_0_5187_1,axiom,
( c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| X1 = X2
| ~ class_OrderedGroup_Ocancel__semigroup__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5187]) ).
cnf(c_0_5187_2,axiom,
( ~ class_OrderedGroup_Ocancel__semigroup__add(X4)
| c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5187]) ).
cnf(c_0_5188_0,axiom,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5188]) ).
cnf(c_0_5188_1,axiom,
( c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| X1 = X2
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5188]) ).
cnf(c_0_5188_2,axiom,
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X4)
| c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5188]) ).
cnf(c_0_5189_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_5189]) ).
cnf(c_0_5189_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_5189]) ).
cnf(c_0_5189_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_5189]) ).
cnf(c_0_5190_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_5190]) ).
cnf(c_0_5190_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_5190]) ).
cnf(c_0_5190_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_5190]) ).
cnf(c_0_5191_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_5191]) ).
cnf(c_0_5191_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_5191]) ).
cnf(c_0_5191_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_5191]) ).
cnf(c_0_5192_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_5192]) ).
cnf(c_0_5192_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_5192]) ).
cnf(c_0_5192_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_5192]) ).
cnf(c_0_5193_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5193]) ).
cnf(c_0_5193_1,axiom,
( ~ c_lessequals(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5193]) ).
cnf(c_0_5193_2,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5193]) ).
cnf(c_0_5194_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5194]) ).
cnf(c_0_5194_1,axiom,
( ~ c_lessequals(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5194]) ).
cnf(c_0_5194_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5194]) ).
cnf(c_0_5195_0,axiom,
( ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5195]) ).
cnf(c_0_5195_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5195]) ).
cnf(c_0_5195_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5195]) ).
cnf(c_0_5196_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ c_lessequals(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5196]) ).
cnf(c_0_5196_1,axiom,
( ~ c_lessequals(X1,X1,X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5196]) ).
cnf(c_0_5196_2,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X1,X1,X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5196]) ).
cnf(c_0_5197_0,axiom,
( X2 = X1
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5197]) ).
cnf(c_0_5197_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| X2 = X1
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5197]) ).
cnf(c_0_5197_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_5197]) ).
cnf(c_0_5198_0,axiom,
( ~ c_lessequals(c_Suc(X1),X2,tc_nat)
| ~ c_lessequals(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5198]) ).
cnf(c_0_5198_1,axiom,
( ~ c_lessequals(X2,X1,tc_nat)
| ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5198]) ).
cnf(c_0_5199_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_5199]) ).
cnf(c_0_5199_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_5199]) ).
cnf(c_0_5200_0,axiom,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5200]) ).
cnf(c_0_5200_1,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = X2
| c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5200]) ).
cnf(c_0_5200_2,axiom,
( c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5200]) ).
cnf(c_0_5201_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5201]) ).
cnf(c_0_5201_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5201]) ).
cnf(c_0_5202_0,axiom,
( c_in(X2,c_SetInterval_Oord__class_OatLeast(X1,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_HOL_Oord(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5202]) ).
cnf(c_0_5202_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_in(X2,c_SetInterval_Oord__class_OatLeast(X1,X3),X3)
| ~ class_HOL_Oord(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5202]) ).
cnf(c_0_5202_2,axiom,
( ~ class_HOL_Oord(X3)
| ~ c_lessequals(X1,X2,X3)
| c_in(X2,c_SetInterval_Oord__class_OatLeast(X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5202]) ).
cnf(c_0_5203_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_5203]) ).
cnf(c_0_5203_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_5203]) ).
cnf(c_0_5204_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_5204]) ).
cnf(c_0_5204_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_5204]) ).
cnf(c_0_5205_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_5205]) ).
cnf(c_0_5205_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_5205]) ).
cnf(c_0_5205_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_5205]) ).
cnf(c_0_5206_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_5206]) ).
cnf(c_0_5206_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_5206]) ).
cnf(c_0_5206_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_5206]) ).
cnf(c_0_5207_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_5207]) ).
cnf(c_0_5207_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_5207]) ).
cnf(c_0_5207_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_5207]) ).
cnf(c_0_5208_0,axiom,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5208]) ).
cnf(c_0_5208_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| X1 = X2
| ~ c_lessequals(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5208]) ).
cnf(c_0_5208_2,axiom,
( ~ c_lessequals(X2,X1,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5208]) ).
cnf(c_0_5209_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_5209]) ).
cnf(c_0_5209_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_5209]) ).
cnf(c_0_5209_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_5209]) ).
cnf(c_0_5210_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_5210]) ).
cnf(c_0_5210_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_5210]) ).
cnf(c_0_5210_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_5210]) ).
cnf(c_0_5211_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_5211]) ).
cnf(c_0_5211_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_5211]) ).
cnf(c_0_5211_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_5211]) ).
cnf(c_0_5212_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_5212]) ).
cnf(c_0_5212_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_5212]) ).
cnf(c_0_5212_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_5212]) ).
cnf(c_0_5213_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_5213]) ).
cnf(c_0_5213_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_5213]) ).
cnf(c_0_5213_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_5213]) ).
cnf(c_0_5214_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_5214]) ).
cnf(c_0_5214_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_5214]) ).
cnf(c_0_5214_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_5214]) ).
cnf(c_0_5215_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_5215]) ).
cnf(c_0_5215_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_5215]) ).
cnf(c_0_5215_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_5215]) ).
cnf(c_0_5216_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X2,X3) = X1
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5216]) ).
cnf(c_0_5216_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X2,X3) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_5216]) ).
cnf(c_0_5217_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X3),X2,X3) = X1
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5217]) ).
cnf(c_0_5217_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X3),X2,X3) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_5217]) ).
cnf(c_0_5218_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X1,X3)
| ~ class_Lattices_Olattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5218]) ).
cnf(c_0_5218_1,axiom,
( ~ class_Lattices_Olattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5218]) ).
cnf(c_0_5219_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X2,X3)
| ~ class_Lattices_Olattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5219]) ).
cnf(c_0_5219_1,axiom,
( ~ class_Lattices_Olattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5219]) ).
cnf(c_0_5220_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5220]) ).
cnf(c_0_5220_1,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5220]) ).
cnf(c_0_5221_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X1,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5221]) ).
cnf(c_0_5221_1,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5221]) ).
cnf(c_0_5222_0,axiom,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5222]) ).
cnf(c_0_5222_1,axiom,
( c_HOL_Oplus__class_Oplus(X3,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5222]) ).
cnf(c_0_5223_0,axiom,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X1,X3,tc_nat) != c_HOL_Oplus__class_Oplus(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5223]) ).
cnf(c_0_5223_1,axiom,
( c_HOL_Oplus__class_Oplus(X1,X3,tc_nat) != c_HOL_Oplus__class_Oplus(X2,X3,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5223]) ).
cnf(c_0_5224_0,axiom,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5224]) ).
cnf(c_0_5224_1,axiom,
( c_HOL_Oplus__class_Oplus(X3,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5224]) ).
cnf(c_0_5225_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_5225]) ).
cnf(c_0_5225_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_5225]) ).
cnf(c_0_5226_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_5226]) ).
cnf(c_0_5226_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_5226]) ).
cnf(c_0_5227_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_5227]) ).
cnf(c_0_5227_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_5227]) ).
cnf(c_0_5233_0,axiom,
( hBOOL(hAPP(X2,X1))
| hBOOL(hAPP(X2,X3))
| ~ c_lessequals(c_Suc(X1),c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5233]) ).
cnf(c_0_5233_1,axiom,
( hBOOL(hAPP(X2,X3))
| hBOOL(hAPP(X2,X1))
| ~ c_lessequals(c_Suc(X1),c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5233]) ).
cnf(c_0_5233_2,axiom,
( ~ c_lessequals(c_Suc(X1),c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1(X2),tc_nat)
| hBOOL(hAPP(X2,X3))
| hBOOL(hAPP(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5233]) ).
cnf(c_0_5238_0,axiom,
( c_Finite__Set_Ofinite(X1,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5238]) ).
cnf(c_0_5238_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Finite__Set_Ofinite(X1,X3)
| ~ c_Finite__Set_Ofinite(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5238]) ).
cnf(c_0_5238_2,axiom,
( ~ c_Finite__Set_Ofinite(X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Finite__Set_Ofinite(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5238]) ).
cnf(c_0_5239_0,axiom,
( c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_5239]) ).
cnf(c_0_5239_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(X3,X2)
| ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_5239]) ).
cnf(c_0_5239_2,axiom,
( ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5239]) ).
cnf(c_0_5250_0,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5250]) ).
cnf(c_0_5250_1,axiom,
( ~ c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat)
| c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5250]) ).
cnf(c_0_5251_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_5251]) ).
cnf(c_0_5251_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_5251]) ).
cnf(c_0_5257_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_5257]) ).
cnf(c_0_5257_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_5257]) ).
cnf(c_0_5257_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_5257]) ).
cnf(c_0_5258_0,axiom,
( c_lessequals(X1,X2,tc_nat)
| X1 = c_Suc(X2)
| ~ c_lessequals(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5258]) ).
cnf(c_0_5258_1,axiom,
( X1 = c_Suc(X2)
| c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5258]) ).
cnf(c_0_5258_2,axiom,
( ~ c_lessequals(X1,c_Suc(X2),tc_nat)
| X1 = c_Suc(X2)
| c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5258]) ).
cnf(c_0_5259_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_5259]) ).
cnf(c_0_5259_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_5259]) ).
cnf(c_0_5259_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_5259]) ).
cnf(c_0_5260_0,axiom,
( c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(X1,X2,X3),X3) = X2
| c_Finite__Set_Ocard(X1,X3) != c_Suc(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5260]) ).
cnf(c_0_5260_1,axiom,
( c_Finite__Set_Ocard(X1,X3) != c_Suc(X2)
| c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(X1,X2,X3),X3) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5260]) ).
cnf(c_0_5261_0,axiom,
( c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(X1,X2,X3),X3) = X2
| c_Finite__Set_Ocard(X1,X3) != c_Suc(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5261]) ).
cnf(c_0_5261_1,axiom,
( c_Finite__Set_Ocard(X1,X3) != c_Suc(X2)
| c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(X1,X2,X3),X3) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5261]) ).
cnf(c_0_5262_0,axiom,
( X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5262]) ).
cnf(c_0_5262_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X2 = X1
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5262]) ).
cnf(c_0_5262_2,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X2 = X1
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5262]) ).
cnf(c_0_5262_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_5262]) ).
cnf(c_0_5263_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5263]) ).
cnf(c_0_5263_1,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5263]) ).
cnf(c_0_5263_2,axiom,
( ~ c_lessequals(X2,X1,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5263]) ).
cnf(c_0_5263_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X2,X1,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5263]) ).
cnf(c_0_5264_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5264]) ).
cnf(c_0_5264_1,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5264]) ).
cnf(c_0_5264_2,axiom,
( ~ c_lessequals(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5264]) ).
cnf(c_0_5264_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5264]) ).
cnf(c_0_5265_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5265]) ).
cnf(c_0_5265_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5265]) ).
cnf(c_0_5265_2,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5265]) ).
cnf(c_0_5265_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5265]) ).
cnf(c_0_5266_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5266]) ).
cnf(c_0_5266_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5266]) ).
cnf(c_0_5266_2,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5266]) ).
cnf(c_0_5266_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5266]) ).
cnf(c_0_5267_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5267]) ).
cnf(c_0_5267_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5267]) ).
cnf(c_0_5267_2,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5267]) ).
cnf(c_0_5267_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5267]) ).
cnf(c_0_5268_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5268]) ).
cnf(c_0_5268_1,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5268]) ).
cnf(c_0_5268_2,axiom,
( ~ c_lessequals(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5268]) ).
cnf(c_0_5268_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5268]) ).
cnf(c_0_5269_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5269]) ).
cnf(c_0_5269_1,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5269]) ).
cnf(c_0_5269_2,axiom,
( ~ c_lessequals(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5269]) ).
cnf(c_0_5269_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5269]) ).
cnf(c_0_5270_0,axiom,
( c_lessequals(X1,X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) != X1
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5270]) ).
cnf(c_0_5270_1,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) != X1
| c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5270]) ).
cnf(c_0_5270_2,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) != X1
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5270]) ).
cnf(c_0_5271_0,axiom,
( c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5271]) ).
cnf(c_0_5271_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5271]) ).
cnf(c_0_5272_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_5272]) ).
cnf(c_0_5272_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_5272]) ).
cnf(c_0_5273_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_5273]) ).
cnf(c_0_5273_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_5273]) ).
cnf(c_0_5274_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_5274]) ).
cnf(c_0_5274_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_5274]) ).
cnf(c_0_5274_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_5274]) ).
cnf(c_0_5275_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_5275]) ).
cnf(c_0_5275_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_5275]) ).
cnf(c_0_5275_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_5275]) ).
cnf(c_0_5276_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_5276]) ).
cnf(c_0_5276_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_5276]) ).
cnf(c_0_5276_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_5276]) ).
cnf(c_0_5277_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3) = X1
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5277]) ).
cnf(c_0_5277_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3) = X1
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5277]) ).
cnf(c_0_5277_2,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| ~ c_lessequals(X1,X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_5277]) ).
cnf(c_0_5278_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = X1
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5278]) ).
cnf(c_0_5278_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = X1
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5278]) ).
cnf(c_0_5278_2,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| ~ c_lessequals(X1,X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_5278]) ).
cnf(c_0_5279_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_5279]) ).
cnf(c_0_5279_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_5279]) ).
cnf(c_0_5279_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_5279]) ).
cnf(c_0_5280_0,axiom,
( c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5280]) ).
cnf(c_0_5280_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5280]) ).
cnf(c_0_5280_2,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5280]) ).
cnf(c_0_5281_0,axiom,
( c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5281]) ).
cnf(c_0_5281_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5281]) ).
cnf(c_0_5281_2,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5281]) ).
cnf(c_0_5282_0,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5282]) ).
cnf(c_0_5282_1,axiom,
( ~ c_lessequals(c_Suc(X1),X2,tc_nat)
| c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5282]) ).
cnf(c_0_5283_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5283]) ).
cnf(c_0_5283_1,axiom,
( ~ c_lessequals(c_Suc(X1),X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5283]) ).
cnf(c_0_5284_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5284]) ).
cnf(c_0_5284_1,axiom,
( ~ c_lessequals(c_Suc(X1),X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5284]) ).
cnf(c_0_5285_0,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5285]) ).
cnf(c_0_5285_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5285]) ).
cnf(c_0_5286_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_5286]) ).
cnf(c_0_5286_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_5286]) ).
cnf(c_0_5287_0,axiom,
( c_Finite__Set_Ofinite(c_Set_Oinsert(X3,X1,X2),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5287]) ).
cnf(c_0_5287_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_Set_Oinsert(X3,X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5287]) ).
cnf(c_0_5288_0,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(X1,X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5288]) ).
cnf(c_0_5288_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(X1,X2),tc_nat)
| c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5288]) ).
cnf(c_0_5289_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_5289]) ).
cnf(c_0_5289_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_5289]) ).
cnf(c_0_5290_0,axiom,
( c_lessequals(X1,c_Suc(X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5290]) ).
cnf(c_0_5290_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5290]) ).
cnf(c_0_5291_0,axiom,
( c_lessequals(c_Suc(X1),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5291]) ).
cnf(c_0_5291_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_lessequals(c_Suc(X1),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5291]) ).
cnf(c_0_5292_0,axiom,
( c_lessequals(c_Suc(X1),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5292]) ).
cnf(c_0_5292_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_lessequals(c_Suc(X1),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5292]) ).
cnf(c_0_5293_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5293]) ).
cnf(c_0_5293_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5293]) ).
cnf(c_0_5294_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)
| ~ c_lessequals(X1,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5294]) ).
cnf(c_0_5294_1,axiom,
( ~ c_lessequals(X1,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5294]) ).
cnf(c_0_5295_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_5295]) ).
cnf(c_0_5295_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_5295]) ).
cnf(c_0_5296_0,axiom,
( c_Set_Oinsert(X1,X2,X3) = X2
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5296]) ).
cnf(c_0_5296_1,axiom,
( ~ c_in(X1,X2,X3)
| c_Set_Oinsert(X1,X2,X3) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5296]) ).
cnf(c_0_5297_0,axiom,
( c_lessequals(X1,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5297]) ).
cnf(c_0_5297_1,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5297]) ).
cnf(c_0_5298_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5298]) ).
cnf(c_0_5298_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5298]) ).
cnf(c_0_5299_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5299]) ).
cnf(c_0_5299_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5299]) ).
cnf(c_0_5299_2,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5299]) ).
cnf(c_0_5300_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5300]) ).
cnf(c_0_5300_1,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5300]) ).
cnf(c_0_5300_2,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5300]) ).
cnf(c_0_5301_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5301]) ).
cnf(c_0_5301_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5301]) ).
cnf(c_0_5301_2,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5301]) ).
cnf(c_0_5302_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_in(c_Finite__Set_Olinorder__class_OMax(X1,X2),X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5302]) ).
cnf(c_0_5302_1,axiom,
( c_in(c_Finite__Set_Olinorder__class_OMax(X1,X2),X1,X2)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5302]) ).
cnf(c_0_5302_2,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_in(c_Finite__Set_Olinorder__class_OMax(X1,X2),X1,X2)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5302]) ).
cnf(c_0_5302_3,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_in(c_Finite__Set_Olinorder__class_OMax(X1,X2),X1,X2)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_5302]) ).
cnf(c_0_5303_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_in(c_Finite__Set_Olinorder__class_OMin(X1,X2),X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5303]) ).
cnf(c_0_5303_1,axiom,
( c_in(c_Finite__Set_Olinorder__class_OMin(X1,X2),X1,X2)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5303]) ).
cnf(c_0_5303_2,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_in(c_Finite__Set_Olinorder__class_OMin(X1,X2),X1,X2)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5303]) ).
cnf(c_0_5303_3,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_in(c_Finite__Set_Olinorder__class_OMin(X1,X2),X1,X2)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_5303]) ).
cnf(c_0_5304_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_5304]) ).
cnf(c_0_5304_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_5304]) ).
cnf(c_0_5305_0,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5305]) ).
cnf(c_0_5305_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5305]) ).
cnf(c_0_5306_0,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5306]) ).
cnf(c_0_5306_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5306]) ).
cnf(c_0_5308_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(X1,X2),tc_nat)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5308]) ).
cnf(c_0_5308_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(X1,X2),tc_nat)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5308]) ).
cnf(c_0_5308_2,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(X1,X2),tc_nat)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_5308]) ).
cnf(c_0_5317_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_5317]) ).
cnf(c_0_5317_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_5317]) ).
cnf(c_0_5317_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_5317]) ).
cnf(c_0_5317_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_5317]) ).
cnf(c_0_5318_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_5318]) ).
cnf(c_0_5318_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_5318]) ).
cnf(c_0_5318_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_5318]) ).
cnf(c_0_5318_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_5318]) ).
cnf(c_0_5319_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_5319]) ).
cnf(c_0_5319_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_5319]) ).
cnf(c_0_5319_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_5319]) ).
cnf(c_0_5319_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_5319]) ).
cnf(c_0_5320_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_5320]) ).
cnf(c_0_5320_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_5320]) ).
cnf(c_0_5320_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_5320]) ).
cnf(c_0_5320_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_5320]) ).
cnf(c_0_5321_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_5321]) ).
cnf(c_0_5321_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_5321]) ).
cnf(c_0_5321_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_5321]) ).
cnf(c_0_5321_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_5321]) ).
cnf(c_0_5324_0,axiom,
( c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Finite__Set_Ocard(X1,X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_5324]) ).
cnf(c_0_5324_1,axiom,
( c_Finite__Set_Ocard(X1,X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_5324]) ).
cnf(c_0_5325_0,axiom,
( c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Finite__Set_Ocard(X1,X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_5325]) ).
cnf(c_0_5325_1,axiom,
( c_Finite__Set_Ocard(X1,X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_5325]) ).
cnf(c_0_5326_0,axiom,
( c_lessequals(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5326]) ).
cnf(c_0_5326_1,axiom,
( c_lessequals(X2,X1,X3)
| c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5326]) ).
cnf(c_0_5326_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X2,X1,X3)
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5326]) ).
cnf(c_0_5327_0,axiom,
( c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5327]) ).
cnf(c_0_5327_1,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5327]) ).
cnf(c_0_5327_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5327]) ).
cnf(c_0_5328_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5328]) ).
cnf(c_0_5328_1,axiom,
( c_lessequals(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5328]) ).
cnf(c_0_5328_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5328]) ).
cnf(c_0_5329_0,axiom,
( c_lessequals(X1,X1,X2)
| c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5329]) ).
cnf(c_0_5329_1,axiom,
( c_HOL_Oord__class_Oless(X1,X1,X2)
| c_lessequals(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5329]) ).
cnf(c_0_5329_2,axiom,
( ~ class_Orderings_Olinorder(X2)
| c_HOL_Oord__class_Oless(X1,X1,X2)
| c_lessequals(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5329]) ).
cnf(c_0_5330_0,axiom,
( c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5330]) ).
cnf(c_0_5330_1,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5330]) ).
cnf(c_0_5330_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5330]) ).
cnf(c_0_5331_0,axiom,
( hBOOL(hAPP(X2,X1))
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5331]) ).
cnf(c_0_5331_1,axiom,
( ~ c_in(X1,X2,X3)
| hBOOL(hAPP(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5331]) ).
cnf(c_0_5332_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3)
| ~ class_Lattices_Olattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5332]) ).
cnf(c_0_5332_1,axiom,
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5332]) ).
cnf(c_0_5333_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5333]) ).
cnf(c_0_5333_1,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5333]) ).
cnf(c_0_5334_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5334]) ).
cnf(c_0_5334_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5334]) ).
cnf(c_0_5335_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5335]) ).
cnf(c_0_5335_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5335]) ).
cnf(c_0_5336_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5336]) ).
cnf(c_0_5336_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5336]) ).
cnf(c_0_5337_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_5337]) ).
cnf(c_0_5337_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_5337]) ).
cnf(c_0_5338_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_5338]) ).
cnf(c_0_5338_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_5338]) ).
cnf(c_0_5339_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),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_5339]) ).
cnf(c_0_5339_1,axiom,
( ~ class_Ring__and__Field_Osemiring__1(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2) = c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5339]) ).
cnf(c_0_5340_0,axiom,
( c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_Suc(X2),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5340]) ).
cnf(c_0_5340_1,axiom,
( c_lessequals(c_Suc(X2),X1,tc_nat)
| c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5340]) ).
cnf(c_0_5341_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_5341]) ).
cnf(c_0_5341_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_5341]) ).
cnf(c_0_5342_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_5342]) ).
cnf(c_0_5342_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_5342]) ).
cnf(c_0_5343_0,axiom,
( ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5343]) ).
cnf(c_0_5343_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5343]) ).
cnf(c_0_5344_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_5344]) ).
cnf(c_0_5344_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_5344]) ).
cnf(c_0_5347_0,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_5347]) ).
cnf(c_0_5347_1,axiom,
( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_5347]) ).
cnf(c_0_5347_2,axiom,
( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != 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_5347]) ).
cnf(c_0_5348_0,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_5348]) ).
cnf(c_0_5348_1,axiom,
( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_5348]) ).
cnf(c_0_5348_2,axiom,
( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != 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_5348]) ).
cnf(c_0_5349_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_5349]) ).
cnf(c_0_5349_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_5349]) ).
cnf(c_0_5350_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_5350]) ).
cnf(c_0_5350_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_5350]) ).
cnf(c_0_5350_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_5350]) ).
cnf(c_0_5350_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_5350]) ).
cnf(c_0_5351_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_5351]) ).
cnf(c_0_5351_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_5351]) ).
cnf(c_0_5351_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_5351]) ).
cnf(c_0_5351_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_5351]) ).
cnf(c_0_5352_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_5352]) ).
cnf(c_0_5352_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_5352]) ).
cnf(c_0_5352_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_5352]) ).
cnf(c_0_5352_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_5352]) ).
cnf(c_0_5353_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_5353]) ).
cnf(c_0_5353_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_5353]) ).
cnf(c_0_5353_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_5353]) ).
cnf(c_0_5354_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_5354]) ).
cnf(c_0_5354_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_5354]) ).
cnf(c_0_5354_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_5354]) ).
cnf(c_0_5355_0,axiom,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5355]) ).
cnf(c_0_5355_1,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5355]) ).
cnf(c_0_5355_2,axiom,
( ~ class_Int_Onumber__ring(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5355]) ).
cnf(c_0_5355_3,axiom,
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5355]) ).
cnf(c_0_5356_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_5356]) ).
cnf(c_0_5356_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_5356]) ).
cnf(c_0_5356_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_5356]) ).
cnf(c_0_5357_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(X3,X1,X2) != X3
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5357]) ).
cnf(c_0_5357_1,axiom,
( c_HOL_Oplus__class_Oplus(X3,X1,X2) != 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_5357]) ).
cnf(c_0_5357_2,axiom,
( ~ class_Int_Onumber__ring(X2)
| c_HOL_Oplus__class_Oplus(X3,X1,X2) != X3
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5357]) ).
cnf(c_0_5357_3,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| c_HOL_Oplus__class_Oplus(X3,X1,X2) != X3
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5357]) ).
cnf(c_0_5358_0,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_5358]) ).
cnf(c_0_5358_1,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_5358]) ).
cnf(c_0_5358_2,axiom,
( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != 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_5358]) ).
cnf(c_0_5359_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_5359]) ).
cnf(c_0_5359_1,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_5359]) ).
cnf(c_0_5359_2,axiom,
( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != 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_5359]) ).
cnf(c_0_5360_0,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_5360]) ).
cnf(c_0_5360_1,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_5360]) ).
cnf(c_0_5360_2,axiom,
( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != 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_5360]) ).
cnf(c_0_5361_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_5361]) ).
cnf(c_0_5361_1,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_5361]) ).
cnf(c_0_5361_2,axiom,
( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != 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_5361]) ).
cnf(c_0_5362_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_5362]) ).
cnf(c_0_5362_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_5362]) ).
cnf(c_0_5363_0,axiom,
( c_lessequals(X1,X2,tc_nat)
| c_lessequals(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5363]) ).
cnf(c_0_5363_1,axiom,
( c_lessequals(X2,X1,tc_nat)
| c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5363]) ).
cnf(c_0_5367_0,axiom,
( c_Suc(c_ATP__Linkup_Osko__Nat__XSuc__le__D__1__1(X2)) = X2
| ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5367]) ).
cnf(c_0_5367_1,axiom,
( ~ c_lessequals(c_Suc(X1),X2,tc_nat)
| c_Suc(c_ATP__Linkup_Osko__Nat__XSuc__le__D__1__1(X2)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5367]) ).
cnf(c_0_5368_0,axiom,
( X1 = c_Orderings_Otop__class_Otop(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X2) != c_Orderings_Otop__class_Otop(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5368]) ).
cnf(c_0_5368_1,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X2) != c_Orderings_Otop__class_Otop(X2)
| X1 = c_Orderings_Otop__class_Otop(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5368]) ).
cnf(c_0_5368_2,axiom,
( ~ class_Lattices_Obounded__lattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X2) != c_Orderings_Otop__class_Otop(X2)
| X1 = c_Orderings_Otop__class_Otop(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5368]) ).
cnf(c_0_5369_0,axiom,
( X1 = c_Orderings_Otop__class_Otop(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X1,X2) != c_Orderings_Otop__class_Otop(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5369]) ).
cnf(c_0_5369_1,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X3,X1,X2) != c_Orderings_Otop__class_Otop(X2)
| X1 = c_Orderings_Otop__class_Otop(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5369]) ).
cnf(c_0_5369_2,axiom,
( ~ class_Lattices_Obounded__lattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X1,X2) != c_Orderings_Otop__class_Otop(X2)
| X1 = c_Orderings_Otop__class_Otop(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5369]) ).
cnf(c_0_5370_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(X1,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5370]) ).
cnf(c_0_5370_1,axiom,
( c_HOL_Oplus__class_Oplus(X1,X1,X2) != 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_5370]) ).
cnf(c_0_5370_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
| c_HOL_Oplus__class_Oplus(X1,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5370]) ).
cnf(c_0_5372_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_5372]) ).
cnf(c_0_5372_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_5372]) ).
cnf(c_0_5373_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_5373]) ).
cnf(c_0_5373_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_5373]) ).
cnf(c_0_5374_0,axiom,
( c_in(X2,X1,X3)
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5374]) ).
cnf(c_0_5374_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| c_in(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5374]) ).
cnf(c_0_5375_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_5375]) ).
cnf(c_0_5375_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_5375]) ).
cnf(c_0_5375_2,axiom,
( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != 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_5375]) ).
cnf(c_0_5376_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_5376]) ).
cnf(c_0_5376_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_5376]) ).
cnf(c_0_5376_2,axiom,
( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != 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_5376]) ).
cnf(c_0_5377_0,axiom,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5377]) ).
cnf(c_0_5377_1,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5377]) ).
cnf(c_0_5377_2,axiom,
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5377]) ).
cnf(c_0_5378_0,axiom,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5378]) ).
cnf(c_0_5378_1,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5378]) ).
cnf(c_0_5378_2,axiom,
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5378]) ).
cnf(c_0_5379_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5379]) ).
cnf(c_0_5379_1,axiom,
( ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1(X1)))
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5379]) ).
cnf(c_0_5380_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_5380]) ).
cnf(c_0_5380_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_5380]) ).
cnf(c_0_5380_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_5380]) ).
cnf(c_0_5381_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5381]) ).
cnf(c_0_5381_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5381]) ).
cnf(c_0_5382_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5382]) ).
cnf(c_0_5382_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5382]) ).
cnf(c_0_5385_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5385]) ).
cnf(c_0_5385_1,axiom,
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5385]) ).
cnf(c_0_5386_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5386]) ).
cnf(c_0_5386_1,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5386]) ).
cnf(c_0_5387_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5387]) ).
cnf(c_0_5387_1,axiom,
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5387]) ).
cnf(c_0_5388_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_5388]) ).
cnf(c_0_5388_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_5388]) ).
cnf(c_0_5388_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_5388]) ).
cnf(c_0_5389_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5389]) ).
cnf(c_0_5389_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5389]) ).
cnf(c_0_5390_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_5390]) ).
cnf(c_0_5390_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_5390]) ).
cnf(c_0_5391_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_5391]) ).
cnf(c_0_5391_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_5391]) ).
cnf(c_0_5392_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_5392]) ).
cnf(c_0_5392_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_5392]) ).
cnf(c_0_5393_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5393]) ).
cnf(c_0_5393_1,axiom,
( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5393]) ).
cnf(c_0_5394_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5394]) ).
cnf(c_0_5394_1,axiom,
( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5394]) ).
cnf(c_0_5395_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_5395]) ).
cnf(c_0_5395_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_5395]) ).
cnf(c_0_5396_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_5396]) ).
cnf(c_0_5396_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_5396]) ).
cnf(c_0_5397_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_5397]) ).
cnf(c_0_5397_1,axiom,
( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != X2
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5397]) ).
cnf(c_0_5398_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_5398]) ).
cnf(c_0_5398_1,axiom,
( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != X2
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5398]) ).
cnf(c_0_5401_0,axiom,
( X1 = X2
| ~ c_fequal(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5401]) ).
cnf(c_0_5401_1,axiom,
( ~ c_fequal(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5401]) ).
cnf(c_0_5407_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5407]) ).
cnf(c_0_5407_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| c_HOL_Oplus__class_Oplus(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_5407]) ).
cnf(c_0_5411_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ocard(X1,X2) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5411]) ).
cnf(c_0_5411_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Finite__Set_Ocard(X1,X2) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5411]) ).
cnf(c_0_5411_2,axiom,
( c_Finite__Set_Ocard(X1,X2) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_Finite__Set_Ofinite(X1,X2)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_5411]) ).
cnf(c_0_5412_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5412]) ).
cnf(c_0_5412_1,axiom,
( ~ class_Int_Onumber__ring(X2)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5412]) ).
cnf(c_0_5412_2,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_5412]) ).
cnf(c_0_5417_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_5417]) ).
cnf(c_0_5417_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_5417]) ).
cnf(c_0_5418_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5418]) ).
cnf(c_0_5418_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5418]) ).
cnf(c_0_5419_0,axiom,
( c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1)
| ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5419]) ).
cnf(c_0_5419_1,axiom,
( ~ class_Finite__Set_Ofinite_Ofinite(X1)
| c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5419]) ).
cnf(c_0_5420_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5420]) ).
cnf(c_0_5420_1,axiom,
( ~ class_Int_Onumber__ring(X2)
| c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5420]) ).
cnf(c_0_5420_2,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5420]) ).
cnf(c_0_5421_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_5421]) ).
cnf(c_0_5421_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_5421]) ).
cnf(c_0_5422_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_5422]) ).
cnf(c_0_5422_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_5422]) ).
cnf(c_0_5423_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_5423]) ).
cnf(c_0_5423_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_5423]) ).
cnf(c_0_5424_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_5424]) ).
cnf(c_0_5424_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_5424]) ).
cnf(c_0_5425_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_5425]) ).
cnf(c_0_5425_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_5425]) ).
cnf(c_0_5426_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_5426]) ).
cnf(c_0_5426_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_5426]) ).
cnf(c_0_5427_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_5427]) ).
cnf(c_0_5427_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_5427]) ).
cnf(c_0_5428_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_5428]) ).
cnf(c_0_5428_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_5428]) ).
cnf(c_0_5429_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X1),X2,X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5429]) ).
cnf(c_0_5429_1,axiom,
( ~ class_Lattices_Obounded__lattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X1),X2,X1) = c_Orderings_Obot__class_Obot(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5429]) ).
cnf(c_0_5430_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(X2),X2) = c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5430]) ).
cnf(c_0_5430_1,axiom,
( ~ class_Lattices_Obounded__lattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(X2),X2) = c_Orderings_Obot__class_Obot(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5430]) ).
cnf(c_0_5431_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_5431]) ).
cnf(c_0_5431_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_5431]) ).
cnf(c_0_5432_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5432]) ).
cnf(c_0_5432_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_5432]) ).
cnf(c_0_5433_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5433]) ).
cnf(c_0_5433_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5433]) ).
cnf(c_0_5434_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5434]) ).
cnf(c_0_5434_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_5434]) ).
cnf(c_0_5435_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Omonoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5435]) ).
cnf(c_0_5435_1,axiom,
( ~ class_OrderedGroup_Omonoid__add(X2)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_5435]) ).
cnf(c_0_5436_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5436]) ).
cnf(c_0_5436_1,axiom,
( ~ class_OrderedGroup_Omonoid__add(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5436]) ).
cnf(c_0_5437_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5437]) ).
cnf(c_0_5437_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_5437]) ).
cnf(c_0_5438_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5438]) ).
cnf(c_0_5438_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5438]) ).
cnf(c_0_5439_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5439]) ).
cnf(c_0_5439_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5439]) ).
cnf(c_0_5440_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(X1),X2,X1) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5440]) ).
cnf(c_0_5440_1,axiom,
( ~ class_Lattices_Obounded__lattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(X1),X2,X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5440]) ).
cnf(c_0_5441_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Otop__class_Otop(X2),X2) = X1
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5441]) ).
cnf(c_0_5441_1,axiom,
( ~ class_Lattices_Obounded__lattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Otop__class_Otop(X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_5441]) ).
cnf(c_0_5442_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_5442]) ).
cnf(c_0_5442_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_5442]) ).
cnf(c_0_5443_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_5443]) ).
cnf(c_0_5443_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_5443]) ).
cnf(c_0_5444_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_5444]) ).
cnf(c_0_5444_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_5444]) ).
cnf(c_0_5445_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_5445]) ).
cnf(c_0_5445_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_5445]) ).
cnf(c_0_5446_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_5446]) ).
cnf(c_0_5446_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_5446]) ).
cnf(c_0_5447_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_5447]) ).
cnf(c_0_5447_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_5447]) ).
cnf(c_0_5448_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_5448]) ).
cnf(c_0_5448_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_5448]) ).
cnf(c_0_5451_0,axiom,
( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
| ~ class_Orderings_Obot(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5451]) ).
cnf(c_0_5451_1,axiom,
( ~ class_Orderings_Obot(X1)
| c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5451]) ).
cnf(c_0_5452_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_5452]) ).
cnf(c_0_5452_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_5452]) ).
cnf(c_0_5453_0,axiom,
( c_lessequals(X1,c_Orderings_Otop__class_Otop(X2),X2)
| ~ class_Orderings_Otop(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5453]) ).
cnf(c_0_5453_1,axiom,
( ~ class_Orderings_Otop(X2)
| c_lessequals(X1,c_Orderings_Otop__class_Otop(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5453]) ).
cnf(c_0_5454_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_5454]) ).
cnf(c_0_5454_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_5454]) ).
cnf(c_0_5457_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5457]) ).
cnf(c_0_5457_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X2)
| c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5457]) ).
cnf(c_0_5458_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5458]) ).
cnf(c_0_5458_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5458]) ).
cnf(c_0_5459_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5459]) ).
cnf(c_0_5459_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5459]) ).
cnf(c_0_5460_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_5460]) ).
cnf(c_0_5460_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_5460]) ).
cnf(c_0_5464_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_5464]) ).
cnf(c_0_5464_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_5464]) ).
cnf(c_0_5465_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X1,X2) = X1
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5465]) ).
cnf(c_0_5465_1,axiom,
( ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X1,X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_5465]) ).
cnf(c_0_5468_0,axiom,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5468]) ).
cnf(c_0_5468_1,axiom,
( ~ class_Orderings_Oorder(X2)
| c_lessequals(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5468]) ).
cnf(c_0_5469_0,axiom,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5469]) ).
cnf(c_0_5469_1,axiom,
( ~ class_Orderings_Opreorder(X2)
| c_lessequals(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5469]) ).
cnf(c_0_5470_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_5470]) ).
cnf(c_0_5470_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_5470]) ).
cnf(c_0_5474_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_5474]) ).
cnf(c_0_5474_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_5474]) ).
cnf(c_0_5493_0,axiom,
( X1 = X2
| c_SetInterval_Oord__class_OatLeast(X1,X3) != c_SetInterval_Oord__class_OatLeast(X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5493]) ).
cnf(c_0_5493_1,axiom,
( c_SetInterval_Oord__class_OatLeast(X1,X3) != c_SetInterval_Oord__class_OatLeast(X2,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5493]) ).
cnf(c_0_5493_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_SetInterval_Oord__class_OatLeast(X1,X3) != c_SetInterval_Oord__class_OatLeast(X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5493]) ).
cnf(c_0_5494_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_5494]) ).
cnf(c_0_5494_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_5494]) ).
cnf(c_0_5494_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_5494]) ).
cnf(c_0_5498_0,axiom,
( class_Finite__Set_Ofinite_Ofinite(tc_fun(X1,X2))
| ~ class_Finite__Set_Ofinite_Ofinite(X1)
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5498]) ).
cnf(c_0_5498_1,axiom,
( ~ class_Finite__Set_Ofinite_Ofinite(X1)
| class_Finite__Set_Ofinite_Ofinite(tc_fun(X1,X2))
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5498]) ).
cnf(c_0_5498_2,axiom,
( ~ class_Finite__Set_Ofinite_Ofinite(X2)
| ~ class_Finite__Set_Ofinite_Ofinite(X1)
| class_Finite__Set_Ofinite_Ofinite(tc_fun(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5498]) ).
cnf(c_0_5499_0,axiom,
( class_HOL_Oord(tc_fun(X2,X1))
| ~ class_HOL_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5499]) ).
cnf(c_0_5499_1,axiom,
( ~ class_HOL_Oord(X1)
| class_HOL_Oord(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5499]) ).
cnf(c_0_5500_0,axiom,
( class_Orderings_Obot(tc_fun(X2,X1))
| ~ class_Orderings_Obot(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5500]) ).
cnf(c_0_5500_1,axiom,
( ~ class_Orderings_Obot(X1)
| class_Orderings_Obot(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5500]) ).
cnf(c_0_5501_0,axiom,
( class_Orderings_Otop(tc_fun(X2,X1))
| ~ class_Orderings_Otop(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5501]) ).
cnf(c_0_5501_1,axiom,
( ~ class_Orderings_Otop(X1)
| class_Orderings_Otop(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5501]) ).
cnf(c_0_5502_0,axiom,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5502]) ).
cnf(c_0_5502_1,axiom,
( ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5502]) ).
cnf(c_0_5503_0,axiom,
( class_Lattices_Olattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5503]) ).
cnf(c_0_5503_1,axiom,
( ~ class_Lattices_Olattice(X1)
| class_Lattices_Olattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5503]) ).
cnf(c_0_5504_0,axiom,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5504]) ).
cnf(c_0_5504_1,axiom,
( ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5504]) ).
cnf(c_0_5505_0,axiom,
( class_Lattices_Obounded__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5505]) ).
cnf(c_0_5505_1,axiom,
( ~ class_Lattices_Obounded__lattice(X1)
| class_Lattices_Obounded__lattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5505]) ).
cnf(c_0_5506_0,axiom,
( class_Lattices_Olower__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5506]) ).
cnf(c_0_5506_1,axiom,
( ~ class_Lattices_Olattice(X1)
| class_Lattices_Olower__semilattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5506]) ).
cnf(c_0_5507_0,axiom,
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5507]) ).
cnf(c_0_5507_1,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5507]) ).
cnf(c_0_5508_0,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ocard(X1,X2) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5508]) ).
cnf(c_0_5508_1,axiom,
( c_Finite__Set_Ocard(X1,X2) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5508]) ).
cnf(c_0_5509_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_5509]) ).
cnf(c_0_5509_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_5509]) ).
cnf(c_0_5510_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_5510]) ).
cnf(c_0_5510_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_5510]) ).
cnf(c_0_5511_0,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5511]) ).
cnf(c_0_5511_1,axiom,
( ~ class_Finite__Set_Ofinite_Ofinite(X2)
| c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5511]) ).
cnf(c_0_5512_0,axiom,
( c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5512]) ).
cnf(c_0_5512_1,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5512]) ).
cnf(c_0_5513_0,axiom,
( c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5513]) ).
cnf(c_0_5513_1,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5513]) ).
cnf(c_0_5514_0,axiom,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5514]) ).
cnf(c_0_5514_1,axiom,
( c_Suc(X1) != c_Suc(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5514]) ).
cnf(c_0_5515_0,axiom,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5515]) ).
cnf(c_0_5515_1,axiom,
( c_Suc(X1) != c_Suc(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5515]) ).
cnf(c_0_5026_0,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5026]) ).
cnf(c_0_5079_0,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5079]) ).
cnf(c_0_5080_0,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5080]) ).
cnf(c_0_5148_0,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
inference(literals_permutation,[status(thm)],[c_0_5148]) ).
cnf(c_0_5152_0,axiom,
~ c_HOL_Oord__class_Oless(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_5152]) ).
cnf(c_0_5228_0,axiom,
~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
inference(literals_permutation,[status(thm)],[c_0_5228]) ).
cnf(c_0_5229_0,axiom,
~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
inference(literals_permutation,[status(thm)],[c_0_5229]) ).
cnf(c_0_5230_0,axiom,
~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
inference(literals_permutation,[status(thm)],[c_0_5230]) ).
cnf(c_0_5314_0,axiom,
c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_5314]) ).
cnf(c_0_5315_0,axiom,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oinsert(X2,X3,X1),
inference(literals_permutation,[status(thm)],[c_0_5315]) ).
cnf(c_0_5316_0,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_fun(X2,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_5316]) ).
cnf(c_0_5383_0,axiom,
~ c_lessequals(c_Suc(X1),X1,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5383]) ).
cnf(c_0_5384_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_5384]) ).
cnf(c_0_5399_0,axiom,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5399]) ).
cnf(c_0_5400_0,axiom,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5400]) ).
cnf(c_0_5402_0,axiom,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_5402]) ).
cnf(c_0_5404_0,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5404]) ).
cnf(c_0_5405_0,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5405]) ).
cnf(c_0_5516_0,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5516]) ).
cnf(c_0_5517_0,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5517]) ).
cnf(c_0_5518_0,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5518]) ).
cnf(c_0_5519_0,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5519]) ).
cnf(c_0_5521_0,axiom,
c_Suc(X1) != X1,
inference(literals_permutation,[status(thm)],[c_0_5521]) ).
cnf(c_0_5522_0,axiom,
c_Suc(X1) != X1,
inference(literals_permutation,[status(thm)],[c_0_5522]) ).
cnf(c_0_4460_0,axiom,
c_Fun_Ofun__upd(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X2,X6,X4,X5) = c_Fun_Ofun__upd(X1,X2,X6,X4,X5),
inference(literals_permutation,[status(thm)],[c_0_4460]) ).
cnf(c_0_4477_0,axiom,
c_lessequals(c_Set_Oimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4,X5),c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,X2,X4,X5),c_Set_Oimage(X1,X3,X4,X5),tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_4477]) ).
cnf(c_0_4478_0,axiom,
c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool)),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X3,tc_bool)),X3,X4),tc_fun(X4,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_4478]) ).
cnf(c_0_4487_0,axiom,
hAPP(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X2) = X3,
inference(literals_permutation,[status(thm)],[c_0_4487]) ).
cnf(c_0_4488_0,axiom,
hAPP(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X2) = X3,
inference(literals_permutation,[status(thm)],[c_0_4488]) ).
cnf(c_0_4521_0,axiom,
c_lessequals(c_Set_Oimage(X1,c_Set_Ovimage(X1,X2,X3,X4),X3,X4),X2,tc_fun(X4,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_4521]) ).
cnf(c_0_4526_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Set_Ovimage(X1,X2,X5,X4),c_Set_Ovimage(X1,X3,X5,X4),tc_fun(X5,tc_bool)) = c_Set_Ovimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X5,X4),
inference(literals_permutation,[status(thm)],[c_0_4526]) ).
cnf(c_0_4527_0,axiom,
c_HOL_Ominus__class_Ominus(c_Set_Ovimage(X1,X2,X5,X4),c_Set_Ovimage(X1,X3,X5,X4),tc_fun(X5,tc_bool)) = c_Set_Ovimage(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X5,X4),
inference(literals_permutation,[status(thm)],[c_0_4527]) ).
cnf(c_0_4532_0,axiom,
c_Set_Oimage(X1,c_Set_Ovimage(X1,X2,X3,X4),X3,X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),tc_fun(X4,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_4532]) ).
cnf(c_0_4543_0,axiom,
c_Fun_Ofun__upd(X1,X2,hAPP(X1,X2),X3,X4) = X1,
inference(literals_permutation,[status(thm)],[c_0_4543]) ).
cnf(c_0_4544_0,axiom,
c_Fun_Ofun__upd(X1,X2,hAPP(X1,X2),X3,X4) = X1,
inference(literals_permutation,[status(thm)],[c_0_4544]) ).
cnf(c_0_4545_0,axiom,
c_Fun_Ofun__upd(X1,X2,hAPP(X1,X2),X3,X4) = X1,
inference(literals_permutation,[status(thm)],[c_0_4545]) ).
cnf(c_0_4565_0,axiom,
c_in(X1,c_Set_Ovimage(X2,c_Set_Oinsert(hAPP(X2,X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X4,X3),X4),
inference(literals_permutation,[status(thm)],[c_0_4565]) ).
cnf(c_0_4584_0,axiom,
c_Set_Oimage(X1,c_Set_Oinsert(X2,X3,X4),X4,X5) = c_Set_Oinsert(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5),
inference(literals_permutation,[status(thm)],[c_0_4584]) ).
cnf(c_0_4597_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_4597]) ).
cnf(c_0_4598_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat),X4,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4598]) ).
cnf(c_0_4609_0,axiom,
c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat)),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X3),X2,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4609]) ).
cnf(c_0_4612_0,axiom,
c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = c_Set_Oinsert(X1,X2,X3),
inference(literals_permutation,[status(thm)],[c_0_4612]) ).
cnf(c_0_4614_0,axiom,
c_in(hAPP(X1,X2),c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X4),
inference(literals_permutation,[status(thm)],[c_0_4614]) ).
cnf(c_0_4639_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool)),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_4639]) ).
cnf(c_0_4640_0,axiom,
c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_4640]) ).
cnf(c_0_4641_0,axiom,
c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_4641]) ).
cnf(c_0_4642_0,axiom,
c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X4,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_4642]) ).
cnf(c_0_4691_0,axiom,
c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),
inference(literals_permutation,[status(thm)],[c_0_4691]) ).
cnf(c_0_4694_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4694]) ).
cnf(c_0_4695_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4695]) ).
cnf(c_0_4705_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3),
inference(literals_permutation,[status(thm)],[c_0_4705]) ).
cnf(c_0_4733_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_4733]) ).
cnf(c_0_4734_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_4734]) ).
cnf(c_0_4735_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_4735]) ).
cnf(c_0_4803_0,axiom,
c_HOL_Ominus__class_Ominus(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_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4803]) ).
cnf(c_0_4804_0,axiom,
c_HOL_Ominus__class_Ominus(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_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4804]) ).
cnf(c_0_4805_0,axiom,
c_HOL_Oplus__class_Oplus(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_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4805]) ).
cnf(c_0_4806_0,axiom,
c_HOL_Oplus__class_Oplus(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_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4806]) ).
cnf(c_0_4807_0,axiom,
c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat),X2,tc_nat) = c_Divides_Odiv__class_Omod(X3,X2,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4807]) ).
cnf(c_0_4808_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_4808]) ).
cnf(c_0_4809_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_4809]) ).
cnf(c_0_4878_0,axiom,
c_lessequals(X1,c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X1,X1,tc_nat),tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4878]) ).
cnf(c_0_4941_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X1),X2,tc_nat),c_Suc(X3),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4941]) ).
cnf(c_0_4965_0,axiom,
c_Set_Oimage(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_4965]) ).
cnf(c_0_4966_0,axiom,
c_Set_Oimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_4966]) ).
cnf(c_0_4967_0,axiom,
c_Set_Ovimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_4967]) ).
cnf(c_0_4968_0,axiom,
c_Set_Ovimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3,X2) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_4968]) ).
cnf(c_0_4971_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_4971]) ).
cnf(c_0_4973_0,axiom,
c_Set_Oinsert(X1,c_Set_Oinsert(X2,X3,X4),X4) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,X3,X4),X4),
inference(literals_permutation,[status(thm)],[c_0_4973]) ).
cnf(c_0_4993_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4993]) ).
cnf(c_0_4994_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4994]) ).
cnf(c_0_4995_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4995]) ).
cnf(c_0_4996_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4996]) ).
cnf(c_0_4997_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_4997]) ).
cnf(c_0_4998_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4998]) ).
cnf(c_0_4999_0,axiom,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4999]) ).
cnf(c_0_5006_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_5006]) ).
cnf(c_0_5007_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_5007]) ).
cnf(c_0_5020_0,axiom,
c_Fun_Oinj__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3),
inference(literals_permutation,[status(thm)],[c_0_5020]) ).
cnf(c_0_5037_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_5037]) ).
cnf(c_0_5044_0,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5044]) ).
cnf(c_0_5045_0,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5045]) ).
cnf(c_0_5046_0,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5046]) ).
cnf(c_0_5048_0,axiom,
c_in(X1,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),
inference(literals_permutation,[status(thm)],[c_0_5048]) ).
cnf(c_0_5061_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_5061]) ).
cnf(c_0_5086_0,axiom,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
inference(literals_permutation,[status(thm)],[c_0_5086]) ).
cnf(c_0_5120_0,axiom,
c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_5120]) ).
cnf(c_0_5121_0,axiom,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_5121]) ).
cnf(c_0_5122_0,axiom,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_5122]) ).
cnf(c_0_5137_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) = c_HOL_Ominus__class_Ominus(X1,c_Suc(X2),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5137]) ).
cnf(c_0_5140_0,axiom,
c_Set_Oinsert(X1,c_Set_Oinsert(X1,X2,X3),X3) = c_Set_Oinsert(X1,X2,X3),
inference(literals_permutation,[status(thm)],[c_0_5140]) ).
cnf(c_0_5141_0,axiom,
c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5141]) ).
cnf(c_0_5142_0,axiom,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_Suc(X2),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5142]) ).
cnf(c_0_5176_0,axiom,
c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_5176]) ).
cnf(c_0_5182_0,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_5182]) ).
cnf(c_0_5231_0,axiom,
c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)) = c_HOL_Oplus__class_Oplus(X1,c_Suc(X2),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5231]) ).
cnf(c_0_5232_0,axiom,
c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(X1),X2,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5232]) ).
cnf(c_0_5234_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_Suc(X1),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5234]) ).
cnf(c_0_5235_0,axiom,
c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
inference(literals_permutation,[status(thm)],[c_0_5235]) ).
cnf(c_0_5236_0,axiom,
c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
inference(literals_permutation,[status(thm)],[c_0_5236]) ).
cnf(c_0_5237_0,axiom,
c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
inference(literals_permutation,[status(thm)],[c_0_5237]) ).
cnf(c_0_5240_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_5240]) ).
cnf(c_0_5241_0,axiom,
c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5241]) ).
cnf(c_0_5242_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat) = X2,
inference(literals_permutation,[status(thm)],[c_0_5242]) ).
cnf(c_0_5243_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat) = X1,
inference(literals_permutation,[status(thm)],[c_0_5243]) ).
cnf(c_0_5244_0,axiom,
c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X1,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5244]) ).
cnf(c_0_5245_0,axiom,
c_lessequals(X1,c_HOL_Otimes__class_Otimes(X1,X1,tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5245]) ).
cnf(c_0_5246_0,axiom,
c_lessequals(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X1,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5246]) ).
cnf(c_0_5247_0,axiom,
c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5247]) ).
cnf(c_0_5248_0,axiom,
c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5248]) ).
cnf(c_0_5249_0,axiom,
c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5249]) ).
cnf(c_0_5252_0,axiom,
c_HOL_Ominus__class_Ominus(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_5252]) ).
cnf(c_0_5253_0,axiom,
c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_5253]) ).
cnf(c_0_5254_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_5254]) ).
cnf(c_0_5255_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_5255]) ).
cnf(c_0_5256_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_5256]) ).
cnf(c_0_5307_0,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
inference(literals_permutation,[status(thm)],[c_0_5307]) ).
cnf(c_0_5309_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
inference(literals_permutation,[status(thm)],[c_0_5309]) ).
cnf(c_0_5310_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = X2,
inference(literals_permutation,[status(thm)],[c_0_5310]) ).
cnf(c_0_5311_0,axiom,
c_HOL_Ominus__class_Ominus(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
inference(literals_permutation,[status(thm)],[c_0_5311]) ).
cnf(c_0_5312_0,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_5312]) ).
cnf(c_0_5313_0,axiom,
c_lessequals(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_5313]) ).
cnf(c_0_5322_0,axiom,
c_HOL_Ominus__class_Ominus(c_Suc(X1),c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5322]) ).
cnf(c_0_5323_0,axiom,
c_HOL_Oplus__class_Oplus(c_Suc(X1),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_Suc(X2),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5323]) ).
cnf(c_0_5345_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_5345]) ).
cnf(c_0_5346_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_5346]) ).
cnf(c_0_5364_0,axiom,
c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2),
inference(literals_permutation,[status(thm)],[c_0_5364]) ).
cnf(c_0_5365_0,axiom,
c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5365]) ).
cnf(c_0_5366_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_5366]) ).
cnf(c_0_5371_0,axiom,
c_HOL_Ominus__class_Ominus(X1,X1,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_5371]) ).
cnf(c_0_5403_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_5403]) ).
cnf(c_0_5406_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,X1,tc_fun(X2,tc_bool)) = X1,
inference(literals_permutation,[status(thm)],[c_0_5406]) ).
cnf(c_0_5408_0,axiom,
c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_5408]) ).
cnf(c_0_5409_0,axiom,
c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_5409]) ).
cnf(c_0_5410_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_5410]) ).
cnf(c_0_5413_0,axiom,
c_HOL_Oplus__class_Oplus(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_5413]) ).
cnf(c_0_5414_0,axiom,
c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),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_5414]) ).
cnf(c_0_5415_0,axiom,
c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),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_5415]) ).
cnf(c_0_5416_0,axiom,
c_HOL_Oplus__class_Oplus(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_5416]) ).
cnf(c_0_5449_0,axiom,
c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5449]) ).
cnf(c_0_5450_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_5450]) ).
cnf(c_0_5455_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_5455]) ).
cnf(c_0_5456_0,axiom,
c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
inference(literals_permutation,[status(thm)],[c_0_5456]) ).
cnf(c_0_5461_0,axiom,
c_lessequals(c_Suc(X1),c_Suc(X1),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5461]) ).
cnf(c_0_5462_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_5462]) ).
cnf(c_0_5463_0,axiom,
c_HOL_Ominus__class_Ominus(c_Suc(X1),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1,
inference(literals_permutation,[status(thm)],[c_0_5463]) ).
cnf(c_0_5466_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_5466]) ).
cnf(c_0_5467_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_5467]) ).
cnf(c_0_5471_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_5471]) ).
cnf(c_0_5472_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_5472]) ).
cnf(c_0_5473_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5473]) ).
cnf(c_0_5475_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) = c_Suc(X1),
inference(literals_permutation,[status(thm)],[c_0_5475]) ).
cnf(c_0_5476_0,axiom,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_Suc(X1),
inference(literals_permutation,[status(thm)],[c_0_5476]) ).
cnf(c_0_5477_0,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5477]) ).
cnf(c_0_5478_0,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5478]) ).
cnf(c_0_5479_0,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5479]) ).
cnf(c_0_5480_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_5480]) ).
cnf(c_0_5481_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5481]) ).
cnf(c_0_5482_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_5482]) ).
cnf(c_0_5483_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_5483]) ).
cnf(c_0_5484_0,axiom,
c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
inference(literals_permutation,[status(thm)],[c_0_5484]) ).
cnf(c_0_5485_0,axiom,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
inference(literals_permutation,[status(thm)],[c_0_5485]) ).
cnf(c_0_5486_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1,
inference(literals_permutation,[status(thm)],[c_0_5486]) ).
cnf(c_0_5487_0,axiom,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
inference(literals_permutation,[status(thm)],[c_0_5487]) ).
cnf(c_0_5488_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_5488]) ).
cnf(c_0_5489_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_5489]) ).
cnf(c_0_5490_0,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5490]) ).
cnf(c_0_5491_0,axiom,
c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5491]) ).
cnf(c_0_5492_0,axiom,
c_fequal(X1,X1,X2),
inference(literals_permutation,[status(thm)],[c_0_5492]) ).
cnf(c_0_5495_0,axiom,
c_lessequals(X1,X1,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5495]) ).
cnf(c_0_5496_0,axiom,
c_lessequals(X1,X1,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5496]) ).
cnf(c_0_5497_0,axiom,
c_Ring__and__Field_Odvd__class_Odvd(X1,X1,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5497]) ).
cnf(c_0_5520_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_5520]) ).
cnf(c_0_5523_0,axiom,
class_HOL_Oord(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_5523]) ).
cnf(c_0_5524_0,axiom,
class_Orderings_Obot(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_5524]) ).
cnf(c_0_5525_0,axiom,
class_Orderings_Otop(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_5525]) ).
cnf(c_0_5526_0,axiom,
class_Orderings_Oorder(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_5526]) ).
cnf(c_0_5527_0,axiom,
class_Lattices_Olattice(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_5527]) ).
cnf(c_0_5528_0,axiom,
class_Orderings_Opreorder(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_5528]) ).
cnf(c_0_5529_0,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_5529]) ).
cnf(c_0_5530_0,axiom,
class_Lattices_Obounded__lattice(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_5530]) ).
cnf(c_0_5531_0,axiom,
class_Lattices_Olower__semilattice(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_5531]) ).
cnf(c_0_5532_0,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_5532]) ).
cnf(c_0_5533_0,axiom,
class_HOL_Oord(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5533]) ).
cnf(c_0_5534_0,axiom,
class_Orderings_Obot(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5534]) ).
cnf(c_0_5535_0,axiom,
class_Orderings_Oorder(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5535]) ).
cnf(c_0_5536_0,axiom,
class_Lattices_Olattice(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5536]) ).
cnf(c_0_5537_0,axiom,
class_Orderings_Olinorder(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5537]) ).
cnf(c_0_5538_0,axiom,
class_Orderings_Opreorder(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5538]) ).
cnf(c_0_5539_0,axiom,
class_Ring__and__Field_Odvd(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5539]) ).
cnf(c_0_5540_0,axiom,
class_Nat_Osemiring__char__0(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5540]) ).
cnf(c_0_5541_0,axiom,
class_Divides_Osemiring__div(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5541]) ).
cnf(c_0_5542_0,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5542]) ).
cnf(c_0_5543_0,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5543]) ).
cnf(c_0_5544_0,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5544]) ).
cnf(c_0_5545_0,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5545]) ).
cnf(c_0_5546_0,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5546]) ).
cnf(c_0_5547_0,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5547]) ).
cnf(c_0_5548_0,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5548]) ).
cnf(c_0_5549_0,axiom,
class_Lattices_Olower__semilattice(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5549]) ).
cnf(c_0_5550_0,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5550]) ).
cnf(c_0_5551_0,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5551]) ).
cnf(c_0_5552_0,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5552]) ).
cnf(c_0_5553_0,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5553]) ).
cnf(c_0_5554_0,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5554]) ).
cnf(c_0_5555_0,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5555]) ).
cnf(c_0_5556_0,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5556]) ).
cnf(c_0_5557_0,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5557]) ).
cnf(c_0_5558_0,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5558]) ).
cnf(c_0_5559_0,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5559]) ).
cnf(c_0_5560_0,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5560]) ).
cnf(c_0_5561_0,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5561]) ).
cnf(c_0_5562_0,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5562]) ).
cnf(c_0_5563_0,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5563]) ).
cnf(c_0_5564_0,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5564]) ).
cnf(c_0_5565_0,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5565]) ).
cnf(c_0_5566_0,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5566]) ).
cnf(c_0_5567_0,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5567]) ).
cnf(c_0_5568_0,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5568]) ).
cnf(c_0_5569_0,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5569]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_001,negated_conjecture,
~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
file('<stdin>',cls_conjecture_6) ).
fof(c_0_1_002,negated_conjecture,
c_Finite__Set_Ocard(v_G,t_a) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat),
file('<stdin>',cls_conjecture_3) ).
fof(c_0_2_003,negated_conjecture,
c_lessequals(c_Suc(v_na),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat),
file('<stdin>',cls_conjecture_2) ).
fof(c_0_3_004,negated_conjecture,
c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
file('<stdin>',cls_conjecture_1) ).
fof(c_0_4_005,negated_conjecture,
~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a),
file('<stdin>',cls_conjecture_5) ).
fof(c_0_5_006,negated_conjecture,
c_in(v_pn,v_U,tc_Com_Opname),
file('<stdin>',cls_conjecture_4) ).
fof(c_0_6_007,negated_conjecture,
c_Finite__Set_Ofinite(v_U,tc_Com_Opname),
file('<stdin>',cls_conjecture_0) ).
fof(c_0_7_008,negated_conjecture,
~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_8_009,negated_conjecture,
c_Finite__Set_Ocard(v_G,t_a) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat),
c_0_1 ).
fof(c_0_9_010,negated_conjecture,
c_lessequals(c_Suc(v_na),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat),
c_0_2 ).
fof(c_0_10_011,negated_conjecture,
c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
c_0_3 ).
fof(c_0_11_012,negated_conjecture,
~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_12_013,negated_conjecture,
c_in(v_pn,v_U,tc_Com_Opname),
c_0_5 ).
fof(c_0_13_014,negated_conjecture,
c_Finite__Set_Ofinite(v_U,tc_Com_Opname),
c_0_6 ).
fof(c_0_14_015,negated_conjecture,
~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
c_0_7 ).
fof(c_0_15_016,negated_conjecture,
c_Finite__Set_Ocard(v_G,t_a) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat),
c_0_8 ).
fof(c_0_16_017,negated_conjecture,
c_lessequals(c_Suc(v_na),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat),
c_0_9 ).
fof(c_0_17_018,negated_conjecture,
c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
c_0_10 ).
fof(c_0_18_019,negated_conjecture,
~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a),
c_0_11 ).
fof(c_0_19_020,negated_conjecture,
c_in(v_pn,v_U,tc_Com_Opname),
c_0_12 ).
fof(c_0_20_021,negated_conjecture,
c_Finite__Set_Ofinite(v_U,tc_Com_Opname),
c_0_13 ).
cnf(c_0_21_022,negated_conjecture,
~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22_023,negated_conjecture,
c_Finite__Set_Ocard(v_G,t_a) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23_024,negated_conjecture,
c_lessequals(c_Suc(v_na),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24_025,negated_conjecture,
c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25_026,negated_conjecture,
~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26_027,negated_conjecture,
c_in(v_pn,v_U,tc_Com_Opname),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27_028,negated_conjecture,
c_Finite__Set_Ofinite(v_U,tc_Com_Opname),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28_029,negated_conjecture,
~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
c_0_21,
[final] ).
cnf(c_0_29_030,negated_conjecture,
c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat) = c_Finite__Set_Ocard(v_G,t_a),
c_0_22,
[final] ).
cnf(c_0_30_031,negated_conjecture,
c_lessequals(c_Suc(v_na),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat),
c_0_23,
[final] ).
cnf(c_0_31_032,negated_conjecture,
c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
c_0_24,
[final] ).
cnf(c_0_32_033,negated_conjecture,
~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a),
c_0_25,
[final] ).
cnf(c_0_33_034,negated_conjecture,
c_in(v_pn,v_U,tc_Com_Opname),
c_0_26,
[final] ).
cnf(c_0_34_035,negated_conjecture,
c_Finite__Set_Ofinite(v_U,tc_Com_Opname),
c_0_27,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_2735,negated_conjecture,
c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
file('/export/starexec/sandbox/tmp/iprover_modulo_cc5f72.p',c_0_31) ).
cnf(c_3488,negated_conjecture,
c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
inference(copy,[status(esa)],[c_2735]) ).
cnf(c_3512,negated_conjecture,
c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
inference(copy,[status(esa)],[c_3488]) ).
cnf(c_3517,negated_conjecture,
c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
inference(copy,[status(esa)],[c_3512]) ).
cnf(c_3524,negated_conjecture,
c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
inference(copy,[status(esa)],[c_3517]) ).
cnf(c_11646,plain,
c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
inference(copy,[status(esa)],[c_3524]) ).
cnf(c_1740,plain,
( c_lessequals(c_Set_Oinsert(X0,X1,X2),X3,tc_fun(X2,tc_bool))
| ~ c_in(X0,X3,X2)
| ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_cc5f72.p',c_0_4828_2) ).
cnf(c_9660,plain,
( c_lessequals(c_Set_Oinsert(X0,X1,X2),X3,tc_fun(X2,tc_bool))
| ~ c_in(X0,X3,X2)
| ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool)) ),
inference(copy,[status(esa)],[c_1740]) ).
cnf(c_9661,plain,
( c_lessequals(c_Set_Oinsert(X0,X1,X2),X3,tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool))
| ~ c_in(X0,X3,X2) ),
inference(rewriting,[status(thm)],[c_9660]) ).
cnf(c_11824,plain,
( c_lessequals(c_Set_Oinsert(X0,v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ c_in(X0,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) ),
inference(resolution,[status(thm)],[c_11646,c_9661]) ).
cnf(c_11827,plain,
( c_lessequals(c_Set_Oinsert(X0,v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ c_in(X0,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) ),
inference(rewriting,[status(thm)],[c_11824]) ).
cnf(c_2731,negated_conjecture,
~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
file('/export/starexec/sandbox/tmp/iprover_modulo_cc5f72.p',c_0_28) ).
cnf(c_3480,negated_conjecture,
~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
inference(copy,[status(esa)],[c_2731]) ).
cnf(c_3508,negated_conjecture,
~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
inference(copy,[status(esa)],[c_3480]) ).
cnf(c_3521,negated_conjecture,
~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
inference(copy,[status(esa)],[c_3508]) ).
cnf(c_3527,negated_conjecture,
~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
inference(copy,[status(esa)],[c_3521]) ).
cnf(c_11652,negated_conjecture,
~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
inference(copy,[status(esa)],[c_3527]) ).
cnf(c_16060,plain,
~ c_in(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),
inference(resolution,[status(thm)],[c_11827,c_11652]) ).
cnf(c_16061,plain,
~ c_in(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),
inference(rewriting,[status(thm)],[c_16060]) ).
cnf(c_2736,negated_conjecture,
c_in(v_pn,v_U,tc_Com_Opname),
file('/export/starexec/sandbox/tmp/iprover_modulo_cc5f72.p',c_0_33) ).
cnf(c_3490,negated_conjecture,
c_in(v_pn,v_U,tc_Com_Opname),
inference(copy,[status(esa)],[c_2736]) ).
cnf(c_3513,negated_conjecture,
c_in(v_pn,v_U,tc_Com_Opname),
inference(copy,[status(esa)],[c_3490]) ).
cnf(c_3516,negated_conjecture,
c_in(v_pn,v_U,tc_Com_Opname),
inference(copy,[status(esa)],[c_3513]) ).
cnf(c_3525,negated_conjecture,
c_in(v_pn,v_U,tc_Com_Opname),
inference(copy,[status(esa)],[c_3516]) ).
cnf(c_11648,plain,
c_in(v_pn,v_U,tc_Com_Opname),
inference(copy,[status(esa)],[c_3525]) ).
cnf(c_2322,plain,
( c_in(hAPP(X0,X1),c_Set_Oimage(X0,X2,X3,X4),X4)
| ~ c_in(X1,X2,X3) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_cc5f72.p',c_0_4624_1) ).
cnf(c_10824,plain,
( c_in(hAPP(X0,X1),c_Set_Oimage(X0,X2,X3,X4),X4)
| ~ c_in(X1,X2,X3) ),
inference(copy,[status(esa)],[c_2322]) ).
cnf(c_11747,plain,
c_in(hAPP(X0,v_pn),c_Set_Oimage(X0,v_U,tc_Com_Opname,X1),X1),
inference(resolution,[status(thm)],[c_11648,c_10824]) ).
cnf(c_11750,plain,
c_in(hAPP(X0,v_pn),c_Set_Oimage(X0,v_U,tc_Com_Opname,X1),X1),
inference(rewriting,[status(thm)],[c_11747]) ).
cnf(c_16063,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_16061,c_11750]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV884-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : iprover_modulo %s %d
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 14 17:55:55 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Running in mono-core mode
% 0.35/0.60 % Orienting using strategy Equiv(ClausalAll)
% 0.35/0.60 % Orientation found
% 0.35/0.60 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_9e98cf.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_cc5f72.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_3192ff | grep -v "SZS"
% 0.35/0.62
% 0.35/0.62 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.35/0.62
% 0.35/0.62 %
% 0.35/0.62 % ------ iProver source info
% 0.35/0.62
% 0.35/0.62 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.35/0.62 % git: non_committed_changes: true
% 0.35/0.62 % git: last_make_outside_of_git: true
% 0.35/0.62
% 0.35/0.62 %
% 0.35/0.62 % ------ Input Options
% 0.35/0.62
% 0.35/0.62 % --out_options all
% 0.35/0.62 % --tptp_safe_out true
% 0.35/0.62 % --problem_path ""
% 0.35/0.62 % --include_path ""
% 0.35/0.62 % --clausifier .//eprover
% 0.35/0.62 % --clausifier_options --tstp-format
% 0.35/0.62 % --stdin false
% 0.35/0.62 % --dbg_backtrace false
% 0.35/0.62 % --dbg_dump_prop_clauses false
% 0.35/0.62 % --dbg_dump_prop_clauses_file -
% 0.35/0.62 % --dbg_out_stat false
% 0.35/0.62
% 0.35/0.62 % ------ General Options
% 0.35/0.62
% 0.35/0.62 % --fof false
% 0.35/0.62 % --time_out_real 150.
% 0.35/0.62 % --time_out_prep_mult 0.2
% 0.35/0.62 % --time_out_virtual -1.
% 0.35/0.62 % --schedule none
% 0.35/0.62 % --ground_splitting input
% 0.35/0.62 % --splitting_nvd 16
% 0.35/0.62 % --non_eq_to_eq false
% 0.35/0.62 % --prep_gs_sim true
% 0.35/0.62 % --prep_unflatten false
% 0.35/0.62 % --prep_res_sim true
% 0.35/0.62 % --prep_upred true
% 0.35/0.62 % --res_sim_input true
% 0.35/0.62 % --clause_weak_htbl true
% 0.35/0.62 % --gc_record_bc_elim false
% 0.35/0.62 % --symbol_type_check false
% 0.35/0.62 % --clausify_out false
% 0.35/0.62 % --large_theory_mode false
% 0.35/0.62 % --prep_sem_filter none
% 0.35/0.62 % --prep_sem_filter_out false
% 0.35/0.62 % --preprocessed_out false
% 0.35/0.62 % --sub_typing false
% 0.35/0.62 % --brand_transform false
% 0.35/0.62 % --pure_diseq_elim true
% 0.35/0.62 % --min_unsat_core false
% 0.35/0.62 % --pred_elim true
% 0.35/0.62 % --add_important_lit false
% 0.35/0.62 % --soft_assumptions false
% 0.35/0.62 % --reset_solvers false
% 0.35/0.62 % --bc_imp_inh []
% 0.35/0.62 % --conj_cone_tolerance 1.5
% 0.35/0.62 % --prolific_symb_bound 500
% 0.35/0.62 % --lt_threshold 2000
% 0.35/0.62
% 0.35/0.62 % ------ SAT Options
% 0.35/0.62
% 0.35/0.62 % --sat_mode false
% 0.35/0.62 % --sat_fm_restart_options ""
% 0.35/0.62 % --sat_gr_def false
% 0.35/0.62 % --sat_epr_types true
% 0.35/0.62 % --sat_non_cyclic_types false
% 0.35/0.62 % --sat_finite_models false
% 0.35/0.62 % --sat_fm_lemmas false
% 0.35/0.62 % --sat_fm_prep false
% 0.35/0.62 % --sat_fm_uc_incr true
% 0.35/0.62 % --sat_out_model small
% 0.35/0.62 % --sat_out_clauses false
% 0.35/0.62
% 0.35/0.62 % ------ QBF Options
% 0.35/0.62
% 0.35/0.62 % --qbf_mode false
% 0.35/0.62 % --qbf_elim_univ true
% 0.35/0.62 % --qbf_sk_in true
% 0.35/0.62 % --qbf_pred_elim true
% 0.35/0.62 % --qbf_split 32
% 0.35/0.62
% 0.35/0.62 % ------ BMC1 Options
% 0.35/0.62
% 0.35/0.62 % --bmc1_incremental false
% 0.35/0.62 % --bmc1_axioms reachable_all
% 0.35/0.62 % --bmc1_min_bound 0
% 0.35/0.62 % --bmc1_max_bound -1
% 0.35/0.62 % --bmc1_max_bound_default -1
% 0.35/0.62 % --bmc1_symbol_reachability true
% 0.35/0.62 % --bmc1_property_lemmas false
% 0.35/0.62 % --bmc1_k_induction false
% 0.35/0.62 % --bmc1_non_equiv_states false
% 0.35/0.62 % --bmc1_deadlock false
% 0.35/0.62 % --bmc1_ucm false
% 0.35/0.62 % --bmc1_add_unsat_core none
% 0.35/0.62 % --bmc1_unsat_core_children false
% 0.35/0.62 % --bmc1_unsat_core_extrapolate_axioms false
% 0.35/0.62 % --bmc1_out_stat full
% 0.35/0.62 % --bmc1_ground_init false
% 0.35/0.62 % --bmc1_pre_inst_next_state false
% 0.35/0.62 % --bmc1_pre_inst_state false
% 0.35/0.62 % --bmc1_pre_inst_reach_state false
% 0.35/0.62 % --bmc1_out_unsat_core false
% 0.35/0.62 % --bmc1_aig_witness_out false
% 0.35/0.62 % --bmc1_verbose false
% 0.35/0.62 % --bmc1_dump_clauses_tptp false
% 150.47/150.64 % --bmc1_dump_unsat_core_tptp false
% 150.47/150.64 % --bmc1_dump_file -
% 150.47/150.64 % --bmc1_ucm_expand_uc_limit 128
% 150.47/150.64 % --bmc1_ucm_n_expand_iterations 6
% 150.47/150.64 % --bmc1_ucm_extend_mode 1
% 150.47/150.64 % --bmc1_ucm_init_mode 2
% 150.47/150.64 % --bmc1_ucm_cone_mode none
% 150.47/150.64 % --bmc1_ucm_reduced_relation_type 0
% 150.47/150.64 % --bmc1_ucm_relax_model 4
% 150.47/150.64 % --bmc1_ucm_full_tr_after_sat true
% 150.47/150.64 % --bmc1_ucm_expand_neg_assumptions false
% 150.47/150.64 % --bmc1_ucm_layered_model none
% 150.47/150.64 % --bmc1_ucm_max_lemma_size 10
% 150.47/150.64
% 150.47/150.64 % ------ AIG Options
% 150.47/150.64
% 150.47/150.64 % --aig_mode false
% 150.47/150.64
% 150.47/150.64 % ------ Instantiation Options
% 150.47/150.64
% 150.47/150.64 % --instantiation_flag true
% 150.47/150.64 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 150.47/150.64 % --inst_solver_per_active 750
% 150.47/150.64 % --inst_solver_calls_frac 0.5
% 150.47/150.64 % --inst_passive_queue_type priority_queues
% 150.47/150.64 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 150.47/150.64 % --inst_passive_queues_freq [25;2]
% 150.47/150.64 % --inst_dismatching true
% 150.47/150.64 % --inst_eager_unprocessed_to_passive true
% 150.47/150.64 % --inst_prop_sim_given true
% 150.47/150.64 % --inst_prop_sim_new false
% 150.47/150.64 % --inst_orphan_elimination true
% 150.47/150.64 % --inst_learning_loop_flag true
% 150.47/150.64 % --inst_learning_start 3000
% 150.47/150.64 % --inst_learning_factor 2
% 150.47/150.64 % --inst_start_prop_sim_after_learn 3
% 150.47/150.64 % --inst_sel_renew solver
% 150.47/150.64 % --inst_lit_activity_flag true
% 150.47/150.64 % --inst_out_proof true
% 150.47/150.64
% 150.47/150.64 % ------ Resolution Options
% 150.47/150.64
% 150.47/150.64 % --resolution_flag true
% 150.47/150.64 % --res_lit_sel kbo_max
% 150.47/150.64 % --res_to_prop_solver none
% 150.47/150.64 % --res_prop_simpl_new false
% 150.47/150.64 % --res_prop_simpl_given false
% 150.47/150.64 % --res_passive_queue_type priority_queues
% 150.47/150.64 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 150.47/150.64 % --res_passive_queues_freq [15;5]
% 150.47/150.64 % --res_forward_subs full
% 150.47/150.64 % --res_backward_subs full
% 150.47/150.64 % --res_forward_subs_resolution true
% 150.47/150.64 % --res_backward_subs_resolution true
% 150.47/150.64 % --res_orphan_elimination false
% 150.47/150.64 % --res_time_limit 1000.
% 150.47/150.64 % --res_out_proof true
% 150.47/150.64 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_9e98cf.s
% 150.47/150.64 % --modulo true
% 150.47/150.64
% 150.47/150.64 % ------ Combination Options
% 150.47/150.64
% 150.47/150.64 % --comb_res_mult 1000
% 150.47/150.64 % --comb_inst_mult 300
% 150.47/150.64 % ------
% 150.47/150.64
% 150.47/150.64 % ------ Parsing...% successful
% 150.47/150.64
% 150.47/150.64 % ------ 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 %
% 150.47/150.64
% 150.47/150.64 % ------ Proving...
% 150.47/150.64 % ------ Problem Properties
% 150.47/150.64
% 150.47/150.64 %
% 150.47/150.64 % EPR false
% 150.47/150.64 % Horn false
% 150.47/150.64 % Has equality true
% 150.47/150.64
% 150.47/150.64 % % ------ Input Options Time Limit: Unbounded
% 150.47/150.64
% 150.47/150.64
% 150.47/150.64 Compiling...
% 150.47/150.64 Loading plugin: done.
% 150.47/150.64 %
% 150.47/150.64
% 150.47/150.64
% 150.47/150.64 % Time Out Real
% 150.47/150.64
% 150.47/150.64 % ------ Statistics
% 150.47/150.64
% 150.47/150.64 % ------ General
% 150.47/150.64
% 150.47/150.64 % num_of_input_clauses: 2738
% 150.47/150.64 % num_of_input_neg_conjectures: 7
% 150.47/150.64 % num_of_splits: 0
% 150.47/150.64 % num_of_split_atoms: 0
% 150.47/150.64 % num_of_sem_filtered_clauses: 0
% 150.47/150.64 % num_of_subtypes: 0
% 150.47/150.64 % monotx_restored_types: 0
% 150.47/150.64 % sat_num_of_epr_types: 0
% 150.47/150.64 % sat_num_of_non_cyclic_types: 0
% 150.47/150.64 % sat_guarded_non_collapsed_types: 0
% 150.47/150.64 % is_epr: 0
% 150.47/150.64 % is_horn: 0
% 150.47/150.64 % has_eq: 1
% 150.47/150.64 % num_pure_diseq_elim: 0
% 150.47/150.64 % simp_replaced_by: 0
% 150.47/150.64 % res_preprocessed: 14
% 150.47/150.64 % prep_upred: 0
% 150.47/150.64 % prep_unflattend: 0
% 150.47/150.64 % pred_elim_cands: 0
% 150.47/150.64 % pred_elim: 0
% 150.47/150.64 % pred_elim_cl: 0
% 150.47/150.64 % pred_elim_cycles: 0
% 150.47/150.64 % forced_gc_time: 0
% 150.47/150.64 % gc_basic_clause_elim: 0
% 150.47/150.64 % parsing_time: 0.127
% 150.47/150.64 % sem_filter_time: 0.
% 150.47/150.64 % pred_elim_time: 0.
% 150.47/150.64 % out_proof_time: 0.
% 150.47/150.64 % monotx_time: 0.
% 150.47/150.64 % subtype_inf_time: 0.
% 150.47/150.64 % unif_index_cands_time: 0.
% 150.47/150.64 % unif_index_add_time: 0.001
% 150.47/150.64 % total_time: 150.03
% 150.47/150.64 % num_of_symbols: 138
% 150.47/150.64 % num_of_terms: 6290
% 150.47/150.64
% 150.47/150.64 % ------ Propositional Solver
% 150.47/150.64
% 150.47/150.64 % prop_solver_calls: 1
% 150.47/150.64 % prop_fast_solver_calls: 21
% 150.47/150.64 % prop_num_of_clauses: 2329
% 150.47/150.64 % prop_preprocess_simplified: 8543
% 150.47/150.64 % prop_fo_subsumed: 0
% 150.47/150.64 % prop_solver_time: 0.
% 150.47/150.64 % prop_fast_solver_time: 0.
% 150.47/150.64 % prop_unsat_core_time: 0.
% 150.47/150.64
% 150.47/150.64 % ------ QBF
% 150.47/150.64
% 150.47/150.64 % qbf_q_res: 0
% 150.47/150.64 % qbf_num_tautologies: 0
% 150.47/150.64 % qbf_prep_cycles: 0
% 150.47/150.64
% 150.47/150.64 % ------ BMC1
% 150.47/150.64
% 150.47/150.64 % bmc1_current_bound: -1
% 150.47/150.64 % bmc1_last_solved_bound: -1
% 150.47/150.64 % bmc1_unsat_core_size: -1
% 150.47/150.64 % bmc1_unsat_core_parents_size: -1
% 150.47/150.64 % bmc1_merge_next_fun: 0
% 150.47/150.64 % bmc1_unsat_core_clauses_time: 0.
% 150.47/150.64
% 150.47/150.64 % ------ Instantiation
% 150.47/150.64
% 150.47/150.64 % inst_num_of_clauses: 2443
% 150.47/150.64 % inst_num_in_passive: 0
% 150.47/150.64 % inst_num_in_active: 0
% 150.47/150.64 % inst_num_in_unprocessed: 2738
% 150.47/150.64 % inst_num_of_loops: 0
% 150.47/150.64 % inst_num_of_learning_restarts: 0
% 150.47/150.64 % inst_num_moves_active_passive: 0
% 150.47/150.64 % inst_lit_activity: 0
% 150.47/150.64 % inst_lit_activity_moves: 0
% 150.47/150.64 % inst_num_tautologies: 0
% 150.47/150.64 % inst_num_prop_implied: 0
% 150.47/150.64 % inst_num_existing_simplified: 0
% 150.47/150.64 % inst_num_eq_res_simplified: 0
% 150.47/150.64 % inst_num_child_elim: 0
% 150.47/150.64 % inst_num_of_dismatching_blockings: 0
% 150.47/150.64 % inst_num_of_non_proper_insts: 0
% 150.47/150.64 % inst_num_of_duplicates: 0
% 150.47/150.64 % inst_inst_num_from_inst_to_res: 0
% 150.47/150.64 % inst_dismatching_checking_time: 0.
% 150.47/150.64
% 150.47/150.64 % ------ Resolution
% 150.47/150.64
% 150.47/150.64 % res_num_of_clauses: 2554
% 150.47/150.64 % res_num_in_passive: 0
% 150.47/150.64 % res_num_in_active: 929
% 150.47/150.64 % res_num_of_loops: 0
% 150.47/150.64 % res_forward_subset_subsumed: 1567
% 150.47/150.64 % res_backward_subset_subsumed: 15
% 150.47/150.64 % res_forward_subsumed: 0
% 150.47/150.64 % res_backward_subsumed: 0
% 150.47/150.64 % res_forward_subsumption_resolution: 0
% 150.47/150.64 % res_backward_subsumption_resolution: 0
% 150.47/150.64 % res_clause_to_clause_subsumption: 0
% 150.47/150.64 % res_orphan_elimination: 0
% 150.47/150.64 % res_tautology_del: 0
% 150.47/150.64 % res_num_eq_res_simplified: 0
% 150.47/150.64 % res_num_sel_changes: 0
% 150.47/150.64 % res_moves_from_active_to_pass: 0
% 150.47/150.64
% 150.47/150.64 % Status Unknown
% 150.50/150.92 % Orienting using strategy ClausalAll
% 150.50/150.92 % Orientation found
% 150.50/150.92 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_9e98cf.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_cc5f72.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_776f64 | grep -v "SZS"
% 150.80/150.94
% 150.80/150.94 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 150.80/150.94
% 150.80/150.94 %
% 150.80/150.94 % ------ iProver source info
% 150.80/150.94
% 150.80/150.94 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 150.80/150.94 % git: non_committed_changes: true
% 150.80/150.94 % git: last_make_outside_of_git: true
% 150.80/150.94
% 150.80/150.94 %
% 150.80/150.94 % ------ Input Options
% 150.80/150.94
% 150.80/150.94 % --out_options all
% 150.80/150.94 % --tptp_safe_out true
% 150.80/150.94 % --problem_path ""
% 150.80/150.94 % --include_path ""
% 150.80/150.94 % --clausifier .//eprover
% 150.80/150.94 % --clausifier_options --tstp-format
% 150.80/150.94 % --stdin false
% 150.80/150.94 % --dbg_backtrace false
% 150.80/150.94 % --dbg_dump_prop_clauses false
% 150.80/150.94 % --dbg_dump_prop_clauses_file -
% 150.80/150.94 % --dbg_out_stat false
% 150.80/150.94
% 150.80/150.94 % ------ General Options
% 150.80/150.94
% 150.80/150.94 % --fof false
% 150.80/150.94 % --time_out_real 150.
% 150.80/150.94 % --time_out_prep_mult 0.2
% 150.80/150.94 % --time_out_virtual -1.
% 150.80/150.94 % --schedule none
% 150.80/150.94 % --ground_splitting input
% 150.80/150.94 % --splitting_nvd 16
% 150.80/150.94 % --non_eq_to_eq false
% 150.80/150.94 % --prep_gs_sim true
% 150.80/150.94 % --prep_unflatten false
% 150.80/150.94 % --prep_res_sim true
% 150.80/150.94 % --prep_upred true
% 150.80/150.94 % --res_sim_input true
% 150.80/150.94 % --clause_weak_htbl true
% 150.80/150.94 % --gc_record_bc_elim false
% 150.80/150.94 % --symbol_type_check false
% 150.80/150.94 % --clausify_out false
% 150.80/150.94 % --large_theory_mode false
% 150.80/150.94 % --prep_sem_filter none
% 150.80/150.94 % --prep_sem_filter_out false
% 150.80/150.94 % --preprocessed_out false
% 150.80/150.94 % --sub_typing false
% 150.80/150.94 % --brand_transform false
% 150.80/150.94 % --pure_diseq_elim true
% 150.80/150.94 % --min_unsat_core false
% 150.80/150.94 % --pred_elim true
% 150.80/150.94 % --add_important_lit false
% 150.80/150.94 % --soft_assumptions false
% 150.80/150.94 % --reset_solvers false
% 150.80/150.94 % --bc_imp_inh []
% 150.80/150.94 % --conj_cone_tolerance 1.5
% 150.80/150.94 % --prolific_symb_bound 500
% 150.80/150.94 % --lt_threshold 2000
% 150.80/150.94
% 150.80/150.94 % ------ SAT Options
% 150.80/150.94
% 150.80/150.94 % --sat_mode false
% 150.80/150.94 % --sat_fm_restart_options ""
% 150.80/150.94 % --sat_gr_def false
% 150.80/150.94 % --sat_epr_types true
% 150.80/150.94 % --sat_non_cyclic_types false
% 150.80/150.94 % --sat_finite_models false
% 150.80/150.94 % --sat_fm_lemmas false
% 150.80/150.94 % --sat_fm_prep false
% 150.80/150.94 % --sat_fm_uc_incr true
% 150.80/150.94 % --sat_out_model small
% 150.80/150.94 % --sat_out_clauses false
% 150.80/150.94
% 150.80/150.94 % ------ QBF Options
% 150.80/150.94
% 150.80/150.94 % --qbf_mode false
% 150.80/150.94 % --qbf_elim_univ true
% 150.80/150.94 % --qbf_sk_in true
% 150.80/150.94 % --qbf_pred_elim true
% 150.80/150.94 % --qbf_split 32
% 150.80/150.94
% 150.80/150.94 % ------ BMC1 Options
% 150.80/150.94
% 150.80/150.94 % --bmc1_incremental false
% 150.80/150.94 % --bmc1_axioms reachable_all
% 150.80/150.94 % --bmc1_min_bound 0
% 150.80/150.94 % --bmc1_max_bound -1
% 150.80/150.94 % --bmc1_max_bound_default -1
% 150.80/150.94 % --bmc1_symbol_reachability true
% 150.80/150.94 % --bmc1_property_lemmas false
% 150.80/150.94 % --bmc1_k_induction false
% 150.80/150.94 % --bmc1_non_equiv_states false
% 150.80/150.94 % --bmc1_deadlock false
% 150.80/150.94 % --bmc1_ucm false
% 150.80/150.94 % --bmc1_add_unsat_core none
% 150.80/150.94 % --bmc1_unsat_core_children false
% 150.80/150.94 % --bmc1_unsat_core_extrapolate_axioms false
% 150.80/150.94 % --bmc1_out_stat full
% 150.80/150.94 % --bmc1_ground_init false
% 150.80/150.94 % --bmc1_pre_inst_next_state false
% 150.80/150.94 % --bmc1_pre_inst_state false
% 150.80/150.94 % --bmc1_pre_inst_reach_state false
% 150.80/150.94 % --bmc1_out_unsat_core false
% 150.80/150.94 % --bmc1_aig_witness_out false
% 150.80/150.94 % --bmc1_verbose false
% 150.80/150.94 % --bmc1_dump_clauses_tptp false
% 157.27/157.46 % --bmc1_dump_unsat_core_tptp false
% 157.27/157.46 % --bmc1_dump_file -
% 157.27/157.46 % --bmc1_ucm_expand_uc_limit 128
% 157.27/157.46 % --bmc1_ucm_n_expand_iterations 6
% 157.27/157.46 % --bmc1_ucm_extend_mode 1
% 157.27/157.46 % --bmc1_ucm_init_mode 2
% 157.27/157.46 % --bmc1_ucm_cone_mode none
% 157.27/157.46 % --bmc1_ucm_reduced_relation_type 0
% 157.27/157.46 % --bmc1_ucm_relax_model 4
% 157.27/157.46 % --bmc1_ucm_full_tr_after_sat true
% 157.27/157.46 % --bmc1_ucm_expand_neg_assumptions false
% 157.27/157.46 % --bmc1_ucm_layered_model none
% 157.27/157.46 % --bmc1_ucm_max_lemma_size 10
% 157.27/157.46
% 157.27/157.46 % ------ AIG Options
% 157.27/157.46
% 157.27/157.46 % --aig_mode false
% 157.27/157.46
% 157.27/157.46 % ------ Instantiation Options
% 157.27/157.46
% 157.27/157.46 % --instantiation_flag true
% 157.27/157.46 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 157.27/157.46 % --inst_solver_per_active 750
% 157.27/157.46 % --inst_solver_calls_frac 0.5
% 157.27/157.46 % --inst_passive_queue_type priority_queues
% 157.27/157.46 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 157.27/157.46 % --inst_passive_queues_freq [25;2]
% 157.27/157.46 % --inst_dismatching true
% 157.27/157.46 % --inst_eager_unprocessed_to_passive true
% 157.27/157.46 % --inst_prop_sim_given true
% 157.27/157.46 % --inst_prop_sim_new false
% 157.27/157.46 % --inst_orphan_elimination true
% 157.27/157.46 % --inst_learning_loop_flag true
% 157.27/157.46 % --inst_learning_start 3000
% 157.27/157.46 % --inst_learning_factor 2
% 157.27/157.46 % --inst_start_prop_sim_after_learn 3
% 157.27/157.46 % --inst_sel_renew solver
% 157.27/157.46 % --inst_lit_activity_flag true
% 157.27/157.46 % --inst_out_proof true
% 157.27/157.46
% 157.27/157.46 % ------ Resolution Options
% 157.27/157.46
% 157.27/157.46 % --resolution_flag true
% 157.27/157.46 % --res_lit_sel kbo_max
% 157.27/157.46 % --res_to_prop_solver none
% 157.27/157.46 % --res_prop_simpl_new false
% 157.27/157.46 % --res_prop_simpl_given false
% 157.27/157.46 % --res_passive_queue_type priority_queues
% 157.27/157.46 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 157.27/157.46 % --res_passive_queues_freq [15;5]
% 157.27/157.46 % --res_forward_subs full
% 157.27/157.46 % --res_backward_subs full
% 157.27/157.46 % --res_forward_subs_resolution true
% 157.27/157.46 % --res_backward_subs_resolution true
% 157.27/157.46 % --res_orphan_elimination false
% 157.27/157.46 % --res_time_limit 1000.
% 157.27/157.46 % --res_out_proof true
% 157.27/157.46 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_9e98cf.s
% 157.27/157.46 % --modulo true
% 157.27/157.46
% 157.27/157.46 % ------ Combination Options
% 157.27/157.46
% 157.27/157.46 % --comb_res_mult 1000
% 157.27/157.46 % --comb_inst_mult 300
% 157.27/157.46 % ------
% 157.27/157.46
% 157.27/157.46 % ------ Parsing...% successful
% 157.27/157.46
% 157.27/157.46 % ------ 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 %
% 157.27/157.46
% 157.27/157.46 % ------ Proving...
% 157.27/157.46 % ------ Problem Properties
% 157.27/157.46
% 157.27/157.46 %
% 157.27/157.46 % EPR false
% 157.27/157.46 % Horn false
% 157.27/157.46 % Has equality true
% 157.27/157.46
% 157.27/157.46 % % ------ Input Options Time Limit: Unbounded
% 157.27/157.46
% 157.27/157.46
% 157.27/157.46 Compiling...
% 157.27/157.46 Loading plugin: done.
% 157.27/157.46 Compiling...
% 157.27/157.46 Loading plugin: done.
% 157.27/157.46 Compiling...
% 157.27/157.46 Loading plugin: done.
% 157.27/157.46 Compiling...
% 157.27/157.46 Loading plugin: done.
% 157.27/157.46 Compiling...
% 157.27/157.46 Loading plugin: done.
% 157.27/157.46 Compiling...
% 157.27/157.46 Loading plugin: done.
% 157.27/157.46 Compiling...
% 157.27/157.46 Loading plugin: done.
% 157.27/157.46 Compiling...
% 157.27/157.46 Loading plugin: done.
% 157.27/157.46 Compiling...
% 157.27/157.46 Loading plugin: done.
% 157.27/157.46 Compiling...
% 157.27/157.46 Loading plugin: done.
% 157.27/157.46 Compiling...
% 157.27/157.46 Loading plugin: done.
% 157.27/157.46 Compiling...
% 157.27/157.46 Loading plugin: done.
% 157.27/157.46 Compiling...
% 157.27/157.46 Loading plugin: done.
% 157.27/157.46 Compiling...
% 157.27/157.46 Loading plugin: done.
% 157.27/157.46 Compiling...
% 157.27/157.46 Loading plugin: done.
% 157.27/157.46 Compiling...
% 157.27/157.46 Loading plugin: done.
% 157.27/157.46 Compiling...
% 157.27/157.46 Loading plugin: done.
% 157.27/157.46 Compiling...
% 157.27/157.46 Loading plugin: done.
% 157.27/157.46 Compiling...
% 157.27/157.46 Loading plugin: done.
% 157.27/157.46 Compiling...
% 157.27/157.46 Loading plugin: done.
% 157.27/157.46 Compiling...
% 157.27/157.46 Loading plugin: done.
% 157.27/157.46 Compiling...
% 157.27/157.46 Loading plugin: done.
% 157.27/157.46 Compiling...
% 157.27/157.46 Loading plugin: done.
% 157.27/157.46 Compiling...
% 157.27/157.46 Loading plugin: done.
% 157.27/157.46 Compiling...
% 157.27/157.46 Loading plugin: done.
% 157.27/157.46 % % ------ Current options:
% 157.27/157.46
% 157.27/157.46 % ------ Input Options
% 157.27/157.46
% 157.27/157.46 % --out_options all
% 157.27/157.46 % --tptp_safe_out true
% 157.27/157.46 % --problem_path ""
% 157.27/157.46 % --include_path ""
% 157.27/157.46 % --clausifier .//eprover
% 157.27/157.46 % --clausifier_options --tstp-format
% 157.27/157.46 % --stdin false
% 157.27/157.46 % --dbg_backtrace false
% 157.27/157.46 % --dbg_dump_prop_clauses false
% 157.27/157.46 % --dbg_dump_prop_clauses_file -
% 157.27/157.46 % --dbg_out_stat false
% 157.27/157.46
% 157.27/157.46 % ------ General Options
% 157.27/157.46
% 157.27/157.46 % --fof false
% 157.27/157.46 % --time_out_real 150.
% 157.27/157.46 % --time_out_prep_mult 0.2
% 157.27/157.46 % --time_out_virtual -1.
% 157.27/157.46 % --schedule none
% 157.27/157.46 % --ground_splitting input
% 157.27/157.46 % --splitting_nvd 16
% 157.27/157.46 % --non_eq_to_eq false
% 157.27/157.46 % --prep_gs_sim true
% 157.27/157.46 % --prep_unflatten false
% 157.27/157.46 % --prep_res_sim true
% 157.27/157.46 % --prep_upred true
% 157.27/157.46 % --res_sim_input true
% 157.27/157.46 % --clause_weak_htbl true
% 157.27/157.46 % --gc_record_bc_elim false
% 157.27/157.46 % --symbol_type_check false
% 157.27/157.46 % --clausify_out false
% 157.27/157.46 % --large_theory_mode false
% 157.27/157.46 % --prep_sem_filter none
% 157.27/157.46 % --prep_sem_filter_out false
% 157.27/157.46 % --preprocessed_out false
% 157.27/157.46 % --sub_typing false
% 157.27/157.46 % --brand_transform false
% 157.27/157.46 % --pure_diseq_elim true
% 157.27/157.46 % --min_unsat_core false
% 157.27/157.46 % --pred_elim true
% 157.27/157.46 % --add_important_lit false
% 157.27/157.46 % --soft_assumptions false
% 157.27/157.46 % --reset_solvers false
% 157.27/157.46 % --bc_imp_inh []
% 157.27/157.46 % --conj_cone_tolerance 1.5
% 157.27/157.46 % --prolific_symb_bound 500
% 157.27/157.46 % --lt_threshold 2000
% 157.27/157.46
% 157.27/157.46 % ------ SAT Options
% 157.27/157.46
% 157.27/157.46 % --sat_mode false
% 157.27/157.46 % --sat_fm_restart_options ""
% 157.27/157.46 % --sat_gr_def false
% 157.27/157.46 % --sat_epr_types true
% 157.27/157.46 % --sat_non_cyclic_types false
% 157.27/157.46 % --sat_finite_models false
% 157.27/157.46 % --sat_fm_lemmas false
% 157.27/157.46 % --sat_fm_prep false
% 157.27/157.46 % --sat_fm_uc_incr true
% 157.27/157.46 % --sat_out_model small
% 157.27/157.46 % --sat_out_clauses false
% 157.27/157.46
% 157.27/157.46 % ------ QBF Options
% 157.27/157.46
% 157.27/157.46 % --qbf_mode false
% 157.27/157.46 % --qbf_elim_univ true
% 157.27/157.46 % --qbf_sk_in true
% 157.27/157.46 % --qbf_pred_elim true
% 157.27/157.46 % --qbf_split 32
% 157.27/157.46
% 157.27/157.46 % ------ BMC1 Options
% 157.27/157.46
% 157.27/157.46 % --bmc1_incremental false
% 157.27/157.46 % --bmc1_axioms reachable_all
% 157.27/157.46 % --bmc1_min_bound 0
% 157.27/157.46 % --bmc1_max_bound -1
% 157.27/157.46 % --bmc1_max_bound_default -1
% 157.27/157.46 % --bmc1_symbol_reachability true
% 157.27/157.46 % --bmc1_property_lemmas false
% 157.27/157.46 % --bmc1_k_induction false
% 157.27/157.46 % --bmc1_non_equiv_states false
% 157.27/157.46 % --bmc1_deadlock false
% 157.27/157.46 % --bmc1_ucm false
% 157.27/157.46 % --bmc1_add_unsat_core none
% 157.27/157.46 % --bmc1_unsat_core_children false
% 157.27/157.46 % --bmc1_unsat_core_extrapolate_axioms false
% 157.27/157.46 % --bmc1_out_stat full
% 157.27/157.46 % --bmc1_ground_init false
% 157.27/157.46 % --bmc1_pre_inst_next_state false
% 157.27/157.46 % --bmc1_pre_inst_state false
% 157.27/157.46 % --bmc1_pre_inst_reach_state false
% 157.27/157.46 % --bmc1_out_unsat_core false
% 157.27/157.46 % --bmc1_aig_witness_out false
% 157.27/157.46 % --bmc1_verbose false
% 157.27/157.46 % --bmc1_dump_clauses_tptp false
% 157.27/157.46 % --bmc1_dump_unsat_core_tptp false
% 157.27/157.46 % --bmc1_dump_file -
% 157.27/157.46 % --bmc1_ucm_expand_uc_limit 128
% 157.27/157.46 % --bmc1_ucm_n_expand_iterations 6
% 157.27/157.46 % --bmc1_ucm_extend_mode 1
% 157.27/157.46 % --bmc1_ucm_init_mode 2
% 157.27/157.46 % --bmc1_ucm_cone_mode none
% 157.27/157.46 % --bmc1_ucm_reduced_relation_type 0
% 157.44/157.59 % --bmc1_ucm_relax_model 4
% 157.44/157.59 % --bmc1_ucm_full_tr_after_sat true
% 157.44/157.59 % --bmc1_ucm_expand_neg_assumptions false
% 157.44/157.59 % --bmc1_ucm_layered_model none
% 157.44/157.59 % --bmc1_ucm_max_lemma_size 10
% 157.44/157.59
% 157.44/157.59 % ------ AIG Options
% 157.44/157.59
% 157.44/157.59 % --aig_mode false
% 157.44/157.59
% 157.44/157.59 % ------ Instantiation Options
% 157.44/157.59
% 157.44/157.59 % --instantiation_flag true
% 157.44/157.59 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 157.44/157.59 % --inst_solver_per_active 750
% 157.44/157.59 % --inst_solver_calls_frac 0.5
% 157.44/157.59 % --inst_passive_queue_type priority_queues
% 157.44/157.59 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 157.44/157.59 % --inst_passive_queues_freq [25;2]
% 157.44/157.59 % --inst_dismatching true
% 157.44/157.59 % --inst_eager_unprocessed_to_passive true
% 157.44/157.59 % --inst_prop_sim_given true
% 157.44/157.59 % --inst_prop_sim_new false
% 157.44/157.59 % --inst_orphan_elimination true
% 157.44/157.59 % --inst_learning_loop_flag true
% 157.44/157.59 % --inst_learning_start 3000
% 157.44/157.59 % --inst_learning_factor 2
% 157.44/157.59 % --inst_start_prop_sim_after_learn 3
% 157.44/157.59 % --inst_sel_renew solver
% 157.44/157.59 % --inst_lit_activity_flag true
% 157.44/157.59 % --inst_out_proof true
% 157.44/157.59
% 157.44/157.59 % ------ Resolution Options
% 157.44/157.59
% 157.44/157.59 % --resolution_flag true
% 157.44/157.59 % --res_lit_sel kbo_max
% 157.44/157.59 % --res_to_prop_solver none
% 157.44/157.59 % --res_prop_simpl_new false
% 157.44/157.59 % --res_prop_simpl_given false
% 157.44/157.59 % --res_passive_queue_type priority_queues
% 157.44/157.59 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 157.44/157.59 % --res_passive_queues_freq [15;5]
% 157.44/157.59 % --res_forward_subs full
% 157.44/157.59 % --res_backward_subs full
% 157.44/157.59 % --res_forward_subs_resolution true
% 157.44/157.59 % --res_backward_subs_resolution true
% 157.44/157.59 % --res_orphan_elimination false
% 157.44/157.59 % --res_time_limit 1000.
% 157.44/157.59 % --res_out_proof true
% 157.44/157.59 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_9e98cf.s
% 157.44/157.59 % --modulo true
% 157.44/157.59
% 157.44/157.59 % ------ Combination Options
% 157.44/157.59
% 157.44/157.59 % --comb_res_mult 1000
% 157.44/157.59 % --comb_inst_mult 300
% 157.44/157.59 % ------
% 157.44/157.59
% 157.44/157.59
% 157.44/157.59
% 157.44/157.59 % ------ Proving...
% 157.44/157.59 %
% 157.44/157.59
% 157.44/157.59
% 157.44/157.59 % Resolution empty clause
% 157.44/157.59
% 157.44/157.59 % ------ Statistics
% 157.44/157.59
% 157.44/157.59 % ------ General
% 157.44/157.59
% 157.44/157.59 % num_of_input_clauses: 2738
% 157.44/157.59 % num_of_input_neg_conjectures: 7
% 157.44/157.59 % num_of_splits: 0
% 157.44/157.59 % num_of_split_atoms: 0
% 157.44/157.59 % num_of_sem_filtered_clauses: 0
% 157.44/157.59 % num_of_subtypes: 0
% 157.44/157.59 % monotx_restored_types: 0
% 157.44/157.59 % sat_num_of_epr_types: 0
% 157.44/157.59 % sat_num_of_non_cyclic_types: 0
% 157.44/157.59 % sat_guarded_non_collapsed_types: 0
% 157.44/157.59 % is_epr: 0
% 157.44/157.59 % is_horn: 0
% 157.44/157.59 % has_eq: 1
% 157.44/157.59 % num_pure_diseq_elim: 0
% 157.44/157.59 % simp_replaced_by: 0
% 157.44/157.59 % res_preprocessed: 14
% 157.44/157.59 % prep_upred: 0
% 157.44/157.59 % prep_unflattend: 0
% 157.44/157.59 % pred_elim_cands: 0
% 157.44/157.59 % pred_elim: 0
% 157.44/157.59 % pred_elim_cl: 0
% 157.44/157.59 % pred_elim_cycles: 0
% 157.44/157.59 % forced_gc_time: 0
% 157.44/157.59 % gc_basic_clause_elim: 0
% 157.44/157.59 % parsing_time: 0.091
% 157.44/157.59 % sem_filter_time: 0.
% 157.44/157.59 % pred_elim_time: 0.
% 157.44/157.59 % out_proof_time: 0.
% 157.44/157.59 % monotx_time: 0.
% 157.44/157.59 % subtype_inf_time: 0.
% 157.44/157.59 % unif_index_cands_time: 0.
% 157.44/157.59 % unif_index_add_time: 0.002
% 157.44/157.59 % total_time: 6.666
% 157.44/157.59 % num_of_symbols: 138
% 157.44/157.59 % num_of_terms: 11789
% 157.44/157.59
% 157.44/157.59 % ------ Propositional Solver
% 157.44/157.59
% 157.44/157.59 % prop_solver_calls: 1
% 157.44/157.59 % prop_fast_solver_calls: 21
% 157.44/157.59 % prop_num_of_clauses: 2526
% 157.44/157.59 % prop_preprocess_simplified: 8346
% 157.44/157.59 % prop_fo_subsumed: 0
% 157.44/157.59 % prop_solver_time: 0.
% 157.44/157.59 % prop_fast_solver_time: 0.
% 157.44/157.59 % prop_unsat_core_time: 0.
% 157.44/157.59
% 157.44/157.59 % ------ QBF
% 157.44/157.59
% 157.44/157.59 % qbf_q_res: 0
% 157.44/157.59 % qbf_num_tautologies: 0
% 157.44/157.59 % qbf_prep_cycles: 0
% 157.44/157.59
% 157.44/157.59 % ------ BMC1
% 157.44/157.59
% 157.44/157.59 % bmc1_current_bound: -1
% 157.44/157.59 % bmc1_last_solved_bound: -1
% 157.44/157.59 % bmc1_unsat_core_size: -1
% 157.44/157.59 % bmc1_unsat_core_parents_size: -1
% 157.44/157.59 % bmc1_merge_next_fun: 0
% 157.44/157.59 % bmc1_unsat_core_clauses_time: 0.
% 157.44/157.59
% 157.44/157.59 % ------ Instantiation
% 157.44/157.59
% 157.44/157.59 % inst_num_of_clauses: 2437
% 157.44/157.59 % inst_num_in_passive: 0
% 157.44/157.59 % inst_num_in_active: 0
% 157.44/157.59 % inst_num_in_unprocessed: 2738
% 157.44/157.59 % inst_num_of_loops: 0
% 157.44/157.59 % inst_num_of_learning_restarts: 0
% 157.44/157.59 % inst_num_moves_active_passive: 0
% 157.44/157.59 % inst_lit_activity: 0
% 157.44/157.59 % inst_lit_activity_moves: 0
% 157.44/157.59 % inst_num_tautologies: 0
% 157.44/157.59 % inst_num_prop_implied: 0
% 157.44/157.59 % inst_num_existing_simplified: 0
% 157.44/157.59 % inst_num_eq_res_simplified: 0
% 157.44/157.59 % inst_num_child_elim: 0
% 157.44/157.59 % inst_num_of_dismatching_blockings: 0
% 157.44/157.59 % inst_num_of_non_proper_insts: 0
% 157.44/157.59 % inst_num_of_duplicates: 0
% 157.44/157.59 % inst_inst_num_from_inst_to_res: 0
% 157.44/157.59 % inst_dismatching_checking_time: 0.
% 157.44/157.59
% 157.44/157.59 % ------ Resolution
% 157.44/157.59
% 157.44/157.59 % res_num_of_clauses: 4656
% 157.44/157.59 % res_num_in_passive: 1909
% 157.44/157.59 % res_num_in_active: 1095
% 157.44/157.59 % res_num_of_loops: 70
% 157.44/157.59 % res_forward_subset_subsumed: 1756
% 157.44/157.59 % res_backward_subset_subsumed: 1
% 157.44/157.59 % res_forward_subsumed: 7
% 157.44/157.59 % res_backward_subsumed: 0
% 157.44/157.59 % res_forward_subsumption_resolution: 1
% 157.44/157.59 % res_backward_subsumption_resolution: 0
% 157.44/157.59 % res_clause_to_clause_subsumption: 145
% 157.44/157.59 % res_orphan_elimination: 0
% 157.44/157.59 % res_tautology_del: 0
% 157.44/157.59 % res_num_eq_res_simplified: 0
% 157.44/157.59 % res_num_sel_changes: 0
% 157.44/157.59 % res_moves_from_active_to_pass: 0
% 157.44/157.59
% 157.44/157.60 % Status Unsatisfiable
% 157.44/157.60 % SZS status Unsatisfiable
% 157.44/157.60 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------